end temperature prediction of molten steel in lf based on cbr

End Temperature Prediction of Molten Steel inLF Based on CBR

Fei He, Anjun Xu, Hongbing Wang, Dongfeng He,� and Naiyuan Tian

In order to improve the temperature control level of molten steel in ladle furnace (LF), a

case-based reasoning (CBR) method has been proposed for predicting end temperature of

molten steel in LF. To predict the temperature accurately and efficiently, this paper

develops two-step retrieval approach and the correlation based feature weighting (CFW)

method for CBR. And, the study evaluates the prediction effect of CBR method by the

experiment of comparison with back propagation neural network (BPNN) model and CBR

model. Experimental results show that CBR model achieves better accuracy than BPNN

model and the CBR method is effective to predict end temperature of molten steel in LF.

1. Introduction

Ladle furnace (LF) is an effective method of secondary

refining, which was in virtue of some measures of heating

up by the electric arc, reductive slag, and argon blowing to

achieve the aims of rapid deoxidation, desulfurization,

mixing the temperature and components of liquid steel,

and removing the inclusion from the molten steel effi-

ciently. LF refining processing not only can improve the

quality of the molten steel and control steel temperature,

but also is a ‘‘lung’’ unit between the LD converter and

continuous casting for the need of sequential production

of continuous casting to attain high productivity. So LF is

more and more necessary in the steel industry.

As known, the main purpose of LF refining processing is

to get the qualified molten steel temperature and compo-

sition. So it is very important to control the temperature of

molten steel in LF accurately. A method of improving the

temperature control level of molten steel in LF is to predict

the temperature of molten steel in LF actively. At present,

the studies for predicting the temperature of molten steel

in LF can be mainly divided into two methods: mechanistic

method and intelligent method.

About mechanistic method, for example, a thermal

model for on-line application was presented for LF by

Nath et al.,[1] where the parameters were evaluated which

can be classified as heat loss to refractory lining, heat loss

due to holding and purging, heat gain due to arcing and

heat effects of additions, and then the total temperature

effect in LF was obtained by calculating the sum of the

parameters. Wu et al.[2] also proposed a prediction model

of molten steel temperature in LF based on energy equi-

librium by the calculation and analysis of energies going

into and out of the LF system. The mechanistic model is

very important for temperature prediction of molten steel

in LF.

But unfortunately, a lot of theoretical assumptions

and too many parameters are involved in the traditional

mechanistic methods, and due to the nonlinearity and

the complexity of the LF process, mechanistic method

is difficult to get better prediction. Therefore, many

researchers proposed intelligent method to predict the

temperature of molten steel in LF for improving the pre-

diction accuracy. For example, Tian et al.[3,4] proposed to

predict the temperature of molten steel in LF by genetic

algorithm combined with BP neural network, and to pre-

dict the molten steel temperature in LF by using hybrid

model which was comprised of a new ensemble ELM

(extreme learning machine)[5] algorithm using the modi-

fied AdaBoost.RT (R stands for regression and T for

threshold)[6] and thermal model. The intelligent methods

have good prediction accuracy for the temperature of

molten steel in LF.

In this research, a case-based reasoning (CBR) method

is proposed for end temperature prediction of molten steel

in LF. Firstly, through the mechanism analysis of LF refin-

ing process and the analysis of energy equilibrium, the

influence factors of molten steel temperature in LF are

determined. Then the CBR prediction model is established

and validated by the experiments. The main idea of CBR is,

[�] F. He, A. Xu, Dr. D. He, N. TianState Key Laboratory of Advanced Metallurgy,University of Science and Technology Beijing, Beijing, 100083, ChinaEmail: [email protected]. WangSchool of Computer and Communication Engineering,University of Science and Technology Beijing, Beijing, 100083, China

DOI: 10.1002/srin.201200028

www.steel-research.de

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim steel research int. 83 (2012) No. 9999 1

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based on the current description of the problem and effec-

tive historical case base, to search cases similar to current

case in the case base, then to make use of the solutions of

similar cases, to construct the solution for current prob-

lem. At present, CBR method has been applied in converter

steelmaking field. For example, Han and Wang[7] has used

CBR for converter steelmaking dynamic oxygen volume

control, and used mutual information CBR for prediction

of oxygen decarburization efficiency.[8] CBR has been

applied widespreadly in many fields, such as computer,[9]

medical diagnosis,[10] and so on.

