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Modeling the Thermal Dynamics of a Single Room in Commercial Buildings and Fault Detection

Permanent Link: http://ufdc.ufl.edu/UFE0044634/00001

Material Information

Title: Modeling the Thermal Dynamics of a Single Room in Commercial Buildings and Fault Detection
Physical Description: 1 online resource (61 p.)
Language: english
Creator: Lin, Yashen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: building -- fdd -- hvac -- modelling
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Modern control strategy in building automation control has large potential of saving energy. This thesis attempts to develop a model which describes the thermal dynamics of a single room that can be used for intelligent control, such as model predictive control. The use of the model in fault detection is discussed in the second part of this thesis. In the first part, three important questions in the modelling problem are discussed: (1) How accurate should the model be to be useful for modern control methods? (2) What model structure should be used so that the desired accuracy can be achieved and yet it is not too complicated? (3) How should we determine the parameters in the model once the model structure is chosen? Various model structures are compared, and a second order model using electrical analogy is found to be a good choice. Experimental data from Pugh Hall on University of Florida are collected for model calibration and validation. It is found that the data is crucial. Normal closed loop operation data may lead to grossly wrong parameter estimation, even with rich excitation. The effect of open door on the model is also discussed, and a modified model is developed. In the second part, the fault caused by occupants is studied. Unknown input observer method (UIO), a model based method, is implemented for fault detection. Using the model we got from the first part, we successfully detected the open door with UIO. However, implementation in another model structure shows that the technique has certain limitation. A tradeoff is found in such situation.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yashen Lin.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Barooah, Prabir.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044634:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044634/00001

Material Information

Title: Modeling the Thermal Dynamics of a Single Room in Commercial Buildings and Fault Detection
Physical Description: 1 online resource (61 p.)
Language: english
Creator: Lin, Yashen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: building -- fdd -- hvac -- modelling
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Modern control strategy in building automation control has large potential of saving energy. This thesis attempts to develop a model which describes the thermal dynamics of a single room that can be used for intelligent control, such as model predictive control. The use of the model in fault detection is discussed in the second part of this thesis. In the first part, three important questions in the modelling problem are discussed: (1) How accurate should the model be to be useful for modern control methods? (2) What model structure should be used so that the desired accuracy can be achieved and yet it is not too complicated? (3) How should we determine the parameters in the model once the model structure is chosen? Various model structures are compared, and a second order model using electrical analogy is found to be a good choice. Experimental data from Pugh Hall on University of Florida are collected for model calibration and validation. It is found that the data is crucial. Normal closed loop operation data may lead to grossly wrong parameter estimation, even with rich excitation. The effect of open door on the model is also discussed, and a modified model is developed. In the second part, the fault caused by occupants is studied. Unknown input observer method (UIO), a model based method, is implemented for fault detection. Using the model we got from the first part, we successfully detected the open door with UIO. However, implementation in another model structure shows that the technique has certain limitation. A tradeoff is found in such situation.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yashen Lin.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Barooah, Prabir.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044634:00001


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MODELINGTHETHERMALDYNAMICSOFASINGLEROOMINCOMMERCIAL BUILDINGSANDFAULTDETECTION By YASHENLIN ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2012

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c r 2012YashenLin 2

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Tomyparentsandwife 3

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ACKNOWLEDGMENTS Firstandforemost,Iwouldliketoexpressmysinceregratitudetom yadvisorDr. PrabirBarooahforguidingmethroughmystudy.Thisthesiswouldha venotbeenpossible withouthissupportandadvice.Henotonlyprovidedinsightfuladvic einresearchtopic, butalsohelpedmebecomearigorousandindependentthinker.Hisem phasisandguidance oncommunicationskillsisespeciallybenecialtomeasaninternational student.Ifeel veryfortunatetohavetheopportunitytoworkwithhimandIwould liketothankhimfor everythinghehasdoneforme. IalsowanttoextendmyspecialgratitudetoDr.TimothyMiddelkoop ,whohasbeen alwayssupportiveandhelpfultome.Iamgratefulforhisconstru ctiveadviceandinspiring discussionsaswellashiscrucialcontributionstomyresearch,esp eciallyintheexperiments part.ItisapleasuretothankDr.HerbertA.Ingley,forsharingh isexpertise.His patience,kindness,andknowledge,isextremelyhelpfulincompletin gmywork.Iwantto givespecialthankstoPederWinkel,SkipRockwell,andothersfromU niversityofFlorida (UF)PhysicalPlantDivisionwhosparedtimehelpingwithourexperimen tsthoughthey havemanyothercommissions. Also,IwouldliketothankmycolleaguesHeHaoandChendaLiao,whopr ovidedme muchneededhelpandusefuladvice,bothinresearchandpersona llife.IthankSiddharth Goyalforhishelpintheexperiments,whichwouldnothavebeenposs ibleotherwise.Last butnottheleast,Iwouldliketothankmyparentsandwife.Iamhear tilythankfulfor theirfaith,devotion,love,supportandencouragement. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................4 LISTOFTABLES .....................................7 LISTOFFIGURES ....................................8 ABSTRACT ........................................9 CHAPTER 1INTRODUCTION ..................................10 1.1Motivation ....................................10 1.2ProblemFormulation ..............................11 1.2.1ModelingASingleRoom ........................11 1.2.1.1Q1:Acceptableaccuracy ...................12 1.2.1.2Q2:Modelstructure .....................12 1.2.1.3Q3:Parameterestimation ..................13 1.2.2FaultDetection .............................14 2MODELSTRUCTURE ...............................16 2.1GeneralSettings ................................16 2.2Full-scaleModel .................................18 2.3Low-orderModels ................................20 2.3.1First-orderModel ............................20 2.3.2Second-orderModel ...........................20 2.3.3TheLinearTimeInvariant(LTI)Case ................21 2.4ModelStructureComparison ..........................21 2.4.1ASHRAEValues ............................22 2.4.2TimeDomainComparison .......................23 2.4.3FrequencyDomainComparison ....................25 3CALIBRATIONANDVALIDATION ........................28 3.1FieldData ....................................28 3.1.1TestBed .................................28 3.1.2DataSets ................................30 3.2IdenticationMethods .............................31 3.2.1Least-squares ..............................31 3.2.2MaximumLikelihood(ML)Method ..................32 3.3ModelCalibrationandValidation .......................35 3.3.1Attempt1:ApparentSuccessButReallyAFailure .........35 3.3.2Attempt2:AMoreReliableCalibration ...............38 3.4EectofOpenDoor ..............................40 3.5Summary ....................................44 4FAULTDETECTION ................................45 4.1UnknownInputObserver ............................45 4.2ImplementationExample ............................47 5

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4.2.1RoomModel ...............................48 4.2.2Implementation .............................49 4.2.3Analysis .................................50 4.3DoorStatusDetection .............................53 4.4Summary ....................................56 5CONCLUSIONANDFUTUREWORK ......................57 REFERENCES .......................................58 BIOGRAPHICALSKETCH ................................61 6

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LISTOFTABLES Table page 3-1BesttparameterswhendatasetAisusedformodelcalibratio n. ........36 3-2BesttparameterswhendatasetCisusedformodelcalibratio n. ........38 7

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LISTOFFIGURES Figure page 2-1Schematicgureoftheroom .............................17 2-2Full-scalemodelstructure ..............................19 2-3SimulationofRoom241withASHRAEvaluesasparameters ...........23 2-4SimulationofRoom243withASHRAEvaluesasparameters ...........23 2-5Timedomaincomparisonofdierentmodels ....................24 2-6Gaincomparisonofthethreemodels ........................26 2-7Theerrordenedin(2{11)forthetwoinputs T s and T sd .............26 3-1ScreenshotofInsightWorkstation .........................29 3-2Floorplanoftestingarea ..............................30 3-3HOBOsensors ....................................30 3-4ThreedatasetscollectedinPughHall. .......................32 3-5Calibration/validationwhendatasetAisusedforcalibration. ..........36 3-6Contourofthecost J denedin(3{2),whichshowsitsnon-convexity. ......37 3-7Calibration/validationwhendatasetCisusedforcalibration. ..........38 3-8DCgaincomparison,leftgureisforrstattempt,rightisfors econdattempt .39 3-9Simulationwithoriginalmodel ...........................41 3-10Structureforthemodelbetweenhallwayandroom ................42 3-11Simulationwithmoderatedmodel ..........................43 3-12Predictionerrorwithrespectto R od .........................43 3-13Predictionerrorwithrespectto R od .........................44 4-1SimulationofUIO ..................................52 4-2EstimatedstatesfromUIO ..............................53 4-3Opendoordetection .................................55 8

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AbstractofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience MODELINGTHETHERMALDYNAMICSOFASINGLEROOMINCOMMERCIAL BUILDINGSANDFAULTDETECTION By YashenLin August2012 Chair:PrabirBarooahMajor:MechanicalEngineering Moderncontrolstrategyinbuildingautomationcontrolhaslargep otentialofsaving energy.Thisthesisattemptstodevelopamodelwhichdescribesth ethermaldynamicsofa singleroomthatcanbeusedforintelligentcontrol,suchasmodelpr edictivecontrol.The useofthemodelinfaultdetectionisdiscussedinthesecondpartof thisthesis. Intherstpart,threeimportantquestionsinthemodelingproblem arediscussed:(1) Howaccurateshouldthemodelbetobeusefulformoderncontro lmethods?(2)What modelstructureshouldbeusedsothatthedesiredaccuracycan beachievedandyetitis nottoocomplicated?(3)Howshouldwedeterminetheparametersin themodeloncethe modelstructureischosen?Variousmodelstructuresarecompa red,andasecondorder modelusingelectricalanalogyisfoundtobeagoodchoice.Experime ntaldatafromPugh HallonUniversityofFloridaarecollectedformodelcalibrationandva lidation.Itisfound thatthedataiscrucial.Normalclosedloopoperationdatamayleadt ogrosslywrong parameterestimation,evenwithrichexcitation.Theeectofopen dooronthemodelis alsodiscussed,andamodiedmodelisdeveloped. Inthesecondpart,thefaultcausedbyoccupantsisstudied.Unk nowninputobserver method(UIO),amodelbasedmethod,isimplementedforfaultdete ction.Usingthemodel wegotfromtherstpart,wesuccessfullydetectedtheopendoo rwithUIO.However, implementationinanothermodelstructureshowsthatthetechniq uehascertainlimitation. Atradeoisfoundinsuchsituation. 9

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CHAPTER1 INTRODUCTION 1.1Motivation Improvingenergyeciencyinbuildingsisatopicthatgarnersmuchat tention nowadays.Asoneoftheprimaryenergyconsumer,buildingsaccou ntfor34%oftotal energyuseintheUnitedStatesandheating,ventilation,andaircon ditioning(HVAC) systemaccountsforroughlyhalfofthat[ 11 ].Inecienttechnologyinoperatingbuildings, inparticular,HVACsystem,causessignicantenergywaste.Comm ercialbuildings, usuallylargeinsize,havegreatpotentialtosaveenergyifmoreec ientcontrolstrategyis implemented.Currently,HVACismostlyoperatedunderapre-desig nedschedulewith xedtemperaturesetpointsforzonesinthebuildingandlocalprop ortionalintegral-derivative(PID)controllerisoftenusedtomaintainsuchz oneclimate.This relativelysimpleoperationstrategyprovideslargeroomforimprove ment,andmodel-based controlofbuildingshasgeneratedexcitementinthecommunityofc ontrolresearchersin recentyears.ThemostpopularcandidateforcontrolofbuildingH VACsystemsisMPC (ModelPredictiveControl),inwhichdynamicalmodelsareusedtopr edictandoptimize systemperformance.Aslewofrecentpapershavebeenpublished onthis topic[ 4 6 15 18 19 23 { 25 27 ]. InordertobeabletoimplementMPC,ormanyothernovelcontrola lgorithms,a goodmodelisrequired.Itisnaturaltostartfromthemostbasicu nit,namely,asingle room.Accuracyandcomplexityaretwomajormetrictomeasureho wgoodamodelis. Clearly,themodelhastohavecertainlevelofaccuracytobeusef ul.Ifthemodelcannot predictthestatesaccurately,wecannotuseitforpredictionorc ontrol.Atthesametime, themodelshouldnotbetoocomplicated.Forthebuildingsystem,th emodelsizecangrow veryfast.Forexample,ifthemodelofasingleroomhas10states, therewillbe1000 statesforabuildingwith100rooms.Moreover,moreintelligentcont rolstrategytendsto havehighercomputationcost.Thusitisvitaltokeepthemodelsize small,sothatsuch controlalgorithmscanbeimplementedinrealtime.Oneoftheobjec tivesofthisthesisis todevelopamodelwithgoodbalancebetweenaccuracyandcomplex ity. 10

