research article the optimization of chiller loading by adaptive...

Research ArticleThe Optimization of Chiller Loading by Adaptive Neuro-FuzzyInference System and Genetic Algorithms

Jyun-Ting Lu Yung-Chung Chang and Cheng-Yi Ho

Department of Energy and Refrigerating Air-Conditioning Engineering National Taipei University of TechnologyNo1 Section 3 Zhongxiao E Road Taipei 10608 Taiwan

Correspondence should be addressed to Jyun-Ting Lu rasheed0701hotmailcom

Received 8 May 2015 Accepted 21 June 2015

Academic Editor Zhike Peng

Copyright copy 2015 Jyun-Ting Lu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A central air-conditioning (AC) system includes the chiller chiller water pump cooling water pump cooling tower and chilledwater secondary pumps Among these devices the chiller consumesmost power of the central AC system In this paper the adaptiveneuro-fuzzy inference system (ANFIS) and genetic algorithm (GA) were utilized for optimizing the chiller loading The ANFIScould construct a power consumptionmodel of the chiller reduce modeling period andmaintain the accuracy GA could optimizethe chiller loading for better energy efficiency The simulating results indicated that ANFIS combined with GA could optimize thechiller loading The power consumption was reduced by 632ndash1896 when partial load ratio was located at the range of 06sim095The chiller power consumption model established by ANFIS could also increase the convergence speedTherefore the ANFIS withGA could optimize the chiller loading for reducing power consumption

1 Introduction

The air-conditioning system is highly demanded in humanrsquoslife and industrial process However it consumes electricalpower with the ratio around 50 [1 2] Therefore how toreduce the power consumption of air-conditioning systemmay be one of the most important issues to utilize the ACsystem and achieve energy The AC system includes windowseparating and central types Among them the central typeis suitable for office and factory and so forth

A central air-conditioning system includes the chillerchiller water pump cooling water pump cooling watertower and chilled water secondary pumps Among thesedevices the chiller consumes most power of the central air-conditioning system The consumed energy is related to theloading of system

There were several literatures discussing how to opti-mize the chiller loading Braun et al (1989) proposed theequal loading distribution (ELD) method This method wasestablished under the same operating characteristics of chiller[3ndash5] Due to the different operating characteristics of thechiller Braun et al suggested that the power consumptionof the chiller was correlated with load of air conditioners

cooling water return temperature and chiller water sup-ply temperature This correlation may explain the optimalchiller loading (OCL) method Chang et al (2005) adoptedpartial load ratio (PLR) method as gene coding principleof genetic algorithm (GA) to minimize power consumptionof the chiller which served as an objective function Theresults showed that Lagrangian multiplier method (LGM)could converge the low load conditions and achieve highaccuracy performance [6] Bonissone et al (2006) discussedimplicit and explicit knowledge representation mechanismsfor evolutionary algorithms and applied domain customizedmutation operators for a well-sampled Pareto front showingall the nondominated solutions [7] Haber and Alique (2007)applied fuzzy-logic for torque control system embedded inan open-architecture computer numerical control (CNC) [8]Martın et al (2009) proposed GA applied to the networkedcontrol of a high performance drilling process for optimaltuning of a linear controller [9] Lee and Lin (2009) appliedparticle swarm optimization (PSO) method for optimizingthe chiller loading design and operating strategies of air-conditioning system [10] Lee et al (2011) compared theresults of differential evolution algorithm with equal loadingdistribution as well as LGM and PSO [11] Gajate et al

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 306401 10 pageshttpdxdoiorg1011552015306401

2 Mathematical Problems in Engineering

(2012) proposed two model-based approaches for tool wearmonitoring on the basis of neuro-fuzzy techniques Thecomparative study demonstrates that the transductive neuro-fuzzymodel provides better error-based performance indices[12] Chen et al (2014) utilize neural networks (NN) toestablish the power consumption model of the chiller andPSO for optimal loading and saving energy [13]

From the previous studies the equal loading distributionmethod was often used to reduce power consumption How-ever the LGMmay cause system divergenceTheNNmethodadopted try-and-error principle to find number of betterneurons on a hidden layer It may cause longer period Hencethere is no single method suitable for all the conditions

In the study the ANFIS combined with GA are utilized tooptimize the chiller loading and reduce the power consump-tion and operating period

2 System Architecture

The general decoupled system of a central air-conditioningsystem is shown in Figure 1 [14] The common piping isthe division line of the central air-conditioning system Forseparating the system into two parts including the firstside (chiller side) and secondary side (load side) the firstside contains the chiller and chiller water pump and thesecondary side is chilled water secondary pumps and airhanding unit The secondary variable frequency pump isinstalled on the secondary side for controlling the flow speedto improve energy efficiencyThe total load of this system canbe expressed by

CL = 119862119901 (119879chwr minus119879chws) (1)

where CL is the cooling load (kW) is the flow rate of chillerwater (kgs) 119862119901 is the specific heat capacity of chilled water(JkgsdotK) 119879chwr is the cooling water return temperature (K)and 119879chws is the chilled water supply temperature (K)

