A State of the Art Review and Case Study of a Residential HVAC System

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Energy and Buildings

jo u r n al h om ep age :w w w . e l s e v i e r . c o m / l o c a t e / e n b u i l d

Artificial neural network (ANN) based model predictive control (MPC) and optimization of HVAC systems: A state of the art review and case study of a residential HVAC system

Abdul Afram

^a,∗

, Farrokh Janabi-Sharifi

^a

, Alan S. Fung

^a

, Kaamran Raahemifar

^b

aDepartmentofMechanicalandIndustrialEngineering,RyersonUniversity,350VictoriaStreet,Toronto,ONM5B2K3,Canada

bDepartmentofElectricalandComputerEngineering,RyersonUniversity,350VictoriaStreet,Toronto,ONM5B2K3,Canada

a r t i c l e i n f o

Articlehistory:

Received5October2016 Receivedinrevisedform 31December2016 Accepted6February2017 Availableonline11February2017

Keywords:

Artificialneuralnetwork(ANN) Modelpredictivecontrol(MPC) ANNbasedMPCreview OptimizationofHVACsystem ResidentialHVACsystem

a b s t r a c t

Inthispaper,acomprehensivereviewoftheartificialneuralnetwork(ANN)basedmodelpredictive control(MPC)systemdesigniscarriedoutfollowedbyacasestudyinwhichANNmodelsofaresidential houselocatedinOntario,Canadaaredevelopedandcalibratedwiththedatameasuredfromsite.A newalgorithmcalledbestnetworkaftermultipleiterations(BNMI)isintroducedtohelpindetermining theappropriateANNarchitecture.ThepredictionperformanceofthedevelopedmodelsusingBNMI algorithmwassignificantlybetter(between6%and59%bettergoodnessoffitforvariousmodels)when comparedtoapreviousstudycarriedoutbytheauthorswhichusedthedefaultsingleiterationANN trainingalgorithmofMATLAB^®.TheANNmodelswerefurtherusedtodesignthesupervisoryMPCfor theresidentialHVACsystem.TheMPCgeneratedthedynamictemperatureset-pointprofilesofthe zoneairandbuffertankwaterwhichresultedintheoperatingcostreductionoftheequipmentwithout violatingthethermalcomfortconstraints.Whencomparedtothefixedset-point(FSP),MPCwasableto saveoperatingcostbetween6%and73%dependingontheseason.

©2017ElsevierB.V.Allrightsreserved.

1. Introduction

Buildingsectorconsumesabout40%and30%oftotalenergyin U.S.andCanadarespectively[1].Spaceheatingcanconsumeupto 60%oftotalsectorenergyincountrieswithextremeweathercon- ditionssuchasCanada[2].Therefore,itisessentialtoinvestigate themethodsforreducingenergyconsumptionandoperatingcost ofthesesystems.Heating,ventilationandair-conditioning(HVAC) systemsareverycomplexandnonlinearsystemsduetotheinter- actionofalargenumberofsubsystems(e.g.,chillers,boilers,heat pumps,pipes,ducts,fans,pumpsandheatexchangers)andther- malinertiaofthebuildings.Inordertocalculatethetotalenergy consumedbyHVACsystem,eachofthesesubsystemsneedtobe modeled preciselytaking intoaccount allthe massand energy transferacrosseach subsystem[3]. Usingconventional forward orphysics-basedmodelingmethods,developingprecisedynamic modelsofeachsubsystemisverydifficultandasignificanteffort

∗Correspondingauthor.

E-mailaddresses:abdul.afram@ryerson.ca

(A.Afram),fsharifi@ryerson.ca(F.Janabi-Sharifi),alanfung@ryerson.ca(A.S.Fung), kraahemi@ryerson.ca(K.Raahemifar).

is required for a detailed understandingof system physics[4].

Ontopofthat,thesemodelshavealargenumberofparameters e.g.,thermalcapacitanceandthermalconductanceforheattrans- fercomponentineachsubsystem.Theseparametersneedtobe eitherextractedfromthemanufacturersupplieddataorestimated usingtheparameterestimationtechniques.Usingmanufacturer supplieddata,theestimatedparametersarelesspreciseifthisdata wasrecordedunderdifferentsetofoperating conditions.Using parameterestimationtechniquesrequiremeasurementsofsystem performancedatafurthercomplicatingthedevelopmentofforward models.Limitationsoftheseforwardmodelingmethodsbecome veryevidentwhenmodelsforavarietyofHVACsystemconfigura- tionsneedtobedevelopedandtunedimpedingthedeploymentof suchmethodsinrealworld.Forwardmodelingmethodsareuseful forsimplersystemsandresearchbasedanalysisofcomplexsys- temsbutfailtosatisfyindustrialusers.Traditionally,industryhas beenveryreluctanttoadaptcomplicatedmethodsinmodelingand controlofHVACsystemsandduetothisreasonmajorityofHVAC systemsarestillusingverysimpleon/offorproportional-integral- derivative(PID) controllersinsteadof more moderncontrollers suchasmodelpredictivecontrol(MPC).Lackofanadvancedcon- trollerresultsinmanyperformanceandeconomicpenaltiessuchas higherenergyconsumption,higheroperatingcost,higherthermal http://dx.doi.org/10.1016/j.enbuild.2017.02.012

0378-7788/©2017ElsevierB.V.Allrightsreserved.

discomfortandhigherequipmentwearandtear[5].Researchers haveshownthatbyaddingasupervisoryMPCcontrollertoHVAC systemscouldresultanywherefrom7%tomorethan50%reduc- tioninenergyconsumptionandoperatingcostreduction[6–11].

OnsomesocalledadvancedHVACsystems,rule-basedsupervisory controllers[12]areimplementedwhichusetheoperatorknowl- edgeandapplyittoreducetheenergyandoperatingcostsuchas appropriatestart/stoptimeofHVAC,nightset-back,precoolingand preheatingetc.Theserule-basedcontrollersaresimpletoimple- mentandrequirenomodelinganddesigneffortandcanprovide significantsavingswhenappliedcorrectly.Problemwiththesesys- temsisthatoperatorhastoconstantlymonitorandadjusttheHVAC operationtomeettheobjectivesofreducingenergyconsumption whilemaintainingthermalcomfort. Rule-basedcontrollersgen- erallyarenot anticipatorycontrollersi.e.,theycannotlookinto thefutureanddecidethecourseofactionappropriatelyandrather workbasedonthecurrentstateofsystem.Maintainingarule-based controllerisatediousprocessandadvancedHVACcontroltaskis bettersuitedforanintelligentcontrollersuchassupervisoryMPC whichcanautomaticallytakeintoaccountthevariationsinweather parametersoverafuturehorizonandcontroltheappropriateset- tingsofHVACsystemsatpresent[13].Furthermore,supervisory MPCcantakeintoaccountthedynamicelectricitypriceandadjust theset-pointsoflocallevelcontrollersforactiveandpassivether- malenergystoragetooffsetthepeakloadtooff-peakhours.

A simpler alternative to forward models is inverse or data-drivenmodels[4,14].Inversemodelscanbedevelopedcom- parativelyeasilysincetheydonotrequiretheunderstandingof systemphysics.Inordertotraintheinversemodels,a compre- hensive setof input-outputdataof systemis neededunder all possibleworkingconditions.Therefore,theeaseofdevelopmentof inversemodelscomesatthecostofreducedgeneralizationcapa- bilitycomparedtotheforwardmodels.Accuracyofinversemodels decreaseswhentrainingdatadeviatesfromtestingdata.There- fore,itiscriticaltotraintheinversemodelswithatrainingdata thatcoversalltheoperatingconditionswhichcouldbechalleng- ingespeciallyforlargescalesystemssuchasHVACsystemswhich operateunderawiderangeofweatherconditionsthroughoutthe year.Forsuchsystems,modelstrainedunderonesetofconditions maynotbeaccurateenoughunderdifferentsetoftestconditions thereforetheadaptivemodelsaresometimesused.Alternatively, manyresearchersusedifferentmodelsinheatingandcoolingsea- sonsforHVACsystems.Researchershavedevelopedmanytypes of inverse modelssuch asfrequency domainmodels (firstand secondorderover-dampedprocesswithdeadtime)[15],datamin- ingalgorithms(artificialneuralnetwork-ANN[16],supportvector machine-SVM[17]),fuzzylogicmodels(fuzzyadaptivenetwork [18], Takagi-Sugenofuzzymodels[19],adaptive networkbased fuzzyinferencesystem[20]), statisticalmodels(regression[21], autoregressionexogenous[22],autoregressionmovingaverage exogenous[23],auto-regressiveintegratedmovingaverage[24]), state-spacemodels(sub-spacestatespaceidentification[25]),geo- metricmodels(thinplatesplineapproximation[26]),case-based reasoning(topologicalcasebasemodeling[26]),stochasticmodels (probabilitydensity function approximation[27])and instanta- neousmodels(justintimemodels[28]).Outofallthesemodeling methods,ANNisthemostpopularmethodduetoitshighaccuracy tomodelnonlinearsystemscomparedtoothermethods.ANNmim- icsthehumanbrainbyusingseveralneuronsinmultiplelayers.The weightsoftheseneuronsaregenerallytrainedbyusingsupervised learningmethods.AppropriatelytrainedANNcanapproximateany nonlinearprocesstoahighdegreeofaccuracy.Therearemanydif- ferenttypesofANNstructuresbutmulti-layerperceptron(MLP) feedforwardstructureisthemostpopularone.OthertypesofANN structuresincluderadialbasisfunctionneuralnetwork,recurrent

