Efficiency in building energy use: Pattern discovery and crisis identification in hot-water consumption data

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Efficiency in building ene gy use: Pa e n disco e y and c isis iden ifica ion
in ho -wa e consump ion da a
Lina Mo kunai e a,∗, Da ius Pupeikisa, Nikolaos Tsalikidisb, Ma ius I aske iciusa,
Fallon Cla e Manhangaa, Ju gi a Ce neckienea, Paulius Spudysa, Pa aske as Kouka as b,c,
Dimos henis Ioannidisb, Agis Papadopoulos d, Pa is Fokaidesa,e
aFacul y o Ci il Enginee ing and A chi ec u e, Kaunas Uni e si y o Technology, Kaunas, 51367, Li huania
bIn o ma ion Technologies Ins i u e, Cen e o Resea ch & Technology, Thessaloniki, 57001, G eece
cSchool o Science and Technology, In e na ional Hellenic Uni e si y, Thessaloniki, 57001, G eece
dP ocess Equipmen Design Labo a o y, Depa men o Mechanical Enginee ing, A is o le Uni e si y, Thessaloniki, 54124, G eece
eSchool o Enginee ing, F ede ick Uni e si y, Nicosia, 1036, Cyp us
a icle i n o
Keywo ds:
P edic i e modelling
Domes ic ho wa e
Con ol op imisa ion
Se e i y le el
a b s a c
As global challenges such as clima e change and pandemics inc easingly dis up u ban sys ems, he need o
efficien and esilien managemen o ene gy esou ces has become c i ical. The ene gy used o p epa e domes ic
ho wa e (DHW) akes a la ge p opo ion o esiden ial buildings’ o al he mal ene gy demand. Howe e , i
is o en o e looked in esea ch due o i s s ochas ic na u e and high dependence on use beha iou . This s udy
explo es he iden ifica ion o he c isis and i s se e i y le el in he DHW consump ion da a and he co esponding
con ol ac ions necessa y o mi iga e i s impac . To iden i y c isis se e i y, we u ilised he mobili y da a o
e ail/ ec ea ion ac i i ies and ansi s a ions, making he esul s gene alisable o any c isis. In addi ion, we used
powe consump ion o DHW p epa a ion da a om 10 esiden ial apa men buildings loca ed in Kaunas ci y o
de elop a machine lea ning-based hyb id ensembling s acking classifie (ESC) capable o p edic ing he c isis and
i s se e i y le el. Finally, we applied p incipal componen analysis (PCA) and k-means clus e ing o ca ego ise
DHW consump ion hou s h oughou he day o each se e i y le el. The esul s showed ha he de eloped
ESC classifie significan ly ou pe o ms (𝑅2= 0.99) he baseline LGBMC classifie (𝑅2= 0.92). Combining he
classifie wi h ex ac ed daily consump ion pa e ns and clus e s allows he op imisa ion o con ol ac ions on
he supply, dis ibu ion, and demand side o he DHW sys em.
1. In oduc ion
Wi h inc easing global empe a u es, he need o op imise ene gy
use and educe ca bon emissions om ene gy gene a ion has become
c i ical [1]. Ensu ing ene gy is used efficien ly, p oduced and deli e ed
p ecisely when and whe e i is needed is one o he key aspec s o ack-
ling clima e change [2]. Gi en ha p oducing ce ain ypes o ene gy o
end use s is o en an ine p ocess, i is necessa y o an icipa e he ene gy
demand in ad ance. Fo example, building hea ing ene gy consump ion
can be p edic ed using i s s ong co ela ion wi h wea he pa e ns [3].
In con as , domes ic ho wa e (DHW) demand is a highly s ochas ic
p ocess [4], which is s ongly dependen on use beha iou , making i a
compelling a ea o u he esea ch. In addi ion, fluc ua ions in ho wa-
e consump ion can e eal changes in ac o s such as popula ion den-
si y and occupancy, which, in u n, may signal changes in u ban use
pa e ns [5]. The sha e o he mal ene gy used o p epa e domes ic ho
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (L. Mo kunai e).
wa e accoun s o a significan po ion o he he mal ene gy consumed
by households. Acco ding o he Li huanian Da a Agency, be ween 2009
and 2018 his sha e inc eased om 10.4 % o 18.6 % o he o al he mal
ene gy [6].
DHW sys ems a e ulne able o a ious c ises igge ed by diffe -
en ac o s, such as na u al disas e s, pandemics, o economic down-
u ns. Fo example, du ing he COVID-19 pandemic, many people had
o swi ch o home offices, leading o significan changes in domes ic wa-
e use [7]. Howe e , o apply a ge ed con ol ac ions, i is impo an
o iden i y he c isis and de e mine i s se e i y le el. In some cases, i
migh be beneficial o adjus con ol measu es aiming o com o o
economic benefi s; in o he s, i migh e en be necessa y o p io i ise
ce ain a eas o e o he s o main ain se ice le els [8].
Iden i ying he change in ene gy consump ion pa e ns is also eco-
nomically significan o consume s, as he ene gy ma ke is no fixed
[9] and can offe mo e a ou able a es du ing ce ain pe iods. To make
h ps://doi.o g/10.1016/j.enbuild.2025.115579
Recei ed 14 No embe 2024; Recei ed in e ised o m 23 Feb ua y 2025; Accep ed 6 Ma ch 2025
Ene gy & Buildings 336 (2025) 115579
A ailable online 10 Ma ch 2025
0378-7788/© 2025 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY license (
h p://c ea i ecommons.o g/licenses/by/4.0/ ).
Mo kunai e e al.
use o ha , he DHW con ol sys ems should be adjus ed o accoun o
cu en consump ion pa e ns in ela ion o he ene gy p ice. Fo ex-
ample, by combining ene gy demand o ecas s wi h ene gy s o age so-
lu ions [10], a mo e sus ainable consump ion model can be achie ed.
Simila ly, ho wa e p oduc ion, suppo ed by ma u e echnologies, can
in eg a e ene gy s o age wi h enewable ene gy sou ces [11].
To imp o e he accu acy o ho wa e demand o ecas s unde c isis
condi ions, i is essen ial o iden i y ac o s ha signal po en ial changes
in DHW usage. In p e ious s udies, he numbe o daily cases o COVID-
19 was used as a ac o [12]. Howe e , such inpu da a highly limi
he applicabili y o he s udy o a specific pandemic e en . In con as ,
ac o s such as a ia ion in mobili y wi hin u ban a eas allow he iden-
ifica ion o a ious c ises ha esul in u ban mobili y change.
Reduced mobili y flows sugges ha mo e people a e spending ime
a home, which in u n inc eases he ho wa e demand o ac i i ies
like household cho es, cooking, and pe sonal hygiene. Unde no mal
condi ions, hese fluc ua ions can be obse ed ac oss diffe en imes o
he yea (e.g., school e sus non-school pe iods) and diffe en days o
he week (e.g., weekdays e sus weekends). A no able example occu ed
du ing he COVID-19 pandemic, when significan shi s in mobili y we e
obse ed o e a ela i ely sho pe iod [12]. The e o e, da a om he
COVID-19 pandemic pe iod can se e as inpu in aining o ecas ing
models o iden i y diffe en modes o DHW sys em ope a ion.