3 Chiller Power Consumption Model

Generally speaking the capacity of the chiller is designed tomeet the need of peak load However most of the chiller isoperated under the condition of partial load and this wouldresult in larger designed capacity and power consumptionThe partial load ratio of a chiller is defined in

PLR =

cooling loadchiller capacity

(2)

The variables of the power consumption model includechilled water supply temperature cooling water return tem-perature and partial load ratio The power consumptionmodel could be presented in [15]

119875ch119894 = 1198860119894 + 1198861119894 (119879chwr119894 minus119879chws119894)

+ 1198862119894 (119879chwr119894 minus119879chws119894)2+ 1198863119894PLRch119894

+ 1198864119894PLR2

ch119894 + 1198865119894 (119879chwr119894 minus119879chws119894)PLRch119894

(3)

ReturnChiller 1

Chiller 2

Chiller 3

Supply

Chiller side

Load side

Constant flowVariable flow

Coolingcoils

2-wayvalves

Bypass pipe

Flowsensor

Tcwri

TchwriTchwsi

Figure 1 Decoupled system of a central AC system [14]

where 1198860119894sim1198865119894 is the regression coefficient 119879chwr119894 is thecooling water return temperature 119879chws119894 is the chilled watersupply temperature and PLRch119894 is the partial load ratio Allof these parameters are for the 119894th chiller

The chiller power consumption model could be estab-lished by ANFIS The program could be expressed by

119875ch119894 = 119891 (119879chwr119894 minus119879chws119894) PLRch119894 (4)

After establishing the power consumption model inorder to satisfy OCL the minimum power consumption ofthe chiller could be viewed as the objective function Theobjective function could be presented by

Objective function = Min119899

sum

119894

119875ch119894 (5)

where 119899 = set number of operating chiller (set)The restrictive limitations could be presented in

CL =

119899

sum

119894=1(PLRch119894 times chillercapacity119894)

05 (Low Limit) ≦ PLRch119894 ≦ 1 (Upper Limit)

(6)

In order to prevent the low operating efficiency and surgeof the chiller the chiller could be set to the lowest load (PLR =

05) Conversely when the PLR was greater than or equal to1 the load of the chiller would be full

Mathematical Problems in Engineering 3

x

y

First layer Second layer Third layer Fourth layer Fifth layer

darr darr

f

N

N

N

NA1

A2

B1

B2

x y

darr darrx y

darr darrx y

darr darrx y

w1

w2

w3

w4

w1

w2

w3

w4

f1w1

f2w2

f3w3

f4w4

prod

prod

prod

prod

sum

Figure 2 ANFIS architecture of the one order Sugeno fuzzy model

4 Analysis Method

41 Adaptive Neuro-Fuzzy Inference System (ANFIS) TheANFIS was proposed by Jang [16] in 1993 and combinedthe NN and fuzzy methods ANFIS has been used to solvethe difficulty of traditional fuzzy system in defining fuzzyrule base using expert experience establish the if-then rulesbased on hybrid learning procedure and adjust suitableregression function to satisfy input-output relationship offuzzy inference Moreover ANFIS have been applied on theNN system to determine the number of neurons in hiddenlayer during initializationThe proper number of neurons canbe found by try-and-error

Figure 2 demonstrated the ANFIS architecture with fuzzyinference of the one order Sugeno fuzzy model In Figure 2the nodes of each layer had the same function

The functions of five layers are described as follows(1) First layer membership function of inputs 119909 and 119910 as

described by

120583119860 (119909) =1

1 +

1003816

1003816

1003816

1003816

(119909 minus 119888119894) 119886119894

1003816

1003816

1003816

1003816

2119887119894 (7)

where 119886119894 119887119894 and 119888119894 are the premise parameters(2) Second layer multiplication of the input signals as

described by (8)It represents the firing strength of each fuzzy rule

119908119894 = 120583119860119895(119909) sdot 120583119861119895

(119910) 119894 = 1 sim 4 119895 = 1 2 (8)

(3) Third layer normalization of 119894th fuzzy rulersquos firingstrength as described by

119908119894 =119908119894

sum

4119894=1 119908119894

119894 = 1 sim 4 (9)

(4) Fourth layer node function described by

119908119894119891119894 = 119908119894 (119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 sim 4 (10)

(5) Fifth layer summation of previous layer as the outputas described by

119891 =

4sum

119894=1119891119894119908119894 119894 = 1 sim 4 (11)

In Figure 2 the ANFIS architecture was composed of twoinput variables (119909 119910) and one output (119891) Each input hadtwo membership functions and composed four fuzzy rulestotally

In this study the temperature differences between cool-ing water return temperature (119879chwr) chilled water supplytemperature (119879chws) and partial load ratio were assumed asthe input variables Power consumption was assumed as theoutput variable Each input had three membership functionsand composed nine fuzzy rules totally

The software programs of Matlab Mathematica 5 andFuzzy Logic Toolbox were adopted to build the modelfor simulation The ANFIS training flow chart was shownin Figure 3 First the operating conditions of chiller werecollected and the proper training data was selected Thenthe ANFIS parameters were set and trained through the loopWhen the iteration numberwas achieved theANFIS trainingwas completed

