Thermal modeling of existing buildings in high-fidelity simulators: A novel, practical methodology

Ene gy & Buildings 292 (2023) 113127 A ailable online 8 May 2023 0378-7788/© 2023 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by- nc-nd/4.0/). Con en s lis s a ailable a ScienceDi ec Ene gy & Buildings jou nal homepage: www.else ie .com/loca e/enbuild The mal modeling o exis ing buildings in high-fideli y simula o s: A no el, p ac ical me hodology J.A. Bo ja-Condea,∗, K. Wi heephanich b, J.F. Co onelc, D. Limona aDepa men o Au oma ic Con ol and Sys em Enginee ing, Uni e si y o Se ille, Se ille, Spain bDepa men o Elec ical and Elec onic Enginee ing, Muns e Technological Uni e si y, Co k, I eland cDepa men o Ene gy Enginee ing, Uni e si y o Se ille, Se ille, Spain A R T I C L E I N F O A B S T R A C T Keywo ds: Simplified building modeling Da a-based g ey-box modeling Building he mal model Au oma ed model iden ifica ion Building ene gy efficiency Exis ing buildings TRNSYS GenOp Op imizing efficiency in he ope a ion o he HVAC sys em o exis ing buildings equi es he cons uc ion o a he mal dynamic model o he building, which may be challenging because a chi ec u al me ada a may be missing o obsole e. Based on a sui able se o measu ed da a, his pape p esen s a no el p ac ical me hodology o c ea e and au oma ically de i e he mal models o exis ing buildings in high-fideli y simula o s o ene gy managemen . To his end, he philosophy o g ey-box s a egies is ollowed o simpli y he modeling and a oid he equi emen o a chi ec u al me ada a, acili a ing and expedi ing he p ocess. Fi s , a building model wi h a highly educed numbe o pa ame e s is cons uc ed by exploi ing he exis ing simila i ies in he ma e ials o he buildings and simpli ying hei elemen s o a simple one-laye pa ame e iza ion. Then, he pa ame e s o he de i ed model a e i e a i ely upda ed while minimizing he e o be ween he eal empe a u e e olu ion and ha gene a ed by he model being iden ified. Fo his pu pose, da a o he oom ai empe a u e, es ima ed occupancy, wea he condi ions, and a iables o he HVAC sys em a e assumed o be a ailable in sui able zones o he building o apply he c ea ion and iden ifica ion p ocesses o he model, allowing ha a whole digi al win o he building is cons uc ed. The me hodology is p esen ed by i s applica ion o a eal case s udy: he Nimbus Resea ch Cen e building a Muns e Technological Uni e si y, loca ed in Co k (I eland). The high-fideli y simula o so wa e TRNSYS is used o he modeling ask, oge he wi h he GenOp op imiza ion p og am. The esul s demons a e ha he p oposed me hodology yields a highly accu a e model o he building, capable o ep esen ing eali y wi h RMSE alues consis en ly below 0.6 ◦C du ing open-loop alida ion pe iods o up o ou days. The findings sugges ha his me hodology may ou pe o m o he modeling echniques epo ed in he li e a u e. Impo an ly, he p oposed echnique is less complex and ime-consuming o implemen han many o he al e na i es. 1. In oduc ion The ene gy consumed in buildings ep esen s up o 40% o he o al ene gy consump ion in de eloped coun ies, o which HVAC (Hea ing, Ven ila ion and Ai Condi ioning) sys ems comp ise abou 50% [1,2]. Fu he mo e, buildings con ibu e o 36% o ene gy- ela ed g eenhouse gas emissions [3]. This has mo i a ed in e na ional policies o imp o e and specifically in hea ing and cooling sys ems.1 *Co esponding au ho . E-mail add esses: [email p o ec ed] (J.A. Bo ja-Conde), [email p o ec ed] (K. Wi heephanich), [email p o ec ed] (J.F. Co onel), [email p o ec ed] (D. Limon). 1Fo ins ance, he Eu opean Union has included he need o inc ease ene gy efficiency in buildings o educe ene gy use in ecen plans o he EU’s clima e ansi ion [4], whe e hea ing and cooling a e p esen ed as one o he key ac o s [5]. To imp o e he ene gy efficiency o buildings, diffe en asks can be pe o med, such as imp o ing he he mal insula ion o buildings [6] o ins alling sola panels o p oduce clean ene gy o sel -consump ion, among o he s. Howe e , hese asks equi e a significan in es men and ime. On he o he hand, a easible solu ion would be o apply ad- anced me hodologies o ope a e HVAC sys ems, which may no equi e new equipmen o a la ge in es men and hus i is app op ia e o ex- is ing buildings: In [7], he g ea po en ial o implemen ing ad anced h ps://doi.o g/10.1016/j.enbuild.2023.113127 Recei ed 20 Feb ua y 2023; Recei ed in e ised o m 21 Ap il 2023; Accep ed 27 Ap il 2023 Ene gy & Buildings 292 (2023) 113127 2 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. managemen me hodologies in exis ing buildings is highligh ed, as ex- is ing buildings ep esen he as majo i y o he en i e building s ock. In pa icula , i has been epo ed ha p ofi ing om new echnologi- cal ad ances in ene gy managemen can educe ene gy use in buildings om 13% o 28% on a e age [8]. The e o e, applying hese echniques only o old buildings would lead o a g ea deal o ene gy sa ings ha could be achie ed in he sho e m. Howe e , he implemen a ion o hese ad anced s a egies is closely linked o he a ailabili y o an ene gy model o he building o ake p e- dic ions in o accoun , o check he iabili y o he managemen policies, e c. In addi ion, he model could be used as a Digi al Twin o he building i i has he capabili y no only o ep esen he eal sys em, con in- uously upda ed wi h eal- ime sys em da a, bu also o allow ai h ul p edic ion o how he sys em will e ol e [9], as long as high accu acy o he model is p o ided. Fu he mo e, i could also be used o o he asks, such as anomaly and aul de ec ion, es ing and aining con ol sys ems be o e applica ion in he eal sys em, e en dimensioning o a new HVAC sys em p io o ins alla ion i i had o be upda ed, e c. [8]. 