i
PREDICTIVE LONG-TERM ASSET MAINTENANCE
STRATEGY: DEVELOPMENT OF A FUZZY LOGIC
CONDITION-BASED CONTROL SYSTEM
Fe nando Almeida
Thesis P oposal p esen ed as pa ial equi emen o
ob aining he Mas e ’s deg ee in In o ma ion Managemen
2
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
PREDICTIVE LONG-TERM ASSET MAINTENANCE STRATEGY:
DEVELOPMENT OF A FUZZY LOGIC CONDITION-BASED CONTROL
SYSTEM
by
Fe nando Ped o Sil a Almeida
Thesis P oposal p esen ed as pa ial equi emen o ob aining he mas e ’s deg ee in in o ma ion
managemen , wi h a specializa ion in Business In elligence
Ad iso : P o . Nadine Cô e-Real
Feb ua y 2022
3
AKNOWLEDGMENTS
Se e al ac o s we e decisi e o he conclusion o his p ojec and o whom I can only be g a e ul.
Fi s , I would like o hank he Uni e sidade No a IMS, all he eache s and colleagues ha helped me
du ing he lea ning p ocess and “equipped me” wi h he necessa y ools o he de elopmen o his
p ojec . My special hanks o P o esso Nadine Cô e-Real o he excellence in he way he p ojec
was conduc ed, p o iding knowledge and ad ice o g ea alue o he success o his wo k. I would
also like o highligh he i eless suppo in he di e en s ages o his challenge, always p onounced
by a con inuous and posi i e encou agemen .
Secondly, I would like o hank he Eu opean Cen al Bank o he en iching expe ience and he
oppo uni y o wo k in a cul u e o excellence. This hesis would no be possible wi hou my colleagues
om he Technical Facili y Managemen depa men who s imula ed me con inuously, wi h g ea
a ailabili y always p esen ing igo and p o essionalism in pe o ming hei ac i i ies, inspi ing me o
be be e .
Finally, and as i could no be any o he way, my deepes hanks o my amily and closes iends o
jumping on boa d wi h his and so many o he challenges wi hou e e hesi a ing and wi hou needing
o be asked.
4
ABSTRACT
Technology has accele a ed he g ow h o he Facili y Managemen indus y and i s oles a e
b oadening o encompass mo e esponsibili ies and skill se s. FM budge s and eams a e becoming
la ge and mo e impac ul as new echnological ends a e inco po a ed in o da a-d i en s a egies.
This new scena io has mo i a ed ins i u ions such as he Eu opean Cen al Bank o ini ia e p ojec s
aimed a op imising he use o da a o imp o e he moni o ing, con ol and p ese a ion o he asse s
ha enable he con inui y o he Bank's ac i i ies. Such p ojec s make i possible o educe cos s, plan,
manage and alloca e esou ces, ein o ce he con ol, and e iciency o sa e y and ope a ional sys ems.
To suppo he long- e m main enance s a egy being de eloped by he Technical Facili y
Managemen sec ion o he ECB, his hesis p oposes a model o calcula e he Le wea ma gin o he
equipmen . This is accomplished h ough he de elopmen o an algo i hm based on a uzzy logic
sys em ha uses Py hon language and p esen s he sys em's s uc u e, i s eliabili y, easibili y,
po en ial, and limi a ions. Fo Facili y Managemen , his p ojec cons i u es a co ne s one o he
ongoing digi al ans o ma ion p og am.
KEYWORDS
Facili y Managemen ; Long-Te m Asse S a egy; Eu opean Cen al Bank; Condi ion-Based
Main enance; Le Wea Ma gin, Fuzzy Logic; Py hon
5
INDEX
1. In oduc ion .................................................................................................................. 8
2. Backg ound ................................................................................................................. 10
2.1. Design Scien i ic Re iew ...................................................................................... 10
2.1.1. Fuzzy Logics .................................................................................................. 10
2.1.2. Fuzzy Sys ems ............................................................................................... 15
2.1.3. In oduc ion o uzzy oolbox in Py hon ...................................................... 21
2.2. Con ex ualiza ion................................................................................................. 23
2.2.1. Facili y Managemen and Technology ......................................................... 23
2.2.2. Asse Main enance S a egy ........................................................................ 27
2.2.3. ECB ................................................................................................................ 31
2.2.4. Applica ions o Fuzzy logics .......................................................................... 37
2.2.5. Resea ch ocus .............................................................................................. 38
3. Me hodology .............................................................................................................. 39
3.1. Selec ion o Equipmen Sample .......................................................................... 41
3.2. Da a collec ion and p ocessing ........................................................................... 42
3.2.1. BAS Da a collec ion and cleaning ................................................................. 43
3.2.2. Technical Reco ds and Equipmen De ails ................................................... 44
3.3. Fuzzy model ......................................................................................................... 46
3.3.1. De ine Uni e se o discou se o he a iables ............................................ 46
3.3.2. Membe ship unc ions o he inpu s and ou pu s ...................................... 47
