Calibrating historic building energy models to hourly indoor air and surface temperatures: Methodology and case study

ContentslistsavailableatScienceDirect

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

Calibrating

historic

building

energy

models

to

hourly

indoor

air

and

surface

temperatures:

Methodology

and

case

study

Francesca

Roberti

,

Ulrich

Filippi

Oberegger

_,

_Andrea

_Gasparella

a

r

t

i

c

l

e

i

n

f

o

Received11June2015

Receivedinrevisedform8September2015

Accepted9September2015

Availableonline10September2015

Keywords: Historicbuilding Casestudy Simulation Monitoring Calibration Sensitivityanalysis

Particleswarmoptimization

EnergyPlus

a

b

s

t

r

a

c

t

Uncalibratedbuildingenergymodels,aswellasmodelscalibratedonlyonasingleperformance indica-torsuchasenergyconsumptionorindoortemperature,canbesignificantlyunreliableregardingmodel parametersandotherperformanceindicators.Theriskofobtainingacalibratedmodelwhoseparameters arefarfromtheactualvaluesisparticularlyhighinhistoricbuildingsbecauseoftheincreaseduncertainty aboutthebuildingconstruction.Inthispaper,weproposeacalibrationmethodologyaimedatreducing thisriskandapplyitonamedievalbuilding.ThebuildingwasmodeledinEnergyPlusbasedonanenergy audit.Asensitivityanalysiswasperformedtoidentifysignificantparametersaffectingtheerrorsbetween simulatedandmonitoredindoorairtemperatures.Themodelwascalibratedonthehourlyindoorair temperaturesinsummerbyminimizingtherootmeansquareerroraveragedoverthebuildingusinga particleswarmoptimizationalgorithm.Asecondcalibrationwasperformedbyvaryingtheparameters ofarepresentativeroom.Bycomparingtheresultsfromthesetwocalibrations,weobtained indica-tionsabouttheaccuracyofthemodelparameters.Finally,themodelwasvalidatedonhourlyindoor airandsurfacetemperaturesinwinterwheretemperaturerootmeansquareerrorsrangedfrom0.4to 0.8K.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction 1.1. Thecontext

Historic buildings represent the cultural identity of our countries,characterizingmanycitiesandgivingcontinuitywith thepast.Energyretrofittingisaneffectivestrategytopreservethis heritage,reducingoperationcostsandimprovingcomfort.Because eachhistoricbuildingisunique,designershavetodevelop spe-cificretrofitsolutionscompatiblewithconservation,takinginto accountrenovationcosts.Energysimulationmodelscanhelpin comparingalternativeretrofitinterventions,buttheymightlead towrongconclusionsifnotcarefullycalibrated.Thechallengeis tobuildamodelthatnotonlyfitsmonitoringdatabutalso repre-sentstherealbuilding,allowingevaluationofalternativeretrofits in a reliable fashion. Thisis particularly important when deal-ingwithhistoricbuildings,aschoosinganinappropriateretrofit action could cause degradation of valuable parts of the build-ingor represent a significant wasteof money. The aim of this

∗Correspondingauthor.Tel.:+390471055644;fax:+390471055699.

E-mailaddress:francesca.roberti@eurac.edu(F.Roberti).

workistopresentamethodologythattacklesthis challengeby performing semi-automatic calibration as the first step in the designofahistoric buildingretrofit.We appliedthis methodol-ogyonavacantmedievalbuildinginnorthernItaly,calibratingthe modelwithrespecttomonitoredindoorairtemperatures.Main issuesrelatedtomodelcomplexityanduncertaintyabouttheinput datawereconsideredandaddressed.First,weperformeda sensitiv-ityanalysisonaninitialmodel,decidingonparameters,parameter ranges,anddesignofexperiment.Second,wecalibratedthemodel, choosingmodeloutputstobecomparedwithmeasureddataand goodness-of-fitindicators.Third,weselectedthemodelwiththe bestgoodness-of-fit.Finally,wevalidatedthemodelanalyzingthe errorsusingadifferentperiodoftheyearfromthecalibration. Fur-thermore,wecalculatedtheerrors ofthesurfacetemperatures, amonitoredparameternotinvolvedinthecalibration.Particular attentionwaspaidtotheenvelopeproperties.Theymayberelated specificallytotheuncertaintyinbuildinggeometry,wall composi-tion(forexample,stone,wood,andmortar)andthickness,andglass propertiesofthewindows.Inhistoricbuildings,envelope proper-tiesoftenvaryconsiderablyfromplacetoplace.Componentscanbe damaged,partiallydestroyedordirty.Therefore,historicbuilding energymodelshaveusuallyeitherimportantlimitationsorhigh complexity,requiringnumerousmeasurementsforcalibration. http://dx.doi.org/10.1016/j.enbuild.2015.09.010

