A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Soft-Sensing Method for Optimizing Combustion Efficiency of Reheating Furnaces

Jian-Guo Wang1 Tiao Shen1 Jing-Hui Zhao1 Shi-Wei Ma1 Xiao-Fei Wang2 Yuan Yao3 Tao

Chen4

1 School of Mechatronical Engineering and Automation Shanghai University Shanghai Key Lab

of Power Station Automation Technology Shanghai 200072 China

2 Shanghai Zhenhua Heavy Industries Company Limited Shanghai 200125 China

3 Department of Chemical Engineering National Tsing Hua University Hsinchu 30013 Taiwan

4 Department of Chemical and Process Engineering University of Surrey Guildford GU2 7XH

United Kingdom

Abstract

Rolling mill reheating furnaces are widely used in large-scale iron and steel plants

the efficient operation of which has been hampered by the complexity of the

combustion mechanism In this paper a soft-sensing method is developed for modeling

and predicting combustion efficiency since it cannot be measured directly Statistical

methods are utilized to ascertain the significance of the proposed derived variables for

the combustion efficiency modeling By employing the nonnegative garrote variable

selection procedure an adaptive scheme for combustion efficiency modeling and

adjustment is proposed and virtually implemented on a rolling mill reheating furnace

The results show that significant energy saving can be achieved when the furnace is

operated with the proposed model-based optimization strategy

Keywords soft-sensing variable selection data-driven statistical analysis reheating

furnace combustion efficiency

1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Correspondence information

J G Wang Tel +86-21-56331278 Email jgwangshueducn

Y Yao Tel +886-3-5713690 Email yyaomxnthuedutw

2

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

1 Introduction

The reheating furnace for a rolling mill is the most energy consumption equipment in

a large-scale iron and steel plant thus it is of great significance to improve the

combustion efficiency and reduce gas consumption [1 2] Since combustion efficiency

cannot be measured directly the adjustment of oxygen content in the exhaust gas is

often used to indirectly control the efficiency Another method is to estimate

combustion efficiency based on oxygen content in the exhaust gas and then implement

control actions [3] However the performance of these methods depends on the

precision and stability of oxygen analyzers which are susceptible to corrosion and wear

of high-temperature gases and difficult to maintain in full operational status for a long

period of time

When quality variables cannot be easily obtained a soft sensor model that can predict

these quality characteristics (as response variables) using readily available sensor

variables (as candidate predictors) will be most desirable A variety of soft sensor

methods and applications have been studied in different fields [4-7]

For a reheating furnace a number of soft sensors have been investigated The feature

of continuous prediction of temperature and composition of the combustion atmosphere

has the potential of acting as a soft sensor thereby leading to a reduced number of

temperature measurements and sampling for chemical analysis [8] The secure

economic and stable control of the combustion process is realized by the cooperation

work of a cascade fuzzy control system for furnace temperature a ratio control system

for air flow with a soft-sensing model plus a fault diagnosis model [9] A data-driven

soft sensor modeling technique for furnace temperature of the Opposition Multi-Burner

(OMB) gasifier is proposed and the selection of secondary variables and model structure

3

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

of a back propagation (BP) neural network is studied which indicates that the furnace

temperature predictive model integrating the principal component analysis (PCA) and

the BP neural network has a promising performance with good predictive precision

[10] A soft sensor modeling method is proposed to predict the billet temperature of the

reheating furnace based on a relevance vector machine (RVM) which has a higher

prediction accuracy and a certain practical significance to the on-site production of a

reheating furnace [11] The least square support vector machine (LSSVM) inductance

model optimized by the particle swarm optimization method with a compression factor

(PSO-CF) algorithm is presented for the difficulty of time prediction which can

improve PSO convergence accuracy and effectively avoid falling into a local optimum

[12] However the soft sensor developed for combustion efficiency was not

investigated in these research efforts which is significant for energy conservation

On the premise of the model prediction accuracy the model-based control makes

optimal operation feasible which can then be successfully employed to operate a

reheating furnace in an efficient way The potential of the nonlinear model predictive

control techniques is explored to improve the temperature control for the metal slabs in

a hot mill reheating furnace and particularly whether or not these control techniques

can be exploited to reduce energy consumption [13] Steinboeck et al developed a

mathematical model of the reheating process of steel slabs in industrial fuel-fired

furnaces in 2010 They exploited a dynamic optimization method for temperature

control of the steel slabs in a continuous reheating furnace and a temperature control

method for reheating steel slabs in an industrial furnace in 2011 They also designed a

nonlinear model predictive controller for a reheating furnace for steel slabs in 2013 [2

14 15]

4

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Obviously the research on the numerical model for the heating performance of

reheating furnace can be done based on basic combustion theory and heat transmission

characteristics Many scholars devote themselves to the simulations of the heat flow

phenomenon in the reheating furnace Zhang et al attempted to apply a computational

fluid dynamic (CFD) simulation to predict the combustion performance for a reheating

furnace by simplifying the furnace to a cuboid and assuming that the slab possesses

infinite length and enters the reheating furnace at a fixed speed [16] The CFD method

has been applied to the study of reaction turbulence radiation heat transmission and the

calculation for the steady state heat transmission rate of the slab under the given

temperature [17] In the works of references [16-20] the authors used the given

temperature data of slabs to compute the steady flow and temperature field However

owing to the changing operating conditions the actual implementation of these

numerical model methods still bristle with difficulties although the methods mentioned

above are feasible for the prediction Thus for an online application it is necessary to

adopt a real time data-driven model to resolve the time varying characteristics

Proper variable selection is an important step in model building for a large-scale

combustion system A well-trimmed variable dimension ensures the acquired model is

transparent comprehensible and robust Some studies reported that the combustion

model built by a selected subset of input variables provide more accurate predictions of

combustion efficiency than the entire set of variables [21-23] Recently shrinkage

methods which conduct variable selection by shrinking or setting some coefficients of a

ldquogreedyrdquo model to zero have received significant attention A popular form of these

methods is the non-negative garrote (NNG) [23 24]

5

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Against this background this paper aims to propose a combustion efficiency index

for the reheating furnace and investigate for room in improvement regarding energy

conservation The primary contribution is a practical combustion efficiency index the

incorporation of the derived variables and soft-sensing method for the optimization of

combustion efficiency of reheating furnaces The derived variables are found more

physically meaningful than the plain variables when constructing the model of

combustion efficiency By employing a NNG variable selection procedure an adaptive

scheme for combustion efficiency modeling and adjustment is proposed and virtually

implemented for a rolling reheating furnace The results show that there is significant

room for energy conservation

The remainder of the paper is organized as follows In the next section the reheating

furnace and the data preprocessing is described In Section 3 the statistics analysis for

different variables and the formation of derived variables are presented In Section 4

the framework of an adaptive model based on NNG variable selection is presented and

two models developed for the temperature and temperature-gas (TG) ratio are

compared according to the model prediction precision A model-based optimization

scheme is provided and applied to the combustion efficiency improvement for an actual

case of a reheating furnace presented in Section 5 Several remarks and a summary

conclude the last section

2 Plant description and data preprocessing

The schematic of the heating process in the rolling mill reheating furnace is shown in