3.3.3. Fuzzi ica ion .................................................................................................. 51
3.3.4. Rules ............................................................................................................. 53
3.3.5. In e ence and de uzzi ica ion ................................................................... 54
4. Discussion ................................................................................................................... 57
4.1. Limi a ions ........................................................................................................... 60
5. Conclusion .................................................................................................................. 62
6. Bibliog aphy ................................................................................................................ 63
7. Annexes ...................................................................................................................... 70
7.1. Annex A – Fuzzy Con ol Sys em Design ............................................................. 70
7.2. Annex B – Inpu s and Ou pu s Resul s ................................................................ 73

6
LIST OF ABBREVIATIONS AND ACRONYMS
AI A i icial In elligence
API Applica ion P og am In e ace
ABS An iskid b ake Sys ems
BAS Building Au oma ion Sys em
BD Big Da a
BOA Bisec o o A ea Me hod
ECB Eu opean Cen al Bank
CBM Condi ion-based Main enance
CM Co ec i e Main enance
CoG Cen e o G a i y/Cen oid Me hod
CoS Cen e o Sums Me hod
CSO Chie Se ice O ice
CV Cooling Val e
DA Di ec o a e Adminis a ion
DoT Deg ees o T u h
DSR Design Science Resea ch
EAD Exhaus Dampe
FCEF F equency Con e e Exhaus Fan
FCSF F equency Con e e Supply Fan
FIS Fuzzy In e ence Sys em
FL Fuzzy Logic
FM Facili y Managemen
FOM Fi s o Maxima Me hod
FS Fuzzy Se
GTS Go e nance & T ans o ma ion Se ices
HVAC Hea ing Ven ila ion Ai Condi ioning
7
HC Humidi ie Con ol
HP Hea e Pump
ICT In o ma ion and Communica ions Technology
MF Membe ship Func ion
ML Machine Lea ning
MOM Mean o Maxima Me hod
LOM Las o Maxima Me hod
LTMS Long-Te m Main enance S a egy
IoT In e ne o Things
OAD Ou side Dampe
PdM P edic i e Main enance
PM P e en i e Main enance
PP P ehea e Pump
PV P ehea e Val e
RAD Reci cula ion Dampe
RCHE Ro o Con olle Hea Exchange
RV Rehea e Val e
SAD Supply Dampe
TEFM Technical Facili y Managemen Sec ion
8
1. INTRODUCTION
The impo ance o acili y managemen (FM) in he s uc u e o o ganiza ions ha e been inc easing in
he las yea s. The ecognised physical and spa ial dependence o ca y ou hei co e ac i i ies, as well
as he need o esponsi e asse pe o mances on success ul ope a ions has led o an inc eased ocus
o e his a ea (Alexande , 1994). Managing long- e m in as uc u al asse s such as eal s a e,
buildings, and equipmen is becoming mo e opical a he s a egic le el. In he wo k en i onmen
such asse s a e epo ed o comp ise a signi ican pa o ope a ing cos s; he e o e, i is c i ical o
e ec i ely manage echnical and adminis a i e ac ions ha ensu e ha all pa s o he building a e
up o s anda d o pe o m hei unc ions. The mos e icien way o ensu e esul s, sa e y, and
sa is ac ion o use s o he physical space is o ha e a main enance ac i i y s a egy, o plan p ope ly
inspec ions, epai s and eplacemen s and as an ou pu o managemen s a , p o iding in o ma ion
abou causes o ailu es and damages (Gackowiec, 2019). De elopmen in con empo a y business
a eas and changes in he wo k en i onmen , besides p og ess o mechanisa ion, compu e iza ion and
highly ad anced echnological de ices c ea e new challenges o main enance pe sonnel o ake up.
The e o e, each o ganiza ion should seek he s a egy ha bes sui s i s needs. Manage s a e becoming
inc easingly awa e o he need o be e unde s and and e eal he ue na u e o hei long- e m asse
base o p omo e i s ac i e managemen o co po a e bene i .
In he las ew yea s, inno a i e solu ions ha e been in oduced, hanks o new echnological ends
such In e ne o Things (IoT) de ices ha a e used as p o ide s o da a abou he cu en s a us o
equipmen and he building i sel . This da a is hen deli e ed o big da a (BD) and A i icial In elligence
(AI) and u he p ocessed by machine lea ning (ML) o ecognise pa e ns, mainly o suppo
p edic i e main enance (PdM), and o de i e ac ions based on hese pa e ns (K ishnamu hy &
Desouza, 2014). The abili y o collec , analyse in o ma ion and con ol emo ely h ough cen alized
and complex sys ems has been a u ning poin in asse main enance wi hin FM. One o Eu ope's
leading ins i u ions, he Eu opean Cen al Bank (ECB), is ully commi ed o i s ision o a mo e digi al
cen ed o ganiza ion, encompassing he di e en a eas o each and depa men s, which a e pa he
co po a e se ices esponsible o he managemen o echnical in as uc u e. Inno a ion on his
speci ic a ea is o he ou mos impo ance as all elemen s ha may in luence he pe o mance o he
employees’ daily esponsibili ies mus be in pe ec condi ion o educe as a as possible he isks o
jeopa dise he execu ion o he bank's co e business ac i i ies.
The bank's headqua e s is equipped wi h a la ge and complex building au oma ion sys em (BAS)
comp ising hund eds o housands o indi idual de ices ha pe o m a wide ange o unc ions c ucial
o he ECB's daily ac i i ies in he Main Building. By cap u ing senso in o ma ion, changes a e made
9
acco ding o he needs o he s a , op imisa ion o esou ces and sus ainabili y o he building i sel .