neural network and feedforwardneuralnetwork withdynamic neutronsetc.

SincemodelsdevelopedwithANNarenonlinear,therefore,MPC approachesbasedonANNarenonlinear.LinearMPCproblemshave guaranteedsolution[29].Minimaofalinearoptimizationproblem canbeefficientlyfoundbyusingoptimizationapproachessuchas activesetmethodorinterior-pointmethod.Ontheotherhand,non- linearoptimizationproblemmaybenon-convexanditmayhave manylocalminima.Analgorithmthatguaranteesglobalminima ofanonlinearoptimizationproblemdoesnotexistintheliterature yet.AnotherproblemwithnonlinearMPCisthattheoptimization solutionmighttakealongtimetoconvergewhichcouldbecritical forfastmovingprocessesthoughinthecaseofsupervisoryMPCfor HVACsystems,thismaynotbeanissuesincesupervisoryMPCout- putonlyupdatesonceeveryfewminutestoeveryfewhours.Global optimizationmethodssuchasevolutionaryalgorithmsandsimu- latedannealingcanworkwithnonlinearoptimizationproblems butpresentconvergenceandcomputationalcomplexityissues.

Thefollowingarethemainobjectivesandcontributionsofthis paper:

iHighlightingthecurrentresearchtrendsinANNbasedMPCand itsapplicationstoHVACcontrolsystems;

iiDevelopmentofanewANNtrainingalgorithmtoappropriately tunethenetworkweights andaidintheselectionofnetwork architecture;

iiiComparisonofdevelopedANNmodelswithapreviousresearch paper fromtheauthors tohighlightthe ANNpredictionper- formance improvements as a result of appropriate training algorithm;

ivSimulationoftheANNbasedMPCcontrollerontheaccurately calibratedresidentialHVACsystemmodel;and

vAnalysisofpotentialenergyandcostsavingsusingMPCcom- paredtothefixedset-pointsonaresidentialHVACsystem.

2. ReviewofANNbasedMPCandoptimizationofHVAC systems

Thissectionpresentsanin-depthreviewof ANNbased MPC and optimization research for various types of HVAC systems.

TheseapproachesdifferbasedonthetypesofbuildingsandHVAC systems,controlobjectives,modelingdatageneration,ANNarchi- tectureandoptimizationmethodselection.Followingsubsections discusseachofthesefactorsindetailwithspecificexamplesfrom literature.Attheendofthissection,theenergyandcostsavings potentialofANN-MPCapproachesispresented.

2.1. BuildingandHVACsystem

SupervisoryandlocallevelANN-MPCforHVACsystemshave beendevelopedforapublicuniversitybuilding(HVACsystemwith anoutdooraircooledinvertedcompressorunitandoneinternal unit foreachofthefourrooms)[6,30],acommercialuniversity building(fiveroomssensitivetothermalloadwithoneairhandling unit(AHU)forthreefloorbuildingwithvariableairvolume(VAV) terminalineachzone)[31],acommercialairportbuilding(check- in hall withfour thermal zonesand constant air volume AHU) [32,7],anexperimentalresearchfacilityofficebuilding(commer- cialHVACsystemwithAHUandVAVterminals)[8,9,33,34–36],an automotiveapplication(autonomousairconditioningsystemwith avariablespeedcompressor)[37],anofficebuilding(integrated daylightingHVACsystem)[11],anofficebuildingwithwarehouse andmanufacturingarea(fourzonebuildingwithoneHVACsub- systemforeachzone)[10]andaschoolbuilding[38].

ThoughANN-MPChavebeendevelopedforavarietyofbuildings byHVACresearchers,ithasnotbeenusedforaresidentialbuilding andparticularlyahouse.Manycommercialbuildingshavesome sortofsupervisorycontrolbutmostofthehousesarelackingany formofsuchsupervisorycontroller.Therefore,thereisanoppor- tunitytodevelopsuchcontrollerforresidentialHVACsystemsto reducetheenergyconsumptionandoperatingcost.Thesecondpart ofthispaperdiscussesthedevelopmentofANN-MPCforresidential HVACsystemofahouse.

2.2. Controlobjective

MPC isoften employed atsupervisory level tooptimizethe energyuseatthebuildingscale.TheideaofusingMPCtosavebuild- ingenergystemsfromtheconceptofsupervisorycontrol[7].When MPCisimplementedinthelocallevelcontroller,thecontrolobjec- tiveisgenerallytominimizethetrackingerrorandcontroleffort.

ButwhenANN-MPCisimplementedinthesupervisorylayer,the controlobjectiveiscommonlystatedasoneoracombinationof thefollowing:

•Minimizeenergyconsumption[6,7,33–35,10,11,39,40],

•Maintainthermalcomfort[6,33–35,10,11],

•Maintainindoorairquality(IAQ)atacceptablelevel[9],

•Minimizeoperatingcost[10,41,7,42,30],

•Maintainvisualcomfortatacceptablelevel[11],

•Minimizeretrofitcost[38],and

•Minimizethermaldiscomforthours[38].

Whencontrolobjectiveisstatedasonlyoneoftheabovestate- ments,thenitiscalledasingleobjectiveoptimizationandwhen morethanoneobjectivesaretobeachievedsimultaneously(e.g., simultaneousminimizationof energyconsumptionand mainte- nanceofthermalcomfort [6]),then theoptimizationiscalleda multi-objectiveoptimization.

Generally,HVACsystemscompriseofmanysubsystemsandthe energyconsumption ofallofthemis calculatedandminimized simultaneously.Thermalcomfortiscalculatedusingthepredicted meanvote(PMV)index.PMVindexpredictsthemeanresponse ofagroupofpeopleaccordingtoASHRAEthermalsensationscale accordingtowhichaPMVof+3ishotand−3iscold.Theneutral valueofPMVis0wheremostofthepeoplewillfeelcomfortable.

Whenusedascontrolobjective,thePMVisgenerallytargetedin the[-0.5,+0.5]range[10].PMViscalculatedusingFanger’sthermal comfortmodelbasedonthefactorsthatdeterminetheheatgain andloss(i.e.,metabolicrate,clothinginsulation,airtemperature, meanradianttemperature,airvelocityandrelativehumidity).

IAQgenerallyreferstotheindoorairtemperature,humidity and carbon dioxide (CO₂)level. Air temperature and humidity depends on internal (occupants and equipment) and external (weather)disturbances actingonthe system.Theair CO2 level dependsontheoccupancyandoccupant’sactivity.Inordertocon- trolthetemperature,humidityandCO₂level,theHVACsystems useheating/cooling, humidification/dehumidification and venti- lation systems respectively. A comfortable indoor temperature and humidity is different for summer and winter seasons and can be adjusted according to ANSI/ASHRAE Standard 55–2013 Thermal Environmental Conditions for Human Occupancy [43]

andANSI/ASHRAEStandard62.1–2013VentilationforAcceptable IndoorAirQuality[44],respectively.AccordingtoStandard55,the temperaturecouldbeapproximatelyintherange[19.5,27.8]^◦C.

According to Standard 62.1, the relative humidity in occupied spacesshouldbecontrolledlessthan65%.Ahigherhumiditycan increase thelikelihood ofconditions that canlead tomicrobial growth.The Standard 62.1alsodeterminesthe ventilationrate basedontheCO₂generationrateinthespace.