1.1. Li e a u e e iew Fo he a o emen ioned pu pose, whi e-box (WB) models a e one o he sui able popula op ions—as long as a good pa ame iza ion o he building is de eloped [10]. The e a e ma u e whi e-box modeling and simula ion ools, highligh ed by hei high fideli y, such as Ene gyPlus [11], Modelica [12], IDA ICE [13], eQUEST [14], o TRNSYS [15]. They ha e been widely used o model he he mal and ene ge ic e olu ion o buildings [16–19]. These ools equi e a de ailed desc ip ion o he building and i s cons uc ion echniques, needing he specifica ion o a la ge se o a chi- ec u al me ada a pa ame e s, such as laye s, hickness, conduc i i y, capaci y, densi y o con ec i e coefficien o ma e ials in walls, win- dows, e c. The e o e, hey will p o ide high fideli y as long as he pa ame e alues a e close o eali y. Acco ding o [20], he e is e - idence ha a mo e de ailed and complex model does no necessa ily ansla e in o a mo e accu a e model o he eal building as a esul o inc easing he quan i y and accu acy o he equi ed se o a chi ec u al design pa ame e s. This is because design pa ame e s a e no eal pa- ame e s due o he eno mous ange o pa icula i ies ha exis in he manu ac u ing o ma e ials, he cons uc ion o he building, i s su - ounding condi ions, unexpec ed ene gy losses, e c. [10,21]. The e o e, i has been shown ha , in o de o enhance he model pe o mance, i is no necessa y o add mo e specific and pa icula a chi ec u al de ails, bu o calib a e a sui able subse o pa ame e s [22]. Because o his, he e a e se e al wo ks in he li e a u e ha couple whi e-box modeling in high-fideli y (HF) simula o s wi h a calib a ion p ocess. Some s udies implemen a calib a ion o ene gy exchanges due o ai infil a ion. In [23], a domes ic building is modeled using TRNSYS, and he ai infil a ion change a e is calib a ed, esul ing in an im- p o ed simula ion-based ene gy assessmen . In [24], he au ho s ha e used TRNSYS o model a school cen e based on comple e a chi ec u al me ada a. They had he added difficul y ha he buildings had de ec i e window insula ion, inc easing ene gy losses due o infil a ion. Then, hey applied a de e minis ic calib a ion app oach o he pa ame e s co - esponding o he infil a ion, yielding a significan educ ion o he he mal model e o . In [25], an ex ensi e wo k is ca ied ou o model a public lib a y in TRNSYS. The cons uc ion p ope ies a e se by he a chi ec u al me ada a, while only infil a ion alues a e used o cali- b a e he he mal model o he building. This s udy is no ably ex ended in [26], whe e he calib a ion pa ame e s o he building he mal model a e no only he infil a ion, bu also he capaci ance o each he mal zone. O he s udies ocus on he calib a ion o he cons uc ion ma e ial p ope ies, bu cons ain he possible esul s o an in e al a ound he alues p o ided by he manu ac u e s. In [27], a wo-s o y es building is modeled in Ene gyPlus in compliance wi h de ailed a chi ec u al doc- umen a ion. They se se e al calib a ion pa ame e s ela ed o in e nal gains, infil a ion, cons uc ion ma e ials, such as hickness o conduc- i i y, e c., which a e cons ained o a maximum fi s design e o o a ound 25%. A simila case s udy is de eloped in [28], whe e he build- ing is modeled in IDA ICE. Simila ly, in [22], an au oma ed p ocedu e o calib a ion is p oposed s a ing om an ini ial de ailed model, which is ocused on powe consump ion. In [29], a his o ical building mod- eled in Ene gyPlus is calib a ed by compa ing wo diffe en me hods. The calib a ion pa ame e s chosen in he s udy a e conduc i i y, he - mal and sola abso p ion, and specific hea o he walls. One me hod calib a es om ai empe a u e measu emen s and he o he me hod es ima es using ai as well as su ace empe a u e measu emen s. Cali- b a ion leads o a significan educ ion in model e o o bo h me hods, al hough he de elopmen o good ini ial models is men ioned as one o he key ac o s. The wo ks men ioned abo e equi e de ailed and comple e echnical in o ma ion ex ac ed om a chi ec u al plans and me ada a o se a s a ing poin in he modeling and calib a ion p ocess. Al hough his in o ma ion is e y use ul, ob aining i is a edious ask, which limi s he applica ion o he me hodology o o he buildings [30]. Fu he mo e, p oblems become pa icula ly challenging in ela i ely old buildings, whe e a chi ec u al me ada a may no be a ailable o no eliable. To a oid his issue, ano he popula op ion is he use o black-box (BB) models ins ead. These a e gene a ed using inpu –ou pu da a in pu e da a-d i en me hods, dis ega ding physical ela ions o a chi ec- u al me ada a, and equi e a limi ed numbe o pa ame e s and com- plexi y [10,31]. To his end, he e a e a wide ange o model s uc u es sui able, such as linea eg ession (LR), neu al ne wo ks (NN), suppo ec o machine (SVM), e c., as e iewed in [10,32–34]. Howe e , black- box echniques ha e clea disad an ages. Fo ins ance, he pa ame e s do no usually ha e physical meaning—so hey a e no in e p e able o building ope a o s. Fu he mo e, hey equi e long aining and alida- ion pe iods and a e limi ed o building ope a ion condi ions co e ed du ing he aining pe iod [10], so ha good accu acy will be ob ained whene e a wide ange o diffe en ope a ing scena ios a e o ced on he eal sys em o e long pe iods o ime, which is no usually desi able o e en possible. In o de o uni y he ad an ages o bo h whi e-box and black-box models, g ey-box (GB) modeling echniques a e used, whe e he model s uc u e is es ablished om physical laws, while model pa ame e s a e iden ified om inpu -ou pu da a [31]. T adi ionally, hese me hods a e based on simple esis ance-capaci ance (RC) model s uc u es, as e- iewed in [32]. O en, he simplifica ion o he modeling is one o hei ocus [35]. In compa ison wi h black-box models, RC models ha e he ad an ages o being physically mo e in e p e able and no equi ing such a wide ange o diffe en ope a ing scena ios. Howe e , non-linea dynamics a e no well modeled, and he e is no consensus on he op- imal model complexi y, since lowe -o de models may no be able o ca ch he he mal dynamics, bu in he same ime, highe -o de models may lead o be o e -fi ed o aining da a [36]. On he o he hand, in compa ison wi h whi e-box models, RC models a e less a duous o de- elop and ha e ewe pa ame e s, a he expense o lowe accu acy and less ep esen a i eness o nonlinea dynamics. Mo e ecen ly, in o de o enhance he adi ional g ey-box model, a u he and deepe app ochemen be ween g ey-box and black-box modeling me hods has been p oposed. To his end, esea che s in o- duce p io physical knowledge in mo e sophis ica ed model s uc u es— ypically used in black-box echniques— han RC ones. Fo example, in [37], a physics-in o med linea eg ession model (PILR) is compa ed o machine lea ning me hods, and he physics-in o med model is con- cluded o be supe io o he o he s. In [38], physically consis en neu al ne wo ks (PCNN) we e p oposed, concluding ha he p oposed model clea ly ou pe o med RC models. Howe e , hey p esen ed i as a limi- a ion ha a e only physically consis en wi h espec o con ol inpu s Ene gy & Buildings 292 (2023) 113127 3 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. Table 1 Compila ion o ad an ages and disad an ages o he diffe en ypes o modeling and hei co esponding s uc u e model. Whi e-Box Black-Box G ey-Box Fea u e HF Sim. NN, LR, SVM, e c. RC PCNN/PILR HF Sim. ∙Easy and quick modeling ✗✓✓✓✓ ∙Physically consis en ✓✗✓✓ ✓ ∙Reduced numbe o pa ame e s ✗∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼✓ ∙Ca ch non-linea dynamics ✓✓✗✓✓ ∙Small numbe o scena ios o aining ✓✗✓✗✓ ∙Good ade-off be ween complexi y and accu acy ✗✗✗∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼✓ ✓I p esen s ad an ages in his ega d. ✗I p esen s disad an ages in his ega d. ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼I depends on o he aspec s. and exogenous empe a u es; o he wise, hey canno gua an ee he o- bus ness o he model anymo e [39]. Also, some exogenous ac o s and non-linea dynamics, such as ca ching he dis u bances o sola gains h ough he windows o o he occupancy, a e also p esen ed as a diffi- cul y. Las ly, simila ly o [40], he quali y o he solu ion can a y sig- nifican ly should an ini ializa ion wi h un ealis ic alues be de eloped; ha is, PCNNs do no always eco e physically consis en pa ame e s om da a. Thus, some le el o enginee ing insigh is equi ed o p op- e ly use he p esen ed me hodologies. O he ecen ly popula field o esea ch o iden i y building he - mal models au oma ically is symbolic eg ession, wi h p omising e- sul s [41–43]. A i s co e, symbolic eg ession could be conside ed a black-box app oach. Howe e , i diffe s om o he black-box me hods because i is ocused on disco e ing ma hema ical models and equa- ions om da a, which can p o ide in e p e abili y by offe ing insigh s in o he ela ionship be ween inpu and ou pu a iables. None heless, symbolic eg ession is a ela i ely new echnique in machine lea ning, and while i has shown p omise in a ious fields, i is s ill unde s udy and he e a e s ill some challenges o o e come, such as scalabili y o la ge da ase s, o e coming o e fi ing, modeling non-linea dynamics, e c. [41]. Recapping he conclusions p esen ed h oughou his sec ion and based pa icula ly on [10,32,33,36,38,39,41], a compila ion o he ad- an ages and disad an ages o each ype o modeling is shown in Ta- ble 1. 1.2. Con ibu ion In his pape a me hodology o de i e s uc u ed G ey-Box models in High-Fideli y Simula o (deno ed as GB-HF Sim. in he igh mos col- umn in Table 1) is p esen ed. The model s uc u e is cons uc ed in high-fideli y simula o s, such as TRNSYS o Ene gyPlus ( ypically used o whi e-box modeling) bu —mo i a ed by he philosophy o g ey-box s a egies—simpli ying he model and a oiding he equi emen o a - chi ec u al me ada a. No ice ha PCNN and PILR models, p esen ed abo e, a e aimed o ge g ey-box models om black-box model ools, while he p oposed me hod in his wo k is also aimed o ge a g ey-box model, bu om he Whi e-Box model ools (i.e. high-fideli y simula- o s). G ey-box RC models a e also aimed a ob aining g ey-box mod- els bu using simple esis ance-capaci ance s uc u es o he building, which canno desc ibe he inhe en non-linea dynamics. In con as , he g ey-box models using high-fideli y simula o , p oposed in his pa- pe , cope wi h his issue, hanks o he use o high-fideli y simula ion ools. This, oge he wi h he p oposed simplified modeling, allows one o achie e a e y good ade-off be ween complexi y o he model and accu acy, as i is demons a ed in he eal case s udy. Fu he mo e, hanks o he e y na u e o such simula o s, a small numbe o ope a ion scena ios o he aining p ocess is sufficien , con a y o he PCNN/PILR me hods. This, oge he wi h he model simplifica ions conside ed in his pape , helps o a oid o e -fi ing p ob- lems. Fig. 1. Nimbus Resea ch Cen e building. In he p oposed me hod, he model o he building is simplified by minimizing he numbe o pa ame e s, hanks o a s a egy ha exploi s he opology o he building, e.g., aking ad an age o he simila i ies be ween ooms and seeking equi alen one-laye walls ha ep esen he mul i-laye ones. This s a egy is compa able o ha o he lumped pa ame e models [35,44]and he echnique o clus e ing zones [45,46]. In addi ion, on he basis o his simplified building model, an au oma ed pa ame e iden ifica ion p ocess2is pe o med using his o - ical ope a ion da a, as does g ey-box modeling, hus, wi hou eso ing o a chi ec u al me ada a, unlike whi e-box me hods. The only eal pa- ame e s ha a e supposed o be known a e p ima y in o ma ion such as he main dimensions o he ooms and windows (heigh , wid h, and dep h), loca ion, o ien a ion, e c.3 The p oposed me hod is applied o a eal case s udy: he Nimbus Re- sea ch Cen e building a Muns e Technological Uni e si y, loca ed in Co k (I eland), shown in Fig. 1. The building is modeled in he TRNSYS simula ion p og am [15]. The alida ion esul s ob ained show high fi- deli y o he model. To he bes knowledge o he au ho , his is he fi s combined use o hese simula o s wi h g ey-box modeling me hods, in addi ion o being applied o a eal building. The es o he pape is o ganized as ollows; Fi s , he case s udy is p esen ed in Sec ion 2, which includes a desc ip ion o i s zones and layou , a ailable da a collec ed based on IoT echnologies [47], and a p oposed classifica ion o zones o modeling. In Sec ion 3, he se up o he model and he main objec i es a e p esen ed. Then, in Sec ion 4, he modeling and iden ifica ion s a egy is explained. A zone-le el oc- cupancy es ima o is p oposed in Sec ion 5. Finally, he pape ends wi h 2No e ha he e m “calib a ion o pa ame e s”—used in he men ioned wo ks ha couple de ailed whi e-box models wi h a calib a ion p ocess—is hence o h a oided, using “iden ifica ion o pa ame e s” ins ead, since, unlike he a icles ci ed abo e, he ini ial alues o he model a e comple ely unknown. 3No e ha his assump ion would no be a d awback in compa ison wi h ypical g ey-box modeling, as mos o hem also need his p ima y in o ma ion, which is no coun ed as using a chi ec u al me ada a [33]. Ene gy & Buildings 292 (2023) 113127 4 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. Fig. 2. Second floo building layou ega ding zones ypes. (Fo in e p e a ion o he colo s in he figu e(s), he eade is e e ed o he web e sion o his a icle.) Fig. 3. Fi s floo building layou ega ding zones ypes. he p esen a ion o he applica ion in a eal case s udy and he discus- sion o he co esponding final esul s in Sec ion 6, ollowed by some conclusions in Sec ion 7. 