Al hough he po en iali ies o he collec ed da a analysis a e ecognised by he eams in ol ed in i s
managemen , no u he de elopmen s ha e been ca ied so a o demons a e he bene i s
unde lying i s exploi a ion. The e o e, his hesis aims o illus a e he a o emen ioned bene i s and i
does so by employing a Design Science Resea ch (DSR) Me hodology h ough a Fuzzy Logic (FL)
algo i hm ha in ends o op imise he classi ica ion o FM asse s based on hei main enance
condi ion. This me hodology seeks o answe ele an ques ions o human p oblems ia he c ea ion
o inno a i e a i ac s, he eby con ibu ing new knowledge o he body o scien i ic e idence ( om
B ocke e al., 2020).The esea ch ou pu is based on a me hod s uc u ed o a s ep-by-s ep app oach
o build a model capable o di ec ly imp o ing he decision-making a ound main enance o he
echnical equipmen o he building. Gi en he FL ap i ude o es ima ing he se ice li e o a gi en
equipmen o a ious condi ions unde which i ope a es and knowing ha a s a emen in na u al
language is o en he bes way o exp ess hem, an academic gap in he esea ch and implemen a ion
o his echnique emains o be illed. This si ua ion is e i ied in wo aspec s:
1. The e y ew s udies u ilizing uzzy concep s in he con ex o Building main enance and FM
(Besik epe e al., 2021). No ele an solu ions p esen simple, easy o implemen and
sus ainable al e na i es o he complex and cos ly sys ems e alua ing equipmen and
ins alla ions, hus his s udy seeks o espond o his esea ch gap.
2. A clea misma ch be ween academic concep s and eal applica ion bene i ing di ec ly a FM
p ojec , specially due o igid co po a e s uc u es ha es ic s di ec collabo a ion be ween
model managemen /de elopmen and echnical expe s, secondly he lack o FM echnical
know-how in he model implemen a ion when compa ed wi h he applica ion o echniques
by p ac i ione s in he main enance communi y (Wu, 2010). By es ablishing a close
ela ionship be ween he echnical specialis s and he acili y manage s wi hin he Bank, a
dynamic cycle o syne gies ha in eg a es all he in e ening pa ies and s eamlines he
implemen ed s a egy can be c ea ed.
Th ough he c ea ion o a p edic i e long- e m main enance s a egy (LTMS) based on uzzy heo y
and eso ing o da a aken om he BAS. This p ojec ep esen s a c i ical piece o he digi aliza ion
ans o ma ion p ocess puzzle inside he ECB. A i s , i is a p ojec ha allows a dynamic and e ec i e
me hod o help suppo in main enance s a egy decision-making and a a la e s age would wo k as a
s a ing poin and connec ion o many o he ools and p ojec s de eloped by he Bank, which a e pa
o he LTMS.
16
1.Fuzzi ica ion
Fuzzi ica ion e e s o ans o ma ion o c isp inpu s in o a membe ship deg ee which exp esses how
well he inpu belongs o he linguis ic e m. In his s ep, expe s’ judgemen and expe ience can be
used o de ine DoM unc ion o a pa icula a iable. Du ing Fuzzi ica ion, a FL con olle ecei es
inpu da a, and de e mines he deg ee o which hey belong o each o he FS acco ding o hei MFs
(Thake & Nago i, 2018).
2.Knowledge Base
The knowledge base desc ibes he c i icali y le el o he sys em o each combina ion o inpu
a iables. I is exp essed by he linguis ic o m I -Then acco ding o in o ma ion ga he ed om he
expe . These ules a e he co e o he FIS and desc ibe a local ela ionship be ween he inpu and
ou pu a iables o he uzzy sys em wi hin he limi s defined by he domain o FS in he ule
an eceden . The comple e inpu –ou pu mapping is ep esen ed by he whole collec ion o uzzy i -
hen ules om he knowledge ule base (Zimme mann, 1996). A well-defined uzzy ule base should
be comple e, consis en , and con inuous. The comple eness means ha o each alue om he inpu
space a leas one ule is ac i a ed. The knowledge base is consis en i he e a e no ules wi h he
same an eceden s bu di e en consequen s. And finally, he knowledge base is con inuous i he e
a e no neighbou ing ules o which he esul o in e sec ion o FS in hei consequen s is an emp y
se . The knowledge base is buil fi s by acqui ing knowledge abou he modelled phenomenon, and
nex by ep esen ing i in a o m o uzzy condi ional ules (P okopowicz e al., 2017).
3. In e ence Engine
The in e ence engine de ines mapping om inpu FS in o ou pu FS. I de e mines he deg ee o which
he an eceden is sa is ied o each ule. I he an eceden o a gi en ule has mo e han one clause i
selec s he mo e sui able DoM used on he implica ion me hod and i akes in o accoun he ac i a ion
o mul iple ules on he consequen esul . The uzzi ied inpu s a e applied o he an eceden s o he
uzzy ules. I a gi en uzzy ule has mul iple an eceden s, he uzzy ope a o (AND o OR) is used o
ob ain a single numbe ha ep esen s he esul o he an eceden e alua ion. To e alua e he
disjunc ion o he ule an eceden s, one uses he OR uzzy ope a ion. Typically, he classical uzzy
ope a ion union is used (μA∪B(x) = max{μA(x), μB(x)}). Simila ly, in o de o e alua e he conjunc ion

17
o he ule an eceden s, he AND uzzy ope a ion in e sec ion is applied (μA∩B(x) = min{μA(x), μB(x)}).
The esul o he an eceden e alua ion can be applied o he MF o he consequen . The mos common
me hod is o cu he consequen MF a he le el o he an eceden u h; his me hod is called clipping.