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Faultdiagnosisisanimportanttaskinbuildingcontrolsystem.Froms afetyaspect, devicefailureinHVACsystemmaycausediscomfortanddangertoth eoccupants.For instance,thesystemmaycooldownorheatupthesupplyairtoomu ch,blowtoolittleair intorooms,etc.Itiscriticaltobeabletodetectthesefaultsandt akecorresponding measurestosolvetheproblem.Fromenergyeciencyaspect,unn ecessaryenergymaybe spentduetomalfunctioningdevices.Forexample,ifthereheatvalv eisstuck,thesystem mayheatupthesupplyairwhileitisactuallytryingtocooldowntheroo m.Anothertype offaultiscausedbyoccupants,suchaswindowsordoorsbeingleft openwhentheA/Cis on,whichwillalsocauseenergywastage.Thelatterpartofthisthe sisdiscussesafault diagnosistechniqueanditsimplementationtodetectifadoorisopeno rclosed. 1.2ProblemFormulation 1.2.1ModelingASingleRoom Wefocusourattentiononthemodelingofasingleroominamulti-zonec ommercial buildingwithVAV(variableairvolume)system,sincesophisticatedcon trolmethods-such asMPC-aremorelikelytomakeanimpactherethaninresidentialbuildin gsorolder commercialbuildingswithCAV(constantairvolume)systems.Somer esearchers attemptedtomodelthebuildingasawhole[ 9 17 32 ].Thesemodelsareusefulforthe analysisoftotalenergyconsumption,butfallshortinzonelevelc ontrol.Othersstudied computationalruiddynamics(CFD)modelsforroomsinbuilding[ 3 16 ].InCFDmodels, theroomisdividedintomanyzones,andtheairrowbetweenzonesins idetheroomis studied.However,formostroomsinbuildings,therearenomechan ismtocontroldierent areasinsidetheroom,especiallyfortypicalocesthatdonothave largespace.Thus,from theperspectiveofroomlevelcontrol,asingleroomisthemostbasic unit.Oncewehave goodunderstandingofthemodelofasingleroom,wecanuseitasa\ buildingblock"to buildmodelforazonewithseveralrooms,oreventhewholebuilding. Therearethreequestionsthatareofimportance:(1)Howaccur ateshouldthemodel besothatitcanbeusedforMPC?(2)Whatmodelstructureshould beusedsothatthe desiredaccuracycanbeachievedyetthemodelisnottoocomplex? (3)Howtodetermine theparametersinthemodeloncethemodelstructureischosen? Wewilltakeacloserlook ateachofthesequestions. 11

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1.2.1.1Q1:Acceptableaccuracy Irrespectiveofwhatmodelstructureischosenorwhatparamet erestimationmethodis used,therewillalwaysbediscrepancybetweenthemodel'spredictio nandwhatis measured.Thetaskofmodelingistondausefulmodel,notacorre ctmodel.Thusthe criteriontomeasureamodelcloselydependsonhowwearegoingtou sethemodel.Inthis roommodelingproblem,ourgoalistouseitforMPC,sotherearetwo majoraspectsthat weconcern:predictionerrorandrateofresponse.Fortheform er,weconsiderthepeakof predictionerrorlessof3 o F tobetheacceptableaccuracy.Thisisbecausetheroom temperatureisnotuniforminreality,thedierencebetweendiere ntareasinsidetheroom canbe3 o F ormore,soaskingforbetteraccuracyinthemodelisunreasonab le.Therate ofresponseisalsoimportant.Itispossiblethatamodelhavesmallp eakerror,butthe temperaturechangesmuchslowerthenreality,whichisclearlynotg oodforcontroldesign. Forexample,MPCpredictsthetemperatureusingthemodeltodet erminetheoptimal inputs.Ifthemodelisslower,thecontrollermaydecidestoblowcon ditionedairintothe roomforlongertimesinceitthinksthatisrequiredtobringtheroomt emperatureto desiredvalue.1.2.1.2Q2:Modelstructure White-boxmodel,black-boxmodel,andgrey-boxmodelarethreet ypesofcommonly usedmodel.White-boxmodelisthemostdetailedinthethree.Itsta rtsfromrst principleinthephysicalprocess,andmakeasfewassumptionsaspo ssible.Itistheclosest descriptionofrealityandiseasytochange.However,theunderlyin gphysicsisusuallyvery complicated,resultinginhighorderandhighdimensionmodelwhichreq uiresenormous computationalresourcewhenapplying.Anotherproblemwiththisa pproachisthatpure white-boxmodeldoesnotexist.Therearealwayssomeunknownan duncertainties,and someinformationinthephysicalprocessmaynotbeavailable.Taket heroommodelingas example,thefurnitureandoccupantsactivityinsidearoomishardt oget,andoftentime varying.Assumptionsareneededinthosecases,andtheymaynot begoodenough. Black-boxmodel,onthecontrary,doesnottouchthephysicalpr ocessalall.Instead, itisdatadriven.Withcertainparameterestimationmethods,Blackboxmodelisobtained directlyfrominputandoutputdata,withoutanyknowledgeoftheu nderlyingphysical 12

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process.Thisfreesusfromthepossiblyverycomplexderivationfr omrstprinciple,and unknowninformationwillnotcauseproblem.Also,black-boxmodelis oftensmallinsize. However,black-boxmodeldoesnothaveanyphysicalinterpreta tionoftherealsystem, whichmakesithardtomakesenseofthemodelparametersorton derrorinthemodel. Lackofrexibilityisanothermajordisadvantageofblack-boxmodel. Iftheprocesswhich themodeldescribeschangedevenjustslightly,alltheparameter shavetobeestimated again,whichisalotofwork. Grey-boxmodelisacombinationoftheabovetwo,whichhasaphysic al representationbutwithsomeapproximation.Someoftheparamet ersinthemodelneedto beidentiedfromdata.Grey-boxmodelispopularsinceitisnotasco mplexaswhite-box model,yetitcanprovidephysicalinsightofthesystemreasonablyw ell.Inthisthesis,we willestablishagrey-boxmodelfortheroomusinganelectricalcircu itanalogy.The resistorandcapacitorvaluesaretheparameterstobeestimated inthemodel.Theneed forhavingR,Cparameters(asopposedtoobtainingablack-boxmod el)inthemodelis manifold.First,R,Cvalueshaveintuitive,physicalmeaning.Second, onecancheckifthe identiedparametersvaluesarereasonable.Thisprovidesasanity checkandcanhelp unearthpotentiallygrosslyinaccuratesystemidentication.Third ,sinceR,Cmodeling paradigmisprevalentintheHVAC/buildingscommunity,itisusefulsimp lyasacommon language.Manyresearchresultscanbefoundonthistopic[ 2 12 { 14 21 ].However,various modelsofdierentstructures,orders,andparametersareuse d.Inthisthesis,weattempt todevelopananalysistondgoodmodelstructureandparameter s. 1.2.1.3Q3:Parameterestimation Theidenticationproblemisnottrivial.Powerfulstate-spaceident icationmethods (suchassubspacemethods[ 30 ])cannotbedirectlyemployedastheydonotleadtoan identicationofR,Cparameters.Rather,theyidentifythesystem matricesinanarbitrary statespace.Frequencydomainandadaptivetechniques[ 29 ]suersimilarproblemsdueto thecomplexrelationshipbetweentheR,Cparametersandthecoec ientsinthe polynomialsthatdescribethetransferfunctions.Also,persisten ceofexcitationmaynotbe guaranteed,especiallywhenmanyparametershavetobeestimate d. 13

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Wepicktwoparameterestimationtechniques,least-squaresmeth odandmaximum likelihoodmethod,toidentifytheR,Cvaluesoflowordermodelsfromda tacollectedfrom abuildingintheUniversityofFloridacampus.Least-squaresmethod canhandlethe nonlinearpropertyinthesystemdynamics.Withthepredictionerro rasitscostfunction, itisstraightforwardandprovidesintuitiveevaluationofhowgoodth emodelpredictionis. Maximumlikelihoodisanotherwidelyusedmethodforparameterestima tionindynamical system,anditisgreatindealingwithmeasurementnoise.Adisadvant ageofitisthatitis onlyapplicabletolinearsystem.However,undersomecircumstance s,whichwewilldiscuss later,ourmodelwillbelinear.Thusmaximumlikelihoodmethodisapplicab le. Modelvalidationisanotherimportantproblem.Afewauthorshavep roposedmethods forestimatingR,Cparametervaluesofbuildingthermalmodels,e.g.,[ 2 8 10 20 22 ]. Suchpapersshowtheeectivenessoftheirproposedmethodsby comparingtheprediction oftheidentiedmodelwithmeasureddata.However,ouranalysiss howsfornormal operatedclosed-loopdata,suchcomparisonisrisky;grosslywron gmodelsmayreproduce suchdataquiteaccurately.Carefulconsiderationhavetobetak en,andwewilldiscussthis indetailinthisthesis.1.2.2FaultDetection Asmoderncontrolsystemsgrowmorecomplex,reliabilitybecomesa major concern[ 7 ].Forsafety-criticalsystems(forexample,aircraft),theresu ltsoffaultscanbe extreme,orevencatastrophic.Theabilitytodiagnosefaultson-lin eisthusobvious.For systemswhicharenotsafety-critical,faultdiagnosecanimproves ystemeciency,indicate needformaintenance,orpreventsystembreakdownwhenfaultis developing.Fault diagnosiscanbeseparatedintothreesteps,namelyfaultdetectio n,faultisolation,and faultcorrection.Faultdetectionistousetheavailableinput/outpu tmeasurementtotell whetherthesystemisoperatingnormally.Thisisabinarydecision,i.e., todetermine whetherthereisfaultinthesystemornot.Faultisolationistoidentif ywhatkindoffault itisandwhereitis,forinstance,whichsensororactuatorisnotwor king.Faultcorrection isratherself-explanatory.Itistoxtheproblemafterthefaultis located.Itisoftenhard toaccomplishthecorrectionautomatically,sincethefaultcanbeca usedbya malfunctioninghardware,whichrequirereplacement. 14

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InaHVACsysteminalargebuilding,faultdiagnosisplaysanimportantr ole.Firstof all,ifdevicesbreakdowninHVACsystem,itcouldcausediscomfortto occupants,oreven bringdangerinseriouscase.Timelydetectionofsuchdevicefailureis criticalforsafety concern.Innotsocriticalconditions,faultdetectionisalsousefu linndingdeteriorating devices,improvingeciency,andintelligentmaintenancescheduling. Inthisthesis,wewill focusonthedetectionofthefaultcausedbyoccupants.Forexa mple,ifthedoorsareleft open,whentheA/Cisstillon,energywillbewastedsincetheA/Cistr yingtocooldown thewholehallwayinsteadoftheroom.Itwouldbedesirableifthesyst emcandetectthis kindoffault,andsignalamessage,sothatpeoplecanxtheproble m.Fromcontrol perspective,thisisalsohelpfulsincethemodelwillbedierentdepe ndingonwhetherthe doorisopenorclosed.Thefaultdetectiontechniquecanhelpuspick therightmodelto useinourcontrolalgorithmwithouttheneedofinstallinganysensor s. Faultdetectionmethodscanbebroadlyclassiedintothreecatego ries.Theyare quantitativemodel-basedmethods,qualitativemodel-basedmetho ds,andprocesshistory databasedmethods[ 31 ].Theadvantagesofthemodel-basedmethodsarethattheyare oftencomputationallylight,andinmanycasestheinput/outputmea surementsrequired forcontrolisalsosucientforfaultdiagnosis.Thesemethodsalso havesomedrawbacks. Theyarelimitedtolinearsystems,havedicultieswithmultiplicativefau lts,requires accurateknowledgeofthemodel.Theprocesshistorydatabased methods,onthe contrary,extractinformationfromdata,withoutknowledgeofa model.Thedisadvantage ofitisthatlargeamountofdataareneededtofortraining,whichma ynotalwaysbe available.Inthisthesis,wepickoneofthecommonlyusedmodel-base dmethod,unknown inputobserver,andimplementittodetecttheabovementionedfau ltinasingleroom. 15