0378-7788/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense

1.2. Reviewofpreviouswork

Inrecentyears,manyauthorshavedemonstratedthe impor-tanceofcalibrating buildingsimulationmodels,inparticularto predicttheeffects ofenergy conservationmeasures.Calibration techniquesincludeiterativerevisionsofaninitialmodel,driven by identified discrepancies, which are corrected based on evi-denceandexpert’sknowledge[1].Calibrationmethodologieshave beenformalizedinthefollowingfivesteps:(a)preparinga pre-liminarysimulationinputfile;(b)identifyingthemostinfluential modelparameters;(c)coarsesearchusingMonte Carlo simula-tion;(d)guidedsearch;and(e)usingasmallnumberofplausible calibrated models to determine the prediction uncertainty [2]. Bayesianapproacheshavebeensuggestedtoquantify uncertain-tiesassociatedwithmodelparametersandretrofitinterventions [3].Rafteryetal.[1]calibratedadetailedEnergyPlusmodelofanew officebuildingconsistingofover100thermalzones.Theauthors graduallyreduced the coefficientof variation ofthe rootmean squareerrorbetweenpredictedand actualenergy consumption basedonasourcehierarchyofinformationorderedbydecreasing presumedaccuracy.Sourceshigherinthehierarchyhavea prior-ityoversourceslowerdown,withloggedmeasurementsatthetop andstandardsandguidelinesatthebottom.Followingthis method-ology, uncertaintiesare not investigated.In contrast,Heoet al. [3]quantifiedtheuncertaintyintheretrofitdecision-making pro-cessbyapplyingBayesiancalibrationtoanofficebuildingmodel. BayesiancalibrationrequiresassigningpriorProbabilityDensity Functions(PDFs)tomodelparametersand computingposterior PDFsfromresults.Thecomputationaleffortrequiredtoquantify uncertaintyisbalancedbyusingquasi-steady-statemodelsinstead of transient models,especially when theobjective is to evalu-atemacro-levelretrofitmeasuresbasedonmonetarysavings.All papersunderlinetheriskofworkingwithacalibratedmodelwhose parametersoroutputsdonotcorrespondtoreality. Recommenda-tionstoreducethisriskare:(a)usinghourlymeasureddataasthe targetfunctionforthecalibration;(b)tighteningtheacceptance criteria;(c)reducingtheamplitudeoftheparameterspacethrough visualinspectionandwalk-throughaudits;(d)calibratingagainst morethanoneoutcomevariable;(e)combiningmoreacceptance criteriatoasinglegoodness-of-fitindicator;and(f)usingasmall numberofcalibratedmodelsratherthanonesinglemodeltoobtain robustpredictionsoftheenergyanddemandreductions.

Onlyafewpapersfocusonhistoricbuildingcalibration.Pernetti etal.[4]calibratedthemodelofa19thcenturymanufacturing facil-ityinItalywithrespecttoindoorairandsurfacetemperaturesusing afullyfactorialcombinationoftheweatherdata,airchangerate andenvelopeproperties.Foreachfactor,twotofourlevelswere selectedaccordingtomeasurementsandstandards,foratotalof 24simulations.Afterthefirstcalibration,asensitivityanalysiswas performedtoidentifyparametersforfurthermodelimprovement. Resultsdemonstratedtheindoortemperaturemitigationeffectby thethermalmassandtheimportanceofreliableweatherdata. Car-dinaleetal.[5]performedanenergyandcomfortassessmentof twovernacularbuildingdistrictsatworldheritagesitesinsouthern Italythroughin-situandlabmeasurementanddynamicsimulation. Themodelparametersweresetaccordingtomeasurements.No explicitcalibrationwasused.Asameansofvalidation,measured andsimulatedindoorairtemperatureswerecompared. Ascione etal.[6] manuallycalibratedanEnergyPlus modelofa historic buildinginsouthernItalytomonthlyenergybills.

Asopposedtomanualcalibration,wefoundonlyacoupleof studies concerned with semi-automatic calibration of historic (or old) buildings. Caucheteux et al. [7] calibrated a transient energymodelofa16thcenturymanorhouseinwesternFrance considering the daily gas consumption monitored during two weeksinDecember.Theauthorsperformedasensitivityanalysis

to identify seven influential model parameters and applied a solvertodeterminethevaluesfortheidentifiedparametersthat minimize the coefficient of variation of the root mean square error.O’NeillandEisenhower[8]performedasensitivityanalysis onatransientenergymodelofanofficebuildingdatingbackto 1901andrefinedtheinfluentialmodelparametersbyapplyingan optimizationalgorithmtoanapproximationmodel.

2. Method

The focus of our workconsisted in the calibrationof a XIII centurybuildingmodel inEnergyPlus7.2,performingtwo opti-mizationswiththeParticleSwarmOptimizationalgorithm(PSO) [9]ondatamonitoredinsummer.Inthefirstcalibration,building propertieswerevarieduniformlyforallzones.Inthesecond cali-bration,wekepttheparametersfromthefirstcalibrationexceptfor asinglereferenceroom.Thedifferencesbetweenthetwo optimiza-tionsgaveindicationsaboutthetrustworthinessoftheoptimized parameters. As furthercontrol, we validated themodel on the airtemperatureinwinterandonthemonitoredtemperaturesof threeinternalsurfacesoftheexteriorwall.Summarizingthewhole methodology,weperformedsixsteps:(1)energydiagnosisofthe building;(2)creationofaninitialmodel(IM)usingthe measure-mentresultsfromtheenergydiagnosisasinputs;(3)definition ofthemostinfluencingparametersalongwithuncertaintyranges through a sensitivity analysis based on the elementary effects method;(4)modelcalibrationusingastargetaveragedindoorair temperaturesmonitoredinsummerweightedontherooms’ vol-umes;(5)modelvalidationcomparingsimulatedandmonitored indoorairtemperaturesinwinter;(6)modelvalidation compar-ingsimulatedandmonitoredinsidesurfacetemperaturesofthe exteriorwallinsummer.