Because he op o he MF is sliced, he clipped FS loses some in o ma ion. Howe e , clipping is
p e e ed because i in ol es less complex and gene a es an agg ega ed ou pu su ace ha is easie
o de uzzi y. Ano he me hod, name, o e s a di e en app oach whe e he o iginal MF o he ule
consequen is adjus ed by mul iplying all i s membe ship deg ees by he u h alue o he ule
an eceden (Iancu, 2012). The MFs o all ule consequen s p e iously clipped o scaled a e combined
in o a single FS.
The e a e di e en ypes o uzzy in e ence me hods among which Mamdani and Sugeno- ype a e he
mos popula ones and he wo a y in he way ou pu s a e de e mined (Alma heel & Abdel ahman,
2017). E en hough hey ollow he same p ocess o uzzi ica ion, he di e ences occu in he second
p ocess when he esul s o all ules a e in eg a ed in o a single p ecise alue o ou pu . The easoning
wi h he Sugeno me hod is almos he same as he Mamdani me hod, only he ou pu sys em is no a
FS bu a he a cons an o a linea equa ion. Mamdani me hod can be conside ed as he ounda ion
o he uzzy model amily based on i - hen ules wi h FS in an eceden s as well as consequen s
(Chaudha i & Pa il, 2014). Mamdani is o en known as he Max-min me hod, due o he in e ence
adop ed, in which he MFs o inpu a iables a e i s combined inside he IF−THEN ules using AND
(∩, o Min) ope a o , and hen he ou pu FS om di e en IF − THEN ules a e combined using OR (∪,
o Max) ope a o o ge he common uzzy ou pu (I ance ic e al., 2010).
Figu e 6: Example o uzzy in e ence using he Mamdani uzzy sys em wi h wo inpu s and he
knowledge base consis ing o wo condi ional uzzy ules as seen in Rus um e al. (2020)
18
4. De uzzi ica ion
A e he ou pu a iable o he Sys em is desc ibed by an accumula ed FS, he inal ou pu mus be
nume ical alues. In Mamdani FIS, an eceden and consequen o he ules a e linguis ic a iables, and
bo h a e uzzy so he e is a need o con e his uzzy ou pu in o c isp o m. Fo his eason, he
accumula ed FS mus be ans o med by applying app op ia e de uzzi ica ion ope a o s (Jaya a hna e
al., 2011). This is achie ed by one o he se e al de uzzi ica ion algo i hms, he ollowing a e he known
me hods (Saman a, n.d.):
• Cen e o Sums Me hod (COS)
• Cen e o g a i y (COG) / Cen oid Me hod
• Cen e o A ea / Bisec o o A ea Me hod (BOA)
• Weigh ed A e age Me hod
• Maxima Me hods
• Fi s o Maxima Me hod (FOM)
• Las o Maxima Me hod (LOM)
• Mean o Maxima Me hod (MOM)
The mos p e alen and physically appealing o all he de uzzi ica ion me hods is he COG which
calcula es he poin whe e a e ical line would slice he agg ega e in o wo equal masses (Godihal,
2009). I is also he me hod used on his p ojec .
Cen e o g a i y (COG) / Cen oid Me hod
This me hod p o ides a c isp alue based on he CoG o he FS. The o al a ea o he MF dis ibu ion
used o ep esen he combined con ol ac ion is di ided in o sub-a eas. The a ea and he CoG o each
sub-a ea is calcula ed and hen he summa ion o all hese sub-a eas is aken o ind he de uzzi ied
alue o a disc e e FS. The o mula o con inuous MF (Codec ucks, 2021), is de ined as:
𝑥=∫𝑥𝜇(𝑥)⋅ⅆ𝑥
∫𝜇(𝑥)⋅ⅆ𝑥
19
Figu e 7: Two ou pu T apezoidal FS adap ed om Codec ucks (2021)
Conside ing wo FS, i s he a eas o he ou pu s need o be agg ega ed by placing hem in he same
axis, hen o compu e he a ea co e ed by his new accumula ed ou pu .
To compu e he a ea co e ed by he agg ega ed FS, he equa ion o each line o ming he egion needs
o be calcula ed:
(𝑦−𝑦1)
(𝑥−𝑥1)=(𝑦2−𝑦1)
(𝑥2−𝑥1)
Figu e 8: Accumula ed Fuzzy Ou pu wi h labels as seen in Codec ucks (2021)
20
• Line ab, (x1, y1) = (0, 0) and (x2, y2) = (1, 0.5) - Line anges om [0, 1] on X-axis
• Line bc, (x1, y1) = (4, 0.8) and (x2, y2) = (6, 0.8) - Ho izon al line has slope ze o, and o any
alue o x, he y coo dina e will emain unchanged
• Line cd, (x1, y1) = (3.5, 0.5) and (x2, y2) = (4, 0.8) - Line anges om [3.5, 4] on X-axis
• Line de, (x1, y1) = (4, 0.8) and (x2, y2) = (6, 0.8)- Line anges om [4, 6] on X-axis
• Line e , (x1, y1) = (6, 0.8) and (x2, y2) = (8, 0) - Line anges om [6, 8] on X-axis
Table 1: Summa y o Line Equa ions adap ed om Codec ucks (2021)
Finally add all he alues in he equa ion o CoG me hod:
𝑪𝒐𝑮=∫(0,5𝑥)𝑥 ⅆ𝑥+∫(0,5)𝑥 ⅆ𝑥+ ∫(3
5𝑥−8
5)𝑥 ⅆ𝑥+ ∫(0,8)𝑥 ⅆ𝑥+ ∫(−0,4𝑥+3,2)𝑥 ⅆ𝑥
6
4
6
4
4
3.5
3.5
1
1
0∫(0,5𝑥)ⅆ𝑥
1
0+∫(0,5)ⅆ𝑥+ ∫(3
5𝑥−8
5)ⅆ𝑥+∫(0,8)ⅆ𝑥+∫(−0,4𝑥+3,2)ⅆ𝑥
6
4
6
4
4
3.5
3.5
1
𝑪𝒐𝑮=4,151
The alue ob ain ep esen s he exac poin whe e he mass o he objec ’s a ea is spli equal
Line
Equa ion
Range
ab
[0,1]
bc
[1,3.5]
cd
[3.5,4]
de
[4,6]
e
[6,8]
𝑦=0,5𝑥
𝑦=0,5
𝑦=3
5𝑥−8
5