Fig 1 There are four zones in the reheating furnace including the preheating zone (P)

the first heating zone (1) the second heating zone (2) and the soaking zone (S) The

6

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Correspondence information

J G Wang Tel +86-21-56331278 Email jgwangshueducn

Y Yao Tel +886-3-5713690 Email yyaomxnthuedutw

2

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

1 Introduction

The reheating furnace for a rolling mill is the most energy consumption equipment in

a large-scale iron and steel plant thus it is of great significance to improve the

combustion efficiency and reduce gas consumption [1 2] Since combustion efficiency

cannot be measured directly the adjustment of oxygen content in the exhaust gas is

often used to indirectly control the efficiency Another method is to estimate

combustion efficiency based on oxygen content in the exhaust gas and then implement

control actions [3] However the performance of these methods depends on the

precision and stability of oxygen analyzers which are susceptible to corrosion and wear

of high-temperature gases and difficult to maintain in full operational status for a long

period of time

When quality variables cannot be easily obtained a soft sensor model that can predict

these quality characteristics (as response variables) using readily available sensor

variables (as candidate predictors) will be most desirable A variety of soft sensor

methods and applications have been studied in different fields [4-7]

For a reheating furnace a number of soft sensors have been investigated The feature

of continuous prediction of temperature and composition of the combustion atmosphere

has the potential of acting as a soft sensor thereby leading to a reduced number of

temperature measurements and sampling for chemical analysis [8] The secure

economic and stable control of the combustion process is realized by the cooperation

work of a cascade fuzzy control system for furnace temperature a ratio control system

for air flow with a soft-sensing model plus a fault diagnosis model [9] A data-driven

soft sensor modeling technique for furnace temperature of the Opposition Multi-Burner

(OMB) gasifier is proposed and the selection of secondary variables and model structure

3

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

of a back propagation (BP) neural network is studied which indicates that the furnace

temperature predictive model integrating the principal component analysis (PCA) and

the BP neural network has a promising performance with good predictive precision

[10] A soft sensor modeling method is proposed to predict the billet temperature of the

reheating furnace based on a relevance vector machine (RVM) which has a higher

prediction accuracy and a certain practical significance to the on-site production of a

reheating furnace [11] The least square support vector machine (LSSVM) inductance

model optimized by the particle swarm optimization method with a compression factor

(PSO-CF) algorithm is presented for the difficulty of time prediction which can

improve PSO convergence accuracy and effectively avoid falling into a local optimum

[12] However the soft sensor developed for combustion efficiency was not

investigated in these research efforts which is significant for energy conservation

On the premise of the model prediction accuracy the model-based control makes

optimal operation feasible which can then be successfully employed to operate a

reheating furnace in an efficient way The potential of the nonlinear model predictive

control techniques is explored to improve the temperature control for the metal slabs in

a hot mill reheating furnace and particularly whether or not these control techniques

can be exploited to reduce energy consumption [13] Steinboeck et al developed a

mathematical model of the reheating process of steel slabs in industrial fuel-fired

furnaces in 2010 They exploited a dynamic optimization method for temperature

control of the steel slabs in a continuous reheating furnace and a temperature control

method for reheating steel slabs in an industrial furnace in 2011 They also designed a

nonlinear model predictive controller for a reheating furnace for steel slabs in 2013 [2

14 15]

4

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Obviously the research on the numerical model for the heating performance of

reheating furnace can be done based on basic combustion theory and heat transmission

characteristics Many scholars devote themselves to the simulations of the heat flow

phenomenon in the reheating furnace Zhang et al attempted to apply a computational

fluid dynamic (CFD) simulation to predict the combustion performance for a reheating

furnace by simplifying the furnace to a cuboid and assuming that the slab possesses

infinite length and enters the reheating furnace at a fixed speed [16] The CFD method

has been applied to the study of reaction turbulence radiation heat transmission and the

calculation for the steady state heat transmission rate of the slab under the given

temperature [17] In the works of references [16-20] the authors used the given

temperature data of slabs to compute the steady flow and temperature field However

owing to the changing operating conditions the actual implementation of these

numerical model methods still bristle with difficulties although the methods mentioned

above are feasible for the prediction Thus for an online application it is necessary to

adopt a real time data-driven model to resolve the time varying characteristics

Proper variable selection is an important step in model building for a large-scale

combustion system A well-trimmed variable dimension ensures the acquired model is

transparent comprehensible and robust Some studies reported that the combustion

model built by a selected subset of input variables provide more accurate predictions of

combustion efficiency than the entire set of variables [21-23] Recently shrinkage

methods which conduct variable selection by shrinking or setting some coefficients of a

ldquogreedyrdquo model to zero have received significant attention A popular form of these

methods is the non-negative garrote (NNG) [23 24]

5

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Against this background this paper aims to propose a combustion efficiency index

for the reheating furnace and investigate for room in improvement regarding energy

conservation The primary contribution is a practical combustion efficiency index the

incorporation of the derived variables and soft-sensing method for the optimization of

combustion efficiency of reheating furnaces The derived variables are found more

physically meaningful than the plain variables when constructing the model of

combustion efficiency By employing a NNG variable selection procedure an adaptive

scheme for combustion efficiency modeling and adjustment is proposed and virtually

implemented for a rolling reheating furnace The results show that there is significant

room for energy conservation

The remainder of the paper is organized as follows In the next section the reheating

furnace and the data preprocessing is described In Section 3 the statistics analysis for

different variables and the formation of derived variables are presented In Section 4

the framework of an adaptive model based on NNG variable selection is presented and

two models developed for the temperature and temperature-gas (TG) ratio are

compared according to the model prediction precision A model-based optimization

scheme is provided and applied to the combustion efficiency improvement for an actual

case of a reheating furnace presented in Section 5 Several remarks and a summary

conclude the last section

2 Plant description and data preprocessing

The schematic of the heating process in the rolling mill reheating furnace is shown in

Fig 1 There are four zones in the reheating furnace including the preheating zone (P)

the first heating zone (1) the second heating zone (2) and the soaking zone (S) The