Ifelectricitypricechangesduringtheday,itismorebeneficial tominimizetheoperatingcostoftheHVACsystemcomparedto minimizingtheenergyconsumption.Inthiscase,thesupervisory MPCstorestheenergyinthebuildingmassbypre-coolingorpre- heatingduringtheoff-peakhoursandtriestominimizetheenergy useduringpeakhours.Itmayincreasetheenergyconsumptionof theHVACsystembuttheoperatingcostwillbereduced[5].

Generally,maintenanceofthevisualcomfortandminimization ofretrofitcostisnotconsideredwhileminimizingtheHVACsystem energyconsumption.Inthisregards[11,38]presentuniqueper- spectivesontheseaspects.In[11],theenergyconsumptionofHVAC systemanddaylightlightingsystemisminimizedusingamulti- objectiveoptimization.In[38],theretrofitcost(costofupgrading windows,addingmoreinsulationandupgradingtheHVACsystem) isconsideredalongwiththeenergyconsumptionandthermalcom- fortandtrade-offsbetweenthesethreecompetingobjectivesare studied.Itwasshownin[38]thatoptimizingonlyoneobjective individuallyresultsinpoorperformanceinotherareastherefore allthreeofthemneedtobeoptimizedsimultaneously.

2.3. Modelingdata

In orderto developdata-driven modelssuchasANN, a rich datasetisrequiredwhichcomprisesofallpossibleworkingcondi- tions.Datacanbemeasuredfromthesiteundernormaloperation or underspecial datagatheringtest conditionsby applyingthe pseudo-randombinarysequence(PRBS)atthecontrolledinputs.

Datacanalsobegeneratedfromthebuildingenergysimulation programssuchasTransientSystemSimulationTool(TRNSYS)and EnergyPlusEnergySimulationSoftwareusingthedesignofexper- imentsmethod.

For example, PRBSwas appliedfor zone set-points and air- conditioneron/offtimesin[6].Similarly,in[31]duringa10-day testperiodPRBSwasappliedtogeneraterandomsupplyairtem- perature and static pressureset-points of AHU.Two controlled set-pointsweremodifiedevery15minanddatawasrecordedat 1minintervals.Datawasaveragedto15minintervalsformod- elingandwasdividedinto80%trainingand20%validationdata sets.In[35],morethan500parameterscomprisingofairtemper- ature,humidity,flowrateandenergyconsumptionwererecorded at1minintervalsfor17days.Eachset-pointwasobservedfor1h.

In[37],amplitudemodulatedPRBSwasusedtogenerateaseriesof amplitude-and-holdtime-varyingcompressorsetspeedsoverthe entireoperatingspace.Adatasetof2000pointswasrecordedout ofwhich75%datawasusedfortrainingand25%datawasusedfor testing.

In[11],thedatabasewasgeneratedbytheEnergyPlusmodel.In total28simulationswerecarriedouttogeneratethedatabaseand 70%datawasusedfortrainingand30%wasusedfortestingand validation.In[38],acomprehensivebuildingmodelwasdeveloped inTRNSYSandsimulationdatabasewasgeneratedfromthismodel totrainandvalidatetheANNmodels.

The forecast of weather parameters can beestimated using thepredictionmodelsordownloadedfromgovernmentservers where available. Three auto-regressive predictive models were usedin[6]topredicttheoutdoorairtemperature,humidityand globalsolar radiation.In [10], theoutdoorair temperatureand solarradiationwasforecastedfor8hintothefuturebasedonthe previousdayvaluescorrectedbycurrentvalues.In[30],anintel- ligentenergyautonomousweatherstationprovided theoutside airtemperature,relativehumidityandglobalradiationmeasure- mentsaswellastheirforecastsovertheuserdefinedprediction horizon.One-dayahead weatherforecast datawasdownloaded fromAustralianBureauofMeteorologyin[32,7].InCanadaandU.S., weatherdatacanbedownloadedfromMeteorologicalServiceof Canada’s(MSC)hypertexttransferprotocol(HTTP)dataserverand

NationalOceanic and Atmospheric Administration(NOAA)data server,respectively.

Occupancycanbeforecastedusingschedulesandcanbemea- sured using occupancy sensors such as passive infrared (PIR) sensors.OccupancycanalsobeestimatedthroughtheCO₂gener- ationrateintheindoorspace.In[30],theoccupancyforecastwas assumedtobeknownduetotheexistenceofschedules.Real-time occupancywasmeasuredusingPIRsensorsandamovementsignal wascalculatedbasedonPIRsensorstobeusedinpredictivecontrol.

In[32,7],occupancyforecastwasestimatedfromflightschedules.

Variable electricity priceis generallyknown inadvance. For example,in[30],pricehadafixedstructurecomprisingof4peri- odsoftaxationi.e.,peak,normal,saverandsupersaverperiods.

InToronto,electricitypricehasthree-tieredstructurei.e.,off-peak, mid-peakandpeakwhichwasusedinthenextpartofthispaper.

Allinput/outputdatashouldbescaledto[−1,1]rangepriorto thetrainingofANNtoimprovetheefficiencyoftraining.Datanor- malizationgivesequalweighttoallvariablesandsuppressesany dominantvariablesduetomagnitudedifferencesinthedata[38].

Someresearchershaveusedthenormalizationofdatawithin[0,1]

range[45]butitislesscommon.

Appropriately selected parameters or variables can improve comprehensibility,scalabilityandpossiblyaccuracyofthemod- els[33].Iftoomanyparametersareselected,theymaycontain redundantparameterswhichmaynotaddanynewinformationto themodelaccuracybutcouldincreaseitsdimensionalityresult- inginincreasedcomputationalexpenseduringtraining.Iftoofew parametersareused,someimportantprocessdynamicsmaybeleft un-modeled.Appropriatenumberofinputvariablesforamodelcan beselectedbasedonthephysicalproperties[32],domainknowl- edge,forwardselectionmethod[32],boostingtreealgorithm[8], wrapperalgorithm[33]andcorrelationcoefficientmatrix[9].For example,in[35],acombination ofdomainknowledge,boosting treealgorithmandwrapperalgorithmwasusedtoselect11param- etersoutof500totalmeasuredparameterstodevelopfourmodels forHVACtotalenergyconsumption,averageindoortemperature, averageindoorhumidityandaverageindoorCO₂concentration.

2.4. ANNarchitecture

ANNmodelswereusedtopredictthePMVindex[6,30],outside weatherparameters(airtemperature,airhumidityandglobalsolar radiation)[6],roomairtemperature[6,30,32],radianttempera- ture,roomairhumidity[6,30],coolingvalveposition[7],outdoor air damper position[7], energy consumed(by chillers[8], fans [8],pumps[8],VAVbox[8],domestichotwaterheaterandHVAC system[9,34]),indoordaylightilluminance[11],averageCO₂con- centration[35]andchilledwaterheadforpipenetworks[39].The followingtypesofANNwereusedforANN-MPCdevelopmentsfor HVACsystems:

•MLP[34,31,10,11,38,40],

•MLPensemble[8,9,33,35],

•Radialbasisfunction(RBF)ANN[6],

•Nonlinearauto-regressivemodelwithexogenousinput(NARX) [7,32,37],

•RBFsusedasNARX[30],

•Feedforwardmulti-layerself-growingANN[10],and

•ArtificialNeuro-FuzzyInferenceSystem(ANFIS)[39].

MLPisthemostcommontypeofANNusedincontrolsystems [7].Ithasaninputlayer,oneormorehiddenlayersandanoutput layer.ANNisusuallytrainedwithback-propagationalgorithm[38], Levenberg-Marquardt(LM)algorithm[6,37,11],Bayesianregular- ization algorithm [7,32] and Broyden-Fletcher-Goldfarb-Shanno (BFGS)algorithm[8,34,35].Back-propagationisthemostcommon

algorithmwhichusesgradientdescenttofindtheminima.Back- propagationsuffersfromlocalminimaandoverfittingproblems reducingthegeneralizationofANN.Bayesianregularizationalgo- rithmhasslowconvergencespeedcomparedtoback-propagation butimprovesthegeneralizationofANNandpreventsoverfitting.

LM algorithm hasfaster convergence speed compared to other commonoptimizationtechniquessuchassteepestdescent,Gauss- Newtonandquasi-Newton.BFGSalgorithmhasgoodperformance forverylargenumbersofvariablesandnon-smoothoptimizations.