𝑦=0,8
𝑦=−0,4𝑥+3,2
21
2.1.3. In oduc ion o uzzy oolbox in Py hon
SciPy is a collec ion o ma hema ical algo i hms and con enience unc ions buil on he NumPy
ex ension o Py hon. I adds signi ican powe o he in e ac i e Py hon session by p o iding he use
wi h high-le el commands and classes o manipula ing and isualizing da a. Wi h SciPy, an in e ac i e
Py hon session becomes a da a-p ocessing and sys em p o o yping en i onmen sys em such as
MATLAB, IDL, Oc a e, R-Lab, and SciLab (SciPy communi y, 2021). The oolbox used in his p ojec is
called Sciki -Fuzzy and i is a collec ion o FL algo i hms in ended o use in he SciPy S ack, w i en in
he Py hon compu ing language. Mos o he unc ionali ies a e ac ually loca ed in sub packages, he
mos ele an o his hesis con ex is sk. uzzy.con ol, also named sk uzzy sub package, which p o ides
a high-le el Applica ion P og am In e ace (API) o uzzy sys em design (The Sciki -image eam, 2016).
Once ins alled and impo ed he FL ool equi es necessa y ca ego ies o be de ined by he use .
• Inpu s
Inpu s a e he uzzy a iables ha ha e p o ound in luence on he expec ed ou pu . Fuzzy a iables
inpu s a e decided o a pa icula uzzy sys em based on he expe ience and knowledge o expe s.
Mos ly, he uzzy inpu s which a e been chosen will o may be ha e ela ion wi h o he Fuzzy inpu
a iables. In sk uzzy he ollowing unc ion is used o de ine he an eceden (inpu s) a iables o a
uzzy con ol sys em, he unc ion mus include he Uni e se o Discou se, de ined as he se o
possible alues ha can ake he a iable and he name o he a iable, label.
sk uzzy.con ol.An eceden (uni e se, label)
• Ou pu
The ou pu is he desi ed esul o whole designed uzzy sys em. As men ioned be o e, he consequen
alue will be a consequence o he in e ence be ween he an eceden s. The unc ion is composed by
he same wo a iables o he p e ious unc ion: Uni e se and label.
sk uzzy.con ol.Consequen (uni e se, label)

22
• Membe ship Func ions Design
Sk uzzy is p eloaded wi h 12 di e en ypes o unc ions which ha e hei own speci ica ions. Only 2
a e ele an o he p ojec as he linguis ic e ms a e cha ac e ized by T iangula and T apezoidal MF.
The unc ion equi es 2 pa ame e s o which he i s ‘x’ associa es he anges de ined o inpu s and
ou pu s o he MF using he co esponden label. The second pa ame e depends on he MF
mo phology o T iangula shaped unc ions a 1-dimension a ay composed by 3 elemen ec o s is
necessa y, abc whe e a <= b <= c, o apezoidal MF, ou -elemen ec o , abcd, wi h a <= b <= c <= d.
sk uzzy.membe ship. im (x, abc)
sk uzzy.membe ship. apm (x, abcd)
• Rules C ea ion
The necessa y ules a e se acco ding o he si ua ion equi emen s, as hey help p oducing expec ed
esul s. This is a p ocedu e usually done sys ema ically: o e e y combina ion o inpu se s o a iables
ha may easonably expec ed o occu in p ac ice, he necessa y ou pu alue is es ima ed by expe
and a ule is w i en exp essing he ela ion, hus i equi es a knowledge ounda ion o he sys em.
Ha ing in mind wo an eceden s each ule should ollow he s uc u e “IF An ecenden 1 is X AND/OR
An ecenden 2 is Y , hen Consequen is Z” As s a ed be o e he “AND” ope a o in he uzzy ule edi o
is modelled wi h uzzy in e sec ion ( he min ope a o ), and he “OR” ope a o is modelled wi h he
union ( he max ope a o ) in FL. The nex unc ions desc ibe he Gene a o which yields Rules in he
sys em, connec ing an eceden (s) o consequen , he “AND” ope a o is ep esen ed wi h a | while he
“OR” is &.
sk uzzy.con ol.Rule(an eceden =[…] | an eceden =[…], consequen =[…]) – AND ope a o
sk uzzy.con ol.Rule(an eceden =[…] & an eceden =[…], consequen =[…]) – OR Ope a o
• Rules Ac i a ion
The sys em is ini ialized and popula ed wi h a se o uzzy Rules by enabling he unc ion. The o al
numbe o ules c ea ed mus be included as he pa ame e sugges s.
sk uzzy.con ol.Con olSys em([ ules])
23
• Ou pu Accumula ion and De uzzi ica ion
Each and e e y ule which has been added o sys em has i s own and unique ou pu se , he e o e
each ule will ha e i s own impac on he ou pu esul . The calcula ion o he sys em is pe o med by
he unc ion con ol.con olsys emsimua ion which accumula es he ou pu s gene a ed h ough he
ac i a ion o ules, caused by he c isp alues o he inpu s. I also compu es he ou pu c isp alue
based on he de aul de uzzi ica ion me hod, CoG.
sk uzzy.con ol.Con olSys emSimula ion(con ol_sys em)
In o de o change i , he pa ame e “de uzzi y_me hod” can be added o he consequen unc ion,
sk uzzy.con ol.Consequen (uni e se, label, de uzzi y_me hod).
