Research Article Support Vector Regression and Genetic ...downloads.hindawi.com/journals/mpe/2016/6212951.pdf · Research Article Support Vector Regression and Genetic Algorithm for

Research ArticleSupport Vector Regression and Genetic Algorithm forHVAC Optimal Operation

Ching-Wei Chen and Yung-Chung Chang

Department of Energy and Refrigerating Air-Conditioning Engineering National Taipei University of Technology No 1 Sec 3Chung-Hsiao E Road Taipei 10608 Taiwan

Correspondence should be addressed to Ching-Wei Chen jasonwei1838gmailcom

Received 11 October 2015 Revised 18 February 2016 Accepted 30 March 2016

Academic Editor Marco Mussetta

Copyright copy 2016 C-W Chen and Y-C ChangThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

This study covers records of various parameters affecting the power consumption of air-conditioning systems Using the SupportVector Machine (SVM) the chiller power consumption model secondary chilled water pump power consumption model airhandling unit fan power consumptionmodel and air handling unit loadmodel were established In addition it was found that1198772 ofthe models all reached 0998 and the training time was far shorter than that of the neural networkThrough genetic programminga combination of operating parameters with the least power consumption of air conditioning operation was searched Moreoverthe air handling unit load in line with the air conditioning cooling load was predicted The experimental results show that for thecombination of operating parameters with the least power consumption in line with the cooling load obtained through geneticalgorithm search the power consumption of the air conditioning systems under said combination of operating parameters wasreduced by 22 compared to the fixed operating parameters thus indicating significant energy efficiency

1 Introduction

Conventional chillers require the highest power consumptionamong components of air conditioning systems In recentyears with the availability of numerous studies on chillerefficiency chillers have continued to become more energyefficient [1ndash3] relatively the power consumption ratios ofpumps and fans have become higher In addition central airconditioning system control involves greater complexity as acentralized air conditioning system comes with many ancil-lary parts Therefore the operating efficiency of pumps andfans has particular importance The main subject of discus-sion in this paper is how to achieve optimized control of waterand air loop load changes through gear control Throughthe thermal load balance equation of the air handling unitthe relationship between the load and relevant variables wasestablished [4] In this equation the variables include theoperating parameters of chiller pump and air handling unitIn other words optimized operation of these three types ofequipment can be simultaneously taken into considerationThrough the powerful search capacity of genetic algorithm[5ndash7] the optimized combination of outlet temperature of

chilled water the air flow of air handling unit and secondarychilled water flow was searched simultaneously to obtain theleast power consumption for cooling load

Schwedler and Bradley [8] proposed the correlationsamong chiller power consumption air conditioning loadcondenser and outlet temperature of chilled water whenthe operating characteristics of each chiller vary The aver-age loading method was adopted to control and solve theoptimized load distribution and chilled water temperaturesetting point of the chiller [9ndash11] Through chilled water flowcontrol the water saving effect can be enhanced Lu et al [12]put forth a comprehensive optimized control method wherethe influential relationships among all controllable variablesand objective functions in the system were expressed usingmathematical equations and the best control setting pointamong them was found Ding and Xianzhong [13] suggestedusing linear regression to establish a load prediction modelOn the other hand Yao et al [14] mentioned the use ofthe RBF neural network to establish a prediction modelChang et al [15] proposed using the cubic polynomialequation to express the performance curve of the chillerand using the gradient method to engage in chiller load

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 6212951 10 pageshttpdxdoiorg10115520166212951

2 Mathematical Problems in Engineering

Pchiller119894

Ppump119895

Tchw119899

Ta119899

ma119899

Figure 1 Illustration of the basic configuration of an air handlingunit together with a chiller and water pump

distribution optimization in order to obtain the least totalpower consumption Beghi et al [16] used the multiobjectivegenetic algorithm to propose ways to manage energy savingof multiple sets of chiller systems

In this paper the chiller chilled water pump loop andair handling unit air loop were integrated and controlledThen the air handling unit thermal balance equation wasadopted to serve as a reference for setting outlet temperatureof chilled water air flow and chilled water flow The powerconsumption model established through the neural networkand SVM replaced the model established through linearregression [17ndash20] Finally genetic algorithm was conjunc-tively used to search the optimized setting values of the threevariables in order to obtain the least power consumption ofthe equipment under the various load conditions

2 System Structure

Figure 1 illustrates the basic configuration of an air handlingunit The air handling unit can be divided into air loopand chilled water loop The principle of cycling involvestransmitting the indoor cooling load to the chilled waterThen through the chilled water pump the chilled water thathas undergone thermal exchange is sent back to the chiller tocomplete one cycle Based on the thermal balance equationof the air handling unit we can express the air handling unitload equation as [21]

119876 =

1198891119890

119886119899

1 + 1198892(119886119899

chw119899

)119890(119879119886119899

minus 119879chw119899

) (1)

The empirical parameters 1198891 1198892 and 119890 need to be identified

from experiment dataThe chiller power consumption through the multiple

regression [22] can be expressed as the following equation

119875chiller119894

= 1198960+ 1198961119894

(119879cwr119894

minus 119879chws119894

)

+ 1198962119894

(119879cwr119894


)2

+ 1198963119894

119876chiller119894

+ 1198964119894

119876chiller119894

2+ 1198965119894

(119879cwr119894


)119876chiller119894

(2)

The air handling unit fan power consumption and thepump power consumption have a cubic relationship with airhandling unit air flow and chilled water flow [23] whichcan be expressed as the following equations throughmultipleregression

119875fan119899

= 1198961015840

0+ 1198961015840

1119886119899

+ 1198961015840

2119886119899

2+ 1198961015840

2119886119899

3

119875pump119895

= 11989610158401015840

0+ 11989610158401015840

1chw

119899

+ 11989610158401015840

2chw

119899

2+ 11989610158401015840

3chw

119899

3

(3)

The empirical parameters 1198960sim 1198965119894 11989610158400sim 1198961015840

2 and 119896

10158401015840

0sim 11989610158401015840

3 are

acquired from regression analysisThe three operating parameters of the air conditioning

system outlet temperature of chilled water of chiller (119879chw)secondary chilled water flow (chw) and air handling unitair flow (