6

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

1 Introduction

The reheating furnace for a rolling mill is the most energy consumption equipment in

a large-scale iron and steel plant thus it is of great significance to improve the

combustion efficiency and reduce gas consumption [1 2] Since combustion efficiency

cannot be measured directly the adjustment of oxygen content in the exhaust gas is

often used to indirectly control the efficiency Another method is to estimate

combustion efficiency based on oxygen content in the exhaust gas and then implement

control actions [3] However the performance of these methods depends on the

precision and stability of oxygen analyzers which are susceptible to corrosion and wear

of high-temperature gases and difficult to maintain in full operational status for a long

period of time

When quality variables cannot be easily obtained a soft sensor model that can predict

these quality characteristics (as response variables) using readily available sensor

variables (as candidate predictors) will be most desirable A variety of soft sensor

methods and applications have been studied in different fields [4-7]

For a reheating furnace a number of soft sensors have been investigated The feature

of continuous prediction of temperature and composition of the combustion atmosphere

has the potential of acting as a soft sensor thereby leading to a reduced number of

temperature measurements and sampling for chemical analysis [8] The secure

economic and stable control of the combustion process is realized by the cooperation

work of a cascade fuzzy control system for furnace temperature a ratio control system

for air flow with a soft-sensing model plus a fault diagnosis model [9] A data-driven

soft sensor modeling technique for furnace temperature of the Opposition Multi-Burner

(OMB) gasifier is proposed and the selection of secondary variables and model structure

3

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

of a back propagation (BP) neural network is studied which indicates that the furnace

temperature predictive model integrating the principal component analysis (PCA) and

the BP neural network has a promising performance with good predictive precision

[10] A soft sensor modeling method is proposed to predict the billet temperature of the

reheating furnace based on a relevance vector machine (RVM) which has a higher

prediction accuracy and a certain practical significance to the on-site production of a

reheating furnace [11] The least square support vector machine (LSSVM) inductance

model optimized by the particle swarm optimization method with a compression factor

(PSO-CF) algorithm is presented for the difficulty of time prediction which can

improve PSO convergence accuracy and effectively avoid falling into a local optimum

[12] However the soft sensor developed for combustion efficiency was not

investigated in these research efforts which is significant for energy conservation

On the premise of the model prediction accuracy the model-based control makes

optimal operation feasible which can then be successfully employed to operate a

reheating furnace in an efficient way The potential of the nonlinear model predictive

control techniques is explored to improve the temperature control for the metal slabs in

a hot mill reheating furnace and particularly whether or not these control techniques

can be exploited to reduce energy consumption [13] Steinboeck et al developed a

mathematical model of the reheating process of steel slabs in industrial fuel-fired

furnaces in 2010 They exploited a dynamic optimization method for temperature

control of the steel slabs in a continuous reheating furnace and a temperature control

method for reheating steel slabs in an industrial furnace in 2011 They also designed a

nonlinear model predictive controller for a reheating furnace for steel slabs in 2013 [2

14 15]

4

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Obviously the research on the numerical model for the heating performance of

reheating furnace can be done based on basic combustion theory and heat transmission

characteristics Many scholars devote themselves to the simulations of the heat flow

phenomenon in the reheating furnace Zhang et al attempted to apply a computational

fluid dynamic (CFD) simulation to predict the combustion performance for a reheating

furnace by simplifying the furnace to a cuboid and assuming that the slab possesses

infinite length and enters the reheating furnace at a fixed speed [16] The CFD method

has been applied to the study of reaction turbulence radiation heat transmission and the

calculation for the steady state heat transmission rate of the slab under the given

temperature [17] In the works of references [16-20] the authors used the given

temperature data of slabs to compute the steady flow and temperature field However

owing to the changing operating conditions the actual implementation of these

numerical model methods still bristle with difficulties although the methods mentioned

above are feasible for the prediction Thus for an online application it is necessary to

adopt a real time data-driven model to resolve the time varying characteristics

Proper variable selection is an important step in model building for a large-scale

combustion system A well-trimmed variable dimension ensures the acquired model is

transparent comprehensible and robust Some studies reported that the combustion

model built by a selected subset of input variables provide more accurate predictions of

combustion efficiency than the entire set of variables [21-23] Recently shrinkage

methods which conduct variable selection by shrinking or setting some coefficients of a

ldquogreedyrdquo model to zero have received significant attention A popular form of these

methods is the non-negative garrote (NNG) [23 24]

5

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Against this background this paper aims to propose a combustion efficiency index

for the reheating furnace and investigate for room in improvement regarding energy

conservation The primary contribution is a practical combustion efficiency index the

incorporation of the derived variables and soft-sensing method for the optimization of

combustion efficiency of reheating furnaces The derived variables are found more

physically meaningful than the plain variables when constructing the model of

combustion efficiency By employing a NNG variable selection procedure an adaptive

scheme for combustion efficiency modeling and adjustment is proposed and virtually

implemented for a rolling reheating furnace The results show that there is significant

room for energy conservation

The remainder of the paper is organized as follows In the next section the reheating

furnace and the data preprocessing is described In Section 3 the statistics analysis for

different variables and the formation of derived variables are presented In Section 4

the framework of an adaptive model based on NNG variable selection is presented and

two models developed for the temperature and temperature-gas (TG) ratio are

compared according to the model prediction precision A model-based optimization

scheme is provided and applied to the combustion efficiency improvement for an actual

case of a reheating furnace presented in Section 5 Several remarks and a summary

conclude the last section

2 Plant description and data preprocessing

The schematic of the heating process in the rolling mill reheating furnace is shown in

Fig 1 There are four zones in the reheating furnace including the preheating zone (P)

the first heating zone (1) the second heating zone (2) and the soaking zone (S) The

6

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

of a back propagation (BP) neural network is studied which indicates that the furnace

temperature predictive model integrating the principal component analysis (PCA) and

the BP neural network has a promising performance with good predictive precision

[10] A soft sensor modeling method is proposed to predict the billet temperature of the

reheating furnace based on a relevance vector machine (RVM) which has a higher

prediction accuracy and a certain practical significance to the on-site production of a

reheating furnace [11] The least square support vector machine (LSSVM) inductance

model optimized by the particle swarm optimization method with a compression factor

(PSO-CF) algorithm is presented for the difficulty of time prediction which can

improve PSO convergence accuracy and effectively avoid falling into a local optimum

[12] However the soft sensor developed for combustion efficiency was not

investigated in these research efforts which is significant for energy conservation