2.2. CONTEXTUALIZATION
2.2.1. Facili y Managemen and Technology
FM is a mul idisciplina y a ea ha co e s di e en anges o ac i i ies, esponsibili ies, and knowledge
o main ain, imp o e and adap he o ganiza ion’s in as uc u es and suppo se ices. The de ini ion
p o ided by he In e na ional Facili y Managemen Associa ion, desc ibes i as “a coo dina ion o he
physical wo kplace wi h he people and wo k o he o ganiza ion, in eg a ing he p inciples o business
adminis a ion, a chi ec u e, and he beha io al and enginee ing sciences” (Wha Is Facili y
Managemen , n.d.). This b oad emb ace many sec o s wi hin he o ganiza ion: building ope a ions,
secu i y, g ounds managemen , space planning, sus ainabili y, p ojec managemen space planning,
wo kplace s a egy and eal es a e managemen . The inc easing ele ance o FM wi hin he
managemen s a egy o companies has been no o ious in ecen yea s, he Global Ma ke o FM was
es ima ed o be alued a €1.2 T illion in 2020 and is es ima ed o be wo h €1.7 T illion by 2027, wi h
a g ow h a e o a ound 50%, despi e o he challenging yea s o 2020 and 2021 caused by he Co id-
19 pandemic (Fo une Business Insigh s Desk and P ima y Resea ch, 2021). The inc ease in he alue
o companies led o a g ea e a en ion a ound he en i onmen whe e he co e ac i i ies a e
24
de eloped. Topics such as sa e y, eadiness in eme gency, well-being a wo k o en i onmen al issues
a e conside ed as a way o ensu e s akeholde s be e condi ions o ob aining high pe o mance in
he wo kplace (A kin & B ooks, 2015; G. Co s e al., 2010). The co ec applica ion o FM echniques
enables he o ganiza ion o p o ide he igh en i onmen o conduc ing i s co e business o deli e
end-use sa is ac ion and bes alue (Ibid.). Fu he mo e, i a acili y is no managed p ope ly i can
impac upon he o ganiza ion’s pe o mance (Ibid.). Con e sely, a well-managed acili y can enhance
pe o mance by con ibu ing owa ds he p o ision o he op imal wo king en i onmen which clea ly
highligh s he impo ance o his a ea o business. None heless, in he ecen pas , pe iods o economic
ins abili y ha e aised awa eness o a managemen ocused on he educ ion o consump ions and
cos s which led o sea ch o sus ainabili y and p ocess op imiza ion. Today, ac oss all indus ies, FM
is ecognized as an impo an pilla o he long- e m su i al and p ospe i y o he business. FM is no
longe ocused on a na ow echnical ield as he di e en needs and business con ex s ha e endowed
his b anch wi h g ea e e sa ili y. I has he expanded iewpoin ha helps he o ganiza ion ake a
s a egic iew o i s acili ies and hei impac on p oduc i i y. Fu he mo e, he e is a g adual end
owa ds he con e gence o FM and asse managemen , om he pe spec i e o a acili y/asse owne ,
he e is li le sense in ha ing sepa a e ope a ions eams, p ocu emen , and main enance egimes
(A kin & Bilds en, 2017).
Figu e 9: FM Ma ke Re enue in Billions o dolla s adap ed om Fo une Business Insigh s Desk and
P ima y Resea ch (2021)
25
One o he main allies o he ad ances in he FM a ea has been echnology. This sec o is unde going
a p o ound ans o ma ion o p ac ices, p ocesses, ools and e e ences due o he adop ion o new
solu ions in In o ma ion and Communica ion Technologies (ICT) ha ha e been imp o ing he
adi ionally concei ed p ocesses, hus making new knowledge bases a ailable o suppo da a-based
decision-making p ocesses. Al hough changes a e isible on he ope a ional side, i is also possible on
he s a egic pe spec i e o c ea e knowledge bases o he scena io cons uc ed, allowing o new
oppo uni ies in he con inuous and gene alized moni o ing o ele an pa ame e s in he conjec u e.
The e olu ion o digi al ools and echnology applied in FM is o ien ed owa ds in eg a ion wi h o he
managemen sys ems (A a & Talamo, 2020). Facili y manage s seek solu ions ha enable
accumula ion, ca ego iza ion, isualiza ion and upda ing o in o ma ion abou he ope a ion and
main enance o a building which should be comple e, p ecise and should loca e an e en in ime and
place wi hin i (A aszkiewicz, 2017).