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CHAPTER2 MODELSTRUCTURE Inthissection,weattempttoanswerQ2,whichisthequestionofwh atisthemodel structureofminimumcomplexitythatcanachieveouraccuracyreq uirement.The underlyingprocessesthatgovernthedynamicsoftemperaturee volutionarecomplexand uncertain,sogrey-boxmodelsareusuallyused.Thelumpedparame termodelsthat researchersusuallyusetomodeltemperaturedynamicsisacombin ationofRCnetwork modelsthatcaptureinter-zoneconduction,whichislinearinstruct ure,andanon-linear termthatcapturestheeectofenthalpyexchangewiththeouts ideduetothesupplyand exhaustair.Werestrictourselvestothisclassofmodels,whichisde notedby M RC ( n;q;p ),where n referstostatedimension, q tothenumberofinputs,and p tothe numberofuncertainparameters.Werstdevelopaveryhighstat edimensionmodelwhich hashighaccuracy.Thenweproposevariouslowordermodelsofthe sameclass,and comparewiththehighorderone.Itturnsoutthatthoughamodel in M RC ( n;q;p )is non-linear,itbecomesLTI(lineartimeinvariant)whenthemassrowr ateofsupplyairis heldconstant.Bothtimeandfrequencyresponsecomparisonispo ssibleinthatcase. 2.1GeneralSettings Inthissection,wewilldiscussthestates,inputs,andparameters ofthreedierent modelsofazoneintheclass M RC ( n;q;p ).Consideratypicalzoneinamulti-zonebuilding withVAVsystem,whichisseparatedfromtheoutsidethroughanex ternalwallanda windowandfromveinternalspaces(roor,ceiling,oneroomoneac hside,andahallway) throughinternalwallsandadoortothehallway.Themajorheattra nsfermechanisms includethefollowing:(1)heatconductionthroughexternalandint ernalwalls,windows, roof,andceiling;(2)radiationandconvectionbetweenthesurfac eandtheairmassin contactwithit;(3)heatconvectionwithoutsideairduetotheairsu ppliedtoand extractedfromtheroombytheHVACsystem;(4)solarradiationt hroughthewindowand externalwall;(5)casualheatgainfromoccupantsandequipment s;and(6)inltrationand exltration.AschematicgureoftheroomisshowninFigure 2-1 Theobjectiveofbuildingcontrolistomaintaincomfortableroomclima te.Naturally, itisourmajorconcernwhenmodeling.Therearethreeaspectsofit thatarerelatively 16

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n r r n Figure2-1.Schematicgureoftheroomimportant,whicharetemperature,humidity,andcontaminants.C ontaminants,suchas CO 2 ,haveminimalimpactonthethermaldynamics,andlowlevelofconta minantscanbe assuredbysupplyingsomexedamountoffreshair.Thus,wedono tconsider contaminantsinthisthesis.However,temperatureandhumidityar ecoupled.Theheat gainfromthesupplyairequalstotheenthalpyofincomingairminusthe enthalpyof exhaustair,i.e.: Q AC = m ( h in h out ) (2{1) where h in = C p T s + W s ( h we + C pw T s )(2{2) h out = C p T i + W i ( h we + C pw T i )(2{3) where m isthesupplyairmassrowrate, C p isthespecicheatofair,and T s isthesupply airtemperature, T i istheinsideroomtemperature, W s isthehumidityofthesupplyair, W i isthehumidityinsidetheroom, h we istheevaporationheatofwaterat0 o C C pw isthe specicheatofwatervapour.Notethatthemainsourceotherth ansupplyairthataects humidityisthewatergeneratedbyoccupants.Whenthereisnoocc upant,thehumidity insidetheroomwillbeequaltothatofthesupplyair.Thisprovidesan opportunityto breakdownandsimplifytheproblem.Supposewecollectdatawhenth eroomis 17

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unoccupied,then W s = W i = W .Wecanrewriteequation( 2{1 )as: Q AC = mC p ( T s T i )+ WC pw ( T s T i )(2{4) wherethersttermisseparatedfromhumidity.Aftercalculation, wefoundthatthe secondtermismuchsmallerthantherstone,thuswecanignoreita ndeliminate humiditydynamicsfromtheproblem. Tofurthersimplifytheproblem,thefollowingassumptionsaremade: 1.Theairinsidetheroomiswellmixed,sothatwehaveoneuniformtem peraturein theroom. 2.Weignorein/ex-ltration.Exltrationhasnoeectonthetempe raturedynamics;it hardlymattersiftheairleavingtheroomisleavingthroughareturna irgrilleor throughcracksinanwindow.Mostcommercialbuildingsaremaintaine datpositive pressuretoprecludethepossibilityofinltrationfromtheoutsidet hroughcracks,so assuminginltrationdoesnotoccurisreasonable.Inthesituationw hendooris open,theremightbeinltrationthroughthedoorfromthehallway. Thiswillbe discussedseparatelyinsection 3.4 3.Weconneourstudytonighttimedatawhenthereisnosolarradia tionand occupantheatgain,whichoftenhavelargeuncertaintyandnotea sytomeasure accurately. Undertheseassumptions,themainvariableofinterestisthetempe ratureofthespace insidethezone,denotedas T i .Thisistherststate,anddependingonthemodel dimension,theremaybeotherstates.Wenowdescribethevarious models. 2.2Full-scaleModel Theinputsthataecttheroomtemperatureareoutsidetempera ture,temperaturesof thesurroundingspaces,andheatgaininsidethezone.Wedeneth einputvectortobe u =[ T o ;T f ;T c ;T n 1 ;T n 2 ;T hw ;T s ;m;Q ] T ,where T o istheoutsidetemperature, T f isthe temperatureofthespacebelowtheroor, T c isthetemperatureofthespaceabovethe ceiling, T n 1 and T n 2 arethetemperatureoftheadjacentroomstotheside, Q isadditional casualheatgainfromappliancesetc., m istherowrateofsupplyairand T s isits temperature.Withthenooccupantsassumption,humiditytermisig nored,sothenetheat gainduetothesupplyairequals: Q AC = mC p T s mC p T i (2{5) 18

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where m isthesupplyairmassrowrate, C p isthespecicheatofair,and T s isthesupply airtemperature.Theconductiveheattransferthroughasolidsu rfaceseparatingtwo roomscanbemodelledaslumpedcapacitanceandresistance.Weemp loythecommonly usedchoiceof3R-2C(3resistorsand2capacitors)[ 13 ]inconstructingthefull-scalemodel. Sincewindowshaveverylowheatcapacitance,itismodelledasasingler esistor.Each surfaceelementisthenconnectedtotheroom\node"toformaRC networkmodel.An additionalcapacitorisincludedtomodeltheheatstoredbytheaira ndotherobjectsin zone.Thestructureofthefull-scalemodelisshowninFigure 2-2 Figure2-2.Full-scalemodelstructureSinceeachwallisa3R-2Ccomponent,therearetwostatesforeac hwall.Togetherwith T i wehavea13-statevector: T =[ T i ;T fw 1 ;T fw 2 ;::: ] T ,where T w 1 ;T w 2 arethetemperatures oftwonodesassociatedwiththesurface .Thedynamicsof T i canbethenexpressedas: C r T i =( 1 R win 1 R ow 1 1 R fw 1 1 R cw 1 1 R n 1 w 1 1 R n 2 w 1 1 R hww 1 ) T i + T o R win + T ow 1 R ow 1 + T fw 1 R fw 1 + T cw 1 R cw 1 + T n 1 w 1 R n 1 w 1 + T n 2 w 1 R n 2 w 1 + T hww 1 R hww 1 + Q AC + Q (2{6) Thedynamicsofthewallnodesofeachwallhavesimilarstructure: C w 1 T w 1 =( 1 R w 1 1 R w 2 ) T w 1 + T i R w 1 + T w 2 R w 2 C w 2 T w 2 =( 1 R w 2 1 R w 3 ) T w 2 + T w 1 R w 2 + T R w 3 19

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Foreachsurface,therearethreeresistancesandtwocapacita nces,whichresultsin30 parametersforallsixsurfaces.Togetherwiththeroomcapacita nceandwindowresistance, thereareatotalof32parametersinthemodel.Thus,thefull-sca lemodelisoftheclass M RC (13 ; 8 ; 32) : Ifweassumethattheresistorsandcapacitorsareuniformlydistr ibuteina surface,i.e., R w 1 = R w 2 = R w 3 ;C w 1 C w 2 ,theparametersofeachsurfacearereducedto two,atotalresistorandatotalcapacitor.Inthiscase,wehave 14parameters,andthe modelisofclass M RC (13 ; 8 ; 14) : 2.3Low-orderModels WenowconsidertwolowordermodelsthatstillemploystheRCnetwor kanalogyof conductiveheattransferasthefull-scalemodeldescribedabove ,butwithfewerstatesand parameters.2.3.1First-orderModel Westartwithamodeloflowestpossiblestatedimension,namely,one .Hereallthe capacitiveelementsofazone(walls,air,furniture)areaggregate dintoasinglecapacitor, sothatthedynamicsof T i become C r T i = T o T i R win + T sd T i R w + Q AC + Q (2{7) where T sd isanaverageofallthesurroundingspacetemperatures.Thismod elhasasingle state T i ,veinputs u =[ T o ;T sd ;T s ;m;Q ] T ,andthreeparameters: =[ C r ;R win ;R w ] T Thus,itisoftheclass M (1 ; 5 ; 3) : 2.3.2Second-orderModel Theresponseoftheroomtemperature T i tochangesinmassrowrateand temperatureofthesupplyairisusuallyfasterthanitsresponseto changesinthe surroundingtemperatures.Anaturalideaistousetwocapacitor storeproducethe two-timescalesoftheprocess.Onecapacitor(roomcapacitance C r )isusedforthelow thermalmassoftheairandotherobjectsintheroom,andtheoth er( C w )isusedforthe heatcapacityofallthewallscombined.Again,therearemanypossib lechoicesofmodel structurefortheintegratedwall.Wechoosetomodeltheintegra tedwallasa2R-1C 20

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element,whichleadsto: C r T i = T o T i R win + T w T i R 1 + Q AC + Q C w T w = T i T w R 1 + T sd T w R 2 (2{8) where T w isthetemperatureofthewallnode.Thismodelhas2states T =[ T i ;T w ] T ,the sameveinputsasthesingle-statemodel,andveparameters =[ C r ;C w ;R win ;R 1 ;R 2 ] T Thus,itisofclass M (2 ; 5 ; 5). 2.3.3TheLinearTimeInvariant(LTI)Case Notethatthe Q AC termin( 2{6 ),( 2{7 ),and( 2{8 )istheonlynonlineartermineachof thethreemodelsdescribedabove.Whenthesupplyairrowrate, m ,isconstant,the Q AC termbecomeslinearinthestate T i andinput T s .ThesystemthenbecomesaLTIsystem: T = AT + Bu;z = CT; (2{9) wherethestate T andinput u variesdependingonwhichofthethreemodelsisunder consideration,theoutput z is T i .Thematrix A dependsontheparameter m .Thenumber ofinputsisreducedbyoneforeachclass(since m hasmovedfrombeinganinputtoa knownxedparameter). 2.4ModelStructureComparison Variousmodelswithintheclass M RC ( n;q;p )canbecomparedamongthemselvesto seehowwelltheycompareagainstoneanotherintermsofspeedof response,gainsetc. Whenthemassrowrateisconstant,themodelsareLTI,soitisposs ibletocomparetheir frequencyresponseaswell.Acomparisonbetweentheirfrequenc yresponseisusefulto determinewhetheralow-ordermodelwithintheclass M RC ( n;q;p )ispowerfulenoughto characterizethetemperaturedynamicswithinarangeofinputfre quenciesaswellasahigh ordermodel.Ifso,thisprovidesjusticationforusingthatloword ermodelintheinterest ofreducedcomplexity.Inaddition,examiningthefrequencyrespo nseisalsousefulfor modelcalibration.Forinstance,thetimeconstantandDCgainwithr espectto controllableinputs(suchassupplyairtemperatureorsurrounding roomtemperatures)can beobtainedthroughforcedresponseexperimentswithoutmaking assumptiononthe 21

