Ene gy & Buildings 292 (2023) 113127
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Ene gy & Buildings
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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.

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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
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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
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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