The main inno a ion ac o ha enables and suppo s he de elopmen and e olu ion o FM is he
abili y o exploi ICT. In pa icula , he mos ecen echnological phenomena’s such as AI embedded
in obo ic de ices and used o FM sma apps ha e been e olu ionizing he sec o . Fu he mo e, he
co ec applica ion o BD echniques allows o p edic i e analy ics and o he ad anced me hods ha
a e used o ex ac ing alue om da a, used in IoT and sma de ices wi h e e lowe implemen a ion
cos s and he inc easing abili y o so wa e o in eg a e and inpu senso da a. These new echnological
ends a e inc easingly being adop ed (A a & Talamo, 2020) al hough BD has always been pa o
in o ma ion-in ensi e FM ope a ions, i has been only ecen ly when he e has been a ecogni ion and
app oach o BD o de elop solu ions ha allow i o be managed in he bes way making i a ailable o
help suppo decision-making. Figu e 10 illus a es he numbe o he used echnologies acco ding o
men ions in publica ion as a pe cen age o he numbe o cases in Facili y Se ices “Main enance and
Ope a ion”, whe e a g owing in e es in IoT, ML and BD is e iden . The e m BD implies da ase s ha
a e ex ensi e in olume, eloci y, a ie y and/o a iabili y, cha ac e is ic which equi e app op ia e
esou ces o ex ac hei ull po en ial. Besides he associa ed in es men , he a e sion o change can
some imes slow down he ans o ma ion o he adi ional p ocess. The low o massi e amoun s o
da a, o en coming om di e en sou ces, leads o he need o se e al s eps and equi emen s o he
co ec s o age, ansmission, and p ocessing o da a (Konanahalli e al., 2018).
32
di ision epo ing di ec ly o he CSO ha , ac ing as a c oss- unc ional se ice pla o m, suppo s he
CSO se ice a eas.
Figu e 12: DA O ganisa ional se -up and in eg a ion o GTS as seen in (ECB Documen a ion, 2021)
The DA is cons i u ed by h ee di isions: Adminis a i e Se ices, P emises and Secu i y, and Sa e y.
Wi hin he di isions he di e en b anches o ac i i ies a e di ided in o sec ions. When i comes o
FM, i is pa o he esponsibili ies o he Technical Facili y Managemen Sec ion (TEFM) is a pa o
he P emises di ision, and i s du ies include ensu ing ope a ion and main enance o buildings, and
echnical in as uc u es wi h he exemp ion o Secu i y ins alla ions and IT sys ems, audio media
se ices, and managemen o u ili ies o ECB owned o leased buildings The sec ion is comp ised by 3
eams:
Figu e 13: TEFM Sec ion O ganisa ional se up

33
The i s eam is esponsible o he echnical FM o ECB, coo dina ion, and execu ion o echnical
main enance (e.g., eme gency powe supply es , i e ala m sys em) and p o ision o ele an
documen a ion. I s esponsibili ies ange om di ec ing se ice p o ide s in main enance ac i i ies and
execu ing quali y checks (e.g., o o ice loo s, ac i i ies held by se ice p o ide s) o ensu e high
s anda ds, o ac i ely collabo a e wi h o he di ision sec ions o he echnical implemen a ion o
o ice layou changes and suppo ing ECB cons uc ion p ojec s.
The second eam is esponsible o he de elopmen and execu ion o concep s o ensu e high
ope a ional sa e y and main enance se ices o he ECB. I s asks ange om managemen o complex
ope a ions, main enance p ojec s and ela ed echnical sys ems o guiding in e nal and ex e nal
specialized eams and assis ing in he managemen o p ojec s wi h ega d o echnical and building
ma e s, including de ini ion o speci ica ions and s anda ds o he ECB’s echnical sys ems and
ins alla ions, ensu ing compliance wi h con ac ual and echnical egula ions. The eam is also leading
he de elopmen , implemen a ion and o e sigh o a long- e m asse main enance s a egy and i
o e sees he BAS and ela ed policies, as well as keeping he sys em knowledge on ECB si e and
manage ex e nal echnical FM p o ide s.
The Audio Media Se ices eam p o ides audio and media se ices (e.g., p ojec o s, lap ops,
ele isions, media playback de ices, ampli ica ion sys ems), i uns and main ains he echnological
ace s o he ECB’s con e ence and mee ing acili ies, and p ocu es audio/media equipmen and
se ices.
The ac i i ies ha comp ise he sec ion's commi men s a e sp ead o e h ee buildings, wo on lease:
Japan Cen e and Eu o Towe and he Main Building, whe e his p ojec is ocused, owned by he bank.