On the premise of the model prediction accuracy the model-based control makes

optimal operation feasible which can then be successfully employed to operate a

reheating furnace in an efficient way The potential of the nonlinear model predictive

control techniques is explored to improve the temperature control for the metal slabs in

a hot mill reheating furnace and particularly whether or not these control techniques

can be exploited to reduce energy consumption [13] Steinboeck et al developed a

mathematical model of the reheating process of steel slabs in industrial fuel-fired

furnaces in 2010 They exploited a dynamic optimization method for temperature

control of the steel slabs in a continuous reheating furnace and a temperature control

method for reheating steel slabs in an industrial furnace in 2011 They also designed a

nonlinear model predictive controller for a reheating furnace for steel slabs in 2013 [2

14 15]

4

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Obviously the research on the numerical model for the heating performance of

reheating furnace can be done based on basic combustion theory and heat transmission

characteristics Many scholars devote themselves to the simulations of the heat flow

phenomenon in the reheating furnace Zhang et al attempted to apply a computational

fluid dynamic (CFD) simulation to predict the combustion performance for a reheating

furnace by simplifying the furnace to a cuboid and assuming that the slab possesses

infinite length and enters the reheating furnace at a fixed speed [16] The CFD method

has been applied to the study of reaction turbulence radiation heat transmission and the

calculation for the steady state heat transmission rate of the slab under the given

temperature [17] In the works of references [16-20] the authors used the given

temperature data of slabs to compute the steady flow and temperature field However

owing to the changing operating conditions the actual implementation of these

numerical model methods still bristle with difficulties although the methods mentioned

above are feasible for the prediction Thus for an online application it is necessary to

adopt a real time data-driven model to resolve the time varying characteristics

Proper variable selection is an important step in model building for a large-scale

combustion system A well-trimmed variable dimension ensures the acquired model is

transparent comprehensible and robust Some studies reported that the combustion

model built by a selected subset of input variables provide more accurate predictions of

combustion efficiency than the entire set of variables [21-23] Recently shrinkage

methods which conduct variable selection by shrinking or setting some coefficients of a

ldquogreedyrdquo model to zero have received significant attention A popular form of these

methods is the non-negative garrote (NNG) [23 24]

5

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Against this background this paper aims to propose a combustion efficiency index

for the reheating furnace and investigate for room in improvement regarding energy

conservation The primary contribution is a practical combustion efficiency index the

incorporation of the derived variables and soft-sensing method for the optimization of

combustion efficiency of reheating furnaces The derived variables are found more

physically meaningful than the plain variables when constructing the model of

combustion efficiency By employing a NNG variable selection procedure an adaptive

scheme for combustion efficiency modeling and adjustment is proposed and virtually

implemented for a rolling reheating furnace The results show that there is significant

room for energy conservation

The remainder of the paper is organized as follows In the next section the reheating

furnace and the data preprocessing is described In Section 3 the statistics analysis for

different variables and the formation of derived variables are presented In Section 4

the framework of an adaptive model based on NNG variable selection is presented and

two models developed for the temperature and temperature-gas (TG) ratio are

compared according to the model prediction precision A model-based optimization

scheme is provided and applied to the combustion efficiency improvement for an actual

case of a reheating furnace presented in Section 5 Several remarks and a summary

conclude the last section

2 Plant description and data preprocessing

The schematic of the heating process in the rolling mill reheating furnace is shown in

Fig 1 There are four zones in the reheating furnace including the preheating zone (P)

the first heating zone (1) the second heating zone (2) and the soaking zone (S) The

6

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Obviously the research on the numerical model for the heating performance of

reheating furnace can be done based on basic combustion theory and heat transmission

characteristics Many scholars devote themselves to the simulations of the heat flow

phenomenon in the reheating furnace Zhang et al attempted to apply a computational

fluid dynamic (CFD) simulation to predict the combustion performance for a reheating

furnace by simplifying the furnace to a cuboid and assuming that the slab possesses

infinite length and enters the reheating furnace at a fixed speed [16] The CFD method

has been applied to the study of reaction turbulence radiation heat transmission and the

calculation for the steady state heat transmission rate of the slab under the given

temperature [17] In the works of references [16-20] the authors used the given

temperature data of slabs to compute the steady flow and temperature field However

owing to the changing operating conditions the actual implementation of these

numerical model methods still bristle with difficulties although the methods mentioned

above are feasible for the prediction Thus for an online application it is necessary to

adopt a real time data-driven model to resolve the time varying characteristics

Proper variable selection is an important step in model building for a large-scale

combustion system A well-trimmed variable dimension ensures the acquired model is

transparent comprehensible and robust Some studies reported that the combustion

model built by a selected subset of input variables provide more accurate predictions of

combustion efficiency than the entire set of variables [21-23] Recently shrinkage

methods which conduct variable selection by shrinking or setting some coefficients of a

ldquogreedyrdquo model to zero have received significant attention A popular form of these

methods is the non-negative garrote (NNG) [23 24]

5

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Against this background this paper aims to propose a combustion efficiency index

for the reheating furnace and investigate for room in improvement regarding energy

conservation The primary contribution is a practical combustion efficiency index the

incorporation of the derived variables and soft-sensing method for the optimization of

combustion efficiency of reheating furnaces The derived variables are found more

physically meaningful than the plain variables when constructing the model of

combustion efficiency By employing a NNG variable selection procedure an adaptive

scheme for combustion efficiency modeling and adjustment is proposed and virtually

implemented for a rolling reheating furnace The results show that there is significant

room for energy conservation

The remainder of the paper is organized as follows In the next section the reheating

furnace and the data preprocessing is described In Section 3 the statistics analysis for

different variables and the formation of derived variables are presented In Section 4

the framework of an adaptive model based on NNG variable selection is presented and

two models developed for the temperature and temperature-gas (TG) ratio are

compared according to the model prediction precision A model-based optimization

scheme is provided and applied to the combustion efficiency improvement for an actual

case of a reheating furnace presented in Section 5 Several remarks and a summary

conclude the last section

2 Plant description and data preprocessing

The schematic of the heating process in the rolling mill reheating furnace is shown in

Fig 1 There are four zones in the reheating furnace including the preheating zone (P)

the first heating zone (1) the second heating zone (2) and the soaking zone (S) The