It also achieves both fast decrease and fast convergence com- paredtobackpropagationalgorithm[40](Zaheeruddin&Ning) (Zaheeruddin&Ning[45]).

When measured, data is used for ANNtraining, it is called supervisedlearningotherwiseitiscalledunsupervisedlearning.

Generally,a costfunctionsuchasmeansquarederror(MSE) or rootmeansquarederror(RMSE)isusedtoterminatethetraining ofANN.ThetrainingofANNterminateswhentheMSEorRMSE eitherstabilizesordropsbelowacertaindesiredvalueorapre- defined numberofepochs haveelapsed.Attheend oftraining, resultingANNweightsareoptimalanditspredictionsareveryclose tomeasureddata.Measureddataisdividedintotrainingandvali- dationdatasetsusuallywith70%trainingdataand30%validation data.AnappropriatelytrainedANNperformsequallywellonboth trainingandtestingdatasets.PerformanceofANNagainstmea- sureddataisanalyzedusingabsoluteerror(AE),meanabsolute error(MAE)[6,8],maximumabsoluteerror(max_AE)[6],normalized relativemeansquarederror(NRMSE)fitness[32],meanabsolute percentageerror(MAPE)[8],standarddeviationofabsoluteerror (StdAE)[8],standarddeviationofabsolutepercentageerror(StdAPE) [8],MSE[37],RMSE[7]andlinearcorrelationcoefficient[37].A moredetaileddiscussionandformulationofthesevarioustypesof performancecomparisonmetricswasprovidedin[4].

SincetheoutputofasingleMLPisdependentonANNweights whicharesensitivetotheinitialconditions,sometimesagroupof MLPscalledtheMLPensembleisused.TheMLPensembleoutputis determinedbymajorityvote.MLPensemblewasshowntooutper- formothermodelingmethodssuchassingleMLP,classificationand regression tree(CART), chi-squareinteractiondetector(CHAID), boosting tree, random forest, multivariate adaptive regression splines(MARSplines)andSVMin[8]and[16].

Activationfunctionsareusedforcomputingtheoutputofaneu- ronin eachlayer.Commonlyusedtypesofactivationfunctions includesigmoidal,hyperbolic,RBFandlinear.IfRBFs(aGaussian) areusedastheactivationfunctionsofANN,thenitiscalledRBF ANN.RBFsusuallyhaveonlyonehiddenlayer.TheoutputofRBF ANNisalinearcombinationofRBFsinhiddenlayer.Comparedto MLP;RBFANNdoesnotsufferfromlocalminima.

MLPisasimplefeedforwardnetworkwhichmeansthatthere is no feedback in the network and output signals are entirely calculated fromthepresent valuesof inputsignals.Sincemany dynamicalsystemsrelyonthepreviousvaluesofinputsignaland outputsignal,anewnetworkstructurecanbeformedbypassing theinputsignalsandoutputsignalsthroughtimedelaynetworks beforeconnectingtothenetwork inputs.Such ANNswhichuse previousvaluesofinputandoutputsignalsarecalledrecurrent networks.NARXis atypeof recurrentnetworkwhosemodelis basedonthelinearauto-regressiveexogenousmodel[7].NARX hasfeedbackconnectionsenclosingseverallayersofthenetwork.

ANNarchitecture(numberofneuronsininput,outputandhid- denlayers)isgenerallyidentifiedbasedontrialanderror[38,40], suggestionin previousempirical studies[37], chosenrandomly [34,35],forwardselection method[32],or automaticidentifica- tion method[6,30,10,11]. Feedforward multi-layerself-growing ANNissimpleMLPstructurewithonehiddenlayerwhosearchi- tecture is defined automatically during the training phase by cascade-correlation algorithm. The number of hidden neurons

determinesthemodel complexity ofANN. Increasingthe num- berofhiddenlayerneuronsincreasesthechancesofover-fitting training data,reducesthegeneralization capabilityof ANNand also minimizes the training error [38]. Therefore, it is impor- tanttochoosethenumberofhiddenlayerneuronsappropriately eithermanuallyorusinganautomaticarchitectureselectionalgo- rithmsuchascascade-correlationalgorithmandmulti-objective geneticalgorithm (MOGA).Cascade-correlationalgorithm starts ANNarchitecturewithonlyonehiddenlayerneuronand mini- mizesthetrainingerror.AfterANNistrained,anotherneuronis addedtothehiddenlayerandANNistrainedagain.IfANNhas lowertrainingerrorafteraddingtheneuroncomparedtotheolder ANN,theANNkeepsgrowinguntiltrainingerrorstopsreducingany further.Thismethodisveryusefulinfindingtheappropriatestruc- tureofANNbutiscomputationallyintensive.Forexample,in[10]

cascade-correlationalgorithmwasusedtofindtheANNstructure forapproximatingairtemperature,radianttemperaturesandelec- tricalpowerconsumedbyHVACsubsystems.Resultingmodelshad 18–24neuronsinthehiddenlayer.Thoughautomatictuningcanbe computationallyexpensive;itisstillmoreefficientthancommonly usedtedioustrialanderrormethodforANNstructureidentifica- tionwhenalargenumberofANNsaretobetrained.MOGAdefines theANNinput/outputstructureandnumberofneurons.MOGAwas usedin[6]tofindtheANNarchitectureforthemodelsofPMVindex, outsideweatherparameters(i.e.,airtemperature,airhumidityand globalsolarradiation)andindoorairparameters(i.e.,temperature andhumidity).ThemodelsfoundwithMOGAhadRBFactivation functionsanddifferentnumberofhiddenlayerneuronsforeach model(i.e.,5neuronsforPMV,14neuronsforroomairtemper- atureinsummer,11neuronsforroomairhumidityinsummer, 7neuronsforroomairtemperatureinwinterand11neuronsfor roomairhumidityinwinter).

ANFISisamorecomplicatedmultilayerhybridmodelstructure basedonbothfuzzylogicandANN.Ithasnolimitationonitsnet- workstructuresandnodefunctionsandcanbeimplementedin theframeworkofadaptiveANNs.UnlikeANN,eachlayerinANFIS performsadifferentfunctionalthoughthenodearchitectureand propertiesremainunchangedinasinglelayerbutvaryacrossthe layers.Geneticalgorithm(GA)basedANFISwasreportedtoper- formbetterthanANNtopredicttheenergyuseoftwobuildingsin [46].Duetomorecomplicatedstructure,trainingtimeforANFISis alsogreaterthanANNonlargedatasets.

2.5. Optimizationmethod

Unlikelinearsystems,findingoptimalsolutionsfornonlinear systemsisadifficulttask,sinceanalyticalsolutionusuallyisnot availablefornonlinearsystems.Therefore,fornonlinearsystems numericaltechniques,suchasdynamicprogrammingandgradient methodshavetobeemployed.ProjectedandaugmentedLagrange multipliermethodsdonotperformwellbecauseoftheequality constraintsusedintheproblemformulationandthegeneralized reduced gradient method providesconsistent results, only if it startswithafeasiblesolution[45].Thefollowingnonlinearopti- mizationmethodsareusedforANN-MPCresearch:

•GA[10,11],

•ModifiedGAorMOGA[39,38],

•Newton-Raphsonmethod[37],

•Interior-pointmethod[34],

•Branchandbound(BaB)method[6,30],

•Particleswarmoptimization(PSO)algorithm[8,31],

•Modifiedormulti-objectivePSO(MOPSO)[35],

•StrengthParetoevolutionaryalgorithm(SPEA)[31],

•SPEAwithlocalsearch(SPEA-LS)[9],

•StrengthMOPSO(S-MOPSO)algorithm[9],

•Fireflyalgorithm[36],and

•Harmonysearch[31].

GAisthemostcommonnonlinearoptimizationmethodamong ANN-MPCresearchers.GAis anumericaloptimizerabletodeal withintegervalues.Itisefficientinthesearchforoptimalsolu- tionandsolvesbothconstrainedandunconstrainedoptimization problems.GAisempiricallyproventoproviderobustsearchesin complexspaces[10].InGA,theobjectivefunctionis minimized withoutcalculatingthederivativesanditisnotrestrictedtothe estimationofuncorrelatedparameters.GAislesssensitivetoini- tializationduetoitsprobabilisticnature.GAproducesmorethan onesolution(individual)orapopulationofgoodindividuals.The drawbackofGAisthatitisslowtoconvergeforcomplexproblems andtherefore,isnotsuitableforreal-timeimplementations.GAis alsolessefficientandslowerthantraditionaloptimizationmethods forsimpleproblems[10].MOGAisusedtosolveoptimizationprob- lemswithmultipleobjectivessuchassimultaneousminimization ofenergyconsumption andthermaldiscomfortwhich areoften conflictingobjectives.