119886) affect the power consumption of the chiller

(119875chiller) secondary water pump power consumption (119875pump)and air handling unit power consumption (119875fan) When thesame load is provided by the air conditioning system thethree operating parameters will have multiple combinationsThe methodology is shown in Figure 2

3 Support Vector Machine (SVM) andSupport Vector Regression (SVR)

Although many methods have been used to predict thepower consumption models of chillers [24] the SVM com-pared to the neural network is a relatively newer artificialintelligence classification method Through the correlationalrelationships of the independent variables and dependentvariables low-dimensional vector spaces are projected tohigh-dimensional vector spaces Unlike the neural networkthere is no need to carry out the massive calculations of thehidden layers during model training thus greatly reducingtraining timeThe disadvantage of excessive learning can alsobe prevented in nonlinear data classification In terms ofclassification the SVM can be divided into linear SVM andnonlinear SVM [25 26] In this study we use nonlinear SVMto do regression

31 Support Vector Machine (SVM) In Figure 3 suppose thatwe have some separating hyperplane to separate data and wehave two support hyperplanes where 119908 is the normal vectorto the hyperplane Let 119889

+ 119889minusbe the shortest distance from

the separating hyperplane to support hyperplane Define theldquomarginrdquo of a separating hyperplane to be 119889

+ 119889minus[27]

In the case of ldquolinear separablerdquo the hyperplane in exis-tence can divide the input space The separating hyperplanein this area can be expressed as 119908119879119909 + 119887 = 0 the hyperplanesolution can be regarded as a quadratic programming solu-tion as the following equation

Minimize 120601 (119908) =1

2119908119879119908

Subject to 119910119894(119908119879119909119894+ 119887) ge 1 119894 = 1 2 119899

(4)

Mathematical Problems in Engineering 3

Collect databaseFigure out the best operating parametersthrough genetic algorithm

Combine the minimumpower consumption andthe satisfied cooling load

Establish power

through SVRconsumption model

Figure 2 The flowchart of this study methodology in optimized operation of chilled water system

Support hyperplane

Support hyperplaneSeparating hyperplane

Margin

w

wTx + b le 1 if y = minus1

wTx + b ge 1 if y = +1

wTx + b = 0

d+

dminus

Figure 3 The hyperplane and margin

Hyperplane

120577

120576

minus120576

120577lowast

Figure 4 The feature space of SVR

This condition is called the primal problemwhenwe throughthe Lagrange [28] the multiplier can be rewritten as thefollowing equation

Minimize 119871119901(119908 119887 120572)

=1

2

10038171003817100381710038171003817119908210038171003817100381710038171003817

minus

119899

sum

119894=1

120572119894[119910119894(119908119879119909119894+ 119887) minus 1]

Subject to 120572119894ge 0 119894 = 1 2 119899

(5)

That can be efficiently solved by quadratic programmingalgorithms and then through KKT (Karush-Kuhn-Tucker)conditions [29] the equation can be converted as

119889 (119909) = 119909 sdot 119908lowast+ 119887lowast=

119899

sum

119894=1

119910119894120572119894(119909 sdot 119909119894) + 119887lowast (6)

32 Support Vector Regression (SVR) SVR is SVM regressionthrough a new type of loss function called 120576-insensitive lossfunction And it can be described by introducing (nonnega-tive) slack variables 120585 120585lowast to measure the deviation of trainingsamples outside 120576-insensitive zone Figure 4 shows the datamap to the high-dimensional feature space [30 31]

Thus SVR is formulated as minimization of the followingfunction

Minimize 120601 (119908 120577 120585lowast) =

1

2119908119879119908 + 119862(

119899

sum

119894=1

120577119894+ 120577lowast

119894)

Subject to 119910119894minus 119908119879119891 (119909119894) minus 119887 le 120576 + 120577

119894

lowast

119894 = 1 2 119899

minus 119910119894+ 119908119879119891 (119909119894) + 119887 ge 120576 + 120577

119894

119894 = 1 2 119899

120585119894 120585lowast

119894ge 0

(7)

The parameter 119862 is a penalty factor to control the degreeof punishment of samples beyond the error 120576 Training errorsabove 120576 are denoted by 120585lowast

119894whereas training errors below 120576 are

denoted by 120585119894

Through the Lagrange and KKT the regression functionis shown as the below function

119891 (119909) =

119899

sum

119894=1

(120572119894+ 120572lowast

119894) 119896 (119909 119909

119894) + 119887lowast (8)

where 119896(119909 119909119894) = 120593(119909)sdot120593(119909

119894) is kernel function Common core

functions are as shown as follows

Linear kernel is

119909119894lowast 119910119894 (9)

Polynomial kernel is

(gamma lowast 119909119894lowast 119910119894+ coef0)degree (10)

Radiation basis function kernel is

exp (minusgamma lowast 1003816100381610038161003816119909119894 minus 119910119894

1003816100381610038161003816

2

) (11)

After SVR training the power consumption for chillerair handling unit secondary chilled water pump and airhandling unit load models can be obtained which can beused to obtain optimized operating parameters by geneticalgorithm [32]


4 Genetic Algorithm

The genetic algorithm (GA) is developed by Holland [33]in his book in 1975 The genetic algorithm is based onDarwinianrsquos theory of survival of the fittest to solve both con-strained and unconstrained optimization problems Geneticalgorithm is analogous to those in the selection processthat mimics biological evolution selection reproductioncrossover and mutation The main advantage of the paral-lelism of GA is having multiple points in search space so thatthe problem of local maximum generally does not exist [34]

41 Initial Population In order to find the best load distri-bution a highly accurate prediction model should be firstestablished to find the objective function of the least powerconsumption as shown in the following equation

kWtotal = Min(

119868

sum

119894=1

119875chiller119894

+

119873

sum

119899=1

119875fan119899 +119869

sum

119895=1

119875pump119895

) (12)

The variables of the objective functions are randomlyselected as shown in the following equations to generate theinitial population made up of 900 sets of solutions

119879chws119894

= (119879chws119894max

minus 119879chws119894min) times random (0 1)

+ 119879chws119894min

119886119899

= (119886119899max minus

119886119899min) times random (0 1)

+ 119886119899min

chw119895

= (chw119895max minus chw


+ chw119895min

(13)