2. Case s udy desc ip ion The me hod p oposed in his pape will be in oduced by means o a eal case s udy: he Nimbus Resea ch Cen e building a Muns e Technological Uni e si y, loca ed in Co k (I eland), shown in Fig. 1 2.1. Desc ip ion o building zones and layou The case s udy is a wo-s o y building whe e he e a e se e al ooms o diffe en uses, such as offices, mee ings, semina s, e c. The building has been used as a es bed case s udy in se e al p ojec s [48,49]. In i , a se o wi eless senso ne wo ks ha e been deployed o measu e ene gy and he mal a iables, which a e sui able o modeling and con ol. In Figs. 2and 3 he layou s o he fi s and second floo s, espec- i ely, a e shown. These a e di ided in o zones, which a e classified acco ding o he se o measu emen s a ailable o each one and wi h associa ed adia o con ol al e (RCV, allows o au oma ed con ol) and he mos a ic adia o al es (TRV, allows o manual con ol). The ones wi h mo e senso s a e shown in colo in he layou and a e de- sc ibed in Sec ion 2.3. •Zone 1 (in ed) is a ki chen. •Zone 2 (in g een) is a oom whe e he e a e app oxima ely hi y compu e wo ks a ions. •Zone 3 (in yellow) is an office o h ee o ou people. •Zone 4 (in blue) is an office o six o se en people. The zones shown in whi e and g ay a e desc ibed in Sec ion 2.3. 2.2. Ins alled senso s and a ailable da a Some o he building zones ha e been equipped wi h senso s o ob- ain sui able measu emen s, based on IoT echnologies [47], o ene gy moni o ing and managemen . The ypes o senso s used a e lis ed be- low. •Zone ai empe a u e senso : Measu es he d y bulb empe a u e in he zone whe e i is ins alled. • Es ima ed occupancy: The numbe o people in a oom is es ima ed by p esence senso s oge he wi h CO2balances. Occupancy may be used o se o he in e nal gains, such as compu e s and ligh ing. • Hea ing sys em exchanges: Hea ans e ed om he HVAC sys em o he oom is es ima ed by combining measu emen s o wa e flow and inle and ou le empe a u es in he an coil. Addi ionally, he ollowing a iables ha affec he whole building a e also measu ed: •Ou side ai empe a u e senso : Measu es he empe a u e o he d y bulb in he ou side ai . •Beam sola adia ion: Di ec adia ion om he Sun on a ho izon al su ace is measu ed using a py anome e . •Diffuse sola adia ion: Diffuse adia ion om he Sun on a ho izon- al su ace is measu ed using a py anome e . Radia ion measu emen s mus be combined wi h sola azimu h and zeni h angles, using imes amp, loca ion, and building o ien a ion. 2.3. Zones classifica ion in modeling Acco ding o he a ailabili y o he a iables measu ed in each zone, hese a e classified in o ou diffe en g oups o zones in e ms o mod- eling: • Full-Senso ized Zones (FS Zones): These a e he zones whe e all ene gy a iables a e measu ed: Zone ai empe a u e, es ima ed oc- cupancy and hea ing sys em exchanges. The e o e, hese a e he zones ha can be ully modeled. Zone 1 and Zone 2 comp ise his g oup. • Almos -Full-Senso ized Zones (AFS Zones): These a e he zones whe e all ene gy a iables bu occupancy a e measu ed: Zone ai empe a u e and hea ing sys em exchanges. Since occupancy is no known, his could be es ima ed. Zone 3 and Zone 4 comp ise his g oup. • Low-Senso ized Zones (LS Zones): These a e he zones whe e only zone ai empe a u e is measu ed. These zones a e ep esen ed by a whi e backg ound colo in Fig. 2. • Non-Senso ized Zones (NS Zones): These a e he zones whe e i is no possible o measu e any a iable. These zones a e ep esen ed by a g ay backg ound colo in Fig. 2. 3. Model se up and objec i es 3.1. Building simplifica ion The de elopmen o a dynamic model o a building is ypically a complex ask, since i usually equi es a p ecise desc ip ion o e e y ma e ial and cons uc ion echnique o he building, such as he laye s o which he walls a e composed and i s ma e ials, he ype o win- dows and he glass p ope ies, e c. In addi ion, hei p ope ies mus be ob ained om a chi ec u al me ada a, which a e ypically difficul o e en impossible o ob ain. This is pa icula ly ha d in exis ing build- ings, whe e echnical in o ma ion is missing o obsole e. The e o e, his me hodology is no app op ia e o ob ain models o exis ing buildings, which is he main objec i e o his pape . To his end, i is p oposed o use a simplified building model based on some assump ions ha a e commonly add essed in p ac ice. Unde his simplifica ion, he model ob ained may p o ide less de ailed e- Ene gy & Buildings 292 (2023) 113127 5 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. sul s, bu his allows one o es ima e he e olu ion o he main a iables o he building necessa y o ene gy analysis and building managemen . These assump ions a e de eloped acco ding o h ee main p inciples. The fi s is o a oid de ailed building geome y, by assuming ha all building elemen s can be modeled as uni o m, wi hou any i egula i y (e.g., a wall ha has p o uding componen s is supposed o be smoo h). The second is o seek simple equi alen elemen s, which means ha in- s ead o modeling he elemen s laye -by-laye , hey can be modeled by an equi alen single laye ha encompasses all. And he hi d p inciple is o ake ad an age o simila i ies be ween he elemen s ha o m he building (e.g., windows, in e nal walls, ex e nal elemen s, as in walls o oo s, and ceilings be ween floo s). These p inciples a e closely ela ed o he philosophy o g ey-box models, as mo i a ed in he In oduc ion. Fo he p oposed modeling p ocess, he ollowing assump ions a e made, which a e alida ed in Sec ion 6: Assump ion 1. Building elemen s wi h mul iple laye s o cons uc ion a e modeled as one-laye elemen s. Assump ion 2. Rooms a e modeled wi h ec angles and smoo h su - aces. Assump ion 3. Building elemen s a e ca ego ized in o a educed num- be o common g oups. Wi hin each g oup, all elemen s a e supposed o ha e he same ma e ials and laye s. The only diffe ence will be hei dimensions (heigh and wid h). Assump ion 4. The na u al ai changes pe hou due o ai infil a ion om ou side he oom a e app oxima ely he same in all ooms. Assump ion 5. The a io be ween zone capaci ance and zone olume is app oxima ely he same in all ooms. These fi e assump ions a e gene ally applicable o mos buildings, g ea ly simpli ying he modeling p ocess. As long as hese assump ions a e me , he me hodology can be scaled. The objec i e is o ob ain a simplified bu analogous model o he eal building o be used o en- e gy analysis and building managemen . Fo example, in he case s udy, acco ding o Assump ion 3 he e a e ou g oups: “Windows”, “In e nal walls”, “Ex e nal elemen s”, and “Ceilings”. 