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model.Therefore,amodelcanbecalibratedbytuningitsparamete rssothatithasthe samepre-speciedspeedofresponseorDCgainasthoseobtained experimentally. Wedonotdealwithcalibrationinthissection.Instead,wechooseth eparametersof thefull-scalemodelaccordingtoASHRAEhandbook.Wecallthesev aluesASHRAE values,andtheywillbediscussedinsection 2.4.1 .Inthelow-ordermodels,however,we needawaytocomputetheeectiveresistanceandcapacitanceof theintegratedwall.We considerthesurfacesthatareaggregatedtoformtheintegrat edwalltobeparallel components,sothatthetotalcapacitanceisthesumofcapacita nceofeachsurface,and thetotalconductanceisthesumofconductance(inverseofres istance)ofeachsurface. 2.4.1ASHRAEValues ASHRAE(AmericanSocietyofHeating,AirconditioningandRefrigera tionengineers) handbook[ 1 ]describeshowtodeterminetheR,C(resistance/capacitance)va luesfora solidsurfacegivenitsmaterialandconstructiontype.Thisinforma tionisnowavailablein softwaresuchasHAP[ 5 ].TheresistancesandcapacitancesofaRCnetworkmodelare carefullychosentomodelthecombinedeectofconductionbetwe entheairmasses separatedbythesurface,aswellaslongwaveradiationandconve ctionbetweenthesurface andtheairmassincontactwithit[ 1 ],[ 14 26 ].Werefertoparametervaluessoobtained as\ASHRAEvalues".However,thereisuncertaintyintheseparam etervalues.First, informationonwallandwindowconstructionandmaterialarenotalw ayseasytoobtainfor existingbuildingsduetopoorrecordkeeping.Second,duetocrack sinwindowsandwalls, theeectiveresistanceofanwindowandwallislikelytobelowerthanw hatisinferred fromconstructiondata.Finally,ifawindoworadoorisopen,theee ctiveresistance couldbefarlowerthantheresistanceestimatedforaclosedwindow ordoor.Therefore althoughbeingavaluablereference,theASHRAEvaluesmaynotbet hebestparameter valuesforagivenroom.Hereweprovidestwosimulationsresultsusin gthefull-scalemodel withASHRAEvaluesastheirR,Cparametervalues.Figure 2-3 andFigure 2-4 arethe simulationsoftwodierentrooms(Room241andRoom243)inPughHa llonUFcampus. 22

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6pm 9pm 12am 3am 6am 68 69 70 71 72 73 74 TimeTemp (F) Simulated Measured Figure2-3.SimulationofRoom241withASHRAEvaluesasparameters 6pm 9pm 12am 3am 6am 68 70 72 74 76 78 TimeTemp (F) Simulated Measured Figure2-4.SimulationofRoom243withASHRAEvaluesasparameters Asshowninthegures,ASHRAEvaluesprovidesgoodpredictionfor Room241,but notforRoom243.Therefore,thereisaneedto identify/estimate R,Cparametersfrom measureddata,aprocessreferredtoasmodelcalibrationand/o rsystemidentication. 2.4.2TimeDomainComparison WepickRoom241forthefollowingcomparison.Thereasonisthatthe ASHRAE valuesalreadyhavegoodpredictionpowerforthisroom,thusweca ncomparethe dierencebetweenmodelstructureswithoutcalibratingthemode ls.Thetimedomain comparisonsofthefull-scaleandreducedmodel(alongwithmeasur edtemperaturesfrom 23

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thethreedatasetsdescribedinSection 3.1 )areshowninFigure 2-5 .Weseethatthe full-scalemodelandsecondordermodelhaveverysimilarprediction .Predictionerrorsare bothsmallerthan1 o F .Firstordermodelunder-predictedthetemperaturealittlemore thantheothertwomodels,butstillwithinreasonablerange,withpr edictionerrorunder 2 o F 6pm 9pm 12am 3am 6am 66 68 70 72 74 Temp (F) Mearsured Full-scale 2nd order 1st order 6pm 9pm 12am 3am 6am 70 72 74 76 78 Temp (F) 6pm 9pm 12am 3am 6am 70 75 80 Temp (F) Data set A Data set C Data set B Figure2-5.TimedomaincomparisonofdierentmodelsRemark2.1. Inalltimedomainsimulationsinthisthesis,weusedaconst antloadof Q ( t ) 50 W .Thoughthethreedatasetswascollectedatnightwithnoocc upants,initial comparisonshowedthatallthemodelsunder-predictedthem easuredtemperature,nomatter whatR,Cparametervaluesarechosen.Weconjecturethatana dditionalheatgaindueto thecomputersintheroomwaspresent.AninactivedesktopPC &monitorcanproduce 20-30Wofheat,andanidledesktopprintercanproduce10-35 W[ 1 ].Sowepicked 50 W asasomewhatad-hocestimate. 24

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2.4.3FrequencyDomainComparison Frequencydomaincomparisonsrevealmorethanasingletime-doma insimulation comparison,andallowsmoregeneralconclusions.Thereforecomp aringthefrequency responseamongmodelsispreferred,whenpossible.Thisisofcours eonlypossibleforLTI systems. ByexaminingthedatafromPughHallforseveralmonths,wendth atthemassrow rateusuallystaysataconstantvalueforadurationofseveralho urs.Thus,consideringthe caseofconstant m thatmakesthemodelLTIisnotaltogetherunreasonable.By examiningthedata,wendthatthesupplyairtemperaturehasthe fastestchangerate amongallinputsignals.Itcanchangefromitsminimumvaluetomaximum valuein5 minutes.Assumingthatthelargestperiodweconsideris5hours,we choosethefrequency ofinteresttobe 1 5 hours (10 5 Hz )to 1 5 mins (10 3 Hz ). Let H ` ( s )bethetransferfunctionfromthe ` -thinputtotheoutput T i .Thesupplyair temperatureisacommoninputinallthemodels.However,inthefull-s calemodel,there arevedierentinputsforthevesurroundingtemperatures;w hileinthelow-order modelsthereisonlyoneinput T sd forallthesurroundingtemperaturessincethewallsare integratedintoonesurface.Forcomparison,wedeneatransfe rfunctionfromasingle surroundingtemperature T sd tooutputinthefullscalemodelasthesumoftransfer functionsofallvesurroundingtemperatures,i.e., H sd ( s ):= 5 X i =1 H sd i ( s )(2{10) where H sd i arethetransferfunctionsfromeachsurroundingtemperature tooutput. Figure 2-6 showsthefrequencyresponsecomparison(onlythemagnitude,n otphase) ofthethreemodels:full-scale(13-thorder),rstorder,andse condorder.Theparameters arechosenasdescribedearlier.Thevalueofthemassrowrateisse ttobethemaximum possiblevalue, m =0 : 12( Kg=s ),aswehaveobservedthatthemaximumerroroccursat themaximumvaluesof m .Wealsoobservedthattheoutsidetemperature T 0 hassmall impactontheoutputcomparedtotheotherinputs,whichisconsist entwiththefactthat commercialbuildingsareusuallywellinsulatedfromtheoutside.Ther efore,weonlyshow theresultofthetwoinputs T s and T sd here.Thefollowingconclusionsaredrawnfromthe 25

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10 -5 10 -4 10 -3 0 0.2 0.4 0.6 0.8 Full-scale 2nd order 1st order ( Hz )j H Ts ( j! ) j 10 -5 10 -4 10 -3 0 0.1 0.2 0.3 0.4 Full-scale 2nd order 1st order ( Hz )j H sd ( j! ) jFigure2-6.Gaincomparisonofthethreemodels 10 -5 10 -4 10 -3 0 1 2 3 4 2nd order 1st order e T s ( Hz ) 10 -5 10 -4 10 -3 0 0.5 1 2nd order 1st order e T sd ( Hz ) Figure2-7.Theerrordenedin( 2{11 )forthetwoinputs T s and T sd gure. First ,fortherangeoffrequenciesdeemedofinterest,thesecondor dermodelis almostasaccurateasthe13-thordermodel. Second ,the1stordermodelisalsoquite accurateintermsofpredictingtheresponseduetosupplyairtemp erature T s ,butlessso incaseofthesurroundingtemperature.However,sincethesurr oundingtemperature changesveryslowly,thehighererrorthatisseeninthehigherfreq uenciesmaynotresult insignicanterrorintheoutputprediction.Inaddition,itispossiblet obringtherst ordermodel'sresponseclosertothatofthehigherordermodelsby `tuning'the parameters. Third ,thegainfromthetwoinputsareofsimilarmagnitude.Thisisin oppositiontotheprevalentbeliefthatsupplyairisthedominantinput .Onereasoncould bethatallthevesurroundingtemperaturesarecombinedintoon e.Theseconclusionsare inconsistentwithwhatthetime-domainsimulationsindicated. Theeectofaninputontheoutputdependsnotonlyonthetransf erfunctionbut alsoonthemagnitudeofinput.Thevariationin T s and T sd canbesignicantlydierent fromeachother.Theerrorinthepredictionof T i maybedierentduetotheseinputseven thoughtheymighthavethesamegain.Thereforewedenethe errorwithrespectto i -th 26

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input as: e i ( )= j H fs i ( j! ) jj H d i ( j! ) j u i ; (2{11) where H fs i ( )and H d i ( )correspondtofull-scaleandlow-ordermodels,and u i isthe maximumvariationinthe i -thinput.ByexaminingthedatafromPughHall,weobserve thatthelargestvariationsinsupplyairtemperatureandsurround ingroomtemperatures are45 0 F and10 0 F Calculationhavebeendonefordierentsupplyairrowrates.Theer ror e i asa functionoffrequencyisshowninFigure 2-7 .Weseefromthethegurethattheprediction errorismostsensitivetotheinput T s .Forrstordermodel,thismaximumerroris3 0 F ;for thesecondordermodel,itislessthan1 0 F .Thereforethe2ndordermodel,forthechosen parametervalues,isclosertothe13-thordermodelbyafactorif three,comparedtothe 1stordermodel,intermsofthepredictionerroracrosstherange offrequenciesofinterest. 27

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CHAPTER3 CALIBRATIONANDVALIDATION 3.1FieldData 3.1.1TestBed ThetestbedweuseforexperimentsanddatacollectionisPughHallo nUniversityof Floridacampus.Finishedin2008,PughHallisa40,000-squarefootfa cility,includesa teachingauditoriumandpublicspaceforlecturesandevents.Asfo rHVACpart,ithas threeairhandlingunits(AHUs),eachofthemmixesoutsideairandre turnair,cooltheair down,maintaincertainhumiditylevel,thensuppliestheconditionedair intodierent rooms.Theterminaldevicesarevariableairvolume(VAV)boxes,wh ichdistributesthe conditionedairintooneorafewrooms.VAVboxescancontrolthem assrowrateofair goingintothetargetrooms,andcanreheattheairifnecessary.N ewlybuilt,PughHallis equippedwithmanypre-installedsensors,whichmakesitanidealtes tbed.Somevery usefulsensorsforthisparticularresearch,suchasroomtempe rature,VAVboxsupplyair temperatureandmassrowrate,VAVdamperandreheatvalvepos ition,andetc.,are alreadyinstalledinthebuilding.Thesensorsareconnectedtobuilding automationsystem (BAS),whichkeepsthebuildingclimatewithinaspecicrange.Thisisre allyhelpful,since installationandwiringsensorsintoexistingsystemisextremelydicult andinecient. SiemensInsightWorkstationisalsoinstalledinPughHall.Itisabuildingmo nitoring, management,andcontrolsoftware,whichhasmanygoodfeatur es.Forexample,it supportsBACnetprotocolandhasfriendlygraphicalinterface, whichmakesmonitoring andcontrollingthebuildingeasier.AscreenshotsofInsightWorkst ationisgivenin gures 3-1 AlthoughInsightWorkstationisanusefultool,itisnoteasytoincor porateourown onlinealgorithm.Torecordonlinedataorimplementmoderncontrols trategy,weneed othermethods.Fortunately,Dr.TimothyMiddelkoopinIndustrial Engineering departmenthasbuiltuppostgreSQLdatabaseswhichrecordsallt hedatapointsinthe BAS.Bysendingqueriestothedatabases,weareabletoobtainlarg eamountofonline dataatafastspeed. 28