Gi en he impo ance o accu a ely p edic ing and adap ing o DHW
consump ion pa e ns, mul iple s akeholde s a e affec ed by hese a i-
a ions. Unde s anding how changes in ho wa e usage influence diffe -
en sec o s unde sco es he need o comp ehensi e analysis and da a-
d i en decision-making. The ollowing poin s highligh he key s ake-
holde s affec ed by he fluc ua ions in DHW demand.
•Ene gy and wa e u ili ies p o ide s: Accu a e DHW consump ion
pa e ns a e essen ial o op imise wa e dis ibu ion and ene gy sup-
ply planning. Sudden usage changes, such as hose caused by lock-
downs, can affec demand o ecas ing and ope a ional efficiency.
•Policy make s: Unde s anding a ia ions in DHW usage helps in-
o m policies ela ed o ene gy efficiency, wa e conse a ion, and
c isis esponse planning. This is pa icula ly ele an o egions an-
si ioning o enewable ene gy sou ces.
•Building enginee s and acili y manage s: De ailed insigh s in o
DHW demand fluc ua ions enable be e sys em op imisa ion, p e-
dic i e con ol, and efficien scheduling o educe ene gy was e and
imp o e sys em pe o mance.
•Real es a e de elope s: Da a on DHW consump ion ends can in-
o m sus ainable building design, ensu ing ha in as uc u e adap s
o bo h no mal condi ions and c isis scena ios.
•Manu ac u e s o DHW sys ems: Insigh s om consump ion pa -
e n changes can guide he de elopmen o mo e adap i e, ene gy-
efficien DHW sys ems, imp o ing hei esponsi eness o a ying
demand le els.
•The esea ch communi y and ene gy planne s: In eg a ion o de-
mand pa e ns in ene gy planning, pa icula ly o enewable-based
DHW sys ems, is c ucial o op imise esou ce alloca ion and ensu e
g id s abili y. In egions whe e sola he mal o hea pump sys ems
a e p edominan , unde s anding peak demand shi s is c i ical o
ene gy s o age and dis ibu ion s a egies.
In his s udy, we employ Communi y Mobili y Repo s [13] da a
collec ed by Google on e ail/ ec ea ion and ansi s a ions o ca e-
go ise he c isis se e i y le els. Fu he , we de elop a hyb id ensembling
s acking classifie (ESC) ha can p edic he c isis and i s se e i y le el
based on DHW consump ion da a collec ed om 10 esiden ial apa -
men buildings loca ed in Kaunas, Li huania. Finally, we pe o m PCA
using he mean and STD alues o hou ly DHW consump ion o each
se e i y le el and clus e hem using he k-means algo i hm. The p o-
posed me hod combines p edic i e modelling and consump ion pa e ns
ex ac ion o enable a ge ed con ol ac ions in dis inc pa s o he DHW
sys em, aiming o mo e esilien and efficien sys ems.
The main no el y o his wo k can be a ibu ed o he ollowing
poin s. Fi s , i add esses an o en o e looked aspec o DHW consump-
ion by ocussing on c isis iden ifica ion and p edic ing he se e i y o
hese e en s, which is ypically challenging due o he unp edic able
na u e o use beha iou . Secondly, i inco po a es mobili y da a om
e ail, ec ea ion, and ansi s a ions, allowing he model o become
adap able o a ious c ises and making i applicable o b oade con ex s
beyond jus ene gy managemen . Thi d, he s udy in oduces a new clas-
sifica ion app oach (a hyb id ensembling s acking classifie (ESC)) ha
pe o ms significan ly be e han s anda d models, achie ing high le -
els o accu acy in c isis and i s se e i y le el p edic ion. Fou h, using
echniques such as PCA and k-means clus e ing enables ca ego isa ion
o ene gy usage pa e ns, allowing a ge ed con ol ac ions o DHW
sys ems supply, dis ibu ion and demand side managemen .
This a icle is s uc u ed as ollows. Sec ion 2 p esen s he p e ious
wo k done on he powe consump ion o DHW p epa a ion o ecas ing
and iden ifica ion o changes in daily consump ion pa e ns du ing c isis
condi ions. Sec ion 3 in oduces he case s udy building and da a used
in his esea ch. Sec ion 4 p o ides all he in o ma ion equi ed o e-
p oduce he esul s p esen ed in his a icle, including he me hods o
c isis and se e i y le els o ecas ing, daily DHW consump ion pe e ns
iden ifica ion, and consump ion hou s clus e ing. Sec ion 5 explo es he
esul s ob ained om he analysis and discuss hei applica ion o DHW
con ol enhancemen . Sec ion 6 concludes he wo k and Sec ion 7 offe s
ecommenda ions o a eas o u u e esea ch.
2. S a e o he a
The COVID-19 pandemic impac ed se e al indus ies, and he ene gy
sec o was no excep ion. The s udy o c isis se e i y in DHW consump-
ion mi o s b oade pandemic-d i en esea ch, including he p edic ion
o heal hca e needs [14] o he public sen imen o COVID-19 [15], high-
ligh ing he impo ance o da a-d i en app oaches in add essing global
heal h challenges. In mos Eu opean coun ies, a s a e o eme gency
was decla ed in Ma ch 2020 and las ed se e al mon hs he ea e , wi h
a s ic e pe iod o lockdown obse ed om mid-Ma ch 2020 h ough
Ap il 2020 [16–18]. One o he mos no able effec s was he ansi ion
o wo king om home, which dec eased indus ial ene gy consump ion
bu inc eased esiden ial/domes ic consump ion in some coun ies [19].
Se e al esea che s ook o analysing he effec o he pandemic on en-
e gy demand wi hin Eu opean coun ies [20,21] and o he na ions such
as Canada [16,19], B azil [22], he USA [23], among o he s [19,24].
Rayash e al. [16], o example, pe o med a comp ehensi e analysis
o he hou ly ene gy demand o he p o ince o On a io, Canada, o
Ap il p e-COVID (2019) and du ing COVID (2020) wi h he assump ion
ha he hea ing ene gy da a a e equi alen o he elec ical load. The e-
sul s p o ed ha he pandemic impac ed elec ici y demand, wi h a o al
dec ease o 14 % and a u he educ ion in demand o e he weekend,
eaching 15–25 %. In addi ion, he esea che s ound ha he elec ici y
demand du ing 2019 inc eased h oughou he week bu dec eased o e
he weekend, while in 2020, he peak would be eached by midweek and
decline h oughou he es o he week [16].
Simila ly, Rouleu e al. [25] analysed he impac o he COVID-19
pandemic on ene gy consump ion, no only conside ing elec ici y, bu
also aking in o accoun ho wa e and space hea ing. The case s udy was
conduc ed on a 40-uni apa men building in Quebec Ci y, which elies
on a dis ic hea ing ho wa e loop ha p o ides hea o he building
and uses na u al en ila ion du ing he ho mon hs. The au ho s ound
ha he peak ho wa e consump ion was eached a 7 PM in he con ol
pe iod. In con as , in he COVID pe iod, he peak was eached in he
a e noon hou s wi h an inc ease 103 %, indica ing ha he lockdown
pe iod du ing he pandemic influenced he ho wa e consump ion pa -
e n [25].