2. Description of LF Refining Process

2.1. Process Flow of LF

High temperature steel in ladle from LD converter is after

many process from reaching LF to exit. The whole process

flow in LF is shown in Figure 1. Here, ladle furnace is twin-LF.

2.2. Analysis of LF Energy Equilibrium

During LF refining process, there is an important principle

– called energy equilibrium, as shown in Figure 2. In other

words, if LF is a system, the input energy, the output

energy, and the energy absorbed by the system should

achieve the balance, as shown in formula (1). The input

energy of LF system are mainly heat gain due to arcing

(Qarc) and heat effects of additions (Qadd). The output

energy of LF system are heat loss from the top surface

(Qsurf), heat loss from ladle refractory lining which is com-

posed of two parts: convection loss to atmosphere from

ladle shell (Qshell) and heat content absorbed by ladle lining

(Qin), and heat loss due to argon stirring (Qargon). The

energy absorbed by LF system (DQ) is used to make the

temperature of molten steel rising.

Qarc þ Qadd ¼ Qsurf þ Qshell þ Qin þ Qargon þ DQ (1)

2.3. Influence Factors of Molten Steel Temperature in LF

Through the analysis of LF energy equilibrium, the influ-

ence factors of molten steel temperature in LF are further

clear. In the paper, based on the analysis of LF energy

equilibrium and the actual production process, they are

the eight factors that mainly affect the end temperature of

molten steel in LF: steel grade, ladle heat status, the starting

temperature of molten steel in LF, the weight of molten

steel, heat effects of additions, power duration time, the

refining time, and the argon consumption. The factors’

characteristics are shown in Table 5 through descriptive

statistics of production data.

Here, the starting temperature of molten steel in LF is

the first temperature being measured in LF refining proc-

ess. The end temperature of molten steel in LF is the last

temperature being measured in LF refining process. Ladle

heat status is comprised of the ladle conditions and the

Treatment Position

Ladle Arrival

Refining Step 1

Adjust Step

connect blow argon tube

1.argon stirring2.furnace cover

lowering

1.temperature measuring and sampling

2.additions adding3. power supply

4.slagging5.argon stirring

6.composition rough adjusting

6. temperature adjusting

1.electrodes prepare2.alloy additions prepare

3.equipment system confirm4.electrifying conditions

permit5.the cooling water flow

confirm6.hydraulic system confirm

Refining Step 2

1.alloy adjusting2.temperature measuring and

sampling3.power supply4.argon stirring

5. composition fine adjusting

6.temperature control1.temperature adjusting

2.wire feeding3.argon stirring

Ladle Exit

End of Treatment

1.electrodes lifting2.power off

3. temperature measuring and

sampling4.furnace cover lifting5.remove blow argon

cube 6.ladle car out

Figure 1. Process flow diagram of LF.

LadleFurnace

QarcQsurf

Qadd

Qshell

Qin

Qargon

Q

Figure 2. The energy equilibrium of LF (Qarc, heat gain due toarcing; Qadd, heat effects of additions; Qsurf, heat loss from thetop surface; Qshell, convection loss to atmosphere from ladleshell; Qin, heat content absorbed by ladle lining; Qargon, heatloss due to argon stirring; DQ, the energy absorbed by thesystem).


2 steel research int. 83 (2012) No. 9999 � 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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residual skull conditions in the ladle bottom, as shown

in Table 1. Total heat effect of alloy and slag additions is

calculated by formula (2), Table 2 and the amount of each

alloy and slag addition. Power duration time represents

the refining power consumption. The refining time is from

the starting time to the ending time of LF refining process.