Newton-Raphsonmethodwasusedin[37]whichisaquadrat- ically converging algorithm. It converges in lower number of iterationscomparedtoothertechniquesandisfaster andmore efficientalgorithmforrealtimecontrolapplications.Interior-point methodsolvesthecontinuouslydifferentiablecostfunctionand constrainsandguaranteestheoptimalsolution[34].BaBisanopti- mizationtechniquewhichisusedfortheoptimizationofdiscrete systems.BaBhasguaranteedoptimalsolution.Itisnotnegatively affectedbytheconstraintsandisnotsensitivetopoorinitialization [6].

PSO is awell-balanced mechanism toenhanceand adapt to globalandlocalexplorationproblems.PSOisexcellentinsolving single-objectiveoptimizationproblemswithfastconvergence[8].

CanonicalPSOcanonlybeusedtosolvethesingle-objectiveopti- mizationproblemswhereasMOPSOcansolvethemulti-objective optimization problems [35]. In general, due to the conflicting objectivefunctionsthereisnouniquesolutiontomulti-objective optimizationsbutasetofnon-dominated(Paretooptimal)solu- tions[38].SPEAhasadvantageinsearchingglobalsolutionwhile PSOisapplicableinsearchingforoptimallocalsolutions.S-MOPSO isthecombinationofSPEAandPSOalgorithmsandiseffectivein findingoptimalsolutionsofnonlinearmulti-objectivemodels[33].

Firefly algorithm isefficient infinding globaloptima.Firefly algorithm outperformedPSOandevolutionarystrategy inmini- mizing theenergy consumptionof HVACsystemin[36].Firefly algorithmwasmoreeffective,efficient,robustandusedlesscen- tralprocessingunit(CPU)timetoconvergecomparedtoPSOand evolutionarystrategy[36].

Harmonysearchwasusedin[31]tominimizetheHVACenergy consumptionandroomtemperatureramprate.Harmonysearch wascompared toPSOandSPEAin[31].BothPSOandHarmony searchhadlowercomputationaltime andhighercomputational frequencycomparedtoSPEA.Therefore,SPEAisnotsuitablefor onlineoptimization.

2.6. Energyandcostsavingspotential

ANN-MPChaveshowntooutperformthemorebasiccontrollers suchasPIDandon/offcontrollers.Duetothesupervisorynatureof MPC,theenergyandcostsavingsrangeanywherefrom7%to50%.

FollowingaretheexamplesfromliteraturewhichuseANN-MPCto reducetheenergyandcostofoperatingHVACsystems.Asummary oftheseANN-MPCapproachesandtheirresultingenergyandcost savingsisprovidedinTable1.

Table1

AsummaryofANN-MPCapproaches.

Reference System SupervisoryControl ANNmodelforMPCdevelopment Costsavingsinvestigation Energy(Cost)Savings [47,32] Airportterminalbuilding √

x x 18%

[7] Airportterminalbuilding √

x √

−5.4%(13%)

[48] Residentialbuilding √

x x 18%

[49] Apartmentbuilding x x x −4.5%

[6] Universitybuilding √ √

x 50%

[42,30] Universitybuilding √ √ √

13.5%(7.8%)

[35,36,31] Officebuilding √ √

x 8.13%

[10] Officebuilding √ √

x 14.7%

[41] Officebuilding x √ √

(31%) Note:Anegativeenergysavingsvaluemeansthatthehigherenergywasconsumedcomparedtobaselineandviceversa.

In[32]and[47],ANNmodelwasusedtosimulatethebehavior ofanairportterminalbuildingwhereastheresistor-capacitor(RC) networkmodelwasusedforthecontrollerdevelopment.TheRC networkbasedMPCsupervisorycontrollerwasusedtoevaluate theenergy-savingspotential.Comparedtothebaselinefixedset- point(FSP)of22^◦C,MPCresultedin5%,18%and13%energysavings whenusedalone,withoptimizedstart-stopcontrolstrategyand withprecoolingstrategyrespectively.Inthispaper,ANNwasnot usedforthedevelopmentofsupervisorycontrollerandcostsavings potentialwerenotinvestigatedunderthevariablepricestructure.

Themethod presentedin [47] wasfurtherdeveloped in[7].

ThenonlinearbuildingandHVACsystemwasmodeledusingthe RCnetworks.The zoneandHVAC systemmodelscontainbilin- eartermswherethecontrolstatesweremultipliedbythecontrol inputsanddisturbances.In ordertoavoidtheuseofnon-linear

optimizationmethods,themodelswerelinearizedbyusingthe ANNbasedfeedbacklinearizationtechnique.Thisresultedinlinear modelswhichwereusedwithMPCbasedonlinearprogramming technique.Thecostsavingsinvestigationswerecarriedoutundera two-tieredpricestructureofSydney.MPCresultedin13%costsav- ingswhencomparedtobaselinecontrol.Sincethermalenergywas storedinthebuildingmassduringtheoff-peakperiod,theenergy consumptionincreasedabout5.4%comparedtobaselinecontrol butsincethisenergywasconsumedduringoff-peakperiodwhen electricitypricewascheap,itresultedin13%lowercosts.Thispaper didnotuseANNmodelduringoptimization.

Researchersin[48]developedarandomneuralnetwork(RNN) based controller tocontrol thetemperature offour roomsin a singlestoryresidentialbuilding.Theintelligentcontrollermanip- ulatedtheflowrateofhotwaterthrougharadiatorconsistingof

Fig.1. MajorsubsystemsofresidentialHVACsystemofTRCA-ASH.

ERV

AHU

BT GSHP

SA Zone RA

OA

EA

SA: Supply Air FA: Fresh Air EA: Exhaust Air RA: Return Air OA: Outside Air FA

RFH System

Ground Loop GSHP

Loop RFH Loop

AHU Loop

Fig.2.BlockdiagramofresidentialHVACsystemofTRCA-ASH.

temperatureregulatingvalvetocontroltheheatinginrooms.RNN basedcontrollerwascomparedtoANNbasedcontrollerandMPC.

MPCwasdevelopedusingthesubspacestatespacesystemidentifi- cation(4SID)model.RNNcontrollerwasbetteratmaintainingthe PMV-basedset-pointscomparedtoANNcontroller.ANNcontroller performedpoorlywhenmetwiththeset-pointsnotincludedinthe trainingdatawhereasRNNwasabletomaintainthoseset-points properly.TheperformanceofRNNwascomparableto4SIDbased MPCcontrollerintermsofenergyconsumptionandprocessreg- ulation.BothRNNand MPCwereabletosave18%moreenergy comparedtoANNcontroller.

In[49],ANNbasedpredictivecontrollerwasdevelopedtocon- troltheradiantfloorheating(RFH)systeminanapartmentbuilding inSouthKorea.ThedevelopedANNbasedpredictivecontrollerwas comparedtoasimpletwo-positionon/offcontroller.Simpleon/off controllerwasunabletoregulatethezonetemperaturewithina desiredbandduetothetimedelayinprocessresponseforhigh thermalinertiaofapartmentbuildingresultingindiscomfortof occupantsandhigherenergyconsumption.ANNbasedpredictive controllerduetoitsanticipatoryaction,wasabletoaccuratelyreg- ulatetheprocessatitsset-pointandeasilyhandledthetimedelay intheresponse.It isimportanttonotethatANNbasedpredic- tivecontrollerproposedin[49]isnotbasedonMPCalgorithm.It ratherusesANNmodeltopredicttheonandofftimesofheatsup- plysothatthezonetemperaturedoesnotoverorundershootthe desireddifferentialtemperaturerange.ANNbasedpredictivecon- trollerwasabletoregulatetheroomtemperaturemoreprecisely comparedtoon/offcontrollerbutatthecostofconsumingabout 4.5%moreenergy.Thisshowsusthattheimplementationoflocal

levelpredictivecontrollercouldresultinhigherenergyconsump- tioniftheobjectiveistoimprovetheprocessregulationinsteadof reducingtheenergyconsumption.