6

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Against this background this paper aims to propose a combustion efficiency index

for the reheating furnace and investigate for room in improvement regarding energy

conservation The primary contribution is a practical combustion efficiency index the

incorporation of the derived variables and soft-sensing method for the optimization of

combustion efficiency of reheating furnaces The derived variables are found more

physically meaningful than the plain variables when constructing the model of

combustion efficiency By employing a NNG variable selection procedure an adaptive

scheme for combustion efficiency modeling and adjustment is proposed and virtually

implemented for a rolling reheating furnace The results show that there is significant

room for energy conservation

The remainder of the paper is organized as follows In the next section the reheating

furnace and the data preprocessing is described In Section 3 the statistics analysis for

different variables and the formation of derived variables are presented In Section 4

the framework of an adaptive model based on NNG variable selection is presented and

two models developed for the temperature and temperature-gas (TG) ratio are

compared according to the model prediction precision A model-based optimization

scheme is provided and applied to the combustion efficiency improvement for an actual

case of a reheating furnace presented in Section 5 Several remarks and a summary

conclude the last section

2 Plant description and data preprocessing

The schematic of the heating process in the rolling mill reheating furnace is shown in

Fig 1 There are four zones in the reheating furnace including the preheating zone (P)

the first heating zone (1) the second heating zone (2) and the soaking zone (S) The

6

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

steel slab moves through the four zones in turn and is heated to the demanded state

using a specific temperature increase curve As is shown in Table 1 the soaking zone

has two areas that are defined as up and down and both of the areas possess the same

five variables including two manipulated variables the air flow (A) and the gas flow

(G) and three temperatures in left center and right sections of the area (T-l T-c and T-

r) The other zones have the same variables as the soaking zone hence there are 40

variables in total for the reheating furnace

Fig 1 The schematic of the heating process in the reheating furnace

Table 1 Variables and descriptions in the soaking zone

Variable Description unit

AS-u Air flow in the lsquouprsquo area Nm3h

AS-d Air flow in the lsquodownrsquo area Nm3h

GS-u Gas flow in the lsquouprsquo area Nm3h

GS-d Gas flow in the lsquodownrsquo area Nm3h

TS-ul Temperature in the left part of the lsquouprsquo area

TS-uc Temperature in the center part of the lsquouprsquo area

TS-ur Temperature in the right part of the lsquouprsquo area

7

143

144

145

146

147

148

149

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

TS-dl Temperature in the left part of the lsquodownrsquo area

TS-dc Temperature in the center part of the lsquodownrsquo area

TS-dr Temperature in the right part of the lsquodownrsquo area

A data set of 20000 samples was used in this study The samples were collected from

an actual reheating furnace in a large iron and steel plant located in Shanghai from

September 14 to September 27 2014 The operational data is taken on a per minute

basis

1

092

093

042

041

046

092

1

091

04

039

045

093

091

1

038

038

045

042

04

038

1

096

096

041

039

038

096

1

096

046

045

045

096

096

1

TS-ul

TS-uc

TS-ur

TS-dl

TS-dc

TS-dr

TS-ul TS-uc TS-ur TS-dl TS-dc TS-dr

04

05

06

07

08

09

1

Fig 2 Correlation between each temperature in the soaking zone

In order to investigate the relation among different temperatures in each zone

correlation analysis is conducted for the soaking zone as illustrated in Fig 2 It can be

seen that the temperature in three parts of the lsquouprsquo area is highly correlated with a

correlation coefficient greater than 09 The similar results exist for the lsquodownrsquo area as

well On the contrary the correlation coefficient between temperatures in one part of

8

150

151

152

153

154

155

156

157

158

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

lsquouprsquo area and any part of lsquodownrsquo area does not exceed 05 Therefore for the reduction

of the data dimension the three temperatures in the lsquouprsquo area or the lsquodownrsquo area can be

treated as only one variable which can be taken as the mean value or the first principal

component acquired from the PCA analysis Considering the reservation of the variable

physical meaning the former is preferred and used

3 Statistics analysis and incorporation of derived variables

In this section in order to uncover the physical knowledge for the actual operation

guidance and confirmation statistical analysis is performed for the 16 input manipulated

variables and the eight output variables (ie the temperatures in the four zones) of a

reheating furnace system For the combustion efficiency evaluation and modeling two

types of derived ratio variables are introduced which is helpful to reveal the

information included in the data

31 Correlation analysis

Correlation analysis between the temperatures (T) in each area and all of the air flows

(A) and the gas flows (G) is performed and shown in Fig 3 It can be seen that only the

temperatures in both areas of the soaking zone are the most highly related to the air flow

and the gas flow in its own zone However this phenomenon does not occur in the other

three zones The temperatures in the second heating zone mainly depend on the air flow

and the gas flow in its own zone as well as the nearby first heating zone As for the

preheating zone and first heating zone no apparent correlation can be observed

Obviously these analysis results could not tell us the explicit information about how to

evaluate the efficiency levels and key manipulated variables

9

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

-101

T P-u

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

-101

T P-d

-101

T 1-u

-101

T 1-d

AP GP A1 G1 A2 G2 AS GS

-101

T 2-u

AP GP A1 G1 A2 G2 AS GS

-101

T 2-d

-101

T S-u

-101

T S-d

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

AP GP A1 G1 A2 G2 AS GS

UPDOWN

Fig 3 Correlation between air flows gas flows and temperatures

32 Incorporation of derived variables

During the stable heating stage the quantity of heat absorbed and removed from the

slabs from each furnace zone is relatively constant Hence the derived variable TG

ratio can be treated as an index for the combustion efficiency level This is because a

higher TG ratio signifies more combustion heat generated from unit gas ie higher

combustion efficiency

Moreover it is known that the appropriate air and fuel ratio is vital for the

combustion efficiency so the air-gas ratio (AG) is utilized as another derived variable

for the research Again the correlation analysis is performed for two types of derived

variables The correlations between different variables including the AG ratio G and

the TG ratio are shown in Fig 4 It can be clearly seen from the four red rectangle

blocks that TG of each zone is only remarkably related to AG and G in the same zone

10

183

184

185

186

187

188

189

190

191

192

193

194

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Furthermore as related to the lsquouprsquo or lsquodownrsquo areas in one zone TG in each area has the

highest correlation with AG and G in the same area while AG and G in the opposite

area of the same zone is secondary This can be easily seen from the red and blue color

markings in each red rectangle block Thus it is of great significance to introduce these

derived ratio variables

-101

TG

P-u

AGP GP AG1G1 AG2 G2 AGS GS

-101

TG

P-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

1-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

2-d

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-u

AGP GP AG1 G1 AG2 G2 AGS GS

-101

TG

S-d

AGP GP AG1 G1 AG2 G2 AGS GS

UPDOWN

Fig 4 Correlation between the air-gas ratio gas flow and TG ratio

33 LDA analysis

Linear discriminant analysis (LDA) aims to finding a projection direction that

maximizes the separation of class means and minimizes the within-class variance [25]