This general calibrationmethodology helps define envelope parametersofa historicbuildingsimulationmodel.Steps1and 2arecrucialasstartingpointfor afairlyaccurateinitialmodel. Step3 isusefultounderstandthemostinfluencingparameters onthecalibrationand isfoundationaltothecalibration,Step4. Steps5and6arevalidationstepsthatcompletethecalibration process.Step5isnecessarytocheckthemodelparametersduring aperiodnotincludedinthecalibration,duringwhichthemodel couldbehavedifferentlythantheactualbuildingbecauseof differ-entclimateconditions.Step6givesindicationsabouttheaccuracy oftheexternalwallmaterialproperties,whichhaveahighimpact onthecalibrationerrors(seetheresultsfromthesensitivity anal-ysis).

3. Casestudy

TheWaaghaus(weighhouse)islocatedinthehistoriccenterof BolzanoinnorthernItaly(Fig.1).Constructedinthe13thcenturyin Romanesquestyle,itwasrebuiltinthe17thand18thcentury.Until 1780itwastheofficialseatofthecityscales.Thebuildinghasthree floors,anatticandabasement,foratotalvolumeof2000m3_.Except fortheroof,theenvelopeismadeofstone.Thelightweightroof iscomposedbytimberbeamsandbadlydamagedmineralwool insulation.Alloriginalwindowswerereplacedbycoupledwindows duringthe1950s/60s.Thebuildinghasbeenvacantsincethe1990s. Afterathoroughstructuralandenergyrenovation,itisgoingtobe transformedintoamuseumofphotography.

3.1. Energyaudit

3.1.1. Thermalconductance

Wemeasuredthethermalconductanceoftheexternalwalls atarepresentativespotonthenorthsideofthebuildingwitha

Fig.1. Themain fac¸ade of the“Waaghaus” located in thehistoriccenter of

Bolzano©_{FlorianBerger/EURAC.}

heatflowmeter,usingtheaveragemethodasperISO9869:1994 [10].Unfortunately,wecouldnotmeasureitatmorespotsbecause of time and sunexposure constraints. We took two measure-ments,thefirst for 4 days obtaininga thermal conductance of 1.355W/m2_{Kandthesecondfor5days,obtaining1.375W/m}2_K. Thestorageeffectofthewallscontributedlessthanthemaximum toleranceof5%allowedbythestandard.

3.1.2. Airinfiltration

We measuredtheinfiltration rateswith a blowerdoor test. Wedidnotsucceedinmaintainingapressuredifferenceof50Pa acrossthewholebuildingenvelopeassuggestedbytheUNIEN 13289:2013 [11] due toinsufficient air tightness, therefore we repeatedthetestatroomlevelwherewecouldreachthispressure difference.Tracergastestsshowedthattheairflowwas predomi-nantlynearthewindows.

3.1.3. Indoortemperatures

In2012we installeda monitoringsystemincludinginternal airandsurfacetemperaturesensorsforeachfloorandforthree fac¸ades.Datawereavailablefrom8thto25thJanuary2012and from1stMayto26thOctober2012.Themaximummeasurement errorofthesensorsasperdatasheetwas0.2◦Cfortherangeof encounteredtemperatures.

3.1.4. Weatherdata

Outdoortemperatureandhumidityweremeasuredonthenorth sideoftherooftop.Solarradiationwastakenfromsatellitedata [19].Forwindspeed,weusedaconstantaveragevalueof1m/s dur-ingsummerandof0.2m/sduringwinterbecauseon-sitemeasured datawasnotavailable.Thesearetheaveragevaluesinthesummer andwinterperiodascalculatedfromtheTypicalMeteorological YearforBolzano.

3.2. Initialmodel(IM)

We modeled theWaaghaus in EnergyPlus v7.2, dividingthe buildinginto29homogeneousthermalzones.Wechose Energy-Plusbecauseit is anopensourcedynamic simulation software thatwasvalidatedaccordingtoANSI/ASHRAEStandard140-2011 [12]andcomparedwithTRNSYS[13].Mostzonescontainedone ormoreairand surfacetemperaturesensors.A measured aver-age of 1.37W/(m2_{K) was used as thermal conductance of the} externalwalls.Tobalancebenefitandcost,wemadesimplifying assumptions regardinggeometry and thermal properties ofthe

envelope.Althoughexteriorwalls,partitionwallsandroof insu-lationhadvariablethicknessesalongtheperimeterandacrossthe heightofthebuilding,weredamagedinplaces,andconsistedof materialswithuncertainproperties,weusedtheaveragethickness andthethermalpropertiesofthepredominantmaterialforeachof thesecomponents.Thewindowsandwindowframeswerevery dirty,crackedordamagedinplaces.Thewindowpaneproperties wereunknown.Wemodeledthewindowsasdirtybutintactand estimatedthewindowpaneparametersfromwindowswith sim-ilarpropertiestakenfromtechnicalliterature.Because,asshown bythetracergastest,theinfiltrationappearedtobeconcentrated nearthewindows,weaveragedtheairflowfromtheblowerdoor testsaccordingtothenumberofwindowsintheroom,obtaining 0.029m3_{/sforasinglewindow.Thisvaluewasthenassignedto} eachwindowintherestofthebuilding.Weusedtheair infiltra-tionmodelproposedbyCoblenzandAchenbach[14]implemented inEnergyPlus:

I=DI×(CTC+TTC×|TZ−TODB|)