AuniversitybuildingwascontrolledusingANN-MPCcontroller in[6].ResearchersdevelopedANNbasedmodelsforPMV,zone temperature and humidity, outside temperature, humidity and solarradiationtobeusedforcontrollerdevelopment.Fourzones werecontrolledbysplitairconditionerseachhavinganoutdoor aircooledinvertercompressorunitandanindoorunit.RBFANNs wereusedtodevelop allthemodels.Theapproachislimitedin thesensethatitdoesnotusecostsavingspotentialandinstead focusedontheenergysavingsonly.Lastbutnotleast,theweather forecastdatawaspredictedon-siteinsteadofdownloadingfroma governmentweatherdataserverwhichpotentiallyhasmoreaccu- rateandreliableprediction.Nevertheless,theresearchersin[6]

showedthattheimplementationofANN-MPCresultedinsavings above50%.Foroptimization,theBaBmethodwasusedinsteadof non-linearoptimizationtechniquessinceitalwaysguaranteesan optimalsolution.

Theresearchers in[42,30]presented ANN-MPCcontroller to control theindoorairtemperature ata universitybuildingand triedtoimprovethecontrollerdesignpresentedin[6].Incontrary tomostotherapproaches,theresearchin[42,30]consideredthe economiccostfunctionrepresentingthecostofoperatingHVAC systeminsteadofenergyconsumption.Usingtheeconomiccost functionresultedin13.5%lowerenergyconsumptionaswellas 7.8%highercostsavingswhencomparedwiththeapproachin[6]

whichonlyminimizedtheenergyconsumption.

In[35],MLPensemblewasusedtomodeltheAHUenergycon- sumption,AHUsupplyairtemperature,AHUstaticpressureand IAQofanofficebuilding.MLPensemblebasedMPCcontrollerwas usedtopredicttheoptimalsettingsofAHU staticpressureand supplyair set-pointswhileminimizingtheenergyconsumption andmaximizingthethermalcomfort.Anevolutionarycomputation algorithm basedonmodified PSO wasusedtosolvethemulti- pleobjectivenonlinearoptimizationproblem.ThedesignofMLP ensemblebasedMLPresultedinanaverageestimatedenergysav- ingsof8.13%comparedwiththebaselinecontrol.Thedevelopment ofMLPtypeANN-MPCforthesamesystemwasalsoreportedin[36]

whereresearchersinvestigatedtheuseofameta-heuristicsearch algorithm (i.e.,fireflyalgorithm) duringoptimizationinsteadof PSO.Fireflyalgorithmwasefficientinfindingglobaloptimaand outperformedPSOin minimizingtheenergyconsumption. Fire- flyalgorithmalsohadloweraverageCPUtimeof12.3sperdata pointcomparedtoPSO’s13.0s.Strengthofmodified-PSOreported in [35] compared to firefly algorithm lies in solving multiple

Fig.3.Inputsandoutputsofeachsubsystem.

Table2 Nomenclature.

Symbol Description

ETOU Electricitytime-of-useprice

G Goodnessoffit

ma,AHU FlowrateofairpassingthroughAHU

mea Flowrateofexhaustair

mfa Flowrateoffreshair

mERV,sp Set-pointofERVair

mra Flowrateofreturnair

msa Flowrateofsupplyair

mw,AHU FlowrateofwaterinAHUloop

mw,GSHP FlowrateofwaterinGSHPloop

mw,RFH FlowrateofwaterinRFHloop

n Numberofsamples

N HorizonsizeofMPCoptimization

t Time

Ta,i TemperatureofmixedairattheinletofAHU Ta,o TemperatureofairattheoutletofAHU Tea,i TemperatureofexhaustairattheinletofERV Tea,o TemperatureofexhaustairattheoutletofERV Tfa Temperatureoffreshairenteringthezone Tfa,i TemperatureoffreshairattheinletofERV Tfa,o TemperatureoffreshairattheoutletofERV Toa Temperatureoftheoutsideair

Tra Temperatureofthereturnair

Trw,GSHP TemperatureofreturnwaterfromGSHPtoBT

Trw,RFH TemperatureofreturnwaterfromRFHtoBT

Ts ExecutiontimeofsupervisoryMPCoptimization

Tsa Temperatureofsupplyair

Tsw,GSHP TemperatureofsupplywaterfromBTtoGSHP

Tsw,RFH TemperatureofsupplywaterfromBTtoRFH

Tw,BT TemperatureofwaterinsideBT

Tw,BT,sp Set-pointtemperatureofwaterinsideBT

Tw,i TemperatureofwaterattheinletofAHUcooling coil

Tw,o TemperatureofwaterattheoutletofAHUcooling coil

Tz Zonetemperature

Tz,sp Set-pointofzonetemperature

uAHU ControlsignalofAHU

uRFH ControlsignalofRFH

uGSHP ControlsignalofGSHP

uRFH ControlsignalofRFH

WAHU PowerconsumptionofAHU

WERV PowerconsumptionofERV

WGSHP PowerconsumptionofGSHP

WRFH PowerconsumptionofRFH

y Measureddata

ˆ

y Estimateddata

Abbreviations

4SID SubspaceStateSpaceSystemIdentification

AE AbsoluteError

AHU AirHandlingUnit

ANFIS ArtificialNeuro-FuzzyInferenceSystem

ANN ArtificialNeuralNetwork

ANSI AmericanNationalStandardsInstitute

ASH ArchetypeSustainableHouse

ASHA ArchetypeSustainableHouseA ASHB ArchetypeSustainableHouseB

ASHRAE AmericanSocietyofHeating,Refrigeratingand Air-ConditioningEngineers

BaB BranchandBound

BFGS Broyden-Fletcher-Goldfarb-Shanno BNMI BestNetworkafterMultipleIterations

BT BufferTank

CART ClassificationandRegressionTree CHAID Chi-squareInteractionDetector

CO2 Carbondioxide

CPU CentralProcessingUnit

DAQ DataAcquisition

ERV EnergyRecoveryVentilator

FSP Fixed-Set-Point

GA GeneticAlgorithm

GSHP GroundSourceHeatPump

HTTP HypertextTransferProtocol

HVAC Heating,VentilationandAir-Conditioning

Table2(Continued)

Symbol Description

IAQ IndoorAirQuality

LM Levenberg-Marquardt

MAE MeanAbsoluteError

MAPE MeanAbsolutePercentageError MARSplines MultivariateAdaptiveRegressionSplines

MLP Multi-LayerPerceptron

MOGA Multi-ObjectiveGeneticAlgorithm MOPSO Multi-ObjectiveParticleSwarmOptimization

MPC ModelPredictiveControl

MSC MeteorologicalServiceofCanada

MSE MeanSquaredError

NARNET NonlinearAuto-RegressiveNeuralNetwork NARX NonlinearAuto-RegressiveExogenous NOAA NationalOceanicaandAtmospheric

Administration

NRMSE NormalizedRelativeMeanSquaredError PID Proportional-Integral-Derivative

PIR PassiveInfrared

PSO ParticleSwarmOptimization

RC Resistor-Capacitor

RFH RadiantFloorHeating

RNN RandomNeuralNetwork

SVM SupportVectorMachine

PMV PredictedMeanVote

PRBS Pseudo-RandomBinarySequence

RBF RadialBasisFunction

RMSE RootMeanSquaredError

S-MOPSO StrengthMulti-ObjectiveParticleSwarm Optimization

SPEA StrengthParetoEvolutionaryAlgorithm SPEA-LS StrengthParetoEvolutionaryAlgorithmwithLocal

Search

TRCA TorontoandRegionConservationAuthority TRNSYS TransientSystemSimulationTool

VAV VariableAirVolume

objectiveoptimizationproblem.Inyetanotherpaper[31],same systemwasinvestigatedand PSOwascompared withharmony searchoptimizationmethodforthedevelopmentofMLPtypeANN- MPC.Harmonysearchconvergedinfeweriterationsandhadlower computationaltimeperiterationaswellwhencomparedtoPSO.

Alloftheseresearches[35,36,31]didnotcarryoutthecostsavings investigationsandonlyfocusedontheenergysavings.

Adaptive online ANN-MPC wasdesigned for automotive air conditioningsystemwithavariablespeedcompressorin[37].Com- paredwithofflineANN-MPCandaPIDcontroller;onlineANN-MPC hadsuperiorreferencetrackinganddisturbancerejection.Newton- Raphsonmethodwasusedtominimizethecostfunction.There wasnosupervisorycontrollerandcostsavingsinvestigationsin thispaper.