The error between the predicted air conditioning coolingload and the actual air conditioning cooling load serves as theraw fitness as shown in the following equation

119865 (119894 119905) =

119873

sum

119895=1

1003816100381610038161003816119876 (119894 119895) minus 119876real (119895)1003816100381610038161003816 (14)

where 119865(119894 119905) is raw fitness of generation 119905 in individual 119894119876(119894 119895) is load prediction value inputted at 119895 in individual and119876real(119895) is actual air conditioning load at 119895

The smaller the fitness is the closer the prediction valueis to the actual value

As shown in the flowchart in Figure 5 under the con-ditions of the known cooling load (119876Load) return air wetbulb temperature (119879

119886) and inlet temperature of cooling water

(119879cwr) three operating parameters were randomly producedthe outlet temperature of chilled water in the chiller (119879chws)secondary chilled water flow (chw) and air handling unitair flow (

119886) Then the equipment power consumption

models were substituted into the equation to obtain thepower consumption (119875chiller) secondary water pump powerconsumption (119875pump) and air handling unit fan power

consumption (119875fan) After computing fitness those nearestto the cooling load and with the least power consumptionin the population were arranged in sequence to retain themoderately superior ones for reproducing a next populationand execute mating and mutation for inferior ones After 500times of iteration we can get the least power consumptionand the cooling load is satisfied Consider the following

119875119903 the reproduction process

119875119888 the crossover process

119875119898 the mutation process

42 Reproduction Through the ranking approach the 900individuals in this paper were ranked according to fitnessThose with the best fitness (ie the top 1 of the smallestfitness) were used as targets for copying

43 Crossover Since it takes two to mate after eliminatingthe top 1 the remaining 98 were used as the length ofmating The chiller power consumption or the air handlingunit power consumption at the functional end was randomlyselected andmated to enter the next population and carry outfitness ranking

44 Mutation Unlike mating it takes only one to mutateas it is a type of asexual reproduction For the remaining 1of the population the chiller power consumption or the airhandling unit power consumption was randomly selectedThrough the outlet temperature of chilled water and airhandling unit air flow mutation was calculated before finallyentering the next population and carrying out fitness ranking

The calculation ends when the population reaches 500through copying mating and mutation In Figure 6 thecalculation has been converged From the subpopulationobtained the best fitness solution will be the best solutionsought

5 Results and Discussion

This experimental system is primary-secondary central airconditioning system with a fixed-frequency scroll compres-sor When the preset outlet temperature of chilled water isreached the onoff control and hot gas bypass methods areused in loading and unloadingThemodel establishment datacomes from the air conditioning experimental system actu-ally operated for three months from 2009417 to 2009611The outlet and inlet temperature of chilledwater in the chillerthe outlet and inlet temperature of chilled water in the airhandling unit the outlet and inlet temperature of coolingwater chilled water flow return air wet bulb temperaturechiller power consumption pump power consumption airhandling unit power consumption and other related datawere compiled to calculate the actual load of the air handlingunit

For three days from 2009614 to 2009616 the datacollected at partial loading rates of 03sim05 075sim1 and 05sim075 were used to crossmatch predicted air conditioning loadand power consumption The experiment was crossmatched


Create initialrandom population

Get minimum powerconsumption or the numberof iterations

End

Evaluatefitness ofpopulation

Randomdecision foroperation

Select twoindividuals

Crossover

Insert offspringinto newpopulation

Select oneindividual

Reproduction

Copy to newpopulation


Mutation


YesNo

Yes

No

I = I + 1 I = I + 1I = I + 2

I = M

N = N + 1

I = 0

N = 0

Pr PmPc

Figure 5 The flowchart of genetic algorithm applied in optimized operation of chilled water system

with the air conditioning system at fixed outlet temperatureof chilled water fixed air handling unit air flow and fixed sec-ondary flow model (hereinafter referred to as fixed operatingparametermodel) from 900 am in themorning to 600 pmin the evening to record the operating parameters Then thedata taken every 20 minutes on average were compiled Asshown in Table 1 there are a total of 81 operating parameterconditions The 3-day operation data serves as the base datafor comparison In addition based on the base data the outlettemperature of chilled water air handling unit air flow andsecondary chilled water flow operation model (hereinafterreferred to as optimized operating parameter model) werecompared

Under the 81 known conditions (inlet temperature ofcooling water return air wet bulb temperature and air

615

616

614

50 100 150 200 250 300 350 400 450 5000Iteration

25

3

35

4

45

5

55

6

Tota

l pow

er co

nsum

ptio

n (k

W)

Figure 6 The convergence diagram of six segments of data formodel establishment


Table 1 Operating parameters

Day Time Wet bulb temperature Inlet temperature of cooling water Load Initial total power consumption∘C ∘C RT kW

2009614 920 2223 2720 248 3712009614 940 1894 2762 249 3742009614 1000 1812 2762 251 3742009614 1020 1759 2757 248 3762009614 1040 1902 2734 265 367

2009614 1620 1948 2482 218 3472009614 1640 1947 2477 215 3462009614 1700 1926 2477 206 3442009614 1720 1920 2485 207 3462009614 1740 1925 2499 210 3462009614 1800 1929 2508 211 3462009615 920 2188 2680 237 3542009615 940 1748 2812 427 6072009615 1000 1689 2820 410 6032009615 1020 1685 2828 413 6042009615 1040 1684 2846 417 606

2009615 1620 1704 2821 403 5992009615 1640 1684 2813 397 5982009615 1700 1689 2807 394 5972009615 1720 1680 2795 393 5952009615 1740 1677 2797 392 5942009615 1800 1670 2791 390 5942009616 920 2191 2689 265 3572009616 940 2157 2712 277 3602009616 1000 2097 2738 273 3622009616 1020 2039 2727 275 3582009616 1040 2090 2766 277 361

2009616 1640 1956 2752 268 3552009616 1700 1943 2762 269 3572009616 1720 1953 2771 268 3602009616 1740 1944 2765 268 3582009616 1800 1948 2759 270 3592009616 1640 1956 2752 268 355

conditioning cooling load) the best outlet temperatures ofchilled water secondary chilled water flow and air handlingunit air flow that are in line with the conditions with the leastcooling load and power consumption were simultaneouslysearched The convergence diagram is as shown in Figure 6Under different partial loads during the 3-day operation500 times of iteration calculation all reached convergenceAs shown in Figure 7 the chiller with the partial loadingrates of 03sim05 through SVR prediction showed the actualpower consumption and simulated power consumption of