Thevariables intheformula denote:DesignInfiltration(DI), Constant Term Coefficient (CTC), Temperature Term Coefficient (TTC),ZoneairTemperature(TZ),andOutdoorDryBulbair Tem-perature(TODB).Thisequationholdsforunoccupiedhouseswhose outsideopeningsareclosed,asinthecaseoftheWaaghaus.Itis asimplemodelcomparedtomodelsbasedonEffectiveLeakage Area(ELA)orComputationalFluidDynamics(CFD).Nevertheless, wedecidedtousethissimplemodelbecauseitgave much bet-ter results in our experiments than the ELA model. Moreover, measurementsofairtightnessandflowratewerenotsufficiently accuratetocreatea reasonableCFDmodelbecauseofthe diffi-cultiesin reachingapressure differenceof50Pa. WesettheDI at4Papressure differencebasedontheair tightness measure-ments,assuminganindependenceofthetemperaturedifference, correspondingto a CTC and TTC of one and zero, respectively. Theseparameterswerethenvariedduringthecalibration.Wind dependence was also neglected as we had no reliable wind speed data. The time step during the simulation was 10min. Table1 summarizes thedifficulties faced during modeling and theparametersusedfor theinitialmodel (IM)along withtheir sources.

3.3. Sensitivityanalysis

Theelementaryeffectsmethod[15]wasappliedtotheIMin ordertoidentifytheinfluence ofthemodel parameters onthe errorsbetweensimulatedandmonitoredindoorairtemperatures insummer2012.Since themethodrequiresrepresentingthese errorsbyasinglevalue,wefirstcalculatedtheabsolutevaluesofthe errorsforeachthermalzoneandthencomputedthespatialaverage weightedbythezonevolumes.Afterwards,wecalculatedthemean absoluteerror(MAE)andtherootmeansquareerror(RMSE)ofthe resultingtimeseriesandusedthemastargetfunctions.Weselected 44modelparametersforscreeninganddefinedrangesaccording topresumeduncertainty.Table1listsallscreenedmodel parame-tersandtheirranges.Rangesweretakenfromtechnicalliterature, normsanddatasheets.

Foreach screenedparameter,theelementaryeffectsmethod computestheaverageinfluenceoftheparameterontheerrors.An elementaryeffectisachangeofthetarget(theerrors)causedbya changeinasinglemodelparameterwhilekeepingallothermodel parametersfixed.Ingeneral,theelementaryeffectofaparameter ontheerrorsdependson:(a)therangeofvaluestheparameter cantake;(b)thebasevalueoftheparameter;(c)themagnitude anddirectionofchange(increaseordecrease)oftheparameter; and (d)thevalues ofthe otherparameters. Therefore,in order

Table1

Modelingdifficulties,parametersusedfortheinitialmodelandparameterrangesusedforthesensitivityanalysis.

Component Modeling

challenge

Parameter Sourceforinitial

modelvalue Initialmodel value Rangefor sensitivityanalysis Exterior wall Varyingfabric andthickness

Extwallconductivity[W/(mK)] Measuredatnorthfac¸ade 0.89 0.75–1.1

Extwallthickness[m] Measuredatnorthfac¸ade 0.65 0.4–0.8

Extwalldensity[kg/m3_{] Measured}* _{2450 1300–2500}

Extwallspecificheat[J/(kgK)] Measured* _{700 600–1000}

Roof insulation

Varyingthickness,

heavilydamaged

Roofmineralwoolthickness[m] Measured 0.03 0.02–0.04

Roofmineralwoolconductivity[W/(mK)] Measured 0.3 0.03–1

Roofmineralwooldensity[kg/m3_{] UNI10351:1994 30 12–100}

Roofmineralwoolspecificheat[J/(kgK)] Datasheets 800 700–1000

Partition wall

Varyingfabricand

thickness

Partitionwallconductivity[W/(mK)] Measured* _{0.89 0.75–1.30}

Partitionwallthickness[m] Averagemeasure 0.2 0.15–0.4

Partitionwalldensity[kg/m3_{] Measured}* _{2450 1300–2500}

Partitionwallspecificheat[J/(kgK)] Measured* _{700 600–1200}

Envelope Varyingairleakage Airinfiltrationofeachzone[m3_{/s] Measured 27values 30%deviationfrom}

measuredvalues

Airinfiltrationtemperaturetermcoefficient(TTC) DefaultvalueinEnergyPlus 0 0–0.04

Airinfiltrationconstanttermcoefficient(CTC) DefaultvalueinEnergyPlus 1 0.50–1

Windows Damagedanddirty

panesandframes

Glassdirt-correctionfactor Guessedfromobservation 0.6 0.4–1

Glasssolartransmittance Typicalclear4mmfloatglass 0.6 0.4–0.95

Windowframeconductance[W/(m2_{K)] WINDOWLBLlibrary(ASHRAE) 2.3 2.0–3.0}

Windowdividerconductance[W/(m2_{K)] WINDOWLBLlibrary(ASHRAE) 2.3 2.0–4.0}

*_{StonesampleanalyzedbyDresdenUniversityofTechnology.}

to obtainrobust sensitivity measures, more elementary effects perparameterhavetobecomputed,varyingdirectionsofchange andbasevalues.Also, onehastofinda compromisebetweena complete,detailedspectrumofinfluencesforallparametersanda limitednumberofsimulationruns.Asthetotalnumberofpossible elementary effects associated with a single parameter grows exponentiallywiththenumberofparameters,inallmeaningful applicationsoftheelementaryeffectsmethodonlyanextremely smallpartofthefullsetofelementaryeffectscanbecomputed.Itis thereforecrucialtochoosethecombinationstoconsidercarefully, withtheobjectiveofuniformlycoveringtheparameterspace.