42 Genetic Algorithm (GA) GA was proposed by Hollandet al in 1970 and based on Darwinrsquos doctrine of evolutionnatural selection and survival of the fittest [6] GA mainlytransforms problems into gene permutation and continu-ously optimizes them through selection or reproductioncrossover and mutation The algorithm could seek optimalsolution through parallel search in wide solution domain andhas been widely applied on various fields

421 Characteristics of GA GA is different from the tra-ditional optimization method and has the characteristics


Collect the requiredinformation

Select the training data

ANFIS parameters setting

Training ANFIS

Whether the trainingis completed

ANFIS training iscompleted

Yes

No

Figure 3 ANFIS training flow chart

of stability and efficiency The main features are shown asfollows

(1) Prevent Complicated Mathematical Model Deviation Forcalculation fitness function is used as themeasuring standardto prevent complicated mathematical model deviation

(2) Convergence Speed for Calculation The parallel searchmethod is used for calculating parameter Instead of single-point method multipoint method can be performed at thesame time to accelerate convergence speed for calculation

(3) Prevent Local Optimal Solution GA includes mutationoperation Chromosomes could practice themutation changeduring evolution to prevent local optimal solution in searchprocess

5 Case Analysis and Results

In this paper a semiconductor factory with five chillers wasunder investigation The specifications of these chillers areshown in Table 1 The operating conditions of these chillersincluding power consumption the temperature at chilledwater supply and cooling water return were recorded every5min during entire experiments There are totally 10580 datasets in the experiments

51 Chiller Power Consumption Model Using Regression Anal-ysis The linear regression (LR) analysis method is utilizedto build and analyze the power consumption model of the

Table 1 Operating conditions of chiller system

Chiller 1 2 3 4 5Chiller water supplytemperature (∘C) 5 5 5 5 5

Cooling water returntemperature (∘C) 28 28 28 28 28

Chiller water flow rate(m3hr) 531 501 567 521 528

Cooling water flow rate(m3hr) 705 742 698 722 674

Cooling capacity (RT) 1280 1280 1280 1250 1250Voltage (V) 4160 4160 4160 4160 4160Input power (kW) 1062 1062 1062 957 957

500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)

Actual power consumption (kW)

Figure 4 Distribution of actual power consumption and simulatedpower consumption of chiller 1 by using regression analysis

chiller system with accurate prediction in short-term period[17] In this study the software of Mathematica 5 was used toestablish regression analysis modelThe calculated regressioncoefficients 1198772 (coefficient of determination) and averagepercentage error (err) are shown in Table 2 In Table 21198860sim1198865 are curve coefficients of the chiller system in (3)by the regression analysis Figure 4 shows the relationshipbetween simulated power consumption and actual powerconsumption of chiller 1 In the actual power consumptionrange from 520 to 920 kW the simulated power consumptionby NN increases from 520 to 920 kW with the averaged 119877

2

and percentage error (err) of 0985 and 0973 respectivelyFor the above main modeling parameters 119877

2 and errthe temperature differences between cooling water returntemperature (119879chwr) chilledwater supply temperature (119879chws)and partial load ratio were assumed as the independentvariables

52 Chiller Power Consumption Model Using NN and ANFISNN method is often adopted to build power consumptionmodel of chiller system by try-and-error principle TheANFIS method is improved from NN method Therefore itis in our interest to compare the chiller power consumptionmodel built by regression analysis NN and ANFIS methods


Table 2 Coefficients of the chiller power consumptionmodels fromquadratic regression analysis

Chiller 1 2 3 4 511988601198860 15080 23617 minus10865 38631 222161198861 1279 minus208 1621 minus619 minus0801198862 minus051 minus056 minus056 018 minus0221198863 minus62023 minus23558 3514 minus67001 minus349201198864 51082 minus36919 minus3455 76331 270521198865 4992 8175 4482 2837 4776119877

2 0984181 0983730 0985550 0985485 0983580Error () 1420413 0854415 0849768 0845402 089693

Table 3 Regression coefficients and average percentage error ofchillers by NN model

Chiller 1 2 4 5 6119877

2119877

2 09998 09998 09999 09998 09998err 088 083 080 082 085

Table 4 Regression coefficients and average percentage error ofchillers by ANFIS model

Chiller 1 2 4 5 6119877

2119877

2 099988 099989 09999 099989 099988err 088 083 081 083 086

in this sectionThemodel of chiller 1 is chosen as an exampleFigure 5 shows the relationship between simulated powerconsumption by NNmethod and actual power consumptionof chiller 1 In the actual power consumption range from 520to 920 kW the simulated power consumption increases from520 to 920 kWThe solid line is the fitting curve by least squareerror method This fitting method would be applied for thefollowing sections 1198772 and averaged err between data andfitting line are 099988 and 08769 respectively

Figure 6 shows the relationship between simulated powerconsumption by ANFIS method and actual power consump-tion of chiller 1 In the actual power consumption range from520 to 920 kW the simulated power consumption increasesfrom 520 to 920 kW 1198772 and averaged err between data andfitting line are 099988 and 088359 respectively