Resea che s in Qa a [24] used machine lea ning echniques o com-
pa e he ac ual usage o elec ici y and he simula ed usage o elec ici y,
hen used hese da a o p edic ene gy consump ion in he yea s 2021
Ene gy & Buildings 336 (2025) 115579
2
Mo kunai e e al.
and 2022. The pandemic was ound o ha e a nega i e effec on elec ic-
i y consump ion in he esiden ial sec o in ha i inc eased du ing he
pandemic due o he s ay-a -home policy. Elec ici y is ee o Qa a i
ci izens and he applica ion o cha ges o i could dec ease he demand
o ene gy in domes ic a eas and cu b he effec s o c ises on he en-
e gy sec o . By analysing he effec s o a c isis such as he COVID-19
pandemic, esea che s and policy make s can p edic , simila ly o he
wo k o Abulibdeh e al. [24], ene gy consump ion pa e ns and be e
p epa e o u u e dis up ions.
Nepal e al. [26] analysed building elec ici y da a using he K-means
app oach; ins ead o andomly selec ed cen oids, he esea che s chose
ini ial cen oids based on he hou ly dis ibu ion o elec ici y da a o
one yea . The pe cen ile me hod was used o selec he ini ial cen oids,
whe e he cumula i e densi y was di ided in o (𝑘+ 2) equally sepa a ed
pe cen iles (k being he numbe o clus e s). The esul s showed ha he
pa e ns among he six buildings analysed we e simila , wi h an inc ease
du ing he day and a dec ease in elec ici y consump ion a nigh . The
au ho de e mined he accu acy o he p oposed me hod by applying he
me hodology on ou diffe en eal-wo ld da a se s and ound ha he
echnique esul ed in much highe accu acy han he andomly selec ed
cen oid o K-means clus e ing.
To unde s and he ull impac o he c isis, i is necessa y o in es i-
ga e all aspec s o ene gy consump ion. DHW usage is o en o e looked
due o i s s ochas ic na u e and high dependency on use beha iou [25].
Howe e , neglec ing his aspec can lead o inaccu a e ene gy manage-
men s a egies.
2.1. Powe consump ion o domes ic ho wa e p epa a ion daily pa e ns
p edic ion
Se e al ac o s, including geog aphic loca ion, ou doo condi ions,
indoo condi ions, numbe o occupan s, and occupan beha iou , in-
fluence DHW use. In o he cases, hese ac o s can ex end o cul u al be-
ha iou o socioeconomic beha iou [27–29]. Mo eo e , as desc ibed in
he li e a u e, ad anced o ecas ing me hods can p o ide use ul insigh s
o imp o ing he managemen o DHW sys ems, aiding in he p edic-
ion o c isis se e i y and enhancing he alloca ion o ene gy esou ces
in esiden ial se ings [30–32]. In esiden ial buildings, DHW accoun s
o 14–25 % o o al ene gy consump ion [4,12,28,33]. Typically, daily
DHW pa e ns ha e wo peaks in he mo ning and e ening [28], which
a e la gely con ibu ed by he ac ha occupan s ei he go o school o
wo k in he mo ning and hen e u n a ound he e ening o con inue
domes ic ac i i ies such as showe ing and cooking. In he design p o-
cess, mos o hese peaks a e o en es ima ed alues. Empi ical models
a e a common me hod o es ima ing DHW demands, whe e, as an ex-
ample, s anda ds like EN 12831-3 p o ide equa ions based on pe capi a
wa e consump ion and sys em efficiency ac o s [28] o de e mine he
demand. Indica o s o he DHW sys em in he design s age, such as peak
powe and he mal ene gy demand, can be de e mined using ele an
s anda ds [34]. Howe e , dynamic simula ions should be used mo e as
hey offe mo e de ails by inco po a ing se e al elemen s, aside om
he heo y-based calcula ions as shown by Rashad e al. [35] h ough
he use o TRNSYS o analysing ene gy demand.
Unde s anding peak powe consump ion om DHW usage is impo -
an in p edic ing he impac o c ises condi ions on daily pa e ns. How-
e e , owing o he a ious ac o s influencing peak powe demand, he
DHW sys ems a e o en no designed o mee he equi emen s o such
fluc ua ing needs, which usually leads o inefficiencies, inc eased ope -
a ional cos s o sys em ailu es, especially in mul iple occupancy build-
ings such as apa men s. As discussed in he e iew by Fuen es e al.
[28], mos DHW sys ems a e designed based on s anda ds and no eal
da a, and as such, many sys ems a e o en o e sized o unde sized. Se -
e al modelling ools [36] a e used in designing DHW sys ems wi h con-
side a ion o occupancy and usage pa e ns h ough ep esen a i e days;
howe e , his app oach doesn’ ake in o accoun he dynamic na u e o
wa e consump ion. Amanowicz [37] highligh s he need o be a en i e
o peak powe selec ion, which, as he au ho desc ibes, affec s cos , size
and efficiency o DHW sys ems. The au ho used h ee diffe en me h-
ods o analyse peak powe consump ion and ound ha he me hod wi h
he highes confidence o esul s is he Sande ’s me hod which uses ho
wa e olume flowing om he wa e de ice, empe a u e o wa e and
ime use o de e mine ene gy equi emen s. Rubina e al. [38] empha-
sized he impo ance o unde s anding peak wa e flow a es in he de-
sign o DHW sys ems, which also influences ac o s like pipe design. The
au ho s used a new empi ical calcula ion o he wa e flow es ima ion
and compa ed ac ual wa e flows wi h he new design wa e flow alues
and ound ha he me hod esul ed in a educ ion in ene gy demands
o wa e hea ing, as well as a educ ion in pipe size, which ul ima ely
educes he cos o manu ac u ing.
Use beha iou plays an impo an ole in powe consump ion o
DHW, and gene ally, his c i e ia is no conside ed ully in he design o
he sys ems and as such would affec he p edic ion o ho wa e usage
in c isis o non-c isis condi ions. Hansen e al. [39] conduc ed an in e -
es ing s udy o de e mine how occupa ion, age, income, and o he can
affec he peak powe usage o a building. I was ound ha households
wi h whi e-colla wo ke s had highe mo ning peaks, whe eas pension-
e s’ homes had lowe and la e peaks. Households wi h ages 41–50 yea s
had highe mo ning peaks wi h 4.5 kWh in he 7 h hou , whe eas age
g oups 18–40 yea s and 51–60 yea s had a lowe powe consump ion
wi h 4 kWh in he 7 h hou as well. High-income households exhibi ed
highe consump ion in he mo ning and e ening peaks, whe eas lowe -
income g oups p esen ed much fla e peaks. These esul s indica e ha
peak powe consump ion is affec ed by occupan s and hei beha iou ,
and as such, i should also be conside ed in design and managemen o
u ili ies.
Cao e al. [33] p edic ed ho wa e demand using se en occupan s’
ho wa e usage beha iou by collec ing showe da a. The esea che s
ained he da a using he Suppo Vec o Machine (SVM), a da a min-
ing echnology, o analyse he showe ing habi s o he occupan s. They
ound ha i was possible o p edic he ho wa e usage and implemen
a ho wa e supply s a egy. Howe e , his p edic i e model achie ed a
oo mean squa e e o (RSME) o 77.63 when he showe habi s o he
occupan s we e analysed indi idually e sus he RSME alue o 58.65
when he da a we e agg ega ed, which led he esea che s o conclude
ha a sepa a e analysis p o ided be e accu acy. The esea che s also
no e ha he diffe en choice o e alua ion c i e ia is he main eason
o his diffe ence.