In this section LDA is utilized to identify the discriminating variables that play an

important role in determining combustion efficiency levels All the data are partitioned

into five groups according to their efficiency levels

11

195

196

197

198

199

200

201

202

203

204

205

206

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Based on a descending order of TG ratios five efficiency levels for the lsquouprsquo area of

the soaking zone are denoted as HH H M L and LL LDA is conducted on the three

groups of the data with levels of HH M and LL

Fig 5 shows the scattering of the LDA projections of the process observations

collected at the three efficiency levels where y1 and y2 correspond to the first two LDA

components that contain most discriminant information The weighting factors ( and

) of the 16 input variables composing the projections y1 and y2 are shown in Fig 6

where and From left to right the 16 input variables are defined as

the eight AG ratio variables and the eight gas flow variables with the order of variables

of each kind P-u P-d 1-u 1-d 2-u 2-d S-u and S-d

-8 -6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

3

4

5

6

Projection y1

Pro

ject

ion

y2

HHMLL

Fig 5 Scattering of LDA projections y1 and y2 for three efficiency levels

12

207

208

209

210

211

212

213

214

215

216

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

AG_S-u-4

-2

0

2

Wei

ghtin

g fa

ctor

for y

1

AG_S-u

-101234

Wei

ghtin

g fa

ctor

for y

2

Fig 6 Weight factors of various input variables for projections y1 and y2

The two figures reveal that the three groups are clearly discriminated by the LDA

projection and the most significant variables for the different efficiency levels are the

derived variables ie the AG in the lsquouprsquo area of the soaking zone A similar result can

be obtained in the lsquodownrsquo area or any area of the other zones Therefore AG in each

heating area is the key manipulated variable that determines the different combustion

efficiency

4 Modeling and prediction of temperature and temperature-gas ratio

For the model-based operation optimization the models for the temperature and TG

ratio based on the NNG algorithm will be developed and compared

41 NNG variable selection algorithm

The NNG method can be generalized into a two-stage shrinkage method In the first

stage the sign for each variable is determined using the ordinary least square procedure

13

217

218

219

220

221

222

223

224

225

226

227

228

229

230

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

and in the second stage the corresponding magnitudes are computed by solving a series

of constrained quadratic programming

A set of observation data is provided where is the input matrix whose

columns represent the measured candidate variables and is the corresponding

vector of the response data The following expression is given with the number of the

response variable being equal to 1 but a similar procedure can be generalized to any

number of variables Let and be normalized to the zero-mean and unit standard

deviation Additionally let be a set of the ordinary least square estimates of the

coefficients of the following linear model then

(1)

The second stage shrinkage can be formulated as the following optimization problem

subject to

(2)

As decreased and the NNG is tightened more of the become zero and the

remaining nonzero coefficients are shrunk A solution path exists with on which

the appropriate shrinkage can be selected Conventionally the v-fold cross-validation is

used to estimate the prediction error and to select the best solution in the solution path

so as to minimize the prediction or model error

42 Modeling and prediction of temperature and TG ratio

The input-output relations change with time as the reheating process develops An

adaptive modeling strategy is often used to resolve time-varying characteristics of

14

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

industrial processes In this paper the NNG-based regression modeling prediction and

optimization is implemented in a moving window manner where the size of the

window and the length of the moving step are selected as 1000 and 100 respectively In

addition the prediction horizon is also set as 100 In each step the NNG regression

model is built based on the data in the current window which is then used for the

prediction and optimization in the subsequent prediction horizon Next the window

moves forward by replacing the oldest 100 samples for model training by the

observations collected in the previous prediction horizon This moving window strategy

is workable because in the reheating process the input-output relation is slowly time-

varying and the model is still valid for the prediction and optimization in the subsequent

short time

The modeling of the temperature T is based on the air flow rates and gas flow rates

while the modeling for the TG ratio is based on the AG ratios and gas flow rates

Taking the lsquouprsquo area of the soaking zone as an example the prediction result for T and

the TG ratio in the lsquouprsquo area of the soaking zone is shown in Figs 7 and 8 respectively

0 02 04 06 08 1 12 14 16 18 2

x 104

1140

1160

1180

1200

1220

1240

1260

1280

1300

1320

Sampling intervals

T S-u (

)

OriginalPredicted

Fig 7 Prediction of temperature in the lsquouprsquo area of the soaking zone

15

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

0 02 04 06 08 1 12 14 16 18 2

x 104

02

04

06

08

1

12

14

16

18

2

Sampling intervals

TG

S-u

OriginalPredicted

Fig 8 Prediction of TG ratio in the lsquouprsquo area of the soaking zone

A comparison between Figs 7 and 8 show that the prediction of the TG ratio is more

accurate than the prediction of temperature The average R2 in 190 NNG regressions is

0935 for the TG ratio while the average R2 is only 0814 for temperature This is

consistent with the statistical analysis which reveals that the correlation between AG

and TG is higher than that between A and T These results indicate that derived

variables are more meaningful for the purpose of prediction and the modeling of the

TG ratio is more appropriate for implementing optimization

The selected frequency for each variable in 190 NNG regressions and the coefficients

of each variable in 20 NNG regressions for the TG ratio modeling of the lsquouprsquo area of

the soaking zone are shown in Figs 9 and 10 respectively Fig 9 shows that the selected

frequency of the variables in the lsquouprsquo area of the soaking zone is much higher than

variables in other zones Similarly as is shown in Fig 10 the NNG regression

coefficients of the variables in the lsquouprsquo area of the soaking zone are much larger than the

variables in the other areas These results indicated that variables in the lsquouprsquo area of

16

269

270

271

272

273

274

275

276

277

278

279

280

281

282

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

soaking zone are mostly contributed to the modeling of the TG ratio in same area

which is quite reasonable Similar results can be obtained for the other areas

0

20

40

60

80

100

120

140

160

180

200

Sel

ecte

d fre

quen

cy

AGP-u AGP-d AG1-u AG1-d AG2-u AG2-d AGS-u AGS-d GP-u GP-d G1-u G1-d G2-u G2-d GS-u GS-d

Fig 9 Variable selected frequency of over 190 runs for the TG ratio model of the lsquouprsquo

area of the soaking zone

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

P-u

0 2 4 6 8 10 12 14 16 18 20-05

05

GP

-u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

P-d

0 2 4 6 8 10 12 14 16 18 20-1

0

GP

-d

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-u

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

1-d

0 2 4 6 8 10 12 14 16 18 20-05

05

G1-

d

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-u

0 2 4 6 8 10 12 14 16 18 200

1

G2-

u

0 2 4 6 8 10 12 14 16 18 20-1

0

AG

2-d

0 2 4 6 8 10 12 14 16 18 20-1

0

G2-

d

0 2 4 6 8 10 12 14 16 18 200

1

AG

S-u

0 2 4 6 8 10 12 14 16 18 20-1

0

GS

-u

0 2 4 6 8 10 12 14 16 18 20-05

05

AG

S-d

0 2 4 6 8 10 12 14 16 18 20-05

05

GS

-d

Fig 10 Part of the NNG regression coefficients of each variable over 190 runs for the