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Figure3-1.ScreenshotofInsightWorkstation Thetestingareaischosentobeasectiononthesecondroor.Itco ntainsseveral typicaloces,aninternalroomwhichisusedasasmallstudio,asma llrestareawhichhas refrigeratorandcookingappliances,asmallmeetingroom,andalar geconferenceroom. Anotheradvantageofthisareaisthat,afewocesareeachsupp liedbyindividualVAV box,whichdecreasestheuncertaintyinsupplyairdistributionafte rairleavetheVAV boxes.Aroorplanisgiveningure 3-2 Hallwaytemperatureisavariableofourinterest,butthereisnopre -installedsensors tomeasureitinthetestarea.Tocollecthallwaytemperature,wede ployedHOBOU10 Dataloggertorecorddata,andTelaire7001sensorasadisplayfor thecurrent measurement.TheleftphotoinFigure 3-3 showsthesensorsanddataloggers(white boxes),therightphotoshowsthesensorsanddataloggersonte steld. Theenvironmenttemperatureoutsidetheroomisanothervariable wewouldliketo measure.Duetotheinstallationandsafetyconcerns,wedecidedn ottoinstalloutdoor sensors.Instead,wegottheweatherdatafromtwowebsites,n amely 29

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Figure3-2.Floorplanoftestingarea Figure3-3.HOBOsensorshttp://www.wunderground.com/andhttp://www.phys.ur.edu/weat her/.Theformerone hashistoryweatherrecordscollectedfromlocalweatherstation ,whichwecanreferto whenwewanttogetdataduringacertainperiodoftime.Thelateron eisthewebsiteof UFPhysicsDepartmentWeatherStation.Itshowsthecurrentwe atherinformation,and updatesevery15minutes.APerlscriptisdevelopedforexactingt heusefulinformation fromthewebsiteinrealtime,suchascurrenttime,temperature, humidityetc.This enablesustogetrealtimedatawhichwecanuseinourcontrolalgor ithm. 3.1.2DataSets Formodelcalibrationandvalidationinthisparticularresearch,wech ooseatypical oce,Room241,inPughHall.Theroomisconnectedtotwoadjacent ocesandthe 30

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hallwaythroughinternalwalls;andtotheoutsidethroughanexter nalwallandwindow. Threedatasetsarestudied.Alldataarecollectedfrom6pminthee veningto6amnext morning.Therstdataset,setA,wascollectedonasummerdayfr omAug.2ndtoAug. 3rd,2011,undernormalclosedloopcontrolstrategy.Theseco nddatasetB,wascollected onawinterdayfromDec.5thtoDec.6th,2011undernormalclose dloopcontrolstrategy. Thesetwodatasetsarechosenamongdatacollectedoversevera lmonthstomeetthe criteriathattheroomandsupplyairtemperaturesshouldhaveasm uchvariationas possible(thelatterensurespersistenceofexcitation),whilethem assrowrateshouldbe constantforlongperiodsoftime(sothatthemodelsbecomeLTI). Thethirddataset,set C,wascollectedfromOct.24thtoOct.25th,2011,underaforce dresponsetest.During thetest,werstheatedupthetargetroomandcooleddownthes urroundingrooms,in ordertogenerateatemperaturedierencebetweentherooman dthesurrounding.Then weshutdowntheairsupplytostudyhowthesurroundingaectthe roomtemperature. Allthesedatasetsarecollectedwiththedoorclosed,andthewindo wscannotbeopen. Theroomtemperature,supplyairtemperature,andsupplyairrow rateofthethreedata setsareplottedinFigure 3-4 Anothertwodatasetsarecollectedforstudyingtheeectofope ningthedoor.Data setDiscollectedonApr.20th,2012,andsetEiscollectedonMay,3r d,2012.Forboth twosets,thebuildingwasoperatedunderdesignedforcedrespon seexperiment.More detailwillbediscussedinsection 3.4 3.2IdenticationMethods Wepicktwomethodsforparameterestimation,whicharedescribed below.Inthe sequel, P denotesaregionintheparameterspace R p where canlie. 3.2.1Least-squares Foragivenmodelstructurewithxedparameters,wedenea predictionerrorcost J as: J = Z 0 ( T i m ( t ) T i p ( t )) 2 dt (3{1) where T i m ( t )isthemeasuredroomtemperatureattime t T i p ( t )istheroomtemperature attime t predictedbythemodelwithagivensetofparametervalues,and isa 31

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6pm 9pm 12am 3am 6am 70 75 80 Room Temperature (F) Data set A Data set B Data set B 6pm 9pm 12am 3am 6am 0 0.05 0.1 0.15 SA Flow Rate (kg/s) 6pm 9pm 12am 3am 6am 60 80 100 SA Temperature (F) Figure3-4.ThreedatasetscollectedinPughHall.user-speciedtimeinterval.Nowtheparameterestimationproblem canbeposedas minimizingthepredictionerrorcost J : ^ =argmin 2P J (3{2) Theminimizationcanbeperformedbyusinganoptimizationalgorithmsu chasgradient descentorbyagainadirectsearch.Anadvantageofthismethodis thatidenticationof parametersofanon-linearmodelispossible.3.2.2MaximumLikelihood(ML)Method Thesecondparameterestimationmethodweuseisthemaximumlikeliho odmethod thatisproposedin[ 20 ].ThismethodisapplicabletoLTImodelsindiscretetime.The continuoustimemodel( 2{9 )isrstconvertedtoadiscretetimewithadditiveprocessnoise andmeasurementnoise.Undersomeassumptions,whichwillbeexpla inedlater,the likelihoodfunctioncanbeformulatedwiththehelpofKalmanlter.The procedureisas follows: 32

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First,discretizethecontinuousdynamics: T ( k +1)= AT ( k )+ Bu ( k )+ ( k ) z ( k )= CT ( k )+ ( k ) (3{3) where T ( k )is n 1statevector, z ( k )is m 1outputvector, ( k ) 2 R n 1 representsthe uncertaintyinstates, ( k ) 2 R m 1 representsthemeasurementerror, A B ,and C are matricescontainingunknownparameters. Beforemovingon,itishelpfultomakesomeGaussianandindependen tassumptions aboutthenoiseandinitialstates,whichisnormalinnoisecharacter ization.Thefollowing assumptionsaremade:1.TheinitialstateisGaussian,i.e., T 0 N (0 ; 0 ); 2.ThenoisesareGaussian,andindependentlydistributed.Thecov ariancesofthe noisesaregivenas: cov ( k ; j )= k kj (3{4) cov ( k ; j )= k kj (3{5) where k 2 R n n and k 2 R m m areknown,and kj istheKroneckermatrixdened by: kj = 1 ;k = j 0 ;k 6 = j (3{6) 3.Theinitialstate,disturbanceandmeasurementnoiseareindepe ndent. Let Z =[ z ( k ) ;z ( k 1) ;:::;z (0)]betheobservationsuptotime k .Thenthelikelihood functionisgivenbythejointdensityfunctionofallobservations,i.e .,: L ( ;Z ( k ))= f ( Z ( k )) = f ( z ( k ) j Z ( k 1)) f ( Z ( k 1)) ... = f ( z ( k ) j Z ( k 1)) f ( z ( k 1) j Z ( k 2)) :::f ( z (0)) (3{7) Notethat L isamultiplicationofconditionaldensityfunctions.Undertheabove assumptions,itcanbeshownthat z ( k )and Z ( k 1)arejointlynormallydistributed,since theyarebothfunctionsof T 0 ( k 1) ;:::; 0 ( k 1) ;:::; 0 ,whicharejointlynormally distributed.By property5and6 inChapterIVof[ 28 ],eachindividualconditionaldensity 33

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in L isalsonormal,andtheconditionalmeanandcovariancecanbecalcula tedusing Kalmanlterinarecursivefashion.Moreprecisely,lettheconditiona lmeanandvariance attimestep k be^ z ( k j k 1)and R ( k j k 1).Notethat,^ z ( k j k 1)isanone-stepprediction and R ( k j k 1)isthecorrespondingvariance.Fornotationsimplicity,wedenet he estimationerrortobe: e ( k )= z ( k ) ^ z ( k j k 1)(3{8) SincetheconditionaldistributionisGaussian,thelikelihoodfunctionc anbewrittenas: L ( ;Z ( N ))= N Yk =1 f (2 ) m 2 j R ( k j k 1) j 1 2 exp( 1 2 e ( k ) T R ( k j k 1) 1 e ( k )) g (3{9) where jj isthedeterminantoperator.Itismoreconvenienttouselogarithm likelihood function: log( L ( ;Z ( N )))= 1 2 N X k =1 f log j R ( k j k 1) j + e ( k ) T R ( k j k 1) 1 e ( k ) g + constant (3{10) Thenextstepistocompute^ z ( k j k 1)and R ( k j k 1).ThisisdoneusingKalman one-steppredictor.Theestimatesofstates ^ T isupdatedbytheequations: ^ T ( k +1 j k )= A ^ T ( k j k 1)+ Bu ( k )+ L k ( z ( k ) CT ( k j k 1)) (3{11) where L k istheKalmangain,whichcanbecalculatedby: L k = AP ( k ) C T ( CP ( k ) C T +) 1 (3{12) Theestimationerrorcovariancematrix P isupdatedby: P ( k +1)= A [ P ( k ) P ( k ) C T ( CP ( k ) C T +) 1 CP ( k )] A T (3{13) Thentheconditionmeanandvarianceweneedtocalculatethelogarit hmlikelihood functioncanbecalculatedby: ^ z ( k +1 j k )= C ^ T ( k +1 j k )(3{14) R ( k +1 j k )= C ( AP ( k +1) A T + k ) C T + k (3{15) 34

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Theestimationproblemthenbecomesoneofnding thatmaximizesthelikelihood functionwithinthesetofallowableparametervalues: ^ =argmin 2P log L; (3{16) Foreachsetofgivenparameter,thelogarithmlikelihoodfunctionca nbecalculatedby equation( 3{10 ).Theminimizationcanbeperformedbydirectsearchorbyother optimizationalgorithms. 3.3ModelCalibrationandValidation ModelcalibrationreferstoestimatingtheR,Cparameters.Thefull scalemodelin 2.2 has32parameters;itisquitediculttoestimatethem.Furthermor e,wesawinthe previoussectionthatthesecondordermodelisclosertothefull-s calemodelthantherst ordermodelintermsofthefrequencyresponsewhensuchacomp arisonispossible.For thisreason(andduetolackofspace),welimitourattentiontothes econdordermodel M RC (2 ; 3 ;p )forthepurposeofidentication.Also,weonlyconsiderthesituat ionwhen doorisclosedinthissection. Thefollowingassumptionsaremadetoreducethenumberofuncert ainparametersin thesecondordermodel:(i)Theresistanceofthewallissymmetric, i.e., R 1 = R 2 = 1 2 R w (ii)Thewallcapacitance C w andwindowresistance R win areassumedknown(ASHRAE values).(iii)Thesurroundingtemperature T sd istakentobetheaverageofallthe surroundingroomtemperatures(abovetheceiling,belowtheroor ,twoadjacentroomsand thehallway).Therstassumptionismadesothatmodelsofmultiplezo nescanbe combinedtocreateamodelofabuildingorsectionofit.Theseconda ssumptionismade sincethecapacitanceofawallchangeslittleduetowearandtearov ertimeorthe appearanceofcracks.Withtheseassumptions,themodelwehav etoidentifyis M (2 ; 3 ; 2): theuncertainparameterstobeestimatedare C r and R w 3.3.1Attempt1:ApparentSuccessButReallyAFailure WeusedatasetAformodelcalibrationanddatasetBformodelver ication.Forthe MLmethodofSection 3.2.2 ,wepickasegmentfromthedatasetwherethemassrowrate isconstantinthatinterval.ThisisrequiredtomakethesystemLTIs incetheMLmethod isonlyapplicabletoLTIsystems.Theminimizationofpredictionerrorc ost( 3{2 )and L 35

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parameter least-squares ML C r ( J=K ) 5 10 4 5 10 4 R w ( K=W ) 6 : 44 10 4 5 : 6 10 4 Table3-1.BesttparameterswhendatasetAisusedformodelca libration. in( 3{16 )arebothdonewithdirectsearch.Theresultingbest-tparamet ervaluesare showninTable 3-1 Theroomtemperaturepredictedbythemodelwiththebest-tpa rametervaluesand themeasuredroomtemperatureareshowninFigure 3-5 fordatasetA.Thefactthatthe predictionerrorissmallisnotsurprisingsincethemodeliscalibrated withthisdataset. Nextweperformvericationoftheidentiedmodelbycomparingits predictionforthe datasetB;seeFigure 3-5 .Againthepredictionerrorisseentobesmall.Atthisstage,we canclaimthatthemodelcalibratedwithsummerdataisabletopredict winterdataquite well,sowecandeclarewehaveacalibratedmodelandmoveon. 6pm 9pm 12am 3am 6am 68 70 72 74 Temp (F) Mearsured Predicted LS Predicted ML 6pm 9pm 12am 3am 6am 72 74 76 78 Temp (F) 6pm 9pm 12am 3am 6am 65 70 75 80 Temp (F) ValidationData set B CalibrationData set A ValidationData Set C Figure3-5.Calibration/validationwhendatasetAisusedforcalibrat ion. 36