The argon consumption represents the heat due to argon

stirring.

DTadd ¼X

i

WiQi (2)

where, DTadd is total heat effect of alloy and slag additions,

or temperature change caused by alloy and slag additions

(8C); i designates a specific addition (metal alloy or slag); Wi

is the weight of addition i (kg); Qi is the temperature change

of molten steel for 1 kg of i (8C). The statistical average of

the heat effect of various additions is shown in Table 2.

Ladle class Code Evaluation criterion

Ladle

conditions

On-line ladle 1 The interval from casting ending to next tapping of converter is in 1.5 h.

2 The interval from casting ending to next tapping of converter is 1.6–3 h.

3 The interval from casting ending to next tapping of converter is 3–5 h.

4 The interval from casting ending to next tapping of converter is more than 5 h,

and then the ladle preheats for 2 h and goes to converter for tapping in 1 h.

5 1. The interval from the second casting ending of repair ladle to next tapping

of converter is in 3 h.

2. The interval from the second casting ending of repair ladle to next tapping

of converter is more than 3 h, and then the ladle preheats for more than 2 h

and goes to converter for tapping in 1 h.

3. Very cold ladle which ladle condition called 7 or 8 is used secondly.

Repair ladle 6 After drying, the ladle must preheat for 2 h continuously and goes to converter

for tapping in 1 h.

Very cold

ladle

7 The interval from casting ending to next tapping of converter is more than 5 h,

and the ladle is unable to realize preheating for 2 h.

8 The interval from the second casting ending of repair ladle to next tapping of

converter is more than 3 h, and the repair ladle is unable to realize preheating

for more than 4 h.

Residual

skull

conditions

Residual

amount

A 0–0.5 t

B 0.6–1.0 t

C 1.1–1.5 t

D 1.6–2.0 t

E 2.1–2.5 t

F �2.6 t

Table 1. The division of ladle heat status.

Serial no. Addition DT [8C]

1 C �2.50

2 HcFeMn �0.90

3 LcFeMn �0.75

4 FeSi þ1.00

5 Slag �0.70

6 Al þ5.00

7 FeNb �0.35

8 FeTi �0.40

9 CaSi �1.05

Table 2. Heat effects of various additions for 100 kg addition for300 t of molten steel.



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3. CBR Prediction Method for EndTemperature of Molten Steel in LF

3.1. Construction of Case Base

3.1.1. Case Representation

Through above analysis, influence factors of end tempera-

ture of molten steel in LF are steel grade, ladle heat status,

the starting temperature of molten steel in LF, the weight of

molten steel, heat effects of additions, power duration

time, the refining time, and the argon consumption.

Steel grade and ladle heat status are discrete attributes,

and other influence factors are continuous attributes. In

the paper, a case represents an attributes-value pair. The

attributes are influence factors. Value is the end tempera-

ture of molten steel in LF. So case representation is shown

in Figure 3.

3.1.2. Construction of Case Base

Based on the case presentation, the production data from

300 t LF in a steel plant which called Q from June to

December in 2011 are collected. And some pre-processing

steps are carried up on the raw data, such as removing the

blank data and deciding a range for each parameter, and so

on. Then, 3847 heats are remained and become the stored

cases of case base.

3.2. Case Retrieval

3.2.1. Case Retrieval Scheme

Based on the characteristics of case attributes, two-step

retrieval scheme is adopted in the research, as shown

in Figure 4. First retrieval is retrieval of discrete attributes.

That is to say the matching cases are selected from the

stored cases according to the rule which matching cases

and the new case should have the same discrete attributes.

Second retrieval is retrieval of continuous attributes. The

core of second retrieval is the similarity calculation

between the new case and the stored cases. In the paper,

k-nearest neighbor retrieval is adopted for second retrieval,

and the correlation based feature weighting (CFW)

method[11,12] is used to compute the weight of each con-

tinuous attribute.