3.2. Iden ifica ion o pa ame e s o he building model The se o pa ame e s o iden i y a e he ones o he one-laye el- emen s, he na u al ai changes pe hou , and he a io be ween zone capaci ance and olume. Since hey a e unknown, hey a e ini ially se as s anda d alues. Then, he a ailable da a collec ed using he ins alled senso s om diffe en expe imen al scena ios a e used o iden i y hem. F om he zones o be iden ified, i is necessa y o know he zone ai empe a u e, he hea ans e ed om he HVAC sys em and he occu- pancy. In addi ion, i is necessa y o know he zone ai empe a u e o he adjacen zones o he iden ified one. Since he zones ha mee hese equi emen s a e he FS Zones, hei pa ame e s a e iden ified and hen analyzed o alida e he ulfillmen o Assump ions 1 o 5, as explained in de ail in Sec ion 4.3. This can be done p o ided ha all he common g oup ypes defined in Assump ion 3 a e p esen in he FS Zones; o he wise, he missing g oups canno be iden ified. Once he abo e assump ions a e alida ed, he esul s o he iden i- fied pa ame e s can be ex apola ed o he en i e building, as explained in Sec ion 4.4. Fig. 4. TRNSYS p ojec in TRNSYS Simula ion S udio. 3.3. Es ima ion o occupancy Once he building model has been iden ified and alida ed, his can be used o es ima e hose signals ha a e no measu ed. Fo ins ance, in he AFS zones, all significan a iables a e measu ed excep occupancy. Based on he model, he occupancy o hese zones can be es ima ed, as shown in Sec ion 5. 4. Modeling and iden ifica ion (based on TRNSYS) The high-fideli y simula o so wa e TRNSYS (TRaNsien SYs em Simula ion p og am) [15]is used o model he building.4This so - wa e is compa ible wi h Ske chUp 3D modeling so wa e [50], which acili a es he in oduc ion o a chi ec u al in o ma ion and dimensions o he building, as will be seen below. No e ha he ea u es o he cons uc ion ma e ials a e unknown a his poin . This means ha hey will fi s be se using gene ic ma e ials. 4.1. TRNSYS p ojec In his p ojec , he plugin o Ske chUp TRNSYS3D [51]has been used o model he building in TRNSYS.5 Based on he layou and main dimensions o he ooms and win- dows (heigh , wid h and dep h), he building can be modeled zone by zone. This hen gene a es a building file o be di ec ly impo ed in o TRNBuild. Once he building model is a ailable in TRNBuild, a TRNSYS p ojec is de eloped in he TRNSYS Simula ion S udio. This p ojec , shown in Fig. 4, has he ollowing blocks: •Collec edDa a: This is a Type9 block ha eads he ex file in which he collec ed da a a e loca ed. In his ex file, he da a his o y o he alues o he a iables measu ed in he zones and ou side he building—p esen ed in Sec ion 2.2—is ound. The co esponding alues o each i e a ion a e he ou pu o he block. •TmyWea he : This is a Type15 block ha eads a ypical me eo o- logical yea file. I is used o comple e wea he da a ha ha e no been measu ed in he building. •Radia ion: This is a Type16 block ha calcula es he adia ion on each wall o ien a ion using he adia ion measu emen s in he build- ing and he sola azimu h and zeni h angles p o ided in he ypical me eo ological yea file. •Building: This is a Type56 block ha impo s he TRNBuild file. •Cos Func ion: This is an Equa ion Block whe e a cos unc ion is cal- cula ed. I ma ches he cos unc ion defined in Equa ion (1), which measu es he disc epancy be ween he eal empe a u e e olu ion collec ed in he zones and he simula ed one. 4The use o TRNSYS is only a p oposal wi hou loss o gene ali y. O he simula ion p og ams, such as Ene gyPlus o IDA ICE, could be used. 5Please no e ha he use o TRNSYS3D and Ske chUp o model he building is op ional. The e a e al e na i e—al hough mo e edious—ways o de eloping he model di ec ly using TRNBuild. The esul would be equally alid. Ene gy & Buildings 292 (2023) 113127 6 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. •Gene a eFile: This is a Type25 block ha gene a es a ex file in which he simula ion esul s a e sa ed. Specifically, he alue o he cos unc ion is sa ed. 4.2. Iden ifica ion a iables The ea u es o he e e ed laye s and he capaci ance- olume a io in he TRNSYS model a e se as decision a iables in an op imiza ion p ocedu e o iden i y he model. Howe e , i is necessa y o de e mine exac ly which iden ifica ion a iables o se du ing he p ocess since a one-laye elemen may ha e se e al physical alues ha can be modi- fied, e.g. hickness, he mal esis ance, capaci ance, e c. No e ha he chosen pa ame e s mus be compa ible so ha hey do no esul in edundancy ha complica es he iden ifica ion p ocess. Since wo diffe en physical alues can influence he same sys em a i- able, e.g. inc easing hickness inc eases he mal esis ance, only one o hem should be se as a iden ifica ion a iable. Unde hese conside a ions, he p oposed iden ifica ion pa ame e s a e as ollows. • Ra io be ween zone olume and capaci ance. • Thickness o he ex e nal wall and oo . • Thickness o he in e nal wall and he ceiling be ween le els.6 •Densi y o he ex e nal wall and oo . •Densi y o he in e nal wall and he ceiling be ween le els.6 • Na u al ai changes pe hou due o infil a ion o ou side ai . • Con ec i e coefficien o he ex e nal wall and oo . • Con ec i e coefficien o he in e nal wall and he ceiling be ween le els.6 Thickness and densi y o he ma e ial a e chosen since he o me will allow he he mal esis ance o be adjus ed and he la e will allow he capaci y. Al e na i ely, al hough less ecommended, he iden ifica- ion pa ame e s co esponding o he ma e ial densi y could be eplaced by he ma e ial con ec i e coefficien , e en hough he esul ing hick- ness will be diffe en . In his case, he con ec i e coefficien would adjus he he mal esis ance, and he hickness would adjus he ca- paci y. I mus be aken in o accoun ha he iden ifica ion pa ame e s mus be adap ed acco ding o he common g oups o building elemen s as specified in Assump ion 3. The pa ame e s o he model a e assumed o be ime in a ian . Al- hough i would be mo e desi able o define some o hem wi h a iable alues du ing simula ion, o ins ance, he na u al ai changes pe hou and he con ec i e coefficien , i has been assumed ha his is an ac- cep able e o , since he complexi y o he op imiza ion p oblem would inc ease exponen ially. This assump ion, adi ionally accep ed in g ey- box modeling [21,52], will be alida ed by checking ha he esul s a e good enough and ha he esul ing alues o hese a iables a e no e y sensi i e depending on he esul s o he o he op imiza ion a iables. 