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However,whenwetrytopredictthetemperatureofdatasetCwit hthis\calibrated" model,whichisshowninthethirdplotinFigure 3-5 ,weseethatthemodelpredictionsare completelyo.Sowhathappened? First,wenotethatthereasonweestimatedtheparametersbydir ectsearchinsteadof usingamoresophisticatedsearchmethodisthatthecostfunction sthatareminimizedto estimatetheparametersarenon-convex.Thisisclearfromtheco ntoursofthecost function J whichareshowninFigure 3-6 fordatasetA.Byperformingdirectsearch, possiblehypothesesthatblamesthesearchmethodforgettingst uckatalocalminimum canbeeliminated.Clearlytheproblemisnotthesearchmethod,bute itherthemodelor thedatausedforcalibration. Rw (K/W)Cr (J/K) 1 2 3 4 5 x 10 -3 2 4 6 8 10 x 10 5 10 11 12 13 Figure3-6.Contourofthecost J denedin( 3{2 ),whichshowsitsnon-convexity. Thereasonforthefailurewasfoundtobethedata.Inthecalibrat iondata(dataset A),thesurroundingroomtemperaturesarealmostthesameasth eroomwestudy.Sothe besttresistancevaluesarethosethataresosmallthattheroo mtemperatureessentially followsthetemperatureofthesurroundings,leadingtosmallpred ictionerror.Invalidation datasetB,thoughtheroomtemperatureproleisquitedierentf romthatinsetA,the surroundingroomtemperaturesarestillclosetotheroomtemper ature,sothemodel predictswell.However,invalidationdatasetC,thesurroundingroo mtemperaturesare signicantlydierentfromtheroomtemperature,soitshowsthat thecalibrated parametervaluesareincorrect. 37

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parameter least-squares ML C r ( J=K ) 7 : 8 10 5 4 : 7 10 5 R w ( K=W ) 0 : 01 0 : 005 Table3-2.BesttparameterswhendatasetCisusedformodelca libration. 3.3.2Attempt2:AMoreReliableCalibration NowweusedatasetCforcalibration,whichleadstobest-tparame tervaluesshown inTable 3-2 .Inthiscase,thebest-tparametersfromthetwomethodsare notsosimilar. Thereasoncouldbethat,thedatathatcanusedfortheMLmetho dcorrespondstoa constantinput(supplyairtemperature),whichisnotsucientlyex citing.Still,whilein thepreviouscasebothmethodsyieldamuchlowervalueoftheresist ancecomparedto theirASHRAEvalues,thistimetheestimatedresistancevalueismuch closertoits ASHRAEvalue.Thetime-domainsimulationsforcalibrationandvalidatio ndatasetsare showninFigure 3-7 .Fromthegures,wecanseethatthoughthemaximumprediction errorislarge(3 0 F ),thissetofparameterspredictthetrendofthetemperaturew ellinall threedatasets. 6pm 9pm 12am 3am 6am 65 70 75 80 Temp (F) 6pm 9pm 12am 3am 6am 68 70 72 74 Temp (F) 6pm 9pm 12am 3am 6am 70 72 74 76 78 Temp (F)Mearsured Predicted LS Predicted ML CalibrationData set C ValidationData set A ValidationData set B Figure3-7.Calibration/validationwhendatasetCisusedforcalibrat ion. 38

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0 0.06 0.12 0 0.2 0.4 0.6 0.8 1 m (kg/s) DC Ts DC To DC Tsd 0 0.06 0.12 0 0.2 0.4 0.6 0.8 1 m (kg/s) DC Ts DC To DC Tsd Figure3-8.DCgaincomparison,leftgureisforrstattempt,righ tisforsecondattempt Wecanalsolookatthisproblemfromanotheraspect.Assumethatt hesupplyair rowrateisconstant,thenthesystembecomeslinear,wecanthen studytheDCgainof thesystemwithrespecttoeachinput.Writethedynamicsinstates paceform,weget T = 264 1 R win C r 1 R 1 C r mC p C r 1 R 1 C r 1 R 1 C w 1 R 1 C w 1 R 2 C w 375 T + 264 mC p C r 1 R win C r 0 00 1 R 2 C w 375 u y = 10 T (3{17) where T = T i T w T ;u = T s T o T sd T .ThenwecancomputethetheDCgainfor eachinput: K s = mC p R win ( R 1 + R 2 ) R 1 + R 2 + R win + mC p R win ( R 1 + R 2 ) K o = R 1 + R 2 R 1 + R 2 + R win + mC p R win ( R 1 + R 2 ) K sd = R win R 1 + R 2 + R win + mC p R win ( R 1 + R 2 ) (3{18) Notethatthecapacitanceofthewallandroomdoesnotaectthe DCgain,andforgiven setof R values,theDCgainisafunctionofthesupplyairrowrate.Weplotthe DCgains forthe R valueswegetfromtherstattempt.ItisshownintheleftofFigure 3-8 .Wecan seethatwiththissetofparameters,evenwhentheA/Cisblowingma ximumamountof air,thedominanteectisstillthesurroundingroomtemperature, whichshouldnot happen,asshowninFigure 3-5 .Ifweinsteadusetheparametersfromsecondattemptand 39

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plottheDCgainintherightofFigure 3-8 .Nowthesupplyairtemperaturewillhave largereectthanthesurroundingroomtemperaturewhentheair rowrateishigh. Thefollowingconclusionsaredrawnfromtheseresults:(1).Calibrationaccuracycruciallydependsonthedatasetchosen .Thisbyitselfis notsurprising.Whatissurprisingisthathavinglargevariationinthem easuredinputs(to havepersistenceofexcitation)andoutputsisnotenough.Theda tashouldbechosenso thattheoutput(roomtemperature)doesnothaveastrongcor relationwithanyofthe surroundingtemperatures.Thefeaturesrequiredinthedatato ensureidenticationof parametersseemtobepossibleonlythroughforcedresponseexp eriments.Ifthese conditionsarenotmet,theusualmethodofcalibrationisnotlikelyto yieldusefulresults, evenwhentheidentiedparametersare\validated"byusingadata setdistinctfromthe calibrationdataset. (2).Itisimportanttokeepthenumberofparameterstoaminimums othatoneisnot forcedtosimplyacceptthebest-tparametersreturnedbysom eoptimizationalgorithm. Instead,smallnumberofparametersmakeitfeasibletoexamine(n on)-convexityofthe costfunctionusedtosearchforparameters.Thecostfunction usedtosearchforthe best-tparameterswasobservedtobenon-convexforbothlea st-squaresandMLmethods. Withamodelwithhighernumberofparameters,thissituationislikelyt obeexacerbated. 3.4EectofOpenDoor Moreoftenthannot,whenanoceisoccupied,thedooriskeptope n.Thiscreatea largeopenarea,throughwhichairexchangeoccursbetweentheh allwayandtheinsideof theroom.Inthatcase,themodelwedevelopedearliermaynotbea pplicable.Moreover, whenMPCisimplemented,therecouldbealargetemperaturedieren cebetweenthe hallwayandinsidetheroom,andtheopeningdoormayhaveasubstan tialeectonthe roomthermaldynamics.Thus,additionworkformodelingtheroomw hendoorisopenis required. Tostudythis,weconductedanexperimentinPughHall.Again,wecho seRoom241 asthetargetroom.Duringtheexperiment,wewouldliketogenerat eatemperature dierencebetweentheroomandthehallway,andmakeitreasonably similartothereal practice.Thus,werstsettheroomtemperaturesetpointofRo om241to70 o F ,and 40

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temperaturesetpointofhallwayto75 o F .Afterthetemperaturesettleddown,weopened thedoor,andwaitforsometimetoobserveitseect. First,westudywhetheropeningthedoorhasanoticeableeecton thethermal dynamicsoftheroom.Todothis,weperformedasimulationwiththea bovementioned calibratedmodelforthewholedurationoftheexperiment.Thesimu lationresultisshown inFigure 3-9 .Duringtheexperiment,thehallwaytemperaturedidnotraiseupto 75 o F Figure3-9.Simulationwithoriginalmodelaswedesigned,however,thetemperaturedierenceisstillgoode noughforustostudythe eectofopeningdoor.Intheplot,theverticallineindicatesthetim edoorwasopened.It isclearthatbeforethattime,thepredictedtemperaturematche sthemeasured temperaturereasonablywell,butafterthattime,itdecreasedwh ilethemeasured temperatureincreased.Thedeviationindicatesthattheeectof theopeningdoorisnot negligible. Naturally,thenextquestionishowtomoderatethemodelwhendoo risopen.One ideaistomodelitasnaturalconvection,thenwhenthedooropen, anotherheattransfer termisadded,anditcanbeexpressedas: Q hw = m hw C p ( T hw T i )(3{19) 41

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where m hw isthemassrowbetweenthehallwayandtheroom.Thevalueof m hw depends onthedensitydierencebetweenthetwospaces.Iftheairpress ureandhumidityarethe sameinthetwospaces,itcanbecalculatedbyanonlinearfunctionof T hw and T i basedon thegeometryoftheopeningarea. AnothersimplerwayistoaddanotherRCcomponenttomodelthehe attransfer throughthedoor.Sincewhenthedoorisopen,thereisnosolidsurf aceseparatingthetwo areas,thecapacitanceissmall.Thuswechoosetouseasingleresist or.Thestructureis showninFigure 3-10 .Inthiscase,theadditionheattransfertermis: n Figure3-10.Structureforthemodelbetweenhallwayandroom Q hw = 1 R od ( T hw T i )(3{20) where R od istheeectiveresistanceofopendoor. Inbothcases,the Q hw termisintheformofacoecientmultiplywiththe temperaturedierencebetweenthehallwayandtheroom,i.e., Q hw = ( T hw T i ).The dierenceisthatinthenaturalconvectioncase,thecoecientisn onlinear,andiscoupled withthe T hw and T i ,whileintheresistorcase,thecoecientisjustaconstantparame ter. Inthisthesis,wewilltakethesecondmethodbecauseofitssimplicity ,anditturnsout thatitissucienttoprovidegoodprediction. Todeterminethevalueor R od ,weagainuseexhaustivesearchmethod.Thereisonly onevariableandwehaveageneralideaoftherangeofit,soexhaus tivesearchishandy. TheresultisshowninFigure 3-11 and 3-12 .Asshowninthegures,withtheadditional resistor,thepredictionmatchedthemeasurementthroughwhole experimentduration.The 42

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Figure3-11.Simulationwithmoderatedmodel 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -3 3 4 5 6 7 8 9 R odError Figure3-12.Predictionerrorwithrespectto R od costfunctionintheexhaustivesearchalsoshowsaclearminimum.Als o,weperformeda validationusingdatafromanotherexperiment.Theresultisshownin Figure 3-13 andthe R od valueworkswell.Sofar,wegotreasonablemodelsforbothdoorclos eanddooropen situations. 43

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19.5 20 20.5 21 21.5 22 22.5 23 65 66 67 68 69 70 71 72 73 Time (h)Temp (F) Ti Simu Ti Measured Thw Figure3-13.Predictionerrorwithrespectto R od 3.5Summary WeexaminedtwoquestionsformodelsofHVACzonesthatcanbeuse dforpredictive control:requiredmodelcomplexityandparameteridentication.W eexaminedmodelsof varyingcomplexitywithinthepopularclassofnon-linearRCnetworkm odels.By comparinglowordermodelswithhighorderones,weconcludethatas econdordermodel reproducestheinput-outputbehaviorofthefull-scale,13thord ermodelquiteaccurately. Evenarstordermodelisaccurateenoughthatitmayverywellsu ceforthepurposeof predictivecontrol.Thus,complexmodelswithhighstatedimensionan dlargenumberof resistance/capacitancemodelsarenotneeded. Theworkreportedhereonparameteridenticationoflow-orderm odelsfrom experimentaldatahasrevealedsomesurprisingresults.Theresu ltsindicatethat calibratingtheparametersoftheR,Cnetworkmodeltoclosed-loop datafromabuildingis likelytoleadtogrosslyinaccurateparameterestimates,sothatth eresultingmodelis unlikelytobeusefulinpredictivecontrol.Evendatawithsucientlye xcitinginputisnot enough.Theresultsrevealthefeaturesthatthedatashouldha vetoenablecorrect identication.Thesefeaturesseemtobepossibletoensureonlyth roughforcedresponse tests. 44