Toreachtheseobjectives,eachparameterrangewasdivided intofourequallyspacedlevels,fromtheminimumtothemaximum value.Weselectedtheparameterstobevariedinrandomorder. Alsothebasevaluesanddirectionsofchangeoftheparameters werechosenrandomly.Thebasevaluesamplingwasperformed undertheassumptionofuniformprobabilitydistributions. Start-ingfromthebasevalue,wealwayschangedaparameterbytwo thirdsofitsrange,therebyensuringthateachelementaryeffect wasselectedwithequalprobability[15].Westartedbycomputing ten elementary effects per parameter. To compute an elemen-taryeffect,twosimulationshave tobeperformedthat differin exactlyone parametervalue. Therefore,880simulations would beneeded to obtainten elementary effects for each of the 44 screened parameters. We created a more economicalsampling plan thatachieves this goal with450simulationsby usingthe sameparametervaluecombinationforthecomputationofmore thanoneelementaryeffect[15].However,theincreasedeconomy comesatthecostofareducedstochasticindependencebetween theelementaryeffects.Tobettercoverthefullrangeofparameter valuecombinationsand,hopefully,elementaryeffects,we gener-atedmorethan200,000combinationsatnegligiblecomputational cost.Forthesimulationsweselectedthe450combinationswith maximumspread.Thespreadwasdefinedandcomputedasin Cam-polongoetal.[16].Foreachparameter,wecomputedtheaverage oftheabsolutevaluesofitselementaryeffects(the“mean abso-luteeffect”).Thisisanindicatoroftheparameter’sinfluenceon theoutputandcanbeused torank theparametersin orderof importance.

To check whether findings were robust to sampling error, wecomputed20additionalelementaryeffectsforeachscreened parameter, corresponding to 900 simulations. Doubling the

numberofsimulationsmadethesensitivitymeasureschangeby lessthan5%oftheirmaximumvalueforeachparameter.

4. Modelcalibrationandvalidation 4.1. Calibration

Wecalibratedtheparametersthatwererelevantaccordingto thesensitivityanalysis,droppingtheroofmineralwoolthickness, conductivity,densityandspecificheat,andthethermal conduc-tanceoftheframeand dividerofthewindowsbecauseoftheir negligibleimportance(seeFig.2).However,wekeptallinfiltration parameters,becausetheirapparentimportanceismainlycaused bythepresenceorabsenceofsensorsinazone.Furthermore,as glasspropertiesshowedhighinfluence,wedecidedtoadd win-dowglassconductivityandwindowsolarreflectance.Theranges weredefinedaccordingtotheuncertaintiesrelatedto measure-mentandbuildingfabric.Startingfromtheinitialmodel(IM),we createdacalibratedmodel(CM)withrespecttotheindoorair tem-peratureaveragedonthevolumeandmeasuredfrom1stMay2012 to26thOctober2012.WecalibratedbyminimizingtheRMSE,using theparticleswarmoptimizationalgorithm[9]implementedinthe softwareGenOpt[17].Table2reportsthecalibrationparameters aswellastheirranges.Toidentifypotentiallyinaccurate parame-ters,weperformedanadditionalwholebuildingcalibration(CM+) where we fixedall parameters obtainedin thefirst calibration exceptforthoserelatedtoonereferenceroomonthefirstfloor. Whenthevaluesassociatedwithaparameterweresimilarinboth calibrations,thisindicatedthattheparametervalueidentifiedfor thewholebuildingwasalsovalidforthisroomandthereforefor mostroomsofthebuilding.

4.2. Validation

WevalidatedtheCMbysimulatingtheperiodfrom8thto25th January 2012and calculating theRMSE of the indoorair tem-peratures.Additionally,wecomparedthreesurfacetemperatures locatedonthefirstandsecondfloortoreducetheriskofusinga modelthatissupposedlycalibratedbutwhoseinputparameters donotcorrespondtotherealbuilding.

Fig.2. MeanabsoluteeffectsontheMAEoftheaverageindoorairtemperature.

Table2

Calibratedvaluesforthetwooptimizedmodels.

Component Parameter IM MIN MAX CM CM+ IM/CM(%) CM/CM+

Exterior wall

Extwallconductivity[W/(mK)] 0.89 0.75 1.10 0.80 0.80 −10 0

Extwallthickness[m] 0.65 0.40 0.80 0.65 0.80 0 19

Extwalldensity[kg/m3_{] 2450 1300 2500 1300 1600 −47 19}

Extwallspecificheat[J/(kgK)] 700 600 1000 600 950 −15 37

Partition wall

Partitionwallconductivity[W/(mK)] 0.89 0.75 1.30 1.16 1.30 31 11

Partitionwallthickness[m] 0.20 0.15 0.40 0.16 0.30 −20 47

Partitionwalldensity[kg/m3_{] 2450 1300 2500 1400 1300 −43 −8}

Partitionwallspecificheat[J/(kgK)] 700 600 1200 650 600 −7 −8

Envelope Airinfiltrationtemperaturetermcoefficient(TTC) 0 0 0.04 0.02 0.03 0 33

Airinfiltrationconstanttermcoefficient(CTC) 1 0.50 1 0.51 0.91 −49 44

Windows Glassdirt-correctionfactor 1 0.40 1 0.40 0.40 −60 0

Glasssolartransmittance 0.6 0.40 0.95 0.40 0.44 −33 9

5. Results

5.1. Sensitivityanalysis

Fig.2showsthemeanabsoluteeffectofeachmodelparameter onthemeanabsoluteerror(MAE)calculatedasperSection3.3. TheparameterthatmostreducedtheMAEwasthethicknessofthe externalwalls,followedbytheCTCintheairinfiltrationmodeland thesolartransmittanceofthewindows.