1198772

= 0999 As shown in Figure 8 the chiller with thepartial loading rates of 05sim10 through SVR predictionshowed the actual power consumption and simulated powerconsumption of 119877

2= 0998 As shown in Figure 9 the

relationship between the power consumption and flow of thechilled water pump as predicted by SVR showed the actualpower consumption and simulated power consumption of1198772

= 0999 As shown in Figure 10 the actual powerconsumption and simulated power consumption of the fanas predicted by SVR showed that 1198772 = 0999 As shown in


Measurement dataRegression data

1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down

Figure 7 The actual power consumption and simulated chillerpower consumption at low load


1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up

Figure 8 Actual load and simulated load of chiller through SVRprediction

Figure 11 the actual load and simulated load of air handlingunit as predicted by SVR showed that 1198772 = 0999 Thussupporting SVM training time is far lower than that of theneural network as shown in Table 2 The best operatingresult of power consumption is as shown in Figure 12 Underdifferent partial loading rates during the 3-day operationthe total power consumption under the best operation waslower than the total power consumption under operation atfixed water temperature thus indicating significant energysaving result As shown in Figure 13 the 3-day total powerconsumption under the best operation and the operation atfixed water temperature was compared On 614 under thecondition of low partial loading rate operation the energyreduction was 2478 kW on 615 under the condition of highpartial loading rate the energy reduction was 3021 kW on616 under the condition of medium partial loading rate2735 kWof energywas savedThrough genetic algorithm thebest operating settings for outlet temperature of chilled waterair handling unit air flow and chilled water flow results are asshown in Table 3

Pump power consumption


00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value

Figure 9 Actual load and simulated load of pump through SVRprediction

Fan power consumption


200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)

Figure 10 Actual load and simulated load of fan through SVRprediction

6 Conclusion

The dependent variables contained in the air handling unitthermal balance equation used in this paper include chillerair handling unit and pump operating parameters At thesame time optimized operation of these three types ofequipment can also be taken into account Through thepowerful search capacity of genetic algorithm the bestcombination of outlet temperature of chilled water airhandling unit air flow and secondary chilled water flow issimultaneously searched With satisfied loading the totalpower consumption is also optimized The 119877

2 values ofthe chiller power consumption model air handling powerconsumption model pump power consumption model andair condition loading model established through the SVM allreached above 0998 They also possess high reliability whenused to predict the power consumption and air conditionload of individual components In terms of training timethey are considered speedier and simpler compared to theneural network Compared to the total power consumptionwhen operated under fixed parameters operating parameters


Table 2 Training time

Model SVR training time (s) 1198772 Neural network training time (s) 119877

2

119875fan 2141 09996 Over 1800 09966119875pump 1384 09998 Over 1800 09999119875chiller up 22103 09976 Over 1800 09981119875chiller down 45563 09997 Over 1800 09997119876fan 3284 09999 Over 1800 09965


500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan

Figure 11 Actual load and simulated load of air handling unitthrough SVR prediction

Total power consumption under optimized operationTotal power consumption under fixed operation

615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)

Figure 12 Curve diagram of total power consumption under fixedoperation and optimized operation

Total power consumption under fixed operationTotal power consumption under optimized operation

0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05

Figure 13 Bar chart of total power consumption before and aftersystem improvement

Table 3 Optimized operation parameters setting

Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2

operated under the optimized model decrease energy con-sumption by 22 on average


It can therefore be confirmed that the SVMcan accuratelypredict power consumption of various equipment and airhandling unit loads Additionally genetic algorithm haspowerful search capacity to find the best combination ofoperating parameters

Nomenclature

kWtotal Total power consumption119886119899

Air flow of air handling unit 119894 (m3hr)chw

119899

Chilled water flow of air handling unit 119899(m3hr)

119875chiller119894

The chiller power consumption 119894 (kW)119875fan119899

The air handling unit power consumption119899 (kW)

119875pump119895

The pump power consumption 119895 (kW)119876 Predicted cooling load of air handling unit

(Ton)119876real Cooling load of air conditioning system

provided to space (Ton)119876chiller

119894

Cooling capacity of chiller 119894 (Ton)119879119886119899

Return air wet bulb temperature of airhandling unit (∘C)

119879chw119899

Inlet temperature of chilled water of airhandling unit 119899 (∘C)

119879cwr119894

Inlet temperature of chilled water ofchiller 119894 (∘C)

119879cws119894

Outlet temperature of chilled water ofchiller 119894 (∘C)

Competing Interests

The authors declare that they have no competing interests

References

[1] J Martin ldquoThe crucial role of inverter drives in the energy-efficient buildingrdquo World Pumps vol 2006 no 483 pp 20ndash212006

[2] Z Li and S Deng ldquoA DDC-based capacity controller of a directexpansion (DX) air conditioning (AC) unit for simultaneousindoor air temperature and humidity controlmdashpart I controlalgorithms and preliminary controllability testsrdquo InternationalJournal of Refrigeration vol 30 no 1 pp 113ndash123 2007

[3] R Saidur ldquoA review on electrical motors energy use and energysavingsrdquo Renewable and Sustainable Energy Reviews vol 14 no3 pp 877ndash898 2010

[4] L Lu W J Cai L Xie S Li and Y C Soh ldquoHVAC systemoptimizationmdashin-building sectionrdquo Energy and Buildings vol37 no 1 pp 11ndash22 2005

[5] J M Link P M Yager and J C Anjos ldquoApplication of geneticprogramming to high energy physics event selectionrdquo NuclearInstruments andMethods in Physics Research A vol 551 no 2-3pp 504ndash527 2005

[6] Y-S Lee and L-I Tong ldquoForecasting energy consumptionusing a grey model improved by incorporating genetic pro-grammingrdquo Energy Conversion and Management vol 52 no 1pp 147ndash152 2011

[7] N Togun and S Baysec ldquoGenetic programming approach topredict torque and brake specific fuel consumption of a gasolineenginerdquo Applied Energy vol 87 no 11 pp 3401ndash3408 2010