In[10],ANN-MPCwasdeveloped fortheHVACsystemofan officebuildinginFrance.Thebuildinghadfourzonesinitcompris- ingoftwoofficezones,onemanufacturingareaandonewarehouse zone. Researchers developed lower order ANN models for the developmentofcontrollerandusedGAtominimizethecostfunc- tion.SupervisoryMPCmeasuredtheairandradianttemperature offourzonesandgeneratedtheset-pointsforlocalzonetemper- aturecontrollers.Thispaperdidnotinvestigatethecostsavings.

Thewholestudywasbasedonthesimulationmodelgeneratedin EnergyPlusand noreal-worlddatawasusedfortrainingorval- idationofmodels.Comparedtoa baselinestrategy usedinreal non-residentialbuildingsinFrance,ANN-MPCresultedin5.2%and 14.7%reducedenergyconsumptionduringheatingandcoolingsea- sonsrespectively.

AmodelofanofficebuildinginUSwasdevelopedusingnonlin- earauto-regressiveneuralnetwork(NARNET)in[41].Thismodel wasusedforthedevelopmentofMPCtominimizetheenergycost consideringadynamicdemandresponsesignal.Thebuildingalso hadanon-siteenergystorageandgeneration.Thecostfunctionwas

Fig.4.ModelingandvalidationdatausedforeachsubsystemANNmodel(a)ERV, (b)AHU,(c)BT,(d)RFHand(e)GSHP.

minimizedbymixed-integernon-linearprogrammingsolvedwith IBM-ILOGCPLEXsolver.Comparedtoabaselinenightsetupstrat- egy(i.e.,twodifferentFSPsduringdayandnight),ANN-MPCwith energystorageandenergygenerationresultedin31%costsavings.

3. Casestudy:residentialHVACsystem

Following section describes the simulation of ANN-MPC on a residentialHVAC systemofToronto and Region Conservation Authority(TRCA) ArchetypeSustainableHouse(ASH)locatedin Vaughan,Ontario,Canada.Therearetwoidenticalsemi-detached

housescalledHouseA(ASHA)andHouseB(ASHB).ASHAhasthe HVACsystemfoundinmanyCanadianhouseholdscomprisingof heatrecoveryventilator,AHUandairsourceheatpump.Whereas, ASHB hasthe futuristic HVAC system focused onreducing the energyconsumptionandoperatingcostreductionofthesystem.

TheASHBsystemisexplainedinmoredetailinthefollowingsub- section.ThispaperonlyfocusesontheHVACsystemofASHB.For furtherdetailsof ASHAandASHBsystems,readerisreferred to [50–59].

3.1. Systemdescription

ResidentialHVACsystemofTRCA-ASHisshowninFigs.1and2.

ResidentialHVAC systemcomprises ofmany subsystems called energyrecoveryventilator(ERV),AHU,groundsourceheatpump (GSHP),buffertank(BT),RFHandzone.Fansareusedtomovethe freshair,returnair,supplyair,exhaustairandoutsideairwhile pumps areused tocirculatethewater in RFH,AHU, GSHPand groundloops.

ERVpreheatsthefreshairduringwinterandprecoolsthefresh airduringsummerbyexchangingenergybetweenoutsideairand exhaustairstreams.Duringsummeroutsideairisatahighertem- peraturecomparedtoreturnairfromthezonewhereasinwinter itisreversed.FreshairentersAHUwhereitismixedwithreturn airfromthezone.Mixedairpassesthroughthecoolingcoiland issuppliedtothezoneduringsummer.Duringwinterseason,the zonetemperatureismaintainedbyRFHsystem.BothAHUandRFH systemsreceivecoldandhotwaterfromBTrespectively.During summerBT stores coldwater whereas, duringwinter seasonit storeshotwater.TemperatureofBTwaterismaintainedbyGSHP duringbothseasons.GSHPhasagroundloopwhereheatisrejected togroundduringsummerandgainedduringwinterandtransferred totheBTwater.

Dataacquisition(DAQ)systemmeasuresthetemperatureand flowrateofeachairandwaterstreamattheinletandoutletof eachsubsystemaswellastheenergyconsumedbyfans,pumpsand GSHPcompressoratanintervalof5sandstoresitintoadatabase.

3.2. Systemmodeling

ERV,AHUandRFHaremultipleinputandmultipleoutputsys- temswhereasBTandGSHParemultipleinputandsingleoutput systems.Datawasextractedfromdatabaseformodelingandvali- dation.Inputsandoutputsofeachofthesubsystemareshownin Fig.3.ThesymbolsaredefinedinTable2.

3.2.1. Pre-processingofdata

SinceDAQsystemrecordsdataat5s’interval,thedatacaptures alltheprocessdynamicsataveryhighresolution.Thedynamics ofHVACsystemarecomparativelyslowandthetemperatureand flowratechangesdonotoccuratsuchafastrate.Therefore,the datawasdownsampledtoreducethenumberofdatapointsand improvetheconvergencespeedofANNtrainingalgorithm.Thedata foreach subsystemwasdownsampledatadifferentresolution dependingonthesystemdynamics.Forexample,thetemperature insidetheERVchangesveryslowlysinceitisdependentonthe outsideairtemperatureandzoneairtemperaturebothofwhich arechangingataslowrate,therefore,amuchlargersamplingtime of500swasusedfordownsamplingtheERVdata.In contrast, thetemperatureandflowrateinsidetheAHUchangesatamuch fasterrate,therefore,ashortersamplingtimeof30swaschosen.

Thesamplingtimeforeachsystemwaschosensuchthatthedown sampleddatacapturesalltheprocessdynamicswhilereducingthe unnecessaryandredundantdata.SamplingtimeforeachoftheBT, RFHandGSHPdatasetswas50s. Inordertoremovethespiked noiseandrandomnoise;medianandmovingaveragesmoothing

Fig.5. FlowchartofBNMIANNTrainingAlgorithm.

filterswereappliedtothedatarespectively.ThedataforANNmodel developmentandvalidationisshowninFig.4.

3.2.2. ANNtrainingalgorithmandarchitectureselection

MLPwithoneinputlayer,onehiddenlayerandoneoutputlayer waschosentomodeleachsubsystem.Sincetwomajorfactorsi.e., startingweightsandnumberofneuronsinthehiddenlayerhave mostinfluenceonANNperformance,theyweredeterminedvery carefully.InordertofindbestweightsforANN,anewalgorithm calledBestNetworkafterMultipleIterations(BNMI)wasdeveloped totraintheANNmultipletimesandrecordthebestweights.

Fig.5showstheflowchartofBNMItrainingalgorithm.Atthe startofalgorithm,pre-processingofdata(i.e.,medianandsmooth filtering)iscarriedout.Afterdatapreprocessing;inputsandtar- getsareidentifiedand dataisnormalizedto[−1,1]range.Then desirednumberofiterationsandnumberofhiddenlayerneurons arespecified.BNMIalgorithmtrainstheANNusing‘fitnet’function inMATLAB^®,andrecordsweightandbiasmatricesoftrainedANN.

Afterthatthegoodnessoffit(G)iscomputedasfollowstoevaluate theperformanceoftrainedANNagainstmeasureddata:

G=

⎛

⎜ ⎜

⎜ ⎜

⎜ ⎜

⎝

1−

ⁿ

i=1

(ˆy_i−y_i)²

ⁿ

i=1

y−^y_n

2

⎞

⎟ ⎟

⎟ ⎟

⎟ ⎟

⎠

×100. (1)

wherey, ˆyandnaremeasureddata,estimateddataandtotalnum- berofdatapointsrespectively.

BNMIalgorithmcomparesthevalueofGforeachtrainedANN againstbestrecordedvalueofGi.e.,G_bestduringprevioustrain- ingiterations.WhenvalueofGofcurrentiterationisbetterthan G_best,thealgorithmupdatesG_bestwithcurrentvalueandrecords thebestANNweightsaswell.Thealgorithmthenkeepsrepeat- inguntilthespecifiednumberofiterationsarecompleted.Inthis paper,thedesirednumberofiterationswassetat1000.Therefore, BNMIalgorithmtrains1000ANNswithrandomstartingweights andrecordstheweightandbiasmatricesofbesttrainedANNout ofthemwhichhashighestvalueofG.