3.2.2. Calculation of the Weights of Continuous Attributes

Correlation based feature weighting (CFW) method[11,12] is

used to compute the weights of continuous attributes. The

calculation takes as the following steps:

(1) Calculate the Pearson correlation coefficient of each

attribute and the end temperature of molten steel in

LF. Here, the Pearson correlation coefficient is calcu-

lated as formula (3). The result is shown in Table 3.

R ¼

Pni¼1

ðXi � X ÞðYi � Y ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1

ðXi � X Þ2s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1

ðYi � Y Þ2s (3)

where, a sample can be expressed as (X)ðXi;YiÞ; R is the

Pearson correlation coefficient between the attribute X

and Y; X and Y are the mean of the samples; n is the

number of the samples.

(2) Calculate the weight of each attribute as formula (4).

The result is shown in Table 4.

wi ¼Rij jP

iRij j

(4)

where, wi is the weight of the ith attribute; Ri is the

correlation between the ith attribute and the end

temperature of molten steel in LF.

3.2.3. Calculation of the Similarity

For continuous attributes, the similarity[13] between

the new case and the stored case can be calculated as

A Case

Attributes

Value

Discrete Attributes

Continuous Attributes

steel grade

ladle heat status

molten steel weight

starting temperature

refining time

argon consumption

power duration time

end temperature

heat effects of addtions

Figure 3. Case representation.

Figure 4. Case retrieval scheme.



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formula (5).

Sim ðCstored;CnewÞ ¼

Pni¼1

wi � sim ðxstoredi ; xnew

i Þ

Pni¼1

wi

(5)

where, n is the number of the attributes; sim ðxstoredi ; xnew

i Þ is

the similarity of the ith attribute between two cases, the

calculation formula is shown as follows. In order to avoid

confusion, Sim refers to the overall similarity and sim refers

to the local similarity.

sim ðxstoredi ; xnew

i Þ ¼ 1�xstored

i � xnewi

�� xmax

i � xmini

(6)

3.2.4. Retrieval of Continuous Attributes

Retrieval of continuous attributes is the core of case

retrieval. k-Nearest neighbor retrieval is adopted for

retrieval of continuous attributes. So the matching cases

are selected according to the size of the similarity. In the

Discrete variables Description

Steel grade 21 kinds of steel, for example, SS400, Q235, SPHC, SPHD, SPHE,

DH36, 510L, X60, X70, X80 and so on.

Ladle heat status 48 kinds of ladle heat status from Table 1, for example, 1A, 2A, 3A,

4A, 5A, 6A, 1B, 2B, 3B, and so on.

Continuous variables Mean Minimum Maximum Standard deviation

Molten steel weight [t] 277.26 210.00 300.07 11.56

Starting temperature [8C] 1575.50 1520.00 1649.00 19.73

Refining time [min] 41.12 7.00 90.00 13.80

Argon consumption [Nl] 42096.44 1017.00 168593.00 21101.84

Power duration time [min] 7.71 1.67 28.15 3.81

Heat effects of additions [8C] 6.70 �38.00 44.00 6.24

End temperature of molten steel in LF [8C] 1571.29 1546.00 1614.00 9.24

Table 5. Descriptive statistics of the process variables.

Molten

steel

weight

Starting

temperature

Refining

time

Argon

consumption

Power

duration

time

Heat

effects of

additions

End temperature �0.0455 0.2524 0.1293 0.0976 0.2012 �0.0470

Symbol R1 R2 R3 R4 R5 R6

Table 3. The correlation between each attribute and the end temperature of molten steel in LF.

The

attributes

Molten

steel

weight

Starting

temperature

Refining

time

Argon

consumption

Power

duration

time

Heat

effects of

additions

The weights, wi 0.0589 0.3265 0.1672 0.1263 0.2603 0.0608

Table 4. The weight of each attribute.