[8] M Schwedler and B Bradley ldquoVariable-primary-flow systemrdquoin HeadingPipingAir Conditioning Engineer pp 41ndash44 2000

[9] 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 pp 663ndash675 1989

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

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

[12] L Lu W Cai Y S Chai and L Xie ldquoGlobal optimizationfor overall HVAC systemsmdashpart I problem formulation andanalysisrdquo Energy Conversion and Management vol 46 no 7-8pp 999ndash1014 2005

[13] S S Ding and D Xianzhong ldquoGrey forecast model and itsapplicationrdquo Journal of Harbin Institute of Technology (NewSeries) vol 10 pp 315ndash320 2003

[14] Y Yao Z Lian Z Hou and W Liu ldquoAn innovative air-conditioning load forecasting model based on RBF neuralnetwork and combined residual error correctionrdquo InternationalJournal of Refrigeration vol 29 no 4 pp 528ndash538 2006

[15] Y-C Chang T-S Chan and W-S Lee ldquoEconomic dispatchof chiller plant by gradient method for saving energyrdquo AppliedEnergy vol 87 no 4 pp 1096ndash1101 2010

[16] A Beghi L Cecchinato and M Rampazzo ldquoA multi-phasegenetic algorithm for the efficient management of multi-chillersystemsrdquo Energy Conversion andManagement vol 52 no 3 pp1650ndash1661 2011

[17] R Z Freire G H C Oliveira and N Mendes ldquoDevelopmentof regression equations for predicting energy and hygrothermalperformance of buildingsrdquo Energy and Buildings vol 40 no 5pp 810ndash820 2008

[18] X-C Xi A-N Poo and S-K Chou ldquoSupport vector regressionmodel predictive control on aHVACplantrdquoControl EngineeringPractice vol 15 no 8 pp 897ndash908 2007

[19] A E Ben-Nakhi andMAMahmoud ldquoCooling load predictionfor buildings using general regression neural networksrdquo EnergyConversion and Management vol 45 no 13-14 pp 2127ndash21412004

[20] Y-C Chang and W-H Chen ldquoOptimal chilled water tem-perature calculation of multiple chiller systems using Hopfieldneural network for saving energyrdquo Energy vol 34 no 4 pp448ndash456 2009

[21] Y-W Wang W-J Cai Y-C Soh S-J Li L Lu and L Xie ldquoAsimplified modeling of cooling coils for control and optimiza-tion of HVAC systemsrdquo Energy Conversion and Managementvol 45 no 18-19 pp 2915ndash2930 2004

[22] Y-C Chang ldquoGenetic algorithm based optimal chiller loadingfor energy conservationrdquo Applied Thermal Engineering vol 25no 17-18 pp 2800ndash2815 2005

[23] M He W-J Cai and S-Y Li ldquoMultiple fuzzy model-basedtemperature predictive control for HVAC systemsrdquo InformationSciences vol 169 no 1-2 pp 155ndash174 2005

[24] D J Swider ldquoA comparison of empirically based steady-statemodels for vapor-compression liquid chillersrdquo AppliedThermalEngineering vol 23 no 5 pp 539ndash556 2003

[25] V N Vapnik Statistical Learning Theory John Wiley amp SonsNew York NY USA 1998


[26] W Y Zhang W-C Hong Y Dong G Tsai J-T Sung and G-F Fan ldquoApplication of SVR with chaotic GASA algorithm incyclic electric load forecastingrdquo Energy vol 45 no 1 pp 850ndash858 2012

[27] T Joachims ldquoText categorizationwith support vectormachineslearning with many relevant featuresrdquo in Machine LearningECML-98 C Nedellec and C Rouveirol Eds vol 1398 ofLecture Notes in Computer Science pp 137ndash142 Springer BerlinGermany 1998

[28] C J C Burges ldquoA tutorial on support vector machines forpattern recognitionrdquo Data Mining and Knowledge Discoveryvol 2 no 2 pp 121ndash167 1998

[29] N Cristianini and J Shawe-Taylor An Introduction to SupportVector Machines and Other Kernel-Based Learning MethodsCambridge University Press Cambridge UK 2000

[30] Z Xu Y Gao and Y Jin ldquoApplication of an optimized SVRmodel of machine learningrdquo International Journal of Multime-dia and Ubiquitous Engineering vol 9 no 6 pp 67ndash80 2014

[31] S Ye G Zhu and Z Xiao ldquoLong term load forecasting and rec-ommendations for china based on support vector regressionrdquoEnergy and Power Engineering vol 4 no 5 pp 380ndash385 2012

[32] Y-C Chang ldquoSequencing of chillers by estimating chiller powerconsumption using artificial neural networksrdquo Building andEnvironment vol 42 no 1 pp 180ndash188 2007

[33] J H Holland Adaptation in Natural and Artificial Systems AnIntroductory Analysis with Applications to Biology Control andArtificial Intelligence University of Michigan Press Ann ArborMich USA 1975

[34] M Melanie An Introduction to Genetic Algorithms A BradfordBook The MIT Press 1999

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


Pchiller119894

Ppump119895

Tchw119899

Ta119899

ma119899

Figure 1 Illustration of the basic configuration of an air handlingunit together with a chiller and water pump

distribution optimization in order to obtain the least totalpower consumption Beghi et al [16] used the multiobjectivegenetic algorithm to propose ways to manage energy savingof multiple sets of chiller systems

In this paper the chiller chilled water pump loop andair handling unit air loop were integrated and controlledThen the air handling unit thermal balance equation wasadopted to serve as a reference for setting outlet temperatureof chilled water air flow and chilled water flow The powerconsumption model established through the neural networkand SVM replaced the model established through linearregression [17ndash20] Finally genetic algorithm was conjunc-tively used to search the optimized setting values of the threevariables in order to obtain the least power consumption ofthe equipment under the various load conditions

2 System Structure

Figure 1 illustrates the basic configuration of an air handlingunit The air handling unit can be divided into air loopand chilled water loop The principle of cycling involvestransmitting the indoor cooling load to the chilled waterThen through the chilled water pump the chilled water thathas undergone thermal exchange is sent back to the chiller tocomplete one cycle Based on the thermal balance equationof the air handling unit we can express the air handling unitload equation as [21]