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CHAPTER4 FAULTDETECTION Faultdiagnosisisanimportanttaskinmanyaspectsofbuildingcontro l.Withthe modelweestablishedintheearlierchapters,weareabletoexploitth euseoffault diagnosistechniques.Oneoftheproblemwiththemodelisthatitcha ngessignicantly whenthedoorisopenedorclosed.Onecancertainlyputsensorsto detectthedoorstatus, howeveritisexpensivetoinstallsensorsforeachroom.Plus,sens orswillfailsooneror later,sothisalsocausesahighermaintenancecost.Thus,itisdesir edtobeabletodetect thatfrommeasurementsfromsensorsthatarealreadyinstalledin abuilding.Inthis section,wewillconsiderdoorclosedstatustobethenormalopera tingmode,whiledoor leftopentobeafaultystatus.Withthissetup,faultdiagnosistech niquescanbeutilized fordetectingwhetherthedoorisopenorclosed. 4.1UnknownInputObserver Unknowninputobserver(UIO)isamodel-basedfaultdiagnosismeth od.Itisa two-stepprocedure:residualgenerationanddecisionmaking.Th ebasicideaistoestimate thestateswithinput/outputmeasurements,usetheestimatione rrorasresidual.Whenthe systemisworkingundernormalcondition,theresidualwillbecloset ozero.Whenfault occurs,theassumedmodelisnolongeraccurate,sotheestimate dstatescannotfollowthe realstates,causingtheresidualtobenon-zero.Athresholdfo rresidualisset.By observingthechangeinresidual,andcomparingwiththethreshold, wecandetectthe fault.Inrealworld,wewillnevergettheexactmodel,duetoallkind sofdisturbances.In UIOmethod,weconsideralldisturbancesasanunknowninput,den otedby d .Bycarefully designtheobserver,UIOmethodisabletoestimatethestateseve nwhendisturbanceis present.Wewillstartfromthesystemmodel. Letthesystemdynamicswithdisturbancetobe: x = Ax + Bu + Ed y = Cx (4{1) 45

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where d isthedisturbanceand E isthedisturbancedistributionmatrix.Theobserveris designtobe z = Fz + TBu + Ky ^ x = z + Hy (4{2) where F;T;K;H aretobedesigned. Denetheestimatorerroras e = x ^ x .Aftersomealgebraicmanipulation,weget e =( A HCA K 1 C ) e +( F ( A HCA K 1 C )) z +( K 2 ( A HCA K 1 C ) H ) y +( T ( I HC )) Bu +( HC I ) Ed (4{3) where K 1 + K 2 = K Ifwecandesignedthematrices,sothatthefollowingaresatised: 8>>>>>>><>>>>>>>: ( HC I ) E =0 T = I HC F = A HCA K 1 C K 2 = FH (4{4) Thenwehave_ e = Fe .Let A HCA = A 1 ,then F = A 1 K 1 C .If( A 1 ;K 1 )isobservable, wecanmaketheobservererrorgotozeroasymptoticallybychoos ing K 1 properly. Nowtheproblembecomessolvingthesetofequations( 4{4 ).Considertherst equation: ( HC I ) E =0 : (4{5) Itcanbeshownthatif rank ( CE )= rank ( E ),thenaspecialsolutionof H isgivenby: H = E [( CE ) T CE ] 1 ( CE ) T (4{6) Withthis H ,wehave T = I HC and A 1 = TA .Thenexttaskistodesign K 1 sothat F = A 1 K 1 C isHurwitz.Ifthepair( A 1 ;C )isobservable,thantheeigenvaluesof F can beassigntoanywhereinthelefthalfplanebystandardpoleplacemen ttechnique.If ( A 1 ;C )isunobservable,wecanperformanobservablecanonicaldecomp osition,whichisa 46

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similaritytransformationtoobtainobservablecanonicalform.Sup pose n 1
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4.2.1RoomModel Intheexample,wechosetousetheroommodelfromM.M.Gouda'spap er(2000).The roomhasveheat-exchangingsurfaces,whicharetwotypesofe xternalwall,oneroor,one ceiling,andoneinternalwall.Eachsurfaceismodelledas2R-1Ccompo nent.Besidesthe heatexchangethroughallsurroundingareas,therearethreeo therheatsources,whichare heatgainfromA/Csystem,solarheatgain,andcasualheatgainfr omoccupantsand appliancesintheroom.Thestates,inputs,andoutputsaredene dasfollows. Thereare6states, x = 2666666666666664 T 1 T 2 T 3 T 4 T 5 T i 3777777777777775 = 2666666666666664 Temperatureofexternalwall1Temperatureofexternalwall2 Temperatureoftheroor Temperatureoftheceiling Temperatureoftheinternalwall Insideroomtemperature 3777777777777775 (4{11) and7inputs, u = 2666666666666666664 T o Q s Q c Q g T z 1 T z 2 T z 3 3777777777777777775 = 2666666666666666664 Outsidetemperature Solarheatgain ACunitheatgain Casualheatgain Groundtemperature Temperatureabovetheceiling Temperatureconnectedtotheinternalwall 3777777777777777775 (4{12) andoneoutput, T i ,whichistheinsideroomtemperature. Thentheroommodelcanbeexpressedinstatespaceform, x = Ax + bu y = Cx (4{13) 48

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where A = 2666666666666664 ( U 1 U 2 ) C 1 0000 U 1 C 1 0 ( U 3 U 4 ) C 2 000 U 3 C 2 00 ( U 5 U 6 ) C 3 00 U 5 C 3 000 ( U 5 U 6 ) C 4 0 U 6 C 4 0000 2 U 7 C 5 U 7 C 5 U 1 C 6 U 3 C 6 U 5 C 6 U 6 C 6 U 7 C 6 1 C 6 ( U 1 U 3 U 5 U 6 U 7 U 8 ) 3777777777777775 B = 2666666666666664 U 2 C 1 000000 U 4 C 2 000000 0 1 C 3 00 U 6 C 3 00 00000 U 5 C 4 0 000000 U 7 C 5 U 8 C 6 0 1 C 6 1 C 6 000 3777777777777775 C = 000001 andparameters C i and U i canbefoundinM.Gouda(2000). 4.2.2Implementation Inthissection,wewilldiscussthesetupandassumptionsweadopte dinthe implementation.Thefaultwearestudyingisthedoorbeingleftopen. Whenthefault occurs,therewillbeanadditionalheatexchangebetweentheout sideandtheroom,which cannotbemeasured.Thisismodelledasanextraheatgainterminto Q c .Thuswehave f a = 00 Q door 0000 T (4{14) Thevalueof Q door canbecomputedby: Q door = m door C p ( T o T i )(4{15) where m door istheairmassrowratebetweenoutsideandinside,whosevalueisdet ermined by T o T i ,andthegeometryofthedoor. Forsimplicity,wealsoassumethefollowing: 1.A/Cunitheatgain Q c ,ismeasured; Q s and Q g aresettozero; 49

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2.Thereisnosensorfault,i.e., f s =0. 3.Thereisonlyonedisturbance,anditonlyaectsthe6thstate T i ,i.e., E = 000001 T .Thisisreasonablesincetheroomtemperatureismore pronetobeaectedbyuncertainties,whilethewallnodesarenot. Thisassumption ensuresthatsolutionsof H exists. 4.Thedisturbanceisnormallydistributedwithzeromean.4.2.3Analysis First,notethatwhenfaultoccurs,theobservererrordynamic( 4{10 )willbeaected bythefaultthroughtheterm TBf a ,andtheerrorwillinturnaecttheresidual r = Ce Notethatinthismodel, C = 000001 ,whichmeansonlythelastentryof theresidual r canbeobserved.Moreover,since f a isnon-zeroonlyonitsthirdentry, TBf a =( TB ) (: ; 3) Nowexaminethematrix T .From( 4{4 ),wehave T = I HC = 266666664 10000 h 1 01000 h 2 ... ... ... ... ... ... 000001 h 6 377777775 (4{16) So TBf a =( TB ) (: ; 3) = Q door 266666664 h 1 1 C 6 ... h 5 1 C 6 (1 h 6 ) 1 C 6 377777775 (4{17) Sinceonlythelastentryisofinterest,wewant(1 h 6 ) 1 C 6 6 =0,so(1 h 6 ) 6 =0. Alsofrom( 4{4 ),weknowthat ( I HC ) E =0 ) (1 h 6 ) e 6 =0(4{18) Herecomesaconrict.Equation( 4{18 )saysthatif e 6 6 =0,then(1 h 6 )=0,whichwill makeusunabletodetectthefault. Inthatcase,weslightlymodifythecondition.Insteadofmaking( I HC ) E =0,we let( I HC ) E = 00000 T .Thentheresidualweobservewillbecorruptedby 50

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thedisturbance.Howeverbyassumption5,thedisturbanceisofz eromean.Thus, althoughcorruptedbydisturbance,theexpectedvalueofthere sidualwillnotbeaected, i.e.,itwillbezeroundernormalcondition,andnon-zerounderfaulty condition. Withthischange,wehave (1 h 6 ) e 6 = ) (1 h 6 )= e 6 (4{19) Then,wehave e = Fe + TBf a +( HC I ) Ed =( A 1 K 1 C ) e + Q door 266666664 h 1 1 C 6 ... h 5 1 C 6 e 6 C 6 377777775 + 266666664 0 ... 0 377777775 d (4{20) ApplyLaplacetransform,weget e ( s )=( sI ( A 1 K 1 C )) 1 ( TBf a ( s )+( HC I ) Ed ( s ))(4{21) Assumethefaulttobeastepsignal,applyFinalValueTheorem,wege t lim t !1 e ( t )=lim s 0 se ( s )= ( A 1 K 1 C ) 1 ( Q door 266666664 h 1 1 C 6 ... h 5 1 C 6 e 6 C 6 377777775 + 266666664 0 ... 0 377777775 d s )(4{22) Notethattheresidualequalstothelastrow.Weseeatradeoher e:ononehand,we wouldliketomaketheeectoffaultlarge,and shouldbelarge;ontheotherhand,we wouldalsoliketomaketheeectofdisturbancesmall,and shouldbesmall.Thus,a tuningprocessisrequired.Inthisparticularexample,wechoose =0 : 1.Anonehour simulationisperformedtostudytheUIO,thedoorisopenedat30min utes.Moreover,the outsidetemperature( T o )issetto85 o F ,thetemperatureofground( T z 1 ),ceiling( T z 2 ),and internalwall( T z 3 )issetto68 o F ,A/Cheatgainissetto 1000 W .Thesimulationresultis showninFigure 4-1 and 4-2 .Inthegures,theverticallineindicatesthetimewhenfault occurs.Figure 4-1 showstheroomtemperatureandresidual.Ascanbeseen,before the 51

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Figure4-1.SimulationofUIOfaultoccurs,theresidualremainsclosetozero,whichindicatesfa ultfreestatus;afterthe faultoccurs,theresidualjumpsup,whichindicatesthedetection offault.Figure 4-2 shows theestimatedsixstatesfromUIOcomparingwiththeactualstate s.Itisclearthatthe observerestimatesthestateswellwhenthesystemisfreeoffau ltbutnotwhenfault occurs.Thesimulationresultshowsthataftertuning,theUIOisab letodetectthedoor beingleftopen. Wewillgiveashortsummaryabouttheissuesweencounteredinthise xample.Dueto thespecialstructureoftheroommodel,UIOcannotbeimplemente ddirectlytodetect thefault.Moregenerally,todetecttheactuatorfaultappearsin the i th rowof f a ,the i th columnof TB mustbenon-zero,thegeneralcondition TB 6 =0isnotsucient.Inthecase whenthe i th columnof TB doesequaltozero,wedevelopedatradeomethod.Insteadof eliminatingtheeectofdisturbancefromtheobserver,werelaxth erestrictionalittle, allowing( I HC ) E tobenon-zero.Bydoingthis,thefaultsignalwillappearinthe estimationerrordynamics,thusaectstheresidual.However,th ismovealsobring disturbanceintotheobserver.Thelargerwemakethefaulteect ,thelargereectof disturbanceoccurs.Becauseofthistradeo,tuningisrequired. Anotherdesignparameter isthepolesoftheobserver.Ascanbeseenfromequation( 4{22 ),thepolelocationsalso 52