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paper, the matching case is not the case with maximum

similarity, but a case set including the cases whose sim-

ilarities are greater than a specific threshold value.

3.3. Case Reuse

Case reuse is to construct the resolve of current problem,

according to the results of case retrieval. The paper uses the

following formula (7) to construct the resolve of current

problem. The resolve of current problem is also the pre-

diction value of the new case.

TCnew ¼

Pi

Sim ðCi;CnewÞ � TiPi

Sim ðCi;CnewÞ ; Sim ðCi;CnewÞ � S (7)

where, TCnew is the prediction value of the new case;

Sim ðCi;CnewÞ is the similarity between the new case and

the case i in case base; Ti is the actual value of the case i, S is

a threshold value of the similarity, and S is 0.85 in the study.

4. Experiments

4.1. Design of Experiments

As mentioned in Section 3.1.2, 3847 heats are remained and

become the stored cases of case base. And other 309 heats

are also obtained from Q steel plant and used to test the

prediction accuracy of CBR model.

In the paper, to validate better the prediction effect, a

prediction model for end temperature of molten steel in LF

based on back propagation neural network (BPNN) is also

established and is compared with CBR prediction model.

Here, BPNN model is designed as follows: BP neural net-

work consists of three layers: the input layer, the hidden

layer, and the output layer. And the transfer function in the

hidden layer is sigmoid tangent function and the transfer

function in the output layer is linear transfer function. BP

network training function is trainlm function. BP neural

network’s input variables are the starting temperature of

molten steel in LF, the weight of molten steel, heat effects

of additions, power duration time, the refining time, and

the argon consumption. BP neural network’s output var-

iable is the end temperature of molten steel in LF. Since

there are six input variables and one output variable, the

input layer of the network contains six neurons and the

output layer contains one neurons. And six BPNN models

have been developed separately for prediction by varying

the number of neurons in the hidden layers and can be

seen in Table 6. Then the training data set of BPNN models

uses the same 3847 heats in case base of CBR model, the

test data set of BPNN models uses the same 309 test heats

of CBR model.

4.2. Results and Discussion

Descriptive statistics for all input and output variables of

the prediction models are showed in Table 5.

The experiments that predict the temperature are car-

ried out according to the above analysis. The 309 test heats

are predicted by CBR model and BPNN models. The results

are shown in Table 6 and Figure 5–8.

Table 6 is hit rate of prediction with CBR model and best

BPNN models. It can be observed that the hit rate of CBR

model is 97.41% with the error limit of 108C, and the hit rate

of the best BPNN model is 95.15% with the error limit of

108C. The hit rate of CBR model is 88.35% with the error

limit of 78C, and the hit rate of the best BPNN model is

82.20% with the error limit of 78C. The hit rate of CBR

model is 76.38% with the error limit of 58C, and the hit rate

of the best BPNN model is 65.37% with the error limit of

58C. Obviously CBR model has better prediction accuracy

than the BPNN models for the end temperature of molten

steel in LF. Here, the hit rate of prediction is the ratio of hit

Model Temperature error range

[�58C, 58C] [�78C, 78C] [�108C, 108C]

CBR 76.38% 88.35% 97.41%

BPNN (MLP 6-5-1) 65.05% 81.23% 94.17%

BPNN (MLP 6-10-1) 65.37% 80.58% 95.15%

BPNN (MLP 6-16-1) 64.40% 81.55% 94.82%

BPNN (MLP 6-6-10-1) 63.43% 82.20% 93.53%

BPNN (MLP 6-10-17-1) 62.78% 81.23% 94.50%

BPNN (MLP 6-15-8-1) 64.72% 79.94% 95.15%

Table 6. Hit rate of predicted temperature with CBR model and best BPNN models.



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heats in all calculated heats which can be calculated as

formula (8).

Hp ¼Nhit

Nall(8)

where, Hp is the hit rate of prediction, Nhit is the number of

heats that hit the target, and Nall is the number of all

calculated heats.