The calculated 119877

2 and err of these chillers simulated byNN and ANFISmethods are shown in Tables 3 and 4 respec-tively In Table 3 the range of 1198772 and err is from 099988to 09999 and from 079796 to 08769 respectively Theaveraged 119877

2 and err are 099988 and 0834472 respectivelyIn Table 4 the range of1198772 and err is from 099988 to 09999and from 081413 to 088359 respectively The averaged 119877

2

and err are 099988 and 0843964 respectivelyFrom Tables 2 to 4 the simulated results by NN and

ANFIS methods had similar accuracy The averaged 119877

2 byNN and ANFIS methods are higher than that by regressionanalysis method However the averaged err by NN andANFIS are lower than that by regression analysis method

In order to understand further the responding time ofthe utilized methods the modeling speeds of the chillers

500

600

700

800

900

1000

500 600 700 800 900 1000Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)


Figure 5 Distribution of actual power consumption and simulatedpower consumption of chiller 1 by using NN

500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)


Figure 6 Distribution of actual power consumption and simulatedpower consumption of chiller 1 by using ANFIS

for semiconductor factory simulated by ANFIS and NN arepresented in Table 5 The chiller power consumption modelby using NNmethod adopted 40 neurons on a single hiddenlayerThe output layer of one neuron is utilized for modelingBased on the results the iteration period by ANFIS in Table 5presentsmore efficientmodeling speed with average of 2min15 sec Therefore the ANFIS is utilized to design the rulebase through automatic learning for achieving optimal outputstatus

53 Loading Distribution Results of LR + ELD LR + GANN + GA and ANFIS + GA LR method could build andanalyse power consumption model of the chiller systemwith accurate predictionThis method includes several ordercalculation principles Here 2nd-order LRmethod is adoptedfor calculating multiple parameters with better accuracy [13]The ELD method of equal load is also commonly adoptedto operate chillers [3ndash5] Therefore it is in our interest tocompare the simulating results by LR + ELD LR + GA NN +GA and ANFIS + GA methods

Table 6 shows the optimal chiller loading by LR + ELDand LR + GA methods under partial load ratio of 055sim095The results indicated that the LR + GA method had betterenergy savings than LR + ELD method by 077 to 225 in


Table 5 Chiller modeling speed of NN and ANFIS methods

Chiller 1 2 4 5 6NN modeling speed 3min 30 sec 3min 27 sec 3min 37 sec 3min 34 sec 3min 30 secANFIS modeling speed 2min 07 sec 2min 17 sec 2min 17 sec 2min 17 sec 2min 17 sec

the partial load ratios of 055 to 095 with the average energysavings of 158Thepower consumption of chiller simulatedby LR + ELD and LR + GA methods increased from 2991 to53013 kW and from 29679 to 52408 kW respectively

Table 7 shows the optimal chiller loading by LR + ELDand NN + GAmethods under partial load ratio of 055sim095The results indicated that the NN + GA method had betterenergy savings than LR + ELD method by 263 to 1695in the partial load ratios of 055 to 095 with the averageenergy savings of 1214 The power consumption of chillersimulated by LR + ELD and NN + GA methods increasedfrom 2991 to 53013 kW and from 291273 to 44052 kWrespectively

Table 8 shows the optimal chiller loading by LR + ELDand ANFIS + GA methods under partial load ratio of 055sim095 The results indicated that the ANFIS + GA methodhad better energy savings than LR + ELD method by 036to 18696 in the partial load ratios of 055 to 095 withthe average energy savings of 1284 The power consump-tion of chiller simulated by LR + ELD and ANFIS + GAmethods increased from 2991 to 53013 kW and from 29802to 42963 kW respectively Table 9 presents the operatingconditions of chiller system by using ANFIS + GA method

From Tables 6 to 8 the chiller operated by ANFIS +GA method would have better energy savings of 1896among these three methods This may be due to the bettercombination capability of GA method for the chiller underpartial load ratios to achieve better energy savings

In order to further understand the relationships ofenergy usages and savings with these methods the powerconsumptions and energy savings of these methods withrespect to the partial load ratios are shown in Figure 7 InFigure 7 in the partial load ratio range of 055 to 095 thepower consumption increased from 29802 to 42963 kWfrom29123 to 44052 kW from29679 to 52408 kW and from2991 to 53013 kW for ANFIS + GA NN + GA LR + GAand LR + ELDmethods respectivelyThe chiller simulated byANFIS + GA method consumed the least power Comparedwith LR + ELD in the partial load ratio range of 055 to 095the energy savings increased from 036 to 1896 from 263to 1690 and from 077 to 114 for the simulating methodsofANFIS+GANN+GA andLR+GA respectively Amongthem the chiller simulated by ANFIS +GA had better energysavings of 1284 This may be due to the better inferencecapability and solving ability of ANFIS method for nonlinearproblems and more flexible combinations and better energysaving effect of GA method

6 Conclusion

A central air-conditioning (AC) system includes the chillerchiller water pump cooling water pump cooling tower and

0

2

4

6

8

10

12

14

16

18

20

2500

3000

3500

4000

4500

5000

5500

055 06 065 07 075 08 085 09 095

Ener

gy sa

ving

()