To o m mo e accu a e p edic i e models o DHW consump ion, i
is necessa y o pe o m an ex ensi e da a e iew when analysing la ge
da a se s o emo e any ou lie s. Sonnekalb e al. [40] used neu al ne -
wo ks and Gaussian p ocesses o e alua e da a se s o lea n and p edic
human beha iou conce ning DHW o adap hea ing imes o educe en-
e gy consump ion. The ini ial da a o he ho wa e p epa a ion we e
p esen ed in minu es; he e o e, da a p e-p ocessing was necessa y o
con e he da a in o hou ly in e als and add o he specific ea u es. In-
comple e da a se s we e elimina ed and he esul s showed ha i would
be possible o educe he window o ho wa e p epa a ion, hus educ-
ing he ene gy consump ion o ho wa e p epa a ion by up o 33–85 %.
Mal ais e al. [4,41] used model p edic i e con ol (MPC) elying
on da a p o ided by neu al ne wo ks ha we e ained om eal da a
o he ene gy managemen o DHW o single- amily esiden ial uni s. I
was ound ha he long- e m p edic ions om machine lea ning models
can show highe inaccu acies compa ed o he heo e ical app oach [4].
Howe e , hese models can s ill be used o p edic DHW demand, and i
used oge he wi h a s o age ank, whe e he MPC is inaccu a e, a supply
would s ill be p esen o mee he demand. The au ho also sugges ed
ha p edic ion inaccu acies a e educed by inc easing he ime in e al
o 2h.
Clus e ing is no limi ed o analysing building elec ici y da a, as
men ioned ea lie . Ri chie e al. [42] used clus e ing and s a is ical
analysis o model DHW usage. The esea che s c ea ed clus e s and
sub-clus e s o ime, olume, and flow a es, and he gene a ed model
Ene gy & Buildings 336 (2025) 115579
3
Mo kunai e e al.
de e mined he p obabili y o occu ence o hese clus e s o e he spe-
cific dis ibu ion. The model showed high accu acy compa ed o he
measu ed da a. Wi h ha in mind, he au ho s p oposed ha he model
could be used o ene gy managemen s a egies as he ene gy d awn
om he g id can be p edic ed.
DHW o ecas ing models can po en ially op imise sys em con ol,
leading o ene gy sa ings and economic benefi s. Howe e , de elop-
ing obus models ha can accoun o he s ochas ic na u e o use be-
ha iou and dis up i e e en s emains a challenge. The e o e, aining
hese models o ecognise and espond o c ises is c ucial.
2.2. Changes in daily pa e ns du ing c isis condi ions
A na ional o global c isis can occu a any momen . Recessions, pan-
demics, o na u al disas e s a e all examples o c ises. Policymake s and
go e nmen s can lea n om c ises such as he COVID-19 pandemic and
be e p epa e by c ea ing o ecas ing and p e en ion s a egies in a i-
ous disciplines o mi iga e u u e disas e s [43]. Gene ally, ene gy con-
sump ion du ing he COVID-19 pandemic saw a change in daily pa -
e ns. The p epandemic condi ions had a peak ene gy consump ion in
he mo ning hou s o he weekday and significan ly lowe alues on
weekends; howe e , du ing he pandemic, no ypical mo ning peaks
we e obse ed, and he ene gy consump ion was lowe [17].
Zhang e al. [20] simula ed he impac o he COVID-19 pandemic on
ene gy demand in a building ma ix in Sweden using he UMI ool. The
buildings we e di ided acco ding o hei a che ype, whe e occupancy
and DHW, among o he pa ame e s, we e conside ed. The esea che s
showed ha he a e age sys em ene gy demand, which includes hea ing,
cooling, and domes ic wa e , dec eases in a ange o 7.1 % o 12.0%. I
was also concluded ha inc easing confinemen cons ain s inc ease he
DHW ene gy demand in esiden ial buildings; howe e , less hea ing is
equi ed due o g ea e in e nal hea gains [20].
Kim e al. [12] analysed eal da a om an apa men complex in
Sou h Ko ea o de e mine changes in DHW demand du ing he pan-
demic. Unlike mos Eu opean coun ies, he s a e o eme gency in Ko ea
was issued on 20 Janua y (2020), almos wo mon hs be o e i was is-
sued in Eu ope. Da a we e collec ed a hou ly in e als and included
DHW accumula ed ene gy, flow a e, supply empe a u e, ou doo em-
pe a u e, and ci y wa e empe a u e. The analysis iden ified a signi -
ican inc ease in DHW demand a e he pandemic, which is due o
changes in he daily consump ion pa e ns o he occupan s as a esul
o he s ay-a -home policy, simila o wha was iden ified by Rouleu e
al. [25].
Abu-Baka e al. [44] used clus e ing o de e mine he impac o he
COVID-19 pandemic on wa e consump ion pa e ns in England. The
pa e ns we e di ided in o ou clus e s: he e ening peak, he la e mo n-
ing, he ea ly mo ning, and mul iple peaks, which we e iden ified using
he “elbow” me hod. The esea che s ound ha he e was an inc ease
in wa e demand in each o he clus e s du ing he lockdown pe iod de-
fined as Janua y o May 2020. Using K-means clus e ing om May 2019
o Oc obe 2020 (conside ing wo kdays, weekends, and holidays), Dz-
iminska e al. [45] e ealed ha he pa e ns ob ained o h ee diffe en
buildings we e simila , diffe ing only in olume o wa e consump ion
in a gi en hou . A change in he mo ning and e ening peak is obse ed,
wi h a shi o abou wo hou s la e in he mo ning hou s and abou
wo hou s ea lie du ing he nigh . The e is also inc eased usage du ing
he a e noon.
2.3. Iden ified challenges in managing DHW consump ion unde c isis
condi ions
The s a e-o - he-a e iew e ealed ha ecen esea ch has ad-
d essed changes in ene gy consump ion pa e ns, including c ises such
as he COVID-19 pandemic, which significan ly al e ed daily ou ines
and subsequen ly affec ed esiden ial ene gy use. S udies ha e demon-
s a ed how mobili y es ic ions du ing lockdowns influenced DHW
demand and o he u ili ies, no ing shi s in peak consump ion imes and
inc eased esiden ial demand due o s ay-a -home policies. In pa icu-
la , esea che s ha e used machine lea ning echniques o p edic en-
e gy consump ion and ca ego ise usage pa e ns, in eg a ing da a om
bo h en i onmen al ac o s and use beha iou . Howe e , se e al gaps
emain unadd essed:
•DHW demand analysis unde c isis condi ions. While a ious
s udies ha e explo ed gene al ene gy consump ion du ing he pan-
demic, ew ha e ocused specifically on DHW demand [16,24,26].
DHW consump ion is highly a iable and use dependen , making
i challenging o manage, especially in c isis condi ions [25]. Mo e
esea ch is needed o iden i y he change in DHW consump ion daily
pa e ns du ing c isis and seg ega e hem based on he se e i y le el.
•Model gene alisabili y o a ious c ises. Exis ing s udies o en
ely on specific da a ela ed o pandemics, such as COVID-19 case
coun s, limi ing hei applicabili y o simila c ises [12]. This educes
he gene alisabili y o he p edic ion models o o he c isis scena ios.
The e is a need o models ha can le e age b oade indica o s, such
as u ban mobili y da a.
•Con ol op imisa ion based on c isis se e i y le el. Cu en mod-
els ocus on o ecas ing ene gy demand [30–32], bu u he discus-
sion on a ge ed con ol ac ions based on he esul s is lacking. E -
ec i e c isis managemen in ene gy sys ems should include dynamic
con ol s a egies ha espond o p edic ed changes in demand, pa -
icula ly conside ing he in e mi en na u e o enewable ene gy
sou ces [35].