Figure 5 and 6 show the comparison of actual tempera-

ture, predicted temperature by CBR model and the best

BPNN model (MLP 6-10-1). From Figure 5 and 6, the

Pearson correlation between actual temperature and pre-

dicted temperature by CBR model is 0.7237, and the Pearson

correlation between actual temperature and predicted

temperature by the BPNN model is 0.6439. Figure 7 and 8

show temperature deviation of prediction of CBR model

and the best BPNN model (MLP 6-10-1). The temperature

deviation of prediction is the difference between the pre-

dicted temperature and the actual temperature. From

Figure 7 and 8, root mean square error (RMSE) of CBR

model is 4.41, and RMSE of the BPNN model is 5.38.

Obviously, the results of the CBR model are better than

the best BPNN model through above analysis. Here, RMSE

is used to evaluate the precision of the model which can be

calculated as follows:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1

ðTpredicted � TactualÞ2

n

vuuut(9)

where, Tpredicted is the predicted value, Tactual is the actual

value, n is the number of the predicted samples.

Through above analysis, some comparisons are carried

on from modeling and test results of using CBR and BPNN

method for predicting end temperature of molten steel in

LF. Firstly, in the paper, one of the biggest differences for

CBR model and BPNN model is selection of input variables.

There are eight input variables in CBR model, and there are

six input variables in BPNN model. Because two discrete

variables – steel grade and ladle heat status cannot be input

variables of BPNN model directly. But steel grade and ladle

Figure 5. The comparison of actual temperature and predictedtemperature using CBR model.

Figure 6. The comparison of actual temperature and predictedtemperature using BPNN (MLP 6-10-1) model.

Figure 7. Temperature deviation of actual and predicted usingCBR model.

Figure 8. Temperature deviation of actual and predicted usingBPNN (MLP 6-10-1) model.



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heat status have very important influence for end tempera-

ture of molten steel in LF, and if the two discrete variables

are ignored, prediction results are also affected. Secondly,

though BPNN method has good prediction effect in many

studies about end temperature prediction of molten steel

in LF, CBR method can obtain better prediction effect than

BPNN method for the practical problem in the study. At

last, about on-line application of prediction model, CBR

method in the study has the advantage of convenience of

modeling, high efficiency, and good robust characteristic.

In addition BPNN method needs long training time and

long-term maintenance.

Therefore, CBR method is more suitable for end

temperature prediction of molten steel in LF. This is mainly

because of the neglecting of two discrete variables in BPNN

method as mentioned above. This is not due to difference

of the methods. If the base data is sorted out according

to the two discrete variables in applying BPNN method,

BPNN method may give better prediction than CBR

method. And in the study the CBR model has good pre-

diction accuracy for the practical problem. In other words,

the CBR method is effective to predict end temperature of

molten steel in LF.

5. Conclusions

In the paper, a CBR method has been proposed for pre-

dicting end temperature of molten steel in LF.

Through the analysis of the actual LF refining process

and energy equilibrium, main influence factors of end

temperature of molten steel in LF are determined.

In the CBR method, the prediction value of end

temperature of molten steel in LF is obtained by construc-

tion of case base, case retrieval, and case reuse. The core of

the CBR method is the calculations of similarity and the

weights of continuous attributes. The paper uses k-nearest

neighbor retrieval and computes the weights by CFW

method for CBR.

To validate the prediction effect, the experiments of

comparison with the CBR model and the BPNN models

are carried on. The results show that the CBR model has

better prediction accuracy than the best BPNN model, and

the CBR method is effective to predict end temperature of

molten steel in LF.

Acknowledgments

This research is supported by Fundamental Research

Funds for the Central Universities of China (no. FRF-BR-

10-027B and no. FRF-TP-12-086A).

Received: February 8, 2012

Keywords: back propagation neural network; case-based

reasoning; end temperature prediction; ladle furnace;

molten steel

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end temperature prediction of molten steel in lf based on cbr

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