5.2. Calibrationandvalidation

Table2 reports theparameters for thetwo calibrated mod-els CM and CM+. Table 3 shows the RMSE and the MAE of the indoor air temperatures over the calibration period

(summer2012) for theinitialmodel (IM),thecalibratedmodel (CM), and the CM where the parameters for a representative thermal zonewerefurtheradjusted(CM+). Thecolumnheaded “CMVP”showstheRMSEandtheMAEoftheindoorair temper-aturesoverthevalidation period(January 2012).Thelast three columnsofTable3showtheRMSEandtheMAEofthreeexternal wallinteriorsurfacetemperatures(STF2NN;STF2NS;STF1NE; ST:surfacetemperature,F2N:secondfloornorthside, N:north faced).

Fig.3showsacarpetplotwiththeRMSEoftheCMasafunction ofthehourofthedayandmonth.

Fig.4reportsthemonitoredandsimulatedair temperatures averagedoverthewholebuildingduringtwoweeksinJune2012.

Fig.5showsthedifferencesbetweenthesimulatedand moni-toredsurfacetemperaturesduringaweekinJuly2012.

Table3

RMSEandMAEfortheinitialmodel(IM),calibratedmodel(CM),calibratedmodelwheretheparametersoftherepresentativezonewerefurtheradjusted(CM+),andforthe

CMoverthevalidationperiod(CMVP).AllreportedvaluesrepresenttemperatureerrorsexpressedinKelvin.

IM CM CM+ CMVP STF2NN STF2NS(brokenwindow) STF1NE

RMSE 0.96 0.66 0.66 0.62 0.48 0.80 0.49

Fig.3. CarpetplotoftheRMSEdependingonthehourofthedayandmonth.

Fig.4.Simulatedandmonitoredairtemperaturesaveragedoverthewholebuilding.Theshadedarearepresentsameasurementuncertaintyof±0.2◦_C.

Fig.5.SimulatedandmonitoredsurfacetemperatureSTF1NE(firstfloor,northernsideofthebuilding,eastexposedwall).Theshadedarearepresentsameasurement uncertaintyof±0.2◦_C.

6. Discussion

6.1. Sensitivityanalysis

From the sensitivity analysis, we understood that the most influentialfactorsontheairtemperatureerrors werethickness andmaterial propertiesof theexteriorwall, airinfiltration (DI, CTC,andTTC),andwindowproperties.Somewhatunexpected,the windowdirtcorrectionfactorinfluencedtheMAEasmuchasthe wallmaterialproperties.Thickness,thermalcapacity,andthermal transmittance of the envelope acted on time shiftand weekly peaksofthesimulatedtemperatures. Instead,infiltrationswere mainlyresponsibleforthehourlyvariationsanddailypeaks.Their influencevariedfromzonetozone.Thisdoesnotnecessarilymean thatinfiltrationwasmoreimportantinsomezonescomparedto others,becauseintheroomswhere theindoorairtemperature wasnotmonitoredtheinfiltrationsdidnotdirectlyinfluencethe temperature sensor readings. Window solar transmittance and dirtcorrectionfactorlargelyimpactedtheMAEbecauseshading devicesweremissing.Parametersrelatedtotheinternalmineral woolinsulationoftheroofwerenegligiblebecausetheinsulation washeavilydamagedandlargelymissing.

6.2. Calibration

TheMAEandtheRMSEoftheCMwereconsiderablylowerthan intheIM(Table3).Toourknowledgetherearenostandardsor guidelinesthatdefineacceptancecriteriaformodelscalibratedto airorsurfacetemperatures.TheASHRAEGUIDELINE[18]defines theacceptancecriteriaonlyintermsofenergyconsumption.