3. Case s udy in oduc ion
3.1. Case s udy buildings
Ten esiden ial apa men buildings in Kaunas (Li huania) we e se-
lec ed as a case s udy (Fig. 1). The u ban block has clea bounda ies
o in ensi e s ee s and na u al elemen s. I con ains mul i-fla housing
buil om he 1960s o he la e 1980s, accommoda ing di e se social
g oups. Se e al mul i-fla esiden ial buildings ha e been mode nised
by inc easing he he mal esis ance o he building en elope and ap-
plying au onomous oom empe a u e con ol. The basic desc ip ion o
building se ice sys ems is as ollows.
•Hea ing sys em. Buildings a e hea ed by he mal ene gy supplied
h ough a cen alised dis ic hea ing (DH) ne wo k ope a ed by he
ci y’s he mal ene gy p o ide . The DH ne wo k in Kaunas ci y co -
e s all he majo popula ed a eas. Fo all buildings, he he mal en-
e gy supply o hea ing is egula ed acco ding o he ou doo em-
pe a u e by a senso .
•Wa e sys em. The cold wa e supply and sewe age sys ems ollow
he same p inciple, i.e. dis ic (cen alised) supply and disposal by
he ci y’s wa e se ices p o ide . Ho wa e is p epa ed wi hin he
Fig. 1. A angemen o selec ed mul i-fla esiden ial buildings.
Ene gy & Buildings 336 (2025) 115579
4
Mo kunai e e al.
Table 1
Cha ac e is ics o selec ed mul i-fla esiden ial buildings.
Building no. Use ul a ea (m2) Numbe o apa men s A e age apa men a ea (m2) Numbe o aps Numbe o occupan s
92 1042 32 32.6 64 32
90 1524 32 47.6 64 44
89 891 18 49.5 36 26
88 1511 32 47.2 64 44
87 812 18 45.1 36 23
86 1416 32 44.3 64 41
82 1517 32 47.4 64 44
80 1530 32 47.8 64 44
79 1423 87 16.4 87 87
75 1400 86 16.3 86 86
building’s hea ing uni , hea ed h ough a dedica ed hea exchange ,
and dis ibu ed h oughou he building’s ho wa e ne wo k o con-
sump ion. Since he buildings con ain many fla s, loca ion and dis-
ance be ween he pipelines a e significan ac o s. To add ess his,
eci cula ion loops a e ins alled in he sys em. These pa allel and
addi ional pipelines, along wi h he eci cula ion pump and o he
necessa y equipmen , con inuously ci cula e ho wa e h ough he
sys em o ensu e a imely ho wa e supply a he mos incon enien
( u hes ) poin ( ap) om he hea exchange . Ho wa e is p epa ed
using he same he mal ene gy sou ced om he DH sys em a he
building’s hea ing dis ibu ion plan . All buildings a e equipped wi h
ins an aneous domes ic ho wa e hea exchange s, wi hou s o age
anks. The p incipal schemes o he sys em a e defined by he ene gy
p o ide [46].
The use ul (hea ed) a ea o he buildings a ies om 812m2 o
1795m2, which co esponds o be ween 18 and 87 apa men s wi h co -
ido s and basemen spaces. The numbe o occupan s anges om 23
o 87 and he numbe o aps o ood p ocessing and hygiene ac i i ies
anges om 26 o 87 (Table 1). The in o ma ion p o ided is based on
da a om he S a e En e p ise Cen e o Regis e s in o ma ion sys em
[47].
3.2. Building da a desc ip ion
Da a on ene gy consump ion o ho wa e p epa a ion and main-
enance ha e been collec ed om sepa a e sma me es, which a e
ins alled in he hea dis ibu ion plan s o buildings and measu e he
he mal ene gy consump ion a 1-h in e als. In addi ion, sma me es
measu e he empe a u e o he inle and ou le hea agen s and he flow
a e. The da a collec ion pe iod o pilo case buildings anges om 2 o
10 yea s be ween 2011-10-01 and 2021-09-30. The whole se consis s o
480,580 en ies ( imes amps) o he mal ene gy o ho wa e measu ed
in kWh.
Da a we e e ie ed om sma me es in he CSV (Comma Sepa a ed
Values) da a o ma . Subsequen ly, i had o be ea ed acco dingly by
fil e ing, cleaning, agg ega ing, and in e pola ing. To ensu e da a com-
pa abili y o objec i e e alua ion and analysis, no malisa ion was ap-
plied based on he mos significan influencing ac o : he numbe o oc-
cupan s. By di iding he ene gy consump ion o ho wa e p epa a ion
by he numbe o occupan s (Table 1), a de i ed uni o kWh∕occupan
is ob ained, elimina ing he influence o building size.
Fig. 2 shows he no malised daily he mal ene gy consump ion o
DHW p epa a ion. The da a collec ed om all buildings and used o
his analysis span om 01/01/2018 o 30/09/2021. The e ical ed
anspa en ba s ma k he lockdown pe iods: he fi s om 16/03/2020
o 16/06/2020, and he second om 7/11/2020 o 30/06/2021. The
g een e ical ba s indica e he co esponding pe iods p io o he lock-
downs. The blue cu e ep esen s he o al daily ene gy consump ion,
while he o ange cu e shows he a e age mon hly daily ene gy con-
sump ion, highligh ing a clea seasonal end.
The inc ease in ene gy consump ion du ing he hea ing season can be
a ibu ed o he lowe empe a u e o cold wa e , as mo e he mal en-
e gy is equi ed o each he ho wa e se -poin empe a u e, i.e. 55◦C.
In addi ion, occupan consump ion habi s and he eci cula ing ho wa-
e loop con ibu e o highe ene gy demand du ing he hea ing sea-
son due o a sligh dec ease in indoo empe a u e. Du ing he hea ing
season, he indoo empe a u e ends o be lowe han du ing he non-
hea ing season pe iod, which inc eases he hea loss o he en i onmen
om he ci cula ing ho wa e loop pipes and hus he ene gy demand,
e en hough he ho wa e loop is used con inuously. Compa ing he
same pe iods be o e and du ing lockdown, he plo does no indica e
significan diffe ences in ene gy consump ion. Howe e , he e a e e-
cu ing ou lie s wi h alues o 0 o significan ly lowe alues du ing he
wa m season. This is likely due o he annual main enance o he build-
ing’s hea ing and ho wa e sys ems when hey a e empo a ily shu
down.
3.3. Mobili y da a desc ip ion
In esponse o he COVID-19 pandemic, Google de eloped Commu-
ni y Mobili y Repo s [13] o p o ide public heal h officials wi h ag-
g ega ed anonymised mobili y da a o in o med c i ical decision mak-
ing. These epo s acked mo emen ends ac oss a ious geog aphic
egions and ca ego ies, including e ail and ec ea ion, g oce ies and
pha macies, pa ks, ansi s a ions, wo kplaces, and esiden ial a eas.
In his s udy, da a specific o Kaunas ci y we e ex ac ed and anal-
ysed, wi h a ocus on changes in mobili y pa e ns in esponse o COVID-
19 ela ed policies. Changes we e examined in wo key ca ego ies: e-
ail and ec ea ion ac i i ies (including places such as es au an s, ca es,
shopping cen es, heme pa ks, museums, lib a ies, and mo ie hea es)
and ansi s a ion ac i i ies (encompassing public anspo hubs such
as bus s a ions). The ca ego ies o e ail ec ea ion and ansi s a ions
we e chosen due o hei significan impac on u ban mobili y and pub-
lic beha iou du ing he COVID-19 pandemic. Re ail and ec ea ion
ac i i ies se e as key indica o s o economic ac i i y and social in e ac-
ion, eflec ing changes in consume beha iou and adhe ence o pub-
lic heal h measu es such as lockdowns o social dis ancing guidelines.