Pow

er co

nsum

ptio

n (k

W)

Partial load ratios (PLR)

ANFIS + GA saving ratio ()


NN + GA saving ratio ()


LR + ELD

LR + ELD

LR + GA

LR + GA

LR + GA saving ratio ()


NN + GA

NN + GA

ANFIS + GA

ANFIS + GA

Figure 7 Power consumption between LR + ELD LR + GA NN +GA and ANFIS + GA methods

chilled water secondary pumps Among these devices thechiller consumesmost power of the central AC system In thispaper the adaptive neuro-fuzzy inference system (ANFIS)and genetic algorithm (GA) were utilized for optimizingthe chiller loading The ANFIS could construct a powerconsumption model of the chiller reduce modeling periodand maintain the accuracy GA could optimize the chillerloading for better energy efficiency The simulating resultsindicated that ANFIS combined with GA could optimizethe chiller loading The power consumption was reducedby 632ndash1896 when partial load ratio was located at therange of 06sim095 The chiller power consumption modelestablished by ANFIS could also increase the convergencespeed Therefore the ANFIS with GA could optimize thechiller loading for reducing power consumption

The chiller power consumption model established byANFIS could also increase the convergence speed withaverage processing period of 2min 15 sec Compared with LR+ ELD ANFIS + GA NN + GA and LR + GA methods thechiller simulated by ANFIS + GA method had better energysavings of 1284 This may be due to the better inferencecapability and solving ability of ANFIS method for nonlinearproblems and more flexible combinations and better energysaving effect of GA method Therefore the ANFIS withGA could optimize the chiller loading for reducing powerconsumption


Table 6 Optimal chiller loading comparison by LRELD and LRGA methods

Cooling load (RT) Chiller LR + ELD LR + GA Saving A minus B ()PLR Load (RT) Total (kW) (A) PLR Load (RT) Total (kW) (B)

6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633


Table 7 Optimal chiller loading comparison by LRELD and NNGAmethods

Cooling load (RT) Chiller LR + ELD NN + GA Saving A minus B ()PLR Load (RT) Total (kW) (A) PLR Load (RT) Total (kW) (B)

6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500


Table 8 Optimal chiller loading comparison by LRELD and ANFIS + GA methods

Cooling load (RT) Chiller LR + ELD ANFIS + GA Saving A minus B ()PLR Load (RT) Total (kW) (A) PLR Load (RT) Total (kW) (B)

6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114


Table 9 Optimal loading conditions of chiller system operated byANFIS + GA method

ANFIS

Type TrainingGenerate FIS Gird partitionMF type psigmfMF type Linear

Train FIS optim methood HybridEpochs 100

GA

Popsize 300Maxgen 400

Crossover rate 05Mutation rate 005

Conflict of Interests

The authors declare no conflict of interests

References

[1] Taiwan Green Productivity Foundation Air Conditioning Sys-tem Management and Energy Saving Manual 2008

[2] S-C Hu and Y K Chuah ldquoPower consumption of semiconduc-tor fabs in Taiwanrdquo Energy vol 28 no 8 pp 895ndash907 2003

[3] J E Braun S A Klein J W Mitcell and W A BeckmanldquoApplications of optimal control to chilled water systems with-out storagerdquo ASHRAE Transactions vol 95 no 1 pp 663ndash6751989

[4] J E BraunMethodologies for the design and control of central ofcooling plants [PhD thesis] University of Wisconsin 1988

[5] R J Hackner J W Mitcell andW A Beckman ldquoHVAC systemdynamaics and energy use in buildingsmdashpart Irdquo ASHRAETransactions vol 90 pp 523ndash535 1984

[6] Y-C Chang J-K Lin and M-H Chuang ldquoOptimal chillerloading by genetic algorithm for reducing energy consump-tionrdquo Energy and Buildings vol 37 no 2 pp 147ndash155 2005

[7] P P Bonissone R Subbu N Eklund and T R KiehlldquoEvolutionary algorithms + domain knowledge = real-worldevolutionary computationrdquo IEEE Transactions on EvolutionaryComputation vol 10 no 3 pp 256ndash280 2006

[8] R E Haber and J R Alique ldquoFuzzy logic-based torque controlsystem for milling process optimizationrdquo IEEE Transactions onSystems Man and Cybernetics Part C Applications and Reviewsvol 37 no 5 pp 941ndash950 2007

[9] D Martın R del Toro R Haber and J Dorronsoro ldquoOpti-mal tuning of a networked linear controller using a multi-objective genetic algorithm and its application to one complexelectromechanical processrdquo International Journal of InnovativeComputing Information and Control vol 5 no 10 pp 3405ndash3414 2009

[10] W-S Lee and L-C Lin ldquoOptimal chiller loading by particleswarm algorithm for reducing energy consumptionrdquo AppliedThermal Engineering vol 29 no 8-9 pp 1730ndash1734 2009

[11] W-S Lee Y-T Chen and Y Kao ldquoOptimal chiller loading bydifferential evolution algorithm for reducing energy consump-tionrdquo Energy and Buildings vol 43 no 2-3 pp 599ndash604 2011