119876 =

1198891119890

119886119899

1 + 1198892(119886119899

chw119899

)119890(119879119886119899

minus 119879chw119899

) (1)

The empirical parameters 1198891 1198892 and 119890 need to be identified

from experiment dataThe chiller power consumption through the multiple

regression [22] can be expressed as the following equation

119875chiller119894

= 1198960+ 1198961119894

(119879cwr119894


)

+ 1198962119894

(119879cwr119894


)2

+ 1198963119894

119876chiller119894

+ 1198964119894

119876chiller119894

2+ 1198965119894

(119879cwr119894


)119876chiller119894

(2)

The air handling unit fan power consumption and thepump power consumption have a cubic relationship with airhandling unit air flow and chilled water flow [23] whichcan be expressed as the following equations throughmultipleregression

119875fan119899

= 1198961015840

0+ 1198961015840

1119886119899

+ 1198961015840

2119886119899

2+ 1198961015840

2119886119899

3

119875pump119895

= 11989610158401015840

0+ 11989610158401015840

1chw

119899

+ 11989610158401015840

2chw

119899

2+ 11989610158401015840

3chw

119899

3

(3)

The empirical parameters 1198960sim 1198965119894 11989610158400sim 1198961015840

2 and 119896

10158401015840

0sim 11989610158401015840

3 are

acquired from regression analysisThe three operating parameters of the air conditioning

system outlet temperature of chilled water of chiller (119879chw)secondary chilled water flow (chw) and air handling unitair flow (

119886) affect the power consumption of the chiller

(119875chiller) secondary water pump power consumption (119875pump)and air handling unit power consumption (119875fan) When thesame load is provided by the air conditioning system thethree operating parameters will have multiple combinationsThe methodology is shown in Figure 2

3 Support Vector Machine (SVM) andSupport Vector Regression (SVR)

Although many methods have been used to predict thepower consumption models of chillers [24] the SVM com-pared to the neural network is a relatively newer artificialintelligence classification method Through the correlationalrelationships of the independent variables and dependentvariables low-dimensional vector spaces are projected tohigh-dimensional vector spaces Unlike the neural networkthere is no need to carry out the massive calculations of thehidden layers during model training thus greatly reducingtraining timeThe disadvantage of excessive learning can alsobe prevented in nonlinear data classification In terms ofclassification the SVM can be divided into linear SVM andnonlinear SVM [25 26] In this study we use nonlinear SVMto do regression

31 Support Vector Machine (SVM) In Figure 3 suppose thatwe have some separating hyperplane to separate data and wehave two support hyperplanes where 119908 is the normal vectorto the hyperplane Let 119889

+ 119889minusbe the shortest distance from

the separating hyperplane to support hyperplane Define theldquomarginrdquo of a separating hyperplane to be 119889

+ 119889minus[27]

In the case of ldquolinear separablerdquo the hyperplane in exis-tence can divide the input space The separating hyperplanein this area can be expressed as 119908119879119909 + 119887 = 0 the hyperplanesolution can be regarded as a quadratic programming solu-tion as the following equation

Minimize 120601 (119908) =1

2119908119879119908

Subject to 119910119894(119908119879119909119894+ 119887) ge 1 119894 = 1 2 119899

(4)




Establish power



Support hyperplane


Margin

w



wTx + b = 0

d+

dminus


Hyperplane

120577

120576

minus120576

120577lowast



Minimize 119871119901(119908 119887 120572)

=1

2

10038171003817100381710038171003817119908210038171003817100381710038171003817

minus

119899

sum

119894=1

120572119894[119910119894(119908119879119909119894+ 119887) minus 1]

Subject to 120572119894ge 0 119894 = 1 2 119899

(5)



119899

sum

119894=1

119910119894120572119894(119909 sdot 119909119894) + 119887lowast (6)



Minimize 120601 (119908 120577 120585lowast) =

1

2119908119879119908 + 119862(

119899

sum

119894=1

120577119894+ 120577lowast

119894)


119894

lowast

119894 = 1 2 119899

minus 119910119894+ 119908119879119891 (119909119894) + 119887 ge 120576 + 120577

119894

119894 = 1 2 119899

120585119894 120585lowast

119894ge 0

(7)



denoted by 120585119894


119891 (119909) =

119899

sum

119894=1

(120572119894+ 120572lowast

119894) 119896 (119909 119909

119894) + 119887lowast (8)

where 119896(119909 119909119894) = 120593(119909)sdot120593(119909



Linear kernel is

119909119894lowast 119910119894 (9)





1003816100381610038161003816

2

) (11)



4 Genetic Algorithm



kWtotal = Min(

119868

sum

119894=1

119875chiller119894

+

119873

sum

119899=1

119875fan119899 +119869

sum

119895=1

119875pump119895

) (12)


119879chws119894

= (119879chws119894max


+ 119879chws119894min

119886119899

= (119886119899max minus


+ 119886119899min

chw119895



+ chw119895min

(13)


119865 (119894 119905) =

119873

sum

119895=1

1003816100381610038161003816119876 (119894 119895) minus 119876real (119895)1003816100381610038161003816 (14)






















End




Crossover



Reproduction



Mutation


YesNo

Yes

No

I = I + 1 I = I + 1I = I + 2

I = M

N = N + 1

I = 0

N = 0

Pr PmPc




615

616

614

50 100 150 200 250 300 350 400 450 5000Iteration

25

3

35

4

45

5

55

6

Tota

l pow

er co

nsum

ptio

n (k

W)





2009614 920 2223 2720 248 3712009614 940 1894 2762 249 3742009614 1000 1812 2762 251 3742009614 1020 1759 2757 248 3762009614 1040 1902 2734 265 367

2009614 1620 1948 2482 218 3472009614 1640 1947 2477 215 3462009614 1700 1926 2477 206 3442009614 1720 1920 2485 207 3462009614 1740 1925 2499 210 3462009614 1800 1929 2508 211 3462009615 920 2188 2680 237 3542009615 940 1748 2812 427 6072009615 1000 1689 2820 410 6032009615 1020 1685 2828 413 6042009615 1040 1684 2846 417 606