Ifamodel parameterdifferedconsiderably betweenCM and CM+(seeTable2),thisindicatedthatitshouldbevariedfromzone tozone.ThisisthecaseoftheexternalwallthicknessandtheCTC. Also,theexternalwalldensityandspecificheatchangedfromCM toCM+by19%and37%,respectively.Thismeansthat,byusingthe samedensityforallstonewalls,thusneglectingthevariabilityof themortar,andbyusingonlyonesampletomeasurethespecific heat,weobtainedaratherbadapproximationoftherealwall.This isatypicalprobleminmodelingtheenvelopeofhistoricbuildings, whichisusuallycomposedofmanydifferentmaterials.Theairflow rateisoftenhighinhistoricbuildingsduetodamagesorcracksin theenvelopeandwindows.Inourcase,theairinfiltrationratefor therepresentativeroomincreasedby38%fromCMtoCM+.This confirmsthataccuratemeasurementsoftheairinfiltrationshould beperformedforeach zone.ThelowestmonthlyaverageRMSE (Fig.3)intheCMwasobtainedinJuly(0.51K),thehighestinJune (0.78K).ThelowestRMSEperhour-of-daywasconcentrated dur-ingthenightandthehighestduringtheday.Thisbehaviorcould notbeconnectedtosolarradiation,becausetheRMSEinJunewas higherthaninJuly,althoughJunehadmorecloudydays(for exam-ple,theperiodfrom9thto12thJune2012presentinFig.3was cloudy).Themonitoredairtemperaturesaveragedoverthe build-ingweresmootherthanthesimulatedones.Thiseffectindicated thatairinfiltrationrateswereprobablyoverestimatedintheIM. Duringthecalibration,thermalmasswasloweredtotheminimum allowedbytheselectedranges.Thisisconnectedtothedifficulty inestimatingthethermal inertiaofexteriorwallscomposedby stonewithhighamounts of unknownfillingmaterial, which is typicalforhistoricalbuildingsofthemedievalperiodinTyrol. Par-ticularattentionis requiredwheneverthecalibrationalgorithm choosesanextremevalueofaparameterinterval.Byjust enlarg-ingtheparameterintervals,onerisksendingupwithunrealisticor improbablevalues.Infact,calibrationisafittingprocessthat mini-mizestheerrorbetweenmeasuredandsimulateddatavaryingaset ofparameters,butisnotabletoevaluatetheaccuracyofasingle parameter.Itisthemodelerwhohastothinkaboutthecausesof

thespecificchoicesmadebythecalibrationalgorithmandtorevise themodelaccordingly.Forexample,thealgorithmmighthave low-eredthethermalinertiaoftheexteriorwallstocompensateforan overestimatedthickness,whichwedidhowevermeasureinmore points.

Otherparameterswerelessthan10%differentbetweenCMand CM+.Thiswasthecasefortheglasssolartransmittanceandglass dirtcorrectionfactor.Duringthecalibration,theywerereducedto theminimumallowed.Hence,solartransmittanceordirtcorrection factorwereprobablyoverestimatedintheIM.Theexteriorwall conductivity,thepartitionwalldensity,andpartitionwallspecific heatalsochangedbylessthan10%betweenCMandCM+.Thismade usconfidentabouttheirvalues.

6.3. Validation

Validatingoveradifferenttimeperiodandperformingthe sur-face temperature comparisons improvedour confidence in the calibratedenvelopeparameters.Inparticular,becausetheRMSEof thesurfacetemperatureswas0.4K,weconcludedthatthe proper-tiesoftheexteriorwallwereappropriatelyset.Theonlyexception isSTF2NS(Table3)whichhasanRMSEcloseto0.8K.Wethinkthat thisRMSEwashighbecauseofthebrokenwindownearthesensor. WedecidedtoretaintheF2NSsurfacetemperaturetounderline thateverypartofthebuildingshouldbetakenintoaccount,even ifdamaged.Modelingbrokenordamagedbuildingcomponentsis oneofthetypicaldifficultiesinhistoricbuildingsimulation.We thinkthatacalibratedmodelshouldalsocapturetheseaspectsas muchaspossible,tobetterrepresenttherealbuildingand con-sequentlyevaluatethebenefitsofaretrofit.The relativelyhigh RMSEofthesurfacetemperaturenearthebrokenwindowreminds ustocontinuouslycompareamodelagainsttheactualbuilding, especiallywhendealingwithcomplexhistoricbuildings.

7. Conclusions

Wepresented a methodologytocalibrateahistoric building simulationmodelandappliedittoamedievalbuildinglocatedin northernItaly.Theaimofthemethodologywastoobtainmodel parameters close to reality, which is not at all trivial for cali-bratedmodelsofhistoricbuildings,astheirbuildingfabricisoften composedof heterogeneous,unknown materials, withvariable dimensions,and partiallyorcompletelydamaged parts.Models thatsimplifytheseaspectscanintroducelargeerrorsinthe simu-lation.Ourmethodologyincludedthreecalibrationstepsafterthe sensitivityanalysistoinvestigatethetrustworthinessofthemodel parameters.

Themostimportantaspectwasperformingtwocalibrations. Inthefirstcalibration,thepropertiesofthebuildingfabricvaried uniformlyforallzones.Inthis way,wecouldreducetheRMSE from0.96KintheIMto0.66KintheCM.Inthesecondcalibration, wevariedonlytheparametersforonerepresentativezoneofthe building,whilekeepingtheparametersfortheotherzonesatthe valuesobtainedduringthefirstcalibration.Thedifferencesinthe parameters’valuesbetweenthefirstandthesecondcalibration gaveusindicationsaboutpossiblemodelingflaws.Inourcase,the highestuncertaintieswererelatedtotheinfiltrationratesandto thedamagedcomponents(roofandwindows).

Thesecondstepwastovalidatethewholebuildingmodelwith respecttoadifferentperiodthantheoneusedforthecalibration. Wecalibratedthemodelusingsummerdataandverifiedits behav-iorwithwinterdata,reachingaRMSEof0.62Kinthevalidation phase.

Thethirdstepwastovalidatethemodelalsowithrespecttothe interiorsurfacetemperaturesoftheexteriorwalls,forwhichwe

obtainedaRMSEof0.4K.Thisconfirmedthattheoverallthermal behaviorofthebuildingenvelopewasmodeledwellintheCM.