[12] A Gajate R Haber R D Toro P Vega and A Bustillo ldquoToolwear monitoring using neuro-fuzzy techniques a comparativestudy in a turning processrdquo Journal of IntelligentManufacturingvol 23 no 3 pp 869ndash882 2012

[13] C-L Chen Y-C Chang and T-S Chan ldquoApplying smartmodels for energy saving in optimal chiller loadingrdquo Energy andBuildings vol 68 pp 364ndash371 2014

[14] ASHRAE ASHRAE Handbook HVAC Systems and EquipmentHandbook ASHRAE 2000

[15] Y-C Chang ldquoOptimal chiller loading by evolution strategy forsaving energyrdquo Energy and Buildings vol 39 no 4 pp 437ndash4442007

[16] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[17] Y C Chang C Y Chen J T Lu J K Lee T S Jan and CL Chen ldquoVerification of chiller performance promotion andenergy savingrdquo Engineering vol 5 no 1A pp 141ndash145 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


(2012) proposed two model-based approaches for tool wearmonitoring on the basis of neuro-fuzzy techniques Thecomparative study demonstrates that the transductive neuro-fuzzymodel provides better error-based performance indices[12] Chen et al (2014) utilize neural networks (NN) toestablish the power consumption model of the chiller andPSO for optimal loading and saving energy [13]

From the previous studies the equal loading distributionmethod was often used to reduce power consumption How-ever the LGMmay cause system divergenceTheNNmethodadopted try-and-error principle to find number of betterneurons on a hidden layer It may cause longer period Hencethere is no single method suitable for all the conditions

In the study the ANFIS combined with GA are utilized tooptimize the chiller loading and reduce the power consump-tion and operating period

2 System Architecture

The general decoupled system of a central air-conditioningsystem is shown in Figure 1 [14] The common piping isthe division line of the central air-conditioning system Forseparating the system into two parts including the firstside (chiller side) and secondary side (load side) the firstside contains the chiller and chiller water pump and thesecondary side is chilled water secondary pumps and airhanding unit The secondary variable frequency pump isinstalled on the secondary side for controlling the flow speedto improve energy efficiencyThe total load of this system canbe expressed by

CL = 119862119901 (119879chwr minus119879chws) (1)

where CL is the cooling load (kW) is the flow rate of chillerwater (kgs) 119862119901 is the specific heat capacity of chilled water(JkgsdotK) 119879chwr is the cooling water return temperature (K)and 119879chws is the chilled water supply temperature (K)

3 Chiller Power Consumption Model

Generally speaking the capacity of the chiller is designed tomeet the need of peak load However most of the chiller isoperated under the condition of partial load and this wouldresult in larger designed capacity and power consumptionThe partial load ratio of a chiller is defined in

PLR =

cooling loadchiller capacity

(2)

The variables of the power consumption model includechilled water supply temperature cooling water return tem-perature and partial load ratio The power consumptionmodel could be presented in [15]

119875ch119894 = 1198860119894 + 1198861119894 (119879chwr119894 minus119879chws119894)

+ 1198862119894 (119879chwr119894 minus119879chws119894)2+ 1198863119894PLRch119894

+ 1198864119894PLR2

ch119894 + 1198865119894 (119879chwr119894 minus119879chws119894)PLRch119894

(3)

ReturnChiller 1

Chiller 2

Chiller 3

Supply

Chiller side

Load side

Constant flowVariable flow

Coolingcoils

2-wayvalves

Bypass pipe

Flowsensor

Tcwri

TchwriTchwsi

Figure 1 Decoupled system of a central AC system [14]

where 1198860119894sim1198865119894 is the regression coefficient 119879chwr119894 is thecooling water return temperature 119879chws119894 is the chilled watersupply temperature and PLRch119894 is the partial load ratio Allof these parameters are for the 119894th chiller

The chiller power consumption model could be estab-lished by ANFIS The program could be expressed by

119875ch119894 = 119891 (119879chwr119894 minus119879chws119894) PLRch119894 (4)

After establishing the power consumption model inorder to satisfy OCL the minimum power consumption ofthe chiller could be viewed as the objective function Theobjective function could be presented by

Objective function = Min119899

sum

119894

119875ch119894 (5)

where 119899 = set number of operating chiller (set)The restrictive limitations could be presented in

CL =

119899

sum

119894=1(PLRch119894 times chillercapacity119894)

05 (Low Limit) ≦ PLRch119894 ≦ 1 (Upper Limit)

(6)

In order to prevent the low operating efficiency and surgeof the chiller the chiller could be set to the lowest load (PLR =

05) Conversely when the PLR was greater than or equal to1 the load of the chiller would be full


x

y


darr darr

f

N

N

N

NA1

A2

B1

B2

x y

darr darrx y

darr darrx y

darr darrx y

w1

w2

w3

w4

w1

w2

w3

w4

f1w1

f2w2

f3w3

f4w4

prod

prod

prod

prod

sum


4 Analysis Method




described by

120583119860 (119909) =1

1 +

1003816

1003816

1003816

1003816

(119909 minus 119888119894) 119886119894

1003816

1003816

1003816

1003816

2119887119894 (7)