2009615 1620 1704 2821 403 5992009615 1640 1684 2813 397 5982009615 1700 1689 2807 394 5972009615 1720 1680 2795 393 5952009615 1740 1677 2797 392 5942009615 1800 1670 2791 390 5942009616 920 2191 2689 265 3572009616 940 2157 2712 277 3602009616 1000 2097 2738 273 3622009616 1020 2039 2727 275 3582009616 1040 2090 2766 277 361

2009616 1640 1956 2752 268 3552009616 1700 1943 2762 269 3572009616 1720 1953 2771 268 3602009616 1740 1944 2765 268 3582009616 1800 1948 2759 270 3592009616 1640 1956 2752 268 355


1198772







1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down



1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up





00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value




200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)


6 Conclusion






2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Establish power



Support hyperplane


Margin

w



wTx + b = 0

d+

dminus


Hyperplane

120577

120576

minus120576

120577lowast



Minimize 119871119901(119908 119887 120572)

=1

2

10038171003817100381710038171003817119908210038171003817100381710038171003817

minus

119899

sum

119894=1

120572119894[119910119894(119908119879119909119894+ 119887) minus 1]

Subject to 120572119894ge 0 119894 = 1 2 119899

(5)



119899

sum

119894=1

119910119894120572119894(119909 sdot 119909119894) + 119887lowast (6)



Minimize 120601 (119908 120577 120585lowast) =

1

2119908119879119908 + 119862(

119899

sum

119894=1

120577119894+ 120577lowast

119894)


119894

lowast

119894 = 1 2 119899

minus 119910119894+ 119908119879119891 (119909119894) + 119887 ge 120576 + 120577

119894

119894 = 1 2 119899

120585119894 120585lowast

119894ge 0

(7)



denoted by 120585119894


119891 (119909) =

119899

sum

119894=1

(120572119894+ 120572lowast

119894) 119896 (119909 119909

119894) + 119887lowast (8)

where 119896(119909 119909119894) = 120593(119909)sdot120593(119909



Linear kernel is

119909119894lowast 119910119894 (9)





1003816100381610038161003816

2

) (11)



4 Genetic Algorithm



kWtotal = Min(

119868

sum

119894=1

119875chiller119894

+

119873

sum

119899=1

119875fan119899 +119869

sum

119895=1

119875pump119895

) (12)


119879chws119894

= (119879chws119894max


+ 119879chws119894min

119886119899

= (119886119899max minus


+ 119886119899min

chw119895



+ chw119895min

(13)


119865 (119894 119905) =

119873

sum

119895=1

1003816100381610038161003816119876 (119894 119895) minus 119876real (119895)1003816100381610038161003816 (14)






















End




Crossover



Reproduction



Mutation


YesNo

Yes

No

I = I + 1 I = I + 1I = I + 2

I = M

N = N + 1

I = 0

N = 0

Pr PmPc




615

616

614

50 100 150 200 250 300 350 400 450 5000Iteration

25

3

35

4

45

5

55

6

Tota

l pow

er co

nsum

ptio

n (k

W)





2009614 920 2223 2720 248 3712009614 940 1894 2762 249 3742009614 1000 1812 2762 251 3742009614 1020 1759 2757 248 3762009614 1040 1902 2734 265 367

2009614 1620 1948 2482 218 3472009614 1640 1947 2477 215 3462009614 1700 1926 2477 206 3442009614 1720 1920 2485 207 3462009614 1740 1925 2499 210 3462009614 1800 1929 2508 211 3462009615 920 2188 2680 237 3542009615 940 1748 2812 427 6072009615 1000 1689 2820 410 6032009615 1020 1685 2828 413 6042009615 1040 1684 2846 417 606

2009615 1620 1704 2821 403 5992009615 1640 1684 2813 397 5982009615 1700 1689 2807 394 5972009615 1720 1680 2795 393 5952009615 1740 1677 2797 392 5942009615 1800 1670 2791 390 5942009616 920 2191 2689 265 3572009616 940 2157 2712 277 3602009616 1000 2097 2738 273 3622009616 1020 2039 2727 275 3582009616 1040 2090 2766 277 361

2009616 1640 1956 2752 268 3552009616 1700 1943 2762 269 3572009616 1720 1953 2771 268 3602009616 1740 1944 2765 268 3582009616 1800 1948 2759 270 3592009616 1640 1956 2752 268 355


1198772







1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down



1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up





00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value




200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)


6 Conclusion






2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










4 Genetic Algorithm



kWtotal = Min(

119868

sum

119894=1

119875chiller119894

+

119873

sum

119899=1

119875fan119899 +119869

sum

119895=1

119875pump119895

) (12)


119879chws119894

= (119879chws119894max


+ 119879chws119894min

119886119899

= (119886119899max minus


+ 119886119899min

chw119895



+ chw119895min

(13)


119865 (119894 119905) =

119873

sum

119895=1

1003816100381610038161003816119876 (119894 119895) minus 119876real (119895)1003816100381610038161003816 (14)






















End




Crossover



Reproduction



Mutation


YesNo

Yes

No

I = I + 1 I = I + 1I = I + 2

I = M

N = N + 1

I = 0

N = 0

Pr PmPc




615

616

614

50 100 150 200 250 300 350 400 450 5000Iteration

25

3

35

4

45

5

55

6

Tota

l pow

er co

nsum

ptio

n (k

W)





2009614 920 2223 2720 248 3712009614 940 1894 2762 249 3742009614 1000 1812 2762 251 3742009614 1020 1759 2757 248 3762009614 1040 1902 2734 265 367

2009614 1620 1948 2482 218 3472009614 1640 1947 2477 215 3462009614 1700 1926 2477 206 3442009614 1720 1920 2485 207 3462009614 1740 1925 2499 210 3462009614 1800 1929 2508 211 3462009615 920 2188 2680 237 3542009615 940 1748 2812 427 6072009615 1000 1689 2820 410 6032009615 1020 1685 2828 413 6042009615 1040 1684 2846 417 606

2009615 1620 1704 2821 403 5992009615 1640 1684 2813 397 5982009615 1700 1689 2807 394 5972009615 1720 1680 2795 393 5952009615 1740 1677 2797 392 5942009615 1800 1670 2791 390 5942009616 920 2191 2689 265 3572009616 940 2157 2712 277 3602009616 1000 2097 2738 273 3622009616 1020 2039 2727 275 3582009616 1040 2090 2766 277 361