Selectionofthenumberofneuronsinhiddenlayerwasalso madesystematicallybytrainingtheANNofeachsubsystemwith numberofneuronsbetween1and50.ThevalueofGincreasesas thenumberofneuronsincreaseinhiddenlayerasseeninFig.6.

Beyondacertainpoint,increasingthenumberofneuronsinhidden layer,thevalueofGdoesnotincreaseanyfurther.Basedonthis, theoptimumnumberofneuronscanbeselectedwhenthevalueof Gstopstoincreaseappreciably.Therefore20hiddenlayerneurons wereselectedforeachoftheERV,AHUandBTmodels,40neurons wereselectedforRFHzonemodeland5neuronswereselectedfor GSHPmodel.

3.2.3. PerformanceofANNmodels

TheperformanceofANNmodelsissummarizedinTable3.The value ofG foreach model is very highand max_AE and MAEis verylow.ComparedtoANNmodelsdevelopedinapreviouspaper Table3

PerformanceofANNModelsontheValidationDataset.

Model ANNArchitecture G(%) maxAE(^◦C) MAE(^◦C) Improvementoverpreviouspaper(%)

ERV Teao

4-20-2 96.8% 1.025 0.077 12.7%

Tfao 96.3% 0.413 0.048 11.3%

AHU Tw,o

4-20-2 86.1% 0.901 0.099 23.9%

Ta,o 85.6% 0.315 0.067 24.7%

BT Tw,BT 4-20-1 97.2% 0.699 0.062 10.0%

RFH Tz

5-40-2 79.3% 0.728 0.053 59.7%

Trw,RFH 87.5% 2.365 0.069 57.0%

GSHP Trw,GSHP 2-5-1 89.4% 4.004 0.185 6.85%

Fig.6.Numberofhiddenlayerneuronsvs.thevalueofGforeachsubsystemmodelwithBNMIAlgorithm.

bytheauthors[14]withoutusingBNMIalgorithm,theimprove- mentsreportedinthispaperaresignificantduetodatafiltering, newBNMI training algorithmand appropriate selection ofhid- denlayerneurons.Thepreviouspaper[14]mainlyfocusedonthe

comparisonofdifferentblack-boxmodelingmethodsavailableby defaultinMATLAB^® SystemIdentificationToolbox^TMandNeural NetworkToolbox^TM.Thecurrentpapershowshowtheauthorshave significantlyimprovedtheANNmodelingresultscomparedtothe

defaultANNtrainingmethodbyintroducingtheBNMIalgorithm andappropriateselectionofhiddenlayerneurons.

VisualcomparisonsoftheperformanceofmodelsalongwithAE plotsarepresentedinFig.7.Itcanbeseenthatthedevelopedmod- elshaveveryhighaccuracyandfollowthemeasureddataclosely.

3.3. Controllerdesign

ResidentialHVACcontroller hasahierarchicalstructurewith MPCusedin supervisorycontrollayerandPIDcontrolusedfor locallevel control.SupervisoryMPCgeneratestheset-pointsof locallevelcontrollersandlocallevelPIDcontrollersregulatethese set-points.ThedetailedarchitectureofresidentialHVACcontroller isshowninFig.8.

3.3.1. SupervisoryMPC

ThepurposeofsupervisoryMPCistoreducetheoperatingcost ofresidentialHVACsystem.Sincedifferentset-pointsmaycause greatdifferencesintheenergyusage,MPCgeneratestheset-points oflocallevelcontrollersinordertostoreenergyinbuildingmass duringoff-peakhoursandreduceequipmentuseduringmid-peak andpeakpricehours.

Fig.9showsinputsandoutputsofMPCcontroller.MPCuses asystemmodeltopredictthefuturestatesofsystemandgener- atesacontrolvectorthatminimizesacertaincostfunctionoverthe predictionhorizoninthepresenceofdisturbancesandconstraints.

Thefirstelementofthecomputedcontrolvectoratanysampling instantisappliedtothesysteminput,andtheremainderisdis- carded.Theentireprocessisrepeatedinthenexttimeinstant.Cost functioncantaketheformoftrackingerror,controleffort,energy cost,demandcost,powerconsumption,oracombinationofthese factors.Constraintscanbeplacedontherateandrangelimitsof actuatorsand manipulatedvariables (e.g.,upperandlowerlim- itsofzonetemperature,supplyairflowratelimits,andrangeand speedlimitsfordamperpositioning).Externalandinternaldistur- bancesactingonthesystemduetoweather,occupantactivities, andequipmentusearealsomodeled,andtheirpredictedeffects onthesystemareusedduringcontrolvectorcomputation. This effortresultsinacontrollerthatisrobusttobothtime-varyingdis- turbancesandsystemparametersandregulatestheprocesstightly withingivenbounds.

Ateachtimeinstant,thesystemoutputisalsomeasuredandis usedasinitialconditionintheoptimizationprocess.Thishelpsin eliminatinganyun-modeleddisturbancesormodelingerrors.The systemanddisturbancemodelcanbewritteninavarietyofforms suchasdifferentialequations,state-spacerepresentation,trans- ferfunctionrepresentationordiscretedifferenceequations.Inthis paper,nonlinearANNsystemmodelisused.

MPCalgorithmworksasfollows:

•Attimet,solveanoptimalcontrolproblemoverafinitefuture horizonofNsteps:

min

ut,....,ut+N−1

J={

N−1 k=0

y_t+k−r(t)²+u_t+k−ur(t)} s.t. x_t+k+1=f(x_t+k,u_t+k),

y_t+k=g(x_t+k,u_t+k), u_min≤u_t+k≤umax), y_min≤y_t+k≤ymax), x_t=x(t),k=0,...,N−1,

(2) Fig.7.Measuredvs.estimatedoutputsof(a)ERV,(b)AHU,(c)BT,(d)RFHand(e) GSHP.

ERV

AHU

BT GSHP

Compressor

Zone Tfa,o

RFH System mfa

Tea,i

mea

Tfa,i

mfa

Tea,o

mea

Tz

Tra

mra

Ta,i

ma,AHU

Ta,o

ma,AHU

Tsa

msa

Tw,i

mw,A HU

Trw,AHU

mw,A HU

Tw,o Trw,RF H

mw,R FH

Tsw,RF H

mw,R FH

Tw,B T

Tw,B T

Tw,B T

Tsw,GSHP

mw,GSHP

Trw,GSHP

mw,GSHP

Local Level Ventilation Controller

Local Level BT Water Temperature

Controller

Local Level Zone Temperature

Controller

Supervisory MPC Controller

T

T

uGSHP uRFH

uAHU

uERV

Tw,B T

Tw,B T

mERV ,sp Tw,B T,sp Tz,sp

Weather Forecast

Electricity TOU Price

Power

Consumption Horizon Size Execution Time Period t,Toa t,ETOU

WERV, WAHU, WRFH, WGSHP

N Ts

Tz

Tw,B T

Tz

Ground Loop Pump

Fig.8. ResidentialHVACcontrollerarchitecture.

Fig.9.InputsandoutputsofMPCbasedcontroller.

whereJisthecostfunction,Nisthepredictionhorizon,u,y,xandr aretheinput,output,stateandreferencetrajectoryofthesystem, andx(t)isthemeasuredstateofthesystemattimet.

•Onlyapplythefirstoptimalmove.

•Attimet+1,getnewmeasurementsandrepeattheoptimization process.

Costfunctionintheaboveformulationtakestheformofsum- mationoftrackingerrorandcontroleffort.Theoptimizationtriesto reducethetrackingerrorandcontroleffortovertheoptimization horizonandproducestheoptimalcontrolvectorinthepresence ofconstraintsonsysteminputandoutput.Thelimitsoncontrol input(i.e.,u_minandumax)andsystemoutput(i.e.,y_minandymax)are definedbytheactuatorconstraintsandrequiredspecificationsof controlobjective,e.g.,incaseofzonetemperaturecontrol,thezone temperaturecanbespecifiedtovarytoacertaindegreearoundthe referenceset-point.

Aboveformofcostfunctionisnotsuitableforsupervisorycon- troland is only usefulfor local level control. In a case where supervisoryMPCoptimizationobjectiveistoreducetheoperating costofHVACsystem,thecostfunctionisre-writtentorepresentthe operatingcostofthesystemasshowninthefollowingsubsection.

3.3.1.1. Cost function. Costfunction representsthe total cost of operatingtheHVACsystem.Itcomprisesoffourtermswhichare