4.3. Pa ame e iden ifica ion based on GenOp Once he TRNSYS model wi h gene ic pa ame e s has been deployed acco ding o Assump ions 1 o 5, and he iden ifica ion a iables ha e been defined, he app op ia e alues o hese a iables a e iden ified using he a ailable da a collec ed wi h he ins alled senso s. 4.3.1. Iden ifica ion p ocess In he iden ifica ion p ocess he pa ame e s o he de i ed model a e i e a i ely upda ed while minimizing he e o be ween he eal em- pe a u e e olu ion and ha gene a ed by he model being iden ified. 6Fo simplici y, ea u es o in e nal walls and ceilings a e lumped. Should he e o be small enough, he esul ing laye may be consid- e ed o ha e he same impac on he zone ai empe a u e as he eal elemen ha i eplaces. Since he e a e se e al ull-senso ized zones, his edundancy can be exploi ed in he iden ifica ion p ocedu e conside ing he ollowing scena ios. Scena io 1: An iden ifica ion p ocess is applied independen ly o each FS Zone in o de o ein o ce he alida ion o he assump ions made, specifically Assump ions 3, 4and 5. Then, diffe en iden ified alues o he same ma e ials will be ob ained in each o hem. This allows one o check he cong uence be ween hese esul s: I he iden i- fied pa ame e s o he same ma e ials a e simila , hen he assump ions a e p obably co ec ; o he wise, some econside a ions should be made, like e iewing he ca ego iza ion o building elemen s ( o example, o analyze i adding ano he kind o building elemen is necessa y), o in- c easing he da a se used, e c. See Rema k 1. Scena io 2: When Scena io 2 is pe o med, a iden ifica ion p ocess is applied simul aneously o all FS Zones, while sha ing he a iables be ween zones o he co esponding common building elemen s in o de o ob ain he in e media e alues ha mos esemble eali y. In he same way as be o e, i will be necessa y o p o e he cong uence be ween he esul s o he applica ion join ly and independen ly. The analysis o he esul an e o be ween he e olu ion o he ai empe a u e o he model zone and he eal building is ano he alida ion me hod ha will be de eloped. I is impo an o no e ha while one o mo e zones a e iden ified, all ex e nal a iables, excep he ai empe a u e o he iden ified zones, a e se o he co esponding ones in he eal sys em using he collec ed da a desc ibed in Sec ion 2.2. Rema k 1. The Iden ifica ion p ocess applied independen ly o each FS Zone (Scena io 1) is an op ional s ep used o ein o ce he alida ion o he assump ions made by p o ing cong uence. I migh be possible o a oid pe o ming his s ep and jus de elop he Iden ifica ion p ocess applied simul aneously o all FS zones (Scena io 2). The assump ions a e alid p o ided ha he e o be ween ac ual and simula ed empe - a u e e olu ion is small enough. In o de o e alua e he pe o mance o he esul ing model, a cos unc ion is defined o measu e he es ima ion e o . The unc ion co - esponds o he oo mean squa e e o (RMSE)—a pe o mance index commonly ound in he li e a u e, as used by [53]—be ween he e olu- ion o eal building measu emen s and he empe a u es based on he simula ion o he model. The cos unc ion is exp essed in Equa ion (1). RMSE𝑝(◦C)=√∑𝑁 𝑖=1(𝑇𝑟𝑒𝑎𝑙,𝑖 −𝑇𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑,𝑖)2 𝑁,(1) whe e 𝑇 eal,𝑖 is he alue o he eal empe a u e o he zone a sample 𝑖exp essed in deg ees Celsius (◦C), and 𝑇es ima ed,𝑖 is he co esponding es ima e. 𝑁is he o al numbe o i e a ions co esponding o a de e - mined ope a ion pe iod 𝑝. 4.3.2. Iden ifica ion p ocess in TRNSYS wi h GenOp Once he iden ifica ion s a egy, i s a iables, and i s pe o mance e alua ion cos unc ion a e defined, pe o ming he iden ifica ion p o- cedu e based on he esul ing TRNSYS p ojec is no immedia e, as TRN- SYS does no allow he physical alues o he elemen s o be changed as use inpu in an au oma ed way. This hinde s he i e a i e p ocess equi ed in he iden ifica ion. Howe e , his issue is sol ed hanks o he GenOp op imiza ion p o- g am [54]. GenOp can au oma ically change he TRNSYS configu a ion files ex e nally o se sui able alues o he pa ame e s, execu e a simu- la ion es and ead he file wi h he simula ion esul s om whe e he cos unc ion is ob ained (see Fig. 5). GenOp p og am ecei es he iden ifica ion pa ame e s and a em- pla e equal o he configu a ion files o he TRNSYS p ojec . No e ha Ene gy & Buildings 292 (2023) 113127 7 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. Fig. 5. Connec ion diag am be ween TRNSYS and GenOp . he alues o he iden ifica ion pa ame e s a e se wi h a label ins ead o i s numbe , which has o be de eloped p e iously. Thus, GenOp can inse he co esponding alues in each i e a ion and send he file o TRNSYS o execu ion. When he execu ion in each i e a ion is comple e, TRNSYS will gen- e a e a file in which he alue co esponding o he cos unc ion is loca ed. Thus, GenOp can adjus he pa ame e s, i.e., he decision a i- ables, and ob ain he alue o he associa ed cos unc ion. Based on his, GenOp can i e a i ely ake app op ia e alues o he pa ame e s in o de o minimize he cos unc ion. Fo his, GenOp allows he use o choose an op imiza ion algo i hm om a wide collec ion a ailable. 4.3.3. T aining and alida ion p ocesses The iden ifica ion p ocess is di ided in o wo phases: • T aining Phase: F om he a ailable da a o he eal building, a sub- se is aken o ca y ou he iden ifica ion o he pa ame e s. These a e he so-called aining da a. No e ha he iden ified pa ame e s a e hose ha make he model fi be e o he aining da a. • Valida ion Phase: In his phase, he iden ified model is alida ed us- ing he so-called alida ion da a, which co esponds o a ime pe iod diffe en om he aining da a. To do his, an open-loop simula ion o he model wi h he iden ified pa ame e s needs o be pe o med, whe e he only alues o be se a e he ini ial empe a u es o he zones being simula ed. The iden ified model is conside ed o be alid i i s simula ed e olu ion fi s sufficien ly well wi h he ali- da ion da a. This p ocedu e can be applied o bo h iden ifica ion scena ios: when he iden ifica ion is pe o med independen ly o e e y FS Zone and when his is done o all he FS Zones oge he . I he alida ion p ocess was no sa is ac o y, i.e. he iden ified model did no fi he eal one, hen, he e would be a need o econ- side some aspec s, such as he ca ego iza ion o building elemen s ( o example, o conside adding o he kinds o building elemen s) o in- c easing he aining da a se acco ding o a sui able analysis o he esiduals. 