Applyingthemethodologypresentedinthispaperrequires con-siderableeffort.However,theeffortisjustifiedbytheimportance ofhavinga calibrated modelof a historicbuilding. In fact, his-toricbuildingsaresubjecttoconservationconstraintsthatforce thedesignertothinkcarefullyaboutspecificretrofitsolutionson a case-by-case basis. Basingthe retrofitting solutionon a non-calibrated model may lead to preservation issues, discomfort, excessiveenergyconsumptionandwastedmoney.Dependingon theapplicationandtimeavailable,it maybepossibleor neces-sarytosimplifytheapproachpresentedinthispaper.Infact,any skippedstepexceptforthesensitivityanalysiswillincreasethe uncertaintyinthecalibratedmodelparameters.Omittingthe sensi-tivityanalysisrequiresacertainexperienceinidentifyingnegligible parameters.

Acknowledgments

Theresearchleadingtotheseresultshasreceivedfundingfrom theEuropeanUnionSeventhFrameworkProgram(FP7/2007-2013) underGAno.260162,project3ENCULT.Theauthorswouldlike tothank solarGIS[19] for providing theradiationdata andthe Dresden University of Technology for the laboratory measure-ments.

References

[1]P.Raftery,M.Keane,A.Costa,Calibratingwholebuildingenergymodels:

detailedcasestudyusinghourlymeasureddata,EnergyBuild.43(2011)

3666–3679,http://dx.doi.org/10.1016/j.enbuild.2011.09.039.

[2]T.AgamiReddy,I.Maor,C.Panjapornpon,Calibratingdetailedbuilding energysimulationprogramswithmeasureddata—PartI:general methodology(RP-1051),HVAC&RRes.13(22)(2007)221–241.

[3]Y.Heo,R.Choudhary,G.A.Augenbroe,Calibrationofbuildingenergymodels

forretrofitanalysisunderuncertainty,EnergyBuild.47(2012)550–560,

http://dx.doi.org/10.1016/j.enbuild.2011.12.029.

[4]R.Pernetti,A.Prada,P.Baggio,Ontheinfluenceofseveralparametersin energymodelcalibration:thecaseofahistoricalbuilding,in:IBPSAItaly,Free UniversityofBolzano,Bolzano,Italy,2013.

[5]N.Cardinale,G.Rospi,P.Stefanizzi,Energyandmicroclimaticperformanceof Mediterraneanvernacularbuildings:theSassidistrictofMateraandtheTrulli districtofAlberobello,Build.Environ.59(2013)590–598.

[6]F.Ascione,F.deRossi,G.P.Vanoli,Energyretrofitofhistoricalbuildings:

theoreticalandexperimentalinvestigationsforthemodellingofreliable

performancescenarios,EnergyBuild.43(2011)1925–1936,http://dx.doi.org/

10.1016/j.enbuild.2011.03.040.

[7]A.Caucheteux,E.Stephan,C.Ouest,Transientsimulationcalibrationofanold buildingusinganexperimentaldesign:evaluatinguncertaintyresults,in: 13thConf.Int.Build.Perform.Simul.Assoc.,Chambery,France,2013,pp. 677–684.

[8]Z.O’Neill,B.Eisenhower,Leveragingtheanalysisofparametricuncertainty

forbuildingenergymodelcalibration,Build.Simul.6(2013)365–377,http://

dx.doi.org/10.1007/s12273-013-0125-8.

[9]J.Kennedy,R.Eberhart,Particleswarmoptimization,in:Proc.ICNN’95—Int.

Conf.NeuralNetworks,IEEE,1995,pp.1942–1948,http://dx.doi.org/10.1109/

ICNN.1995.488968.

[10]ISOStandard,ThermalInsulation—BuildingElements—In-SituMeasurement ofThermalResistanceandThermalTransmittance,1994.

[11]UNIEN,UNIEN13829:Determinazionedellapermeabilitàall’ariadegliedifici (DeterminationofAirPermeabilityofBuildings),2002.

[12]ASHRAE,ANSI/ASHRAEStandard140-2011,StandardMethodofTestforthe EvaluationofBuildingEnergyAnalysisComputerPrograms,ASHRAE,Atlanta, GA,2011.

[13]G.Pernigotto,A.Gasparella,Extensivecomparativeanalysisofbuilding

energysimulationcodes:heatingandcoolingenergyneedsandpeakloads

calculationinTRNSYSandEnergyPlusforSouthernEuropeanclimates,

HVAC&RRes.19(2013)481–492,http://dx.doi.org/10.1080/10789669.2013.

794088.

[14]C.W.Coblenz,P.R.Achenbach,Fieldmeasurementoftenelectrically-heated houses,ASHRAETrans.69(1963)358–365.

[15]M.D.Morris,Factorialsamplingplansforpreliminarycomputational

experiments,Technometrics33(1991)161–174,http://dx.doi.org/10.2307/

1269043.

[16]F.Campolongo,J.Cariboni,A.Saltelli,Aneffectivescreeningdesignfor

sensitivityanalysisoflargemodels,Environ.Modell.Softw.22(2007)

1509–1518,http://dx.doi.org/10.1016/j.envsoft.2006.10.004.

[17]GenOpt,GenericOptimizationProgram,1998–2011,2015, http://simulationresearch.lbl.gov/GO(accessedJanuary15,2015).

[18]ASHRAE,ASHRAEGUIDELINE14-2002MeasurementofEnergyandDemand Savings,8400,2002.

[19]SolarGIS,OnlineDataandToolsforSolarEnergyProjects(solargis.info), 2010–2015,2014(n.d.)http://solargis.info(accessedFebruary10,2015).