Meanwhile, ansi s a ion ac i i ies p o ide c i ical insigh s in o pub-
lic anspo usage, which is di ec ly co ela ed wi h mobili y pa e ns,
access o essen ial se ices, and he b oade unc ioning o he u ban
economy. By concen a ing on hese wo ca ego ies, he s udy aimed o
cap u e he mos influen ial aspec s o daily li e in Kaunas affec ed by
COVID-19 ela ed policies. The da a, p o ided in he o m o ime se ies,
span om Feb ua y 2020 o Decembe 2021.
Mobili y da a, including he ca ego ies o e ail / ec ea ional and
ansi s a ions om Google mobili y epo s, clea ly indica es he s a
o bo h lockdown pe iods in Kaunas, Li huania, du ing he COVID-19
pandemic (Fig. 3). The pe cen age change om baseline, depic ed in
he g aph, highligh s he sha p declines in mobili y co esponding o
he onse o he fi s and second lockdown pe iods. These lockdown
pe iods a e eflec ed in he diffe en se e i y le els o es ic ions, ep-
esen ed by colou -coded bands anging om baseline (no mal ac i i y)
o se e i y 5 ( he mos s ingen es ic ions). The da a show ha mobil-
i y dec eased significan ly a he beginning o he pandemic, especially
Ene gy & Buildings 336 (2025) 115579
5

Mo kunai e e al.
Fig. 2. No malised daily he mal ene gy consump ion o domes ic ho wa e p epa a ion.
Fig. 3. Mobili y changes in e ail/ ec ea ion ac i i ies and ansi s a ions in ela ion o c isis se e i y le els.
du ing he s ic es lockdown phases, be o e g adually eco e ing in line
wi h he easing o es ic ions. Howe e , mobili y le els emained below
baseline h oughou he s udy pe iod, indica ing a p olonged impac o
he pandemic on public ac i i y, pa icula ly in ansi and ec ea ional
spaces. The ex ac ion o he Se e i y le els a e u he de ailed in he
Me hodology sec ion.
4. Me hodology
The o e all esea ch app oach is illus a ed in Fig. 4. I consis s o
h ee main pa s: da a collec ion and p epa a ion, c isis and se e i y
o ecas ing, and pa e n ex ac ion and clus e ing. The fi s pa in ol es
da a om wo main sou ces: 10 case s udy buildings in Kaunas (Li hua-
nia) and Google Communi y Mobili y Repo s [13]. In his phase, he
building da a unde go he usual da a cleaning, no malisa ion, and p e-
p ocessing s eps. C isis se e i y le els a e ex ac ed om he da ase s on
e ail/leisu e ac i i y and ansi s a ions collec ed in he Google Com-
muni y Repo s. Finally, he p e-p ocessed da a a e me ged in o a single
da ase ha includes addi ional empo al ea u es.
In he nex phase, he ESC classifie is used o o ecas he c isis
and i s se e i y le el. The o ecas ing model is u he c oss- alida ed
o ensu e i s eliabili y and accu acy.Fu he , daily DHW consump ion
pa e ns a e ex ac ed o each o he c isis se e i y le els. Addi ion-
ally, PCA and k-means clus e ing a e used o define he clus e s o daily
consump ion hou s.
The esul s o o ecas ing, pa e n ex ac ion and clus e ing ac s as an
inpu o DHW sys ems con ol op imisa ion. Each pa o he me hod-
ology is u he de ailed in his chap e .
4.1. Da a collec ion and p epa a ion
4.1.1. Calcula ion o ho wa e consump ion
The collec ed aw da a pe ain he amoun o he mal ene gy used
o ho wa e p epa a ion. Howe e , o de e mine he dis inc ho wa e
consump ion pa e ns, he DHW consump ion da a a e needed. The main
ac o de e mining he amoun o he mal ene gy is he empe a u e o
he cold wa e o be hea ed, which a ies h oughou he yea due o
he changing empe a u e o he ou doo ai . Howe e , he cold wa e
empe a u e a ia ion is significan ly influenced by he he mal ine ia
Ene gy & Buildings 336 (2025) 115579
6
Mo kunai e e al.
Fig. 4. Resea ch app oach.
o he g ound (soil), as he supply pipelines a e laid a a dep h o a
leas 1,8m unde g ound o p e en eezing du ing he coldes pe iods
o win e . The a e age dep h o he pipelines in Kaunas a ies be ween
2 and 2.5m.
Kaunas (cen al Li huania) is in he cold- empe a u e zone, wi h
mode a ely wa m summe s and cold win e s. The ci y o Kaunas has
an a e age long- e m ou doo empe a u e o a ound 7–8 ◦C. The a -
e age ou doo empe a u e in July is a ound 17◦C, and in win e
a ound −5◦C. Li huania has ela i ely ho summe s, day ime highs
abo e +35◦C, and cold win e s, wi h nigh ime lows below −30 ◦C.
The e o e, he amoun o ho wa e consumed 𝑉ℎ𝑤, 𝑚3 knowing he
he mal ene gy consumed 𝑄ℎ𝑤, 𝐽 was calcula ed using Eq. (1).
𝑉hw =𝑄hw
𝐶𝑣⋅(𝜃hw −𝜃cw)(1)
whe e:
–𝐶𝑣 is he olume ic hea capaci y o he wa e . The s anda d alue
is 4,160,000 J∕(m3◦C).
–𝜃ℎ𝑤 is he s anda dised ho wa e empe a u e (◦C). A empe a u e
o 55 ◦C should be main ained, conside ing he Building Regula ions’
equi emen s.
–𝜃𝑐𝑤 is he supplied cold wa e empe a u e (◦C), which a ies be-
ween 4◦C and 16◦C o e he yea .
The cold wa e empe a u e in he ne wo k h oughou he yea is
de e mined based on he a e age daily ou doo empe a u e. To ake
in o accoun he he mal ine ia o he soil, i.e. he a ia ion in ou doo
empe a u e, which is no mally mos significan o e 24h, a mo ing
a e age me hod was adop ed. The ela ionship be ween he cold wa-
e empe a u e and he mo ing a e age ou doo empe a u e is based
on he cold wa e empe a u e measu emen s decla ed by he p o ide ,
whe e a lowe limi o −4◦C wa e empe a u e co esponds o an ou -
doo empe a u e o −20◦C and an uppe bounda y o −16◦C co e-
sponds o +25 ◦C. The cold wa e and ou doo ai empe a u e mea-
su emen s we e used o apply a linea eg ession me hod and de i e he
Eq. (2).
𝜃𝑐𝑤 =𝜃𝑜𝑢𝑡 ⋅0.2667 + 9.3333 (2)
whe e:
–𝜃𝑜𝑢𝑡 is he 24-h mo ing a e age o daily ou doo empe a u e, ◦C.
Table 2
Lockdown se e i y cha ac e iza ion based on mobili y
changes (Kaunas).