4.4. Modeling he whole building Once Assump ions 1 o 5a e alida ed o FS Zones, he en i e building can be modeled using he esul ing iden ified pa ame e s in hose zones. In i ue o Assump ion 3, all g oups o building elemen s ha e he same ma e ials and laye s, so he ma e ials iden ified in FS Zones will ma ch wi h hose o he o he zones (AFS, LS and NS Zones). And analogously, because Assump ions 4and 5speci y ha na u al ai changes pe hou due o infil a ion and ha he a io be ween zone ca- paci ance and olume is he same in all zones, so infil a ion and zone capaci ance can be calcula ed. The esul is ha he en i e building is modeled and iden ified. 5. Da a-based occupancy es ima ion Based on he iden ified model o he building, i is possible o design an es ima o o de e mine he alues o missing a iables o in e es ha ha e no been measu ed. Fo ins ance, in he AFS Zones he occupancy is he only a iable o in e es ha has no been measu ed, and his could be es ima ed. In his case, he empe a u e measu emen s o some su ounding zones a e missing (abou 30%, due o NS zones), bu hey can be app oxima ed by he measu ed empe a u e o i s neighbo s o es ima ion pu poses, since he con ibu ion o his e o o he e olu ion o he empe a u e o he AFS-zone is negligible compa ed o he effec o he occupancy.7 5.1. Occupancy es ima o In o de o demons a e his, a simple es ima ion policy has been used. In his case, he pa ame e o be es ima ed, he occupancy, is calcula ed as he linea combina ion o he es ima ion e o and he accumula ed es ima ion e o . The es ima ion e o is he misma ch be- ween he eal measu ed empe a u e and he es ima ed one. This is desc ibed as ollows. e o 𝑖=𝑇 eal,𝑖 −𝑇model,𝑖,(2) Occ𝑖=𝐾1⋅e o 𝑖+𝐾2⋅ 𝑖 ∑ 𝑘=0 e o 𝑘,(3) whe e 𝑇𝑟𝑒𝑎𝑙,𝑖 is he alue o he eal empe a u e o he zone and 𝑇𝑚𝑜𝑑𝑒𝑙,𝑖 is he alue o he simula ed empe a u e o he zone wi h he es ima ed occupancy 𝑂𝑐𝑐𝑖−1 a sample 𝑖. 𝐾1and 𝐾2a e he sui able gains. 5.2. Valida ion o he es ima ed occupancy A byp oduc o he occupancy es ima o is he possibili y o im- plemen ing an addi ional s ep o ein o ce he alida ion o Assump- ions 3,4and 5, ha is, he ex ension o he iden ified pa ame e s in FS Zones o he en i e building. This can be done, o example: (i) by ana- lyzing i s consis ency wi h he use o he building, e.g., checking i he esul ing es ima ed occupancy is cohe en wi h he occupancy sched- ule o offices and he numbe o people who usually occupy he oom), (ii) by compa ing i wi h he occupancy measu emen s in o he zones, e c. 6. Applica ion o he case s udy and esul s The p oposed me hodology is applied o a eal case s udy: he Nim- bus Resea ch Cen e building a Muns e Technological Uni e si y, lo- ca ed in Co k (I eland), shown in Fig. 1. In his case s udy, by exploi ing he simila i ies be ween building elemen s, acco ding o Assump ion 3, ou common g oups can be con- side ed: Windows, in e nal walls, ex e nal elemen s (walls and oo s) and ceilings be ween floo s. Then he whole model is cha ac e ized by only he six pa ame e s desc ibed in Table 2. The a ailable da a o modeling ha e been collec ed o 13 days in No embe , since his is a mon h when he HVAC sys em is needed o be ope a ing and he wea he is less egula , so he ope a ing ange is g ea e . 7In addi ion, no e ha an ai -condi ioned building has all he zone empe a- u es wi hin a small ange, so empe a u e jump be ween bounda y zones will always be less han 5 ◦C app oxima ely, whe eas he jump be ween inside and ou side empe a u es is going o be clea ly highe . In his case, hei dis u - bances can be igno ed. Ene gy & Buildings 292 (2023) 113127 8 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. Fig. 6. 3D model in Ske chUp using TRNSYS3D plugin. 6.1. TRNSYS p ojec de elopmen As explained in Sec ion 4.1, TRNSYS3D is used o model he build- ing. Then, he cons uc ion elemen s a e d awn wi h Ske chUp, and, nex , TRNSYS3D au oma ically se s he ypes o cons uc ion by analyz- ing hei posi ions and shapes ( oo s, floo s, in e nal and ex e nal walls, ceilings, windows, e c.). I is impo an o no e ha hese ypes mus be classified acco ding o Assump ion 3(common g oups o building elemen s). Acco ding o hese ypes, elemen s a e assigned gene ic ma- e ials o a p o ided empla e (in he case s udy, a gene ic I ish empla e is used). The ea u es o hese ma e ials a e no manually changed o ma ch hose o he ac ual building since, ini ially, he ma e ials a e as- sumed o be unknown and a e se as andom gene ic ma e ials. Then, a ea u e o TRNSYS3D is used o su ace ma ching, au oma ically iden- i ying he adjacen elemen s be ween zones, hei ex e nal elemen s, he bounda ies, e c. This is essen ial in o ma ion when analyzing he he mal e olu ion o he building. The esul ing building is shown in Fig. 6. Once he building is modeled in Ske chUp and impo ed in o TRN- Build, he esul ing file is se in he building block (Type56) o he TRNSYS p ojec in TRNSYS Simula ion S udio, Fig. 4. Then, he files o be se in he TRNSYS Simula ion S udio would be he collec ed da a file (Type 9)—which con ains he senso s measu e- men s a he Nimbus Cen e —and he ypical me eo ological yea file (Type 15)—which con ains wea he da a collec ed a Co k Ai po [55]. The sample ime o he da a and simula ion is 10 minu es. To simula e in e nal gains o he building, he ollowing conside a- ions a e aken: •Pe sons: The numbe o people is se using he es ima ed occupancy da a (done by p esence senso s oge he wi h CO2balances). The ene gy gain o each pe son in he oom is se acco ding o ISO 7730:2005 [56]wi h he ype o ac i i y sea ed, ligh wo k, yping. •Compu e s: The numbe o compu e s unning in he offices is equal o he numbe o people in he oom. The compu e powe is se o 230 W acco ding o he TRNSYS documen a ion. •A ificial ligh ing: he ligh s a e on whe e e he e is someone in he oom. Consump ion is 13 W∕m2(EVG di ec ). •Hea ing powe : Hea ans e ed om he HVAC sys em o he oom (es ima ed by combining measu emen s o wa e flow and inle and ou le empe a u es in he an coil) is se as a con ec i e gain. 6.2. Resul s o pa ame e iden ifica ion using ull-senso ized zones The iden ifica ion p oblem is pe o med acco ding o a hyb id gen- e alized pa e n sea ch algo i hm wi h a pa icle swa m op imiza ion algo i hm, a ailable in GenOp [54]. The da a collec ed a ailable a e di ided in o a nine-day pe iod o he T aining Phase ( om 6 o 15 o No embe ), and a ou -day pe iod o he Valida ion Phase ( om 15 o 19 o No embe ). 