TG ratio model of the lsquouprsquo area of the soaking zone

It is remarkable that the NNG regression coefficients corresponding to the AG ratio

in the lsquouprsquo area of the soaking zone are consistently positive On the contrary the

coefficients of the gas flow rate in the same area are consistently negative This

indicates that under this condition the rise of the AG leads to the increase of the TG

17

283

284

285

286

287

288

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

while the rise of the G leads to the drop of the TG This property is helpful for

performing optimization and improve combustion efficiency

For comparison the modeling results for two other algorithms artificial neural

network (ANN) and partial least squares (PLS) [26] are compared with the NNG

algorithm in the following three aspects [27]

(1) Model Size the number of variables selected for modeling

(2) Model Magnitude the mean of the L1 norm of the regression coefficients

(3) Prediction Precision the mean squared prediction error (MSPE)

Summary of the algorithm comparison is shown in Table 2 It can be seen that the

superiorities of the NNG regression in model size model magnitude and model

precision are remarkable

Table 2 Summary of algorithm comparison

Index NNG ANN PLS

Model Size 849 16 16

Model Magnitude 10075 -- 12150

MSPE 00093 00108 00140

5 Model-based optimization

51 Implemention of model-based optimization operation

The goal of optimization is to seek an optimal combination of AG and G in the lsquouprsquo

area of the soaking zone so as to minimize the gas consumption while keeping the

temperature at the target value According to the heating schedule the most expected

temperature in the soaking zone is 1200 Therefore the target temperature

is set at this value to achieve the desired heating effect As shown in Fig 11 in the real

18

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

operation the temperature fluctuates around the target value because of the imperfect

control performance However in order to simplify the analysis and compute the

maximum possible energy saving perfect temperature control is assumed when

adopting the model-based optimization strategy In other words it is assumed that the

actual temperature in the lsquouprsquo area of the soaking zone can be adjusted to the expected

temperature ie 1200

0 02 04 06 08 1 12 14 16 18 2

x 104

1150

1200

1250

1300

Sampling intervals

T S-u (

)

OriginalTarget

Fig 11 Original and target temperature in the lsquouprsquo area of the soaking zone

The adjustment scheme takes the maximum value and minimum value of the original

operation data as the upper and lower bounds for the adjustment Moreover in order to

assure the validity of the linear model the increment or decrement of AG and G should

not beyond of the original value (considered as 10 for the purposes of this paper)

The adjustment strategy can be formulated as

19

307

308

309

310

311

312

313

314

315

316

317

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(3)

where NNG() denotes the NNG regression model of the TG ratio and are the

NNG regression coefficients of the AG and G in the lsquouprsquo area of the soaking zone for

modeling TG in same area

With the model-based strategy and adaptive model of the TG ratio given in Section

42 the optimization adjustment results can be obtained as follows

The adjustment of gas flow in the lsquouprsquo area of the soaking zone shown in Fig 12

illustrates that the implementation of the model-based optimization operation can reduce

the consumption of the gas flow Compared with the original case 938 of the gas can

be saved on average by utilizing the model-based adjustment

0 02 04 06 08 1 12 14 16 18 2

x 104

-800

-700

-600

-500

-400

-300

-200

-100

0

Sampling intervals

Adj

ustm

ent o

f gas

flow

m（

3 h）

20

318

319

320

321

322

323

324

325

326

327

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

(a) Adjustment amount of gas flow

0 02 04 06 08 1 12 14 16 18 2

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000G

as fl

owm

（3 h

）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted gas flow

095 096 097 098 099 1 101 102 103 104 105

x 104

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Gas

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted gas flow in interval [9501-10500]

Fig 12 Adjustment of gas flow in the lsquouprsquo area of the soaking zone

The adjustment of the air flow in the lsquouprsquo area of the soaking zone given in Fig 13

shows that the air flow is reduced in most cases and only increased for a few cases In

21

328

329

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

general 681 of the air flow is reduced after the implementation of the model-based

optimization

0 02 04 06 08 1 12 14 16 18 2

x 104

-2000

-1500

-1000

-500

0

500

1000

Sampling intervals

Adj

ustm

ent o

f air

flow

(m3 h

)

(a) Adjustment amount of air flow

0 02 04 06 08 1 12 14 16 18 2

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(b) Comparison of original and adjusted air flow

22

330

331

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

095 096 097 098 099 1 101 102 103 104 105

x 104

4000

5000

6000

7000

8000

9000

10000

Air

flow

m（

3 h）

Sampling intervals

OriginalAdjusted

(c) Comparison of original and adjusted air flow in interval [9501-10500]

Fig 13 Adjustment of air flow in the lsquouprsquo area of the soaking zone

52 Discussions

In this section detailed analysis for the optimization operation results is provided

The statistics of optimization at the boundary conditions shown in Table 3 illustrates

that the adjusted value for G reaches its lower limit in most cases (8045 for

and 687 for ) which is the most energy-efficient point In a number of cases

(1079 for and 001 for ) the adjusted AG reaches its upper

limit These results indicate that the optimization operations maximize the combustion

efficiency by decreasing G and increasing the AG ratio up to the boundary conditions

However the lower limit is also unexpectedly attained in a small number of cases

(110 for and 078 for ) for which a more detailed analysis is

given below

23

332

333

334

335

336

337

338

339

340

341

342

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

Table 3 Statistics of optimization at boundary conditions

Total

Amount 0 1374 0 16090 17464

Percentag

e 0 687 0 8045

8732

Total

Amount 2 220 2158 156 2536

Percentag

e 001 110 1079 078

1268

Table 4 Statistics for different optimization operations

Adjustment

Gdarr

Guarr TotalAGuarr AGdarr

Tdarr Tuarr Tdarr Tuarr

Amount 9548 3744 6328 380 0 20000

Percentage 4774 1872 3164 190 0 100

The statistics for different optimization operations is performed and shown in Table

4 It can be seen that all the adjusted operations result in the reduction of gas

consumption In over half the cases (4774 with decreased temperature and 1872

with increased temperature) AG is adjusted to higher levels Meanwhile a number of

the adjustments (3164) lower the temperature by reducing the G and AG at the same

time This result indicates that the original temperature cannot be adjusted to the target

by only reducing G in the constraint conditions The remaining cases (19) are

24

343

344

345

346

347

348

349

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

relatively special in which an excess of air is supplied in the original operation and the

adjusted operation thereby increasing the temperature by a smaller AG with less gas

consumption

6 Conclusion

Based on the actual operation data this paper aims to explore the improvement of the

combustion efficiency and the room for energy conservation Correlation analysis and