Labels Desc ip ion
Baseline Pe cen age change equal o g ea e han 0
Se e i y1 Pe cen age change be ween −1 % and −20 %
Se e i y2 Pe cen age change be ween −20 % and −40 %
Se e i y3 Pe cen age change be ween −40 % and −60 %
Se e i y4 Pe cen age change be ween −60 % and −80 %
Se e i y5 Pe cen age change be ween −80 % and −100 %
Fig. 5 shows he a ia ion o he cold wa e empe a u e in he supply
ne wo ks acco ding o he fluc ua ion o he ou doo ai empe a u e.
The esul s a e plo ed o he pe iod, s a ing om 2016 o he end o
Sep embe 2021.
4.1.2. Cha ac e isa ion o se e i y based on local mobili y pa e ns
Google mobili y da a include pe cen age changes measu ed agains
a baseline ha ep esen s ypical mobili y le els be o e he COVID-19
pandemic. Using p edefined h esholds, a cha ac e isa ion scheme was
implemen ed o hese de ia ions o illus a e he a ying le els o de-
pa u e om baseline mobili y pa e ns (Table 2):
•I he mobili y change o e ail/ ec ea ion and ansi s a ions was
he same, his alue was assigned o he subsequen label.
•I he mobili y change diffe ed, only he mobili y change alue o
e ail/ ec ea ion was used as he subsequen label.
The Google mobili y da a begins in Feb ua y 2020, while he wa-
e usage olume da a begins in Feb ua y 2019. Hence, all da a poin s
o 2019 we e labelled wi h he “Baseline” label o dis inguish he
p e-COVID-19 pe iod when mobili y pa e ns we e unaffec ed by lock-
downs.
This cha ac e isa ion de e mines he se e i y o COVID-19 lock-
downs and he gene al es ic ions imposed on local esiden s. The
“Baseline” label ep esen s no mal condi ions, i.e. indica ing he p e-
COVID le el o mobili y. In con as , se e i y le els (Se e i y 1 h ough
Se e i y 5) deno e inc easing le els o es ic ed mobili y co ela ing
wi h he in ensi y o lockdown measu es and o he es ic ions in he
u ban a ea o Kaunas. Al hough mobili y changes a e eco ded daily,
he cha ac e isa ions we e applied o ep esen condi ions o all subse-
quen hou s o each day. Fig. 6 shows an agg ega ed iew o he hou ly
coun s o COVID-19 qua an ine se e i y le els impac ing mobili y da a
o each mon h om Janua y 2020 o May 2021. I is highligh ed ha
he e is a clea ise in hou s cha ac e ised as mo e se e e in e ms o he
lockdown effec , pa icula ly in Ap il 2020 and Decembe 2020, whe e
he mos ins ances o Se e i y 5 a e eco ded, which is in line wi h he
his o ical imeline o he aus e i y o he lockdown measu es.
4.1.3. Combined da ase and ea u e ex ac ion
Following he cha ac e isa ion scheme o each imes amp desc ibed
in Sec ion 4.1.2, he esul ing hou ly labels we e me ged wi h he hou ly
domes ic wa e olume in ake da a. Consequen ly, he combined da a
se spans om Feb ua y 6, 2019, o Sep embe 29, 2021, o each build-
ing.
The domes ic wa e olume in ake da a o each o he en buildings
(as desc ibed in Sec ion 4.1.1) we e sequen ially combined in o a single
da ase . Using he cha ac e isa ion scheme ou lined in Sec ion 4.1.2 o
each imes amp, he esul ing hou ly labels we e me ged concu en ly
wi h he co esponding wa e in ake da a.
Fo he analysed da ase , ime was inco po a ed as a ea u e by spli -
ing he imes amp in o ca ego ical alues o c ea e addi ional empo al
ea u es. In addi ion o s anda d empo al ea u es, such as he hou
o he day, day o he week, and mon h, specific ea u es we e syn he-
sised based on he unique cha ac e is ics o ou da ase , eflec ing he
loca ion o he case s udy. Li huanian holiday da a o 2019 o 2021
we e included using he ‘holiday’ Py hon lib a y. An addi ional ea u e
Ene gy & Buildings 336 (2025) 115579
7
Mo kunai e e al.
Fig. 5. Rela ionship be ween ou doo ai empe a u e and cold wa e empe a u e in supply ne wo ks.
Fig. 6. Qua an ine se e i y cha ac e is ic ins ances (hou ly coun ).
Table 3
P edic i e modelling: ea u es desc ip ion.
Fea u e Labelling
lockdSe e i y Baseline: 0, Se e i y1: 1,…Se e i y5: 5
W_ ol Wa e in ake o each building (m3)
Qua e 1 o 4
Mon h 1 o 12
Dayo Mon h 1 o 31
Weekday 0 o 6
Hou 0 o 23
IsWknd_Holiday 0, 1
(IsWknd_Holiday) was c ea ed o iden i y whe he a gi en da e alls on
a Sa u day o Sunday and coincides wi h any Li huanian holiday.
An ou lie de ec ion s a egy was applied o he wa e olume da a,
iden i ying alues abo e he 99.99 h pe cen ile o each o he en build-
ings and eplacing hem wi h he maximum alue co esponding o his
pe cen ile.
The final da a se o he ESC o ecas was di ided in o aining and
es se s, wi h 80% aining and 20 % o es ing [48].
4.2. C isis and se e i y o ecas ing
4.2.1. P edic i e modelling o lockdown- ype eme gencies
As indica ed in he ele an li e a u e, he COVID-19 lockdown and
i s consequences on daily ou ines di ec ly affec ed esiden s’ ene gy
and ho wa e consump ion pa e ns. The e o e, i has become c i ical
o iden i y such ab up u u e eme gencies so ha u ili y p o ide s can
make immedia e adjus men s and p epa a ions o ensu e ha no se e e
dis up ions occu o enan s.
In his s udy, a da a-d i en pa e n ecogni ion mechanism was de-
eloped o iden i y po en ial u u e i egula i ies in esiden ial wa e
demand unde un o eseen ci cums ances esembling a lockdown e en ,
such as he pos -COVID-19 pe iod. Using se e i y le el labels, a ma-
chine lea ning-based classifie was c ea ed o p edic whe he such an
eme gency migh be imminen and, i so, o es ima e he expec ed se e -
i y o he si ua ion. To achie e his, a hyb id ensemble s acking classifie
(ESC) was implemen ed. This me a-ensemble lea ning model combines
he s eng hs o mul iple indi idual classifie s h ough a wo-le el s ack-
ing app oach, enhancing p edic i e accu acy o i egula demand pa -
e ns.
Ene gy & Buildings 336 (2025) 115579
8
Mo kunai e e al.
The fi s laye consis s o wo base classifie s: LGBMClassifie
(LGBMC) and His G adien Boos ingClassifie (HGBC). The LGBMC clas-
sifie op imises he ollowing objec i e unc ion:
𝐿(𝜃) =
𝑛
∑
𝑖=1
𝑙(𝑦𝑖, 𝑓(𝑥𝑖;𝜃)) + Ω(𝑓)(3)
whe e:
–𝐿(𝜃) is he o e all loss unc ion.
–𝑙 is he loss unc ion.
–𝑦𝑖 is he ue label.
–𝑓(𝑥𝑖;𝜃) is he p edic ed alue.
–Ω(𝑓) is he egula isa ion e m o a oid o e fi ing.
His G adien Boos ingClassifie uses he g adien boos ing ame-
wo k:
𝐹𝑚(𝑥) = 𝐹𝑚−1(𝑥) + 𝛾𝑚ℎ𝑚(𝑥)(4)
whe e:
–𝐹𝑚(𝑥) is he cu en model a i e a ion 𝑚.