6.2.1. Resul ing pa ame e alues As men ioned in Sec ion 3.2, o iden i y he ea u es o he equi - alen one-laye elemen s and he a io be ween zone capaci ance and olume, he FS zones a e used. And acco ding o Sec ion 4.3, he pa- ame e iden ifica ion p ocess is applied bo h independen ly o each FS Zone and simul aneously o all FS Zones o analyze he cong uence be- ween all he esul s, as ollows. Scena io 1: In Table 2 he esul ing alues o he iden ifica ion p o- cess o each FS Zone a e shown in he fi s wo columns (Zone 1and Zone 2). Taking in o accoun ha i is possible o p o e cong uence i esul s o he zones ha e simila alues o he same and equi alen pa- ame e s, i can be checked ha he diffe ences be ween he esul s a e small enough o conside ha hey a e cong uen . The e o e, Assump- ions 1 o 5would be alida ed in his case. Specifically Assump ion 3, whe e all elemen s o each defined g oup a e supposed o ha e he same ma e ials and laye s, and Assump ions 4and 5, whe e all zones ha e he same na u al ai changes pe hou due o infil a ion and he same a io be ween zone capaci ance and olume. Scena io 2: Once he FS Zones ha e been iden ified and e ified o cong uence, he nex s ep is o iden i y hese zones wi h he same pa- ame e s simul aneously o ob ain in e media e alues ha minimize he sum o cos unc ions o each zone. The esul s a e shown in Ta- ble 2in ou h column (Zones 1 and 2 oge he ), in compa ison wi h he mean alues be ween he Zone 1 and Zone 2 independen ly, shown in hi d column ((Zone1 +Zone2)∕2). Again, i can be checked ha he diffe ences be ween he esul s a e small enough o conside hem con- g uen . 6.2.2. Zone empe a u e e olu ion fi ing In he modeling and iden ifica ion p ocess, he e a e wo ypes o esul s o show: (i) model esponse a e he T aining Phase is applied and (ii) model esponse when he Valida ion Phase is pe o med. To compa e he esul s be ween simula ions, he cos acco ding o Equa ion (1)is aken in o accoun . The esul s shown in his sec ion a e hose co esponding o Scena io 2 (modeling and iden ifica ion o bo h FS Zones simul aneously). Zone 1: Resul s co esponding o T aining Phase a e shown in Fig. 7. In he uppe plo , he eal zone empe a u e e olu ion is shown in ed, and he simula ed one is shown in blue. In he lowe plo , he main hea gains o he eal building a e shown (hea ing sys em exchange is shown in ed, and occupancy is shown in blue). The maximum e o be ween he empe a u e o he eal and simula ed zone is less han 1 ◦C, he mean absolu e e o (MAE) is 0.3 ◦C, and he median absolu e de ia ion is 0.26 ◦C, wi h a RMSE9days alue o 0.381 ◦C. Simila ly, in Fig. 8 he esul s a e shown when he Valida ion Phase is applied. The maximum e o be ween he empe a u e o he eal and simula ed zone is less han 1 ◦C, he mean absolu e e o is 0.27 ◦C, and he median absolu e de ia ion is 0.25 ◦C, wi h a RMSE4days alue o 0.349 ◦C. Zone 2: Ob ained esul s a e simila o hose o Zone 1, as shown in Fig. 9, o T aining Phase, and Fig. 10, o Valida ion Phase. In he fi s , he maximum e o be ween empe a u es is less han 1.2 ◦C, he mean absolu e e o is 0.36 ◦C, and he median absolu e de ia ion is 0.33 ◦C, wi h a RMSE9days alue o 0.449 ◦C. In alida ion, he maximum e o is less han 1.5 ◦C, he mean absolu e e o is 0.46 ◦C, and he median absolu e de ia ion is 0.38 ◦C, wi h a RMSE4days alue o 0.587 ◦C. The e o e, i can be concluded ha he esul ing e o be ween he empe a u e e olu ion o he eal da a and hose gene a ed wi h he iden ified model is small enough (RMSE4days <0.6 ◦C). In whi e-box models, o example, in [53], al hough wi h a se en-day alida ion pe iod, using a highly mo e complex model and s a ing om a chi- ec u al d awings and ab ica ion de ails a ailable, he RMSE alue (0.27 ◦C≤RMSE7days≤1.5 ◦C) is compa able o ha o his pape . In [57], o a wo-day pe iod, wi h a o ally de ailed model in e ms o a chi- ec u al me ada a, he RMSE alue (RMSE2𝑑𝑎𝑦𝑠≤1.59 ◦C) is also o he same o de . On he o he hand, o PCNN and RC models, o exam- ple in [38], he mean absolu e e o is 0.88 ◦Cand 1.48 ◦C, espec i ely, Ene gy & Buildings 292 (2023) 113127 9 J.A. Bo ja-Conde, K. Wi heephanich, J.F. Co onel e al. Table 2 Iden ifica ion esul s. Values o pa ame e s. Ini ial Scena io 1 Scena io 2 - Final Pa ame e Random Values Zone 1 Zone 2 (Zone1+Zone2)∕2 Zones 1&2 oge he Ra io Capaci ance/Volume (kJ∕m3⋅K) 5.00 28.52 23.56 26.04 26.09 Thickness Ex e nal Elem. (cm) 0.50 0.110 0.125 0.118 0.093 Con ec . Coe . Ex . Elem. (W∕m2⋅K) 50.014.34 19.10 16.73 15.33 Thickness In e nal Elem. (cm) 0.50 0.123 0.130 0.127 0.128 Con ec . Coe . In . Elemen s (W∕m2⋅K) 50.023.31 21.90 22.64 21.63 Na u al ai changes pe hou (l∕h) 0.50 0.175 0.198 0.188 0.180 Open-loop RMSE9days in aining (◦C) 0.377 0.433 0.405 0.415 Open-loop RMSE4days in alida ion (◦C) 0.360 0.562 0.461 0.468 Fig. 7. Iden ified s. Real model acco ding T aining Phase: Open-loop simula- ion om 6 o 15 o No embe . Zone 1. Fig. 8. Iden ified s. Real model acco ding Valida ion Phase: Open-loop simu- la ion om 15 o 19 o No embe . Zone 1. o a h ee-day alida ion pe iod, simila o ha ob ained in his wo k (0.36 ◦C o a ou -day open-loop alida ion pe iod). 6.3. Resul s o es ima ion o occupancy o AFS zones In his case, he e olu ion o he esul ing es ima ed occupancy ac oss he en i e ime pe iod mus be analyzed. To do ha , he known Fig. 9. Iden ified s. Real model acco ding T aining Phase: Open-loop simula- ion om 6 o 15 o No embe . Zone 2. Fig. 10. Iden ified s. Real model acco ding Valida ion Phase: Open-loop simu- la ion om 15 o 19 o No embe . Zone 2. eal occupancy o o he zones is used o compa e hem wi h he iden- ified ones, along wi h he numbe o people who usually occupy he zones. Zone 3: The esul s a e shown in Fig. 11. In he uppe plo , he eal zone empe a u e e olu ion is shown in ed, and he simula ed one is shown in blue. As can be seen, he es ima o upda es he occupancy in o de o fi he simula ed empe a u e wi h he eal one. In he lowe