2009616 1640 1956 2752 268 3552009616 1700 1943 2762 269 3572009616 1720 1953 2771 268 3602009616 1740 1944 2765 268 3582009616 1800 1948 2759 270 3592009616 1640 1956 2752 268 355


1198772







1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down



1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up





00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value




200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)


6 Conclusion






2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












End




Crossover



Reproduction



Mutation


YesNo

Yes

No

I = I + 1 I = I + 1I = I + 2

I = M

N = N + 1

I = 0

N = 0

Pr PmPc




615

616

614

50 100 150 200 250 300 350 400 450 5000Iteration

25

3

35

4

45

5

55

6

Tota

l pow

er co

nsum

ptio

n (k

W)





2009614 920 2223 2720 248 3712009614 940 1894 2762 249 3742009614 1000 1812 2762 251 3742009614 1020 1759 2757 248 3762009614 1040 1902 2734 265 367

2009614 1620 1948 2482 218 3472009614 1640 1947 2477 215 3462009614 1700 1926 2477 206 3442009614 1720 1920 2485 207 3462009614 1740 1925 2499 210 3462009614 1800 1929 2508 211 3462009615 920 2188 2680 237 3542009615 940 1748 2812 427 6072009615 1000 1689 2820 410 6032009615 1020 1685 2828 413 6042009615 1040 1684 2846 417 606

2009615 1620 1704 2821 403 5992009615 1640 1684 2813 397 5982009615 1700 1689 2807 394 5972009615 1720 1680 2795 393 5952009615 1740 1677 2797 392 5942009615 1800 1670 2791 390 5942009616 920 2191 2689 265 3572009616 940 2157 2712 277 3602009616 1000 2097 2738 273 3622009616 1020 2039 2727 275 3582009616 1040 2090 2766 277 361

2009616 1640 1956 2752 268 3552009616 1700 1943 2762 269 3572009616 1720 1953 2771 268 3602009616 1740 1944 2765 268 3582009616 1800 1948 2759 270 3592009616 1640 1956 2752 268 355


1198772







1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down



1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up





00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value




200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)


6 Conclusion






2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












2009614 920 2223 2720 248 3712009614 940 1894 2762 249 3742009614 1000 1812 2762 251 3742009614 1020 1759 2757 248 3762009614 1040 1902 2734 265 367

2009614 1620 1948 2482 218 3472009614 1640 1947 2477 215 3462009614 1700 1926 2477 206 3442009614 1720 1920 2485 207 3462009614 1740 1925 2499 210 3462009614 1800 1929 2508 211 3462009615 920 2188 2680 237 3542009615 940 1748 2812 427 6072009615 1000 1689 2820 410 6032009615 1020 1685 2828 413 6042009615 1040 1684 2846 417 606

2009615 1620 1704 2821 403 5992009615 1640 1684 2813 397 5982009615 1700 1689 2807 394 5972009615 1720 1680 2795 393 5952009615 1740 1677 2797 392 5942009615 1800 1670 2791 390 5942009616 920 2191 2689 265 3572009616 940 2157 2712 277 3602009616 1000 2097 2738 273 3622009616 1020 2039 2727 275 3582009616 1040 2090 2766 277 361

2009616 1640 1956 2752 268 3552009616 1700 1943 2762 269 3572009616 1720 1953 2771 268 3602009616 1740 1944 2765 268 3582009616 1800 1948 2759 270 3592009616 1640 1956 2752 268 355


1198772







1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down



1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up





00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value




200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)


6 Conclusion






2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

1

15

2

25

3

35

4

45

Pow

er co

nsum

ptio

n (k

W)

Pchiller_down



1000 2000 3000 4000 5000 6000 7000 8000 90000Simulated value

115

225

335

445

5

Pow

er co

nsum

ptio

n (k

W)

Pchiller_up





00501

01502

02503

03504

04505

055

Pow

er co

nsum

ptio

n (k

W)

2 4 6 8 10 12 14 16 180Simulated value




200 400 600 800 1000 12000Simulated value

00501

01502

02503

03504

04505

Pow

er co

nsum

ptio

n (k

W)


6 Conclusion






2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












2



500 1000 1500 2000 2500 3000 3500 40000Simulated value

152

253

354

455

556

65

Air

hand

ling

unit

load

(kW

)

Qfan



615 616614

1220 1520 920 1220 1520 920 1220 1520 1800920Time

2

3

4

5

6

7

8

Tota

l pow

er co

nsum

ptio

n (k

W)



0

50

100

150

200

250

Tota

l pow

er co

nsum

ptio

n (k

W)

615 616614Date

9677 kW7199 kW

9726 kW12461 kW13254 kW

16275 kW PLR = 05sim075PLR = 075sim10

PLR = 03sim05



Day Time 119879chw119904 119886

chw∘C CMH CMH

2009614 920 1294 96288 192009614 940 1044 99745 1922009614 1000 1025 10317 192009614 1020 1006 10401 22009614 1040 105 10943 194

2009614 1620 1089 95879 1892009614 1640 1298 11011 1992009614 1700 1312 1068 2012009614 1720 1339 1124 2042009614 1740 1322 11058 2032009614 1800 1305 10799 22009615 920 1226 96327 192009615 940 66 14171 192009615 1000 787 15893 1862009615 1020 675 14992 2152009615 1040 67 14516 185

2009615 1620 649 10717 2722009615 1640 643 13327 2082009615 1700 655 13465 2092009615 1720 749 11254 2532009615 1740 724 10822 2592009615 1800 713 15351 2042009616 920 104 10028 1882009616 940 1098 99285 1972009616 1000 1114 1142 1852009616 1020 105 11153 2012009616 1040 1062 10483 199

2009616 1640 1053 10905 22009616 1700 1061 12377 1912009616 1720 1062 11028 2032009616 1740 1057 12295 22009616 1800 1049 11994 2012009616 1640 1053 10905 2




Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Nomenclature



119899


119875chiller119894



119875pump119895




119894



119879chw119899


119879cwr119894


119879cws119894


Competing Interests


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Support Vector Regression and Genetic ...downloads.hindawi.com/journals/mpe/2016/6212951.pdf · Research Article Support Vector Regression and Genetic Algorithm for