–𝐹𝑚−1(𝑥) is he p e ious model.
–𝛾𝑚 is he lea ning a e.
–ℎ𝑚(𝑥) is he base lea ne a i e a ion 𝑚.
The second laye , he me a-lea ne , in eg a es he ou pu om he
base-le el classifie s. The me a-lea ne chosen is XGBClassifie (XGBC).
The XGBoos classifie can be o mula ed as ollows:
𝐿(𝜃) =
𝑛
∑
𝑖=1
𝑙(𝑦𝑖, 𝑓(𝑥𝑖;𝜃)) +
𝐾
∑
𝑘=1
Ω(𝑓𝑘)(5)
whe e:
–𝐿(𝜃) is he o e all loss unc ion.
–𝑙 is he loss unc ion.
–𝑦𝑖 is he ue label.
–𝑓(𝑥𝑖;𝜃) is he p edic ed alue.
–Ω(𝑓𝑘) is he egula isa ion e m o he 𝑘 h ee.
The s acking p ocess in ol es wo laye s:
•Fi s laye :
𝑦𝐿𝐺𝐵𝑀𝐶 =𝐿𝐺𝐵𝑀𝐶(𝑋)(6)
𝑦𝐻𝐺𝐵𝐶 =𝐻𝐺𝐵𝐶(𝑋)(7)
•Second laye (me a lea ne ). The me a-lea ne 𝑋𝐺𝐵𝐶 uses he p e-
dic ions o he base classifie s as i s inpu :
𝑦𝑚𝑒𝑡𝑎 =𝑋𝐺𝐵𝐶([ 𝑦𝐿𝐺𝐵𝑀𝐶 , 𝑦𝐻𝐺𝐵𝐶 ]) (8)
4.2.2. C oss- alida ion
All models we e used o one-s ep (i.e. 1 h) o ecas ing. Addi ionally,
he ESC employs 5- old c oss- alida ion du ing he aining o he me a-
lea ne (Eqs. (9) and (10)). The da a we e spli in o 5-equal olds in
5- old CV and hence in each old, 20 % o he da a is a ailable. One old
is le o es ing, and he emaining ou olds a e used o aining.
The decision o use 5- old c oss- alida ion is commonly made because
i achie es a good balance be ween compu a ional efficiency and model
e alua ion eliabili y. I is less compu a ionally expensi e han highe -
old c oss- alida ion, especially when dealing wi h la ge da a se s o
complex models such as me a-lea ning.
𝐶𝑉𝐸𝑆𝐶 =1
𝐾
𝐾
∑
𝑘=1
𝑦(𝑘)
𝑚𝑒𝑡𝑎 (9)
whe e:
–𝐾 is he numbe o olds (in his case, 5).
–𝑦(𝑘)
𝑚𝑒𝑡𝑎 is he p edic ion o he me a-lea ne on he 𝑘 h old.
Table 4
ESC hype pa ame e s.
Classifie Hype pa ame e s
LGBMC eg_alpha=0.7, eg_lambda=0.7
lea ning_ a e=0.07
HGBC max_lea _nodes=30, lea ning_ a e=0.07
XGBC max_dep h=6, subsample=0.8
Combining he base classifie s and me a-lea ne in a wo-le el s ack-
ing amewo k can be exp essed as:
𝑦 =𝑋𝐺𝐵𝐶([ 𝑦𝐿𝐺𝐵𝑀𝐶 , 𝑦𝐻𝐺𝐵𝐶 ]) (10)
He e 𝑦 is he final p edic ion o he ESC model. The hype pa ame-
e s o each base classifie we e ca e ully selec ed o balance bias and
a iance, aiming o educe o e -fi ing. Specific alues we e de e mined
using g id o andom sea ch me hods along wi h selec ed ial and e o
compiles, ensu ing op imal pe o mance on he es se s (Table 4).
4.3. Pa e n ex ac ion and clus e ing
Fo he fi e defined c ises se e i y le els and he baseline (no mal
condi ions), daily pa e ns o DHW consump ion we e ex ac ed using
he mean alues o each hou o he day. The s anda d de ia ion (STD)
was calcula ed o e alua e he possible high a ia ion in he da a. In
addi ion, weekends and holidays we e excluded, while daily pa e ns
we e ex ac ed based on obse a ions du ing da a explo a o y analysis.
The da a poin s co esponding o each se e i y le el and he baseline
we e spli in o six da a se s ha we e u he used o clus e ing. Each
da a se included 24 ows ep esen ing alues o ho wa e consump ion
o each hou o he day; howe e , he numbe o dimensions diffe ed
o each da a se since no all mon hs showed he six se e i y le els. The
s uc u e and mon hs included in each da a se a e p esen ed in Table 5.
P incipal componen analysis (PCA) and he k-means me hod we e
used o clus e sepa a e hou s in a day o ene gy consump ion o DHW
p epa a ion. The da a se used included mean and STD alues o all
in es iga ed buildings. Using he mean and STD allowed us o conside
possible s ong disc epancies be ween sepa a e buildings’ ho -wa e con-
sump ion pa e ns.
5. Resul s and discussion
5.1. P edic i e modelling esul s
The pe o mance me ics conside ed o he es ed classifie s a e Ac-
cu acy, P ecision, Recall, and F1 Sco e (Table 6). O e all, he de eloped
ESC exhibi s e y good pe o mance, achie ing high accu acy. The ac-
cu acy o he es da a is aligned wi h he accu acy o he aining da a,
indica ing ha he model is no o e fi ing and gene alises e y well o
unseen da a. The high p ecision, ecall, and F1 sco es in bo h da ase s
unde sco e he obus ness o he model and i s abili y o classi y posi-
i e ins ances co ec ly. Compa ed o a base classifie , he ESC signi -
ican ly ou pe o ms he LGBMC in all pe o mance me ics. Al hough
LGBMC and HGBC a e g adien -boos ing algo i hms, hey op imise di -
e en ly and ha e diffe en biases. Combining hei ou pu s h ough a
me a-lea ne like XGBC, a powe ul boos ing algo i hm, allows he ESC
o lea n mo e complex pa e ns in he da a. An o e iew o ESC pe -
o mance is also illus a ed in a con usion ma ix (Fig. 7); i ep esen s
he esul s o a classifica ion ask, di iding es samples in o ou ca e-
go ies, depending on hei ue and p edic ed labels: ue posi i es (TP),
ue nega i es (TN), alse posi i es (FP), alse nega i es (FN). The only
misclassifica ions a e limi ed o Label 0 (Baseline), while he e a e no
misclassifica ions o any o he se e i y le els.
Ene gy & Buildings 336 (2025) 115579
9
Mo kunai e e al.
– o iginal d a , Me hodology, In es iga ion, Concep ualiza ion; Paulius
Spudys: W i ing – e iew & edi ing, Me hodology, Da a cu a ion, Con-
cep ualiza ion; Pa aske as Kouka as: W i ing – e iew & edi ing, Su-
pe ision, Resou ces; Dimos henis Ioannidis: W i ing – e iew & edi -
ing, Valida ion, Resou ces, P ojec adminis a ion, Concep ualiza ion;
Agis Papadopoulos: W i ing – e iew & edi ing, Valida ion, Resou ces,
P ojec adminis a ion; Pa is Fokaides: W i ing – e iew & edi ing, Val-
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