119908119894 = 120583119860119895(119909) sdot 120583119861119895

(119910) 119894 = 1 sim 4 119895 = 1 2 (8)


119908119894 =119908119894

sum

4119894=1 119908119894

119894 = 1 sim 4 (9)


119908119894119891119894 = 119908119894 (119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 sim 4 (10)


119891 =

4sum

119894=1119891119894119908119894 119894 = 1 sim 4 (11)










Training ANFIS



Yes

No















500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)




2







2 0984181 0983730 0985550 0985485 0983580Error () 1420413 0854415 0849768 0845402 089693


Chiller 1 2 4 5 6119877

2119877

2 09998 09998 09999 09998 09998err 088 083 080 082 085


Chiller 1 2 4 5 6119877

2119877

2 099988 099989 09999 099989 099988err 088 083 081 083 086






2





500

600

700

800

900

1000

500 600 700 800 900 1000Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)



500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)














6 Conclusion


0

2

4

6

8

10

12

14

16

18

20

2500

3000

3500

4000

4500

5000

5500

055 06 065 07 075 08 085 09 095

Ener

gy sa

ving

()

Pow

er co

nsum

ptio

n (k

W)






LR + ELD

LR + ELD

LR + GA

LR + GA



NN + GA

NN + GA

ANFIS + GA

ANFIS + GA







6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633




6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










x

y


darr darr

f

N

N

N

NA1

A2

B1

B2

x y

darr darrx y

darr darrx y

darr darrx y

w1

w2

w3

w4

w1

w2

w3

w4

f1w1

f2w2

f3w3

f4w4

prod

prod

prod

prod

sum


4 Analysis Method




described by

120583119860 (119909) =1

1 +

1003816

1003816

1003816

1003816

(119909 minus 119888119894) 119886119894

1003816

1003816

1003816

1003816

2119887119894 (7)



119908119894 = 120583119860119895(119909) sdot 120583119861119895

(119910) 119894 = 1 sim 4 119895 = 1 2 (8)


119908119894 =119908119894

sum

4119894=1 119908119894

119894 = 1 sim 4 (9)


119908119894119891119894 = 119908119894 (119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 sim 4 (10)


119891 =

4sum

119894=1119891119894119908119894 119894 = 1 sim 4 (11)










Training ANFIS



Yes

No















500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)




2







2 0984181 0983730 0985550 0985485 0983580Error () 1420413 0854415 0849768 0845402 089693


Chiller 1 2 4 5 6119877

2119877

2 09998 09998 09999 09998 09998err 088 083 080 082 085


Chiller 1 2 4 5 6119877

2119877

2 099988 099989 09999 099989 099988err 088 083 081 083 086






2





500

600

700

800

900

1000

500 600 700 800 900 1000Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)



500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)














6 Conclusion


0

2

4

6

8

10

12

14

16

18

20

2500

3000

3500

4000

4500

5000

5500

055 06 065 07 075 08 085 09 095

Ener

gy sa

ving

()

Pow

er co

nsum

ptio

n (k

W)






LR + ELD

LR + ELD

LR + GA

LR + GA



NN + GA

NN + GA

ANFIS + GA

ANFIS + GA







6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633




6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Training ANFIS



Yes

No















500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)




2







2 0984181 0983730 0985550 0985485 0983580Error () 1420413 0854415 0849768 0845402 089693


Chiller 1 2 4 5 6119877

2119877

2 09998 09998 09999 09998 09998err 088 083 080 082 085


Chiller 1 2 4 5 6119877

2119877

2 099988 099989 09999 099989 099988err 088 083 081 083 086






2





500

600

700

800

900

1000

500 600 700 800 900 1000Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)



500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)














6 Conclusion


0

2

4

6

8

10

12

14

16

18

20

2500

3000

3500

4000

4500

5000

5500

055 06 065 07 075 08 085 09 095

Ener

gy sa

ving

()

Pow

er co

nsum

ptio

n (k

W)






LR + ELD

LR + ELD

LR + GA

LR + GA



NN + GA

NN + GA

ANFIS + GA

ANFIS + GA







6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633




6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












2 0984181 0983730 0985550 0985485 0983580Error () 1420413 0854415 0849768 0845402 089693


Chiller 1 2 4 5 6119877

2119877

2 09998 09998 09999 09998 09998err 088 083 080 082 085


Chiller 1 2 4 5 6119877

2119877

2 099988 099989 09999 099989 099988err 088 083 081 083 086






2





500

600

700

800

900

1000

500 600 700 800 900 1000Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)



500

600

700

800

900

1000

500 600 700 800 900 1000

Sim

ulat

ed p

ower

cons

umpt

ion

(kW

)














6 Conclusion


0

2

4

6

8

10

12

14

16

18

20

2500

3000

3500

4000

4500

5000

5500

055 06 065 07 075 08 085 09 095

Ener

gy sa

ving

()

Pow

er co

nsum

ptio

n (k

W)






LR + ELD

LR + ELD

LR + GA

LR + GA



NN + GA

NN + GA

ANFIS + GA

ANFIS + GA







6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633




6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















6 Conclusion


0

2

4

6

8

10

12

14

16

18

20

2500

3000

3500

4000

4500

5000

5500

055 06 065 07 075 08 085 09 095

Ener

gy sa

ving

()