LDA show that it is of great significance to introduce two derived ratio variables which

are the AG ratio and the TG ratio A type of combustion efficiency utilizing an on-line

soft sensor is put forward by employing a NNG variable selection algorithm which

provides a good solution to the combustion efficiency real-time measurement problem

of a reheating furnace The implementation of the model-based optimization is studied

based on the actual operational data Detailed analysis for the optimization results is

given for the different cases The results show that significant energy conservation can

be achieved when the furnace operation is optimized by using the developed soft sensor

model

Acknowledgement

The authors would like to thank the financial support provided by the National Nature

Science Foundation of China under Grant 61171145 Y Yao was supported by Ministry

of Science amp Technology ROC under Grant number MOST 104-2221-E-007-129

References

25

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[1] Z J Wang Q D Wu and T Y Chai Optimal-setting control for complicated

industrial processes and its application studyControl Engineering Practice vol

12 pp 65-74 2004

[2] A Steinboeck K Graichen and A Kugi Dynamic Optimization of a Slab

Reheating Furnace With Consistent Approximation of Control VariablesIEEE

Transactions on Control Systems Technology vol 19 pp 1444-1456 2011

[3] B T Zhang C Y Wang Q Qin and L Li Influence of Boiler Combustion

Adjustment on NOxEmission and Boiler EfficiencyAdvanced Materials

Research vol 732-733 pp 234-237 2013

[4] C K Yoo and IB Lee Soft Sensor and Adaptive Model-Based Dissolved

Oxygen Control for Biological Wastewater Treatment ProcessesEnvironmental

Engineering Science vol 21 pp 331-340 2004

[5] S A Bhat D N Saraf S Gupta and S K Gupta Use of Agitator Power as a

Soft Sensor for Bulk Free-Radical Polymerization of Methyl Methacrylate in

Batch ReactorsIndustrial amp Engineering Chemistry Research vol 45 pp 4243-

4255 2006

[6] K Desai Y Badhe S S Tambe and B D Kulkarni Soft-sensor development

for fed-batch bioreactors using support vector regressionBiochemical

Engineering Journal vol 27 pp 225-239 2006

[7] Y P Badhe Lonari J Tambe S S amp Kulkarni B D Improve polyethylene

process control and product qualityHydrocarbon Processing vol 86 pp 53-60

2007

26

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[8] N K Nath K Mandal A K Singh B Basu C Bhanu S Kumar et al Ladle

furnace on-line reckoner for prediction and control of steel temperature and

compositionIronmaking amp Steelmaking vol 33 pp 140-150 2006

[9] A J Yan T Y Chai F H Wu and P Wang Hybrid intelligent control of

combustion process for ore-roasting furnaceJournal of Control Theory and

Applications vol 6 pp 80-85 2008

[10] J Li W M Zhong H Cheng X D Kong and F Qian A data-driven soft

sensor modeling for furnace temperature of Opposed Multi-Burner gasifier pp

705-710 2011

[11] Y H Yang Y H Liu X Z Liu and S K Qin Billet temperature soft sensor

model of reheating furnace based on RVM method pp 4003-4006 2011

[12] J H Wang C Wang X F Zhu and X K Fang Application of soft sensor in

welding seam tracking prediction based on LSSVM and PSO with compression

factor pp 2441-2446 2013

[13] L Balbis J Balderud and M J Grimble Nonlinear predictive control of steel

slab reheating furnace pp 1679-1684 2008

[14] A Steinboeck D Wild T Kiefer and A Kugi A mathematical model of a slab

reheating furnace with radiative heat transfer and non-participating gaseous

media International Journal Of Heat And Mass Transfer vol 53 pp 5933-

5946 Dec 2010

[15] A Steinboeck D Wild and A Kugi Nonlinear model predictive control of a

continuous slab reheating furnace Control Engineering Practice vol 21 pp

495-508 2013

27

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[16] C Zhang T Ishii and S Sugiyama Numerical Modeling Of the Thermal

Performance Of Regenerative Slab Reheat Furnaces Numerical Heat Transfer

Part A Applications vol 32 pp 613-631 1997

[17] J G Kim and K Y Huh Prediction of Transient Slab Temperature Distribution

in the Re-heating Furnace of a Walking-beam Type for Rolling of Steel Slabs

ISIJ International vol 40 pp 1115-1123 2000

[18] J G Kim K Y and H I T K Three-Dimensional Analysis Of the Walking-

Beam-Type Slab Reheating Furnace In Hot Strip Mills Numerical Heat

Transfer Part A Applications vol 38 pp 589-609 2000

[19] CT Hsieh MJ Huang ST Lee and CH Wang Numerical Modeling of a

Walking-Beam-Type Slab Reheating Furnace Numerical Heat Transfer Part A

Applications vol 53 pp 966-981 2008

[20] MJ Huang CT Hsieh ST Lee and CH Wang A Coupled Numerical Study

of Slab Temperature and Gas Temperature in the Walking-Beam-Type Slab

Reheating Furnace Numerical Heat Transfer Part A Applications vol 54 pp

625-646 2008

[21] Z Song and A Kusiak Constraint-Based Control of Boiler Efficiency A Data-

Mining Approach IEEE Transactions on Industrial Informatics vol 3 pp 73-

83 2007

[22] J Q Li J J Gu and C L Niu The Operation Optimization based on

Correlation Analysis of Operation Parameters in Power Plant pp 138-141

2008

28

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451

A Soft-Sensing Method for Optimization of Combustion Efficiency of Reheating Furnaces

[23] J G Wang S S Shieh S S Jang D S H Wong and C W Wu A two-tier

approach to the data-driven modeling on thermal efficiency of a BFGcoal co-

firing boiler Fuel vol 111 pp 528-534 Sep 2013

[24] L Breiman Better Subset Regression Using the Nonnegative Garrote

Technometrics vol 37 pp 373-384 1995

[25] R A Fisher The use of multiple measurements in taxonomic problems

AnnHum Genet vol 7 pp 179-188 1936

[26] J Liu Developing a soft sensor based on sparse partial least squares with

variable selection Journal of Process Control vol 24 pp 1046-1056 2014

[27] K Sun J Liu JL Kang SS Jang D SH Wong and DS Chen

Development of a variable selection method for soft sensor using artificial

neural network and nonnegative garrote Journal of Process Control vol 24 pp

1068-1075 2014

29

439

440

441

442

443

444

445

446

447

448

449

450

451