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Figure4-2.EstimatedstatesfromUIOaectthenalvalueoftheestimationerror,thusaectthevalue ofresidualwhenfault occurs.Normally,wewouldlikethepolestobeawayfromtheimaginary axissothatthe observerwillconvergefaster,however,duringourtuning,weob servedthatmovingthe polestotheleftwilldecreasethenalvalueofresidual.Thisindicate sthereisanother tradeowehavetotakeintoaccountwhenapplyingUIOmethodfor faultdiagnosis. 4.3DoorStatusDetection NowweattempttodetectopeningdoorwithUIO.Wetakethesecon dordermodelfor theroominequation( 2{8 ),andweassumethatthemassrowrateisconstantforshort period.Let x =[ T i ;T w ] T bethestates, u =[ T sd ;T o ;T s ;Q ]betheinputvector,and y = T i betheoutput,thenthesystemcanbewriteas: x = Ax + Bu y = Cx (4{23) 53

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where A = 264 1 R win C r 1 R 1 C r mC p C r 1 R 1 C r 1 R 1 C w 1 R 1 C w 1 R 2 C w 375 B = 264 0 1 R win C r mC p C r 1 C r 1 R 2 C w 000 375 C =[1 ; 0] (4{24) Thenweadddisturbanceandfaultintothesystem.Againweassume thedisturbance entersthesystemonlythrough T i ,i.e.,thedisturbancedistributionmatrix E =[1 ; 0] T .We havediscussedinsection 3.4 ,whendoorisopen,theheatexchangecanbemodelledasan additionalresistorbetweenthehallwayandtheroom.Duringthisan alysis,wemakea littlemodication:considerthefaultasanadditiontermintotheinput T sd .Thereasoning isthatwhenthedoorisopen,moreheattransferoccurs.Bychan ging T sd ,thesameeect canbeappliedtothesystem.Forexample,when T sd >T i ,thefaultcanbeconsideredto beapositivetermaddedto T sd ,whichincreasesthetemperaturedierence,andthus increasetheheattransfer.Bymakingthismodication,openingth edoorcanbemodelled asanactuatorfault.Moreprecisely,wehave f a =[ ; 0 ; 0 ; 0] T .Thewholesystembecomes: x = Ax + B ( u + f a )+ Ed y = Cx (4{25) WefollowtheproceduredescribedearliertodesignaUIO.First, H = E [( CE ) T CE ] 1 ( CE ) T = 264 10 375 (4{26) and TB =( I HC ) B = 264 0000 1 R 2 C w 000 375 (4{27) Notethatthefaulthappenedtobeattherstinput,sothat TBf a = 264 0 R 2 C w 375 (4{28) 54

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isnonzero,whichmeansthefaultwillentertheerrordynamics,and thestandardUIOcan beapplied.Allthedesignmatrices, F;T;K;H ,canbecomputedbythestandard procedureinsection 4.1 TotesttheUIOwedesigned,weapplyittoPughHalldatasetE.Wepic kthetime periodfrom9pmto11pm,duringwhichthesupplyairrowratewaskep tclosetoa constant.Thedoorwasopenedat10:08pm.TheresultisgiveninFigu re 4-3 9pm 9:30pm 10pm 10:30pm 11pm 67 68 69 70 71 Temp (F) 9pm 9:30pm 10pm 10:30pm 11pm -1 0 1 2 TimeResidual Estimated Measured Figure4-3.Opendoordetection Theverticallineinthegureindicatesthetimewhendoorwasopened .Beforethat timepoint,theobserverestimationcatchesrealtemperaturewe ll,andtheresidualisclose tozero.Afterthedoorwasopened,themodelchangedduetoth efault,theobserverno longercatchestherealtemperature,whichcausestheresidual tojumpup. Inthedoorstatusdetectioncase,standardUIOcanbeapplieddir ectly.Theresidual showsaclearchangewhenthedoorisopened,whichindicatetheimple mentationofUIO todetectthedoorstatusissuccessful. 55

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4.4Summary Wediscussedthedesignofunknowninputobserver,whichestimate sstateswiththe presenceofunknowninputs.Thenaresidualisgeneratetodetec tactuatorfaultsand sensorsfault.AnexampleforimplementationofUIOinfaultdiagnosis ispresented,where itcannotbeapplieddirectlyandtuningisrequired.Moreimportantly, weappliedthis methodtodetectwhetherthedoorofaroomisopen.Theexperime ntaldatacollected fromPughHallshowstheattemptissuccessful. 56

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CHAPTER5 CONCLUSIONANDFUTUREWORK Inthisthesis,werstdevelopedahighordermodel(fullscalemode l)withelectrical analogy.Thenweproposedafewlowordermodels,startingwiththe lowestorderpossible (rstordermodel).Comparisonshowsthatsecondordermodelis agoodchoiceformodel structure.Higherordermodelsdonothavesignicantimprovemen t.Afterthemodel structureischosen,weusedatafromPughHallonUniversityofFlo ridacampusto calibrateandvalidatethemodel.Itisfoundthatthedatasetsmust beselectedvery carefully.Normalclosedloopoperationdatamayleadtogrosslywro ngparameter estimation.Speciallydesignedforcedresponseexperimentsarere quired.Wealsousean additionalresistortomodeltheeectofopendoor,whichprovide sgoodpredictioninthe dooropenscenario.Withthemodelwedeveloped,unknowninputob serverissuccessfully implementedtodetecttheopendoor. Somedirectionsforfutureworkinclude:developmodeloflargerzo newithmultiple rooms;applyMPCtominimizeenergyconsumption;transformthepa rameterestimation problemintoaconvexoptimizationproblem,sothatuniquesolutionisg uaranteed;study theidentiabilityoftheproblem,establishcriterionforcalibrationda ta,sothatenough informationisprovidedinthedatatondthecorrectparameters. 57

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REFERENCES [1]ASHRAE.TheASHRAEhandbookfundamentals(SIEdition),2005 [2]PederBacherandHenrikMadsen.Identifyingsuitablemodelsfor theheatdynamics ofbuildings. EnergyandBuildings ,43(7):1511{1522,July2011. [3]M.Bartak,I.Beausoleil-Morrison,J.A.Clarke,andetal.Integr atingcfdandbuilding simulation. BuildingandEnvironment ,37,2002. [4]SBengea,VAdetola,KKang,MJLiba,DVrabie,RBitmead,andSNa rayanan. Parameterestimationofabuildingsystemmodelandimpactofestima tionerroron closed-loopperformance.In IEEEConferenceonDecisionandControl ,December 2011. [5]Carriercorp.Hourlyanalysisprogram(HAP).[6]VChandanandAGAlleyne.Optimalcontrolarchitectureselectio nforthermal controlofbuildings.In AmericanControlConference(ACC) ,July2011. [7]J.ChenandR.J.Patton. Robustmodel-basedfaultdiagnosisfordynamicsystems KluwerAcademicPublishers,1999. [8]TYChenandAKAthienitis.Investigationofpracticalissuesinbuild ingthermal parameterestimation. BuildingandEnvironment ,38(8):1027{1038,June2003. [9]D.E.Claridge,M.Liu,andW.D.Turner.Wholebuildingdiagnostics,19 99.Available from: http://poet.lbl.gov/diagworkshop/proceedings/clarid ge.pdf [10]FDeque,FOllivier,andAPoblador.Greyboxesusedtorepresen tbuildingswitha minimumnumberofgeometricandthermalparameters. EnergyandBuildings 31(1):29{35,jan2000. [11]UnitedStatesGovernmentEnergyUseAdministration.Electric ityexplained-useof electricity,2010.Availablefrom: http://www.eia.gov/energyexplained/index.cfm?page=e lectricity_use [12]G.Fraisse,C.Viardot,O.Lafabrie,andG.Achard.Developme ntofasimpliedand accuratebuildingmodelbasedonelectricalanalogy. [13]M.M.GoudaandS.DanaherC.P.Underwood.Low-ordermode lforthesimulation ofabuildinganditsheatingsystem. BuildingServicesEnergyResearchTechnology 21:199{208,Aug2000. [14]MMGouda,SDanaher,andCPUnderwood.Buildingthermalmode lreductionusing nonlinearconstrainedoptimization. BuildingandEnvironment ,37:1255{1265,2002. [15]SiddharthGoyal,HerbertIngley,andPrabirBarooah.Zone-le velcontrolalgorithms basedonoccupancyinformationforenergyecientbuildings.In AmericanControl Conference ,June2012.accepted. [16]F.Haghighat,Y.Lin,andA.C.Megri.Developmentandvalidationo fazonalmodelpoma. BuildingandEnvironment ,36,2001. 58

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[17]Z.LiaoandA.L.Dexter.Asimpliedphysicalmodelforestimating theaverageair temperatureinmulti-zoneheatingsystems. BuildingandEnvironment ,39,2004. [18]YMa,GAnderson,andFBorrelli.Adistributedpredictivecontro lapproachto buildingtemperatureregulation.In AmericanControlConference(ACC) ,July2011. [19]Y.Ma,A.Kelman,A.Daly,andF.Borrelli.Predictivecontrolfor energyecient buildingswiththermalstorage:Modeling,stimulation,andexperimen ts. Control Systems,IEEE ,32(1):44{64,feb.2012. [20]HenrikMadsenandJ.Hoist.Estimationofcontinuous-timemode lsfortheheat dynamicsofabuildings. EnergyandBuildings ,22:67{79,1995. [21]E.H.Mathews,P.G.Richards,andC.Lombard.Arst-orderth ermalmodelfor buildingdesign. EnergyandBuildings ,21,1994. [22]EHMathews,PGRousseau,PGRichards,andCLombard.Aproc eduretoestimate theeectiveheatstoragecapabilityofabuilding. EnergyandBuildings ,26:179{188, 1991. [23]MMorari,FOldewurtel,andDSturzenegger.ImportanceofOc cupancyInformation forBuildingClimateControl. AppliedEnergy ,January2012.Availablefrom: http://control.ee.ethz.ch/index.cgi?page=publicatio ns;action=details;id=3984 [24]PDMorosan,RBourdais,DDumur,andJBuisson.Distributedmo delpredictive controlbasedonbenders'decompositionappliedtomultisourcemu ltizonebuilding temperatureregulation.In 49thIEEEConferenceonDecisionandControl(CDC) Dec2010. [25]TXNghiemandGJPappas.Receding-horizonsupervisorycontr olofgreenbuildings. In AmericanControlConference(ACC) ,July2011. [26]TRNielsen.Simpletooltoevaluateenergydemandandindoorenv ironmentinthe earlystagesofbuildingdesign. SolarEnergy ,78:73{83,January2005. [27]F.Oldewurtel,D.Gyalistras,M.Gwerder,C.N.Jones,A.Parisio ,V.Stauch, B.Lehmann,andM.Morari.IncreasingEnergyEciencyinBuildingClim ate ControlusingWeatherForecastsandModelPredictiveControl.I n Clima-RHEVA WorldCongress ,Antalya,Turkey,May2010.Availablefrom: http://control.ee.ethz.ch/index.cgi?page=publicatio ns;action=details;id=3545 [28]IanB.Rhodes.Atutorialintroductiontoestimationandlterin g. IEEETransaction onAutomaticControl ,AC-16(6),1971. [29]GangTao. AdaptiveControlDesignandAnalysis .JohnWiley&Sons,2003. [30]PetervanOverscheeandB.L.Moor. SubspaceIdenticationforLinearSystems: Theory-Implementation-Applications .Springer,1996. [31]V.Venkatasubramanian,R.Rengaswamy,K.Yin,andS.N.Kavu ri.Areviwof processfaultdetectionanddiagnosis,parti:Quantitativemodel-b asedmethods. ComputersandChemicalEngineering ,27,2003. 59

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BIOGRAPHICALSKETCH YashenLinwasbornin1987inBeijing,China.HereceivedhisBacheloro fScience degreeinautomationin2009fromUniversityofScienceandTechnolo gyBeijing.Hethen joinedtheDistributedControlGroupatUniversityofFloridatopur suehisdoctoraldegree undertheadvisementofDr.PrabirBarooah.Hisresearchinteres tliesintheeldof modelingandintelligentcontrolofheating,ventilation,andaircondit ioning(HVAC) systeminbuildings. 61