Pow

er co

nsum

ptio

n (k

W)






LR + ELD

LR + ELD

LR + GA

LR + GA



NN + GA

NN + GA

ANFIS + GA

ANFIS + GA







6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633




6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












6023 (95)

1 095 1216

53013

083431 106792

524082 095 1216 099902 1278754 095 1216 099951 127937 1145 095 11875 092864 1160806 095 11875 098925 123656

5706 (90)

1 09 1152

49865

076197 97532

489432 09 1152 1 1280004 09 1152 099951 127937 1855 09 1125 085924 1074056 09 1125 087781 109726

5389 (85)

1 085 1088

46791

067253 86084

457442 085 1088 1 1280004 085 1088 1 128000 2245 085 10625 080303 1003796 085 10625 077175 96469

5072 (80)

1 08 1024

43792

058798 75261

428062 08 1024 099902 1278754 08 1024 099902 127875 2255 08 1000 074145 926816 08 1000 066813 83516

4755 (75)

1 075 960

40867

053666 68692

401212 075 960 099902 1278754 075 960 1 128000 1835 075 9375 066569 832116 075 9375 054203 67754

4438 (70)

1 07 896

38016

060068 76887

373762 07 896 050098 641254 07 896 099951 127937 1685 07 875 074633 932916 07 875 065249 81561

4121 (65)

1 065 832

35239

05176 66253

346892 065 832 05 640004 065 832 099951 127937 1565 065 8125 066618 832736 065 8125 056549 70686

3804 (60)

1 06 768

32537

052981 67816

322322 06 768 050098 641254 06 768 074438 95281 0945 06 750 067302 841286 06 750 055279 69099

3487 (55)

1 055 704

2991

052884 67692

296792 055 704 05 640004 055 704 051222 65564 0775 055 6875 067058 838236 055 6875 054106 67633




6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












6023 (95)

1 095 1216

53013

099658 127562

440522 095 1216 1 1280004 095 1216 1 128000 16905 095 11875 1 1250006 095 11875 075024 93780

5706 (90)

1 09 1152

49865

099316 127124

414142 09 1152 1 1280004 09 1152 1 128000 16955 09 1125 1 1250006 09 1125 05 62500

5389 (85)

1 085 1088

46791

074536 95406

393732 085 1088 1 1280004 085 1088 1 128000 15855 085 10625 1 1250006 085 10625 05 62500

5072 (80)

1 08 1024

43792

05 64000

36962 08 1024 1 1280004 08 1024 1 128000 15605 08 1000 099804 1247556 08 1000 05 62500

4755 (75)

1 075 960

40867

050489 64626

354772 075 960 1 1280004 075 960 1 128000 13195 075 9375 067791 847396 075 9375 056109 70136

4438 (70)

1 07 896

38016

05 64000

33442 07 896 1 1280004 07 896 099071 126811 12045 07 875 05 625006 07 875 05 62500

4121 (65)

1 065 832

35239

05 64000

317792 065 832 1 1280004 065 832 061193 78327 9825 065 8125 05826 728256 065 8125 055279 69099

3804 (60)

1 06 768

32537

05 64000

30482 06 768 09956 1274374 06 768 05 64000 6325 06 750 05 625006 06 750 05 62500

3487 (55)

1 055 704

2991

05 64000

291232 055 704 069208 885864 055 704 055572 71132 2635 055 6875 05 625006 055 6875 05 62500




6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












6023 (95)

1 095 1216

53013

087537 112047

429632 095 1216 087732 1122974 095 1216 1 1280 18965 095 11875 1 12506 095 11875 1 1250

5706 (90)

1 09 1152

49865

056549 7238272

405292 09 1152 093939 1202424 09 1152 1 1280 18725 09 1125 1 12506 09 1125 1 1250

5389 (85)

1 085 1088

46791

05 640

383132 085 1088 075806 9703324 085 1088 1 1280 18125 085 10625 099902 1248786 085 10625 1 1250

5072 (80)

1 08 1024

43792

051075 65376

362582 08 1024 05 6404 08 1024 1 1280 17205 08 1000 099902 1248786 08 1000 1 1250

4755 (75)

1 075 960

40867

05 640

347832 075 960 05 6404 075 960 1 1280 14895 075 9375 088416 110526 075 9375 087195 108994

4438 (70)

1 07 896

38016

05 640

328432 07 896 05 6404 07 896 1 1280 11665 07 875 093744 117186 07 875 0565 70625

4121 (65)

1 065 832

35239

055034 70444

319582 065 832 05 6404 065 832 063099 80767 9315 065 8125 1 12506 065 8125 057527 71909

3804 (60)

1 06 768

32537

05 640

304822 06 768 05 6404 06 768 059677 76387 6325 06 750 088172 109366 06 750 052639 66655

3487 (55)

1 055 704

2991

05 640

298022 055 704 05 6404 055 704 061975 79328 0365 055 6875 056207 702596 055 6875 056891 71114



ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











ANFIS



GA





References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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