The main building comp ises h ee main elemen s: he G ossma k halle, F ank u ’s o me wholesale
ma ke hall wi h new in e nal s uc u es; a high- ise consis ing o wo o ice owe s joined by an
a ium; and he en ance building, which c ea es a isual link be ween he G ossma k halle and he
high- ise and ma ks he main en ance o he Bank acili ies. Looking a he numbe s, he e a e a ound
3000 wo kplaces, sp ead o e 42 loo s in a o al a ea o app oxima ely 120,000 m2, which equi es a
o al coo dina ion o esou ces as well as a combined e o be ween he di ision's eams and se ice
p o ide s (ECB PREMISES, 2014). When con on ed wi h he con ex o he o ganiza ion, he TEFM
eams need o assu e he a ailabili y, eliabili y, and pe o mance o he cu en asse s, bu also o
p epa e and plan he equi ed esou ces and p ocedu es o secu e he u u e s a egic objec i es. The
ex eme impo ance o all he ac i i y ca ied ou wi hin he building en ails ha he isks associa ed
wi h a down ime caused by he ailu e o a echnical ins alla ion may esul in de as a ing
consequences, he e o e he main enance s a egy canno ully ely on CM. A he same ime, he
34
necessa y in e en ions should be s a egically planned so as no o jeopa dize he Bank’s no mal
ope a ions. No o men ion, he ixed in e al schedule has an impo an ole on he plani ica ion o
asse main enance. Howe e , budge a y cons ain s and o he a eas o in e en ion o equal
impo ance can limi he in es men and esou ces a ailable, in his sense he bank seeks o implemen
a PdM s a egy based on he equipmen condi ion whe e epai o eplacemen decisions a e based
on he cu en and p ojec ed u u e heal h o he equipmen , allowing less down imes, longe use ul
li e cycles o equipmen , educ ion o cos s and maximum main enance impac . Ne e heless, i is s ill
impo an o unde s and ha eac i e assis ance will ne e cease o exis , e en when a success ul PdM
has been implemen ed. A sus ainable asse managemen is c ucial o ensu e he alignmen o
co po a e and in as uc u e s a egies and needs o connec hem wi h he asse managemen
ope a ional le el (Whi ield, 2020). Taking hese s a egies in o accoun , i is impo an o balance he
business needs, isks and he ope a ing and main enance cos s and c ea e a delibe a e plan o ac ion
con aining a se o ules used o p o ide guidance o conduc ing an e ec i e main enance (Ding &
Kama uddin, 2015). The ECB decision-making bodies ecognize he need o de ine Long Te m Asse
Main enance S a egy wi h he objec i e o de e mine op imum iming o main enance, e u bishmen
and eplacemen o asse s, in o de o cope wi h needs o he o ganiza ion and op imiza ion o
esou ce. The key s eps in de elopmen o a main enance s a egy ha e been de ined in he ollowing
way:
1. Ini ial Pilo model Kick-o , wi h a sample o asse s ha ha e been p io i ized.
2. Implemen a ion o a PdM s a egy o all c i ical and Heal h Sa e y and En i onmen .
3. E alua ion o he demand o PdM o o he equipmen and a eas o he building.
4. Conside a ions and implemen a ion o u u e applica ions.
An ini ial pilo model was es ablished, and a sample o asse s was selec ed acco ding o hei c i icali y
on he o e all bank’s ac i i ies pe o mance. Rele an pa ame e s in he assessmen o he condi ion
o he asse s ha e been de ined and da a ela ing o he same ha e been collec ed and p epa ed, hen
a uzzy model ha e been applied in o de o calcula e he cu en condi ion o he equipmen . The
second s ep akes in o conside a ion a PdM s a egy o all c i ical and Heal h Sa e y and En i onmen
35
plan s. In he hi d s ep, an e alua ion o he demand o PdM o o he plan s is made. The s ep also
conside s which senso s need o be ins alled o imp o e he quali y o he ou pu s. The ou h s ep
conside s he u u e o he s a egy and long- e m decisions. I includes a long- e m asse s a egy ha
has a da a d i en decision making p ocess. Real ime da a will be accessible. This will ensu e accu acy
and quali y o he long- e m asse s a egy.
Be o e he s a o he pilo model, he se ice p o ide ca ied ou an in en o y o he equipmen
unde he esponsibili y o he sec ion and which a e pa o he con ac ed ou sou ced main enance
se ices, hen he componen s o an Hea ing Ven ila ion Ai Condi ioning (HVAC) sys ems ha e been
chosen as he es sample. They a e high- alue asse s o buildings wi h a high impac on building
pe o mance and ene gy e iciency. De ec s, imp ope ope a ion o ailu e o he HVAC sys em may
esul in poo heal h and low p oduc i i y. Fu he mo e, ine icien ope a ion and main enance o he
HVAC sys em can cause ene gy was age, cus ome complain s, poo indoo ai quali y and e en
en i onmen al damage (Wu, 2010). Besides he HVAC sys ems end o be isola ed in echnical ooms,
making i possible o echnical pe sonnel o pe o m he main enance asks wi hou in e up ing he
daily ac i i y wi hin he building (Au-Yong e al., 2014).
The pilo model, de eloped by he se ice p o ide , is based on wo pa ame e s (Inpu s) ha when
combined calcula e he le el o s ess o which he equipmen has been subjec ed. This is done by
means o ules aimed a e-c ea ing a logical and echnically based easoning. The pa ame e s a e
based on he expe ience and echnical knowledge o he echnicians esponsible o he main enance
o he equipmen . The i s pa ame e is he numbe o imes he equipmen is ac i e; in o he wo ds,
how o en a gi en componen is eques ed and in which i s s a e changes om a es ing posi ion o
he execu ion o a gi en unc ion, he alues mi o he mon hly ac i i y. The second pa ame e is he
age componen in hou s. Each de ice has i s expec ed longe i y which can a y acco ding o he
ypology, ma e ial, exposu e and expec ed use le els. High usage on olde equipmen will ha e a highe
impac on he de e io a ion han on new componen s. The i s is collec ed by he SP expe s om he
BAS, a con ol and complex co e sys em ha ecei es in o ma ion collec ed by senso s sp ead o e he
main building o moni o he ac i i y o equipmen . The sys em has he con ol o all sa e y and secu i y
de ices; hus, i is isola ed om any in e ace, causing he da a collec ed by he sys em o be only
accessible h ough manual ex ac ion - a ask ca ied exclusi ely by specialized and au ho ized s a
membe s due o secu i y p o ocols. The second pa ame e is p o ided by SP and manu ac u e s - he
wo in e enien pa ies wi h access o de ailed asse in o ma ion. The inal objec i e o he eams is
o es ima e he pe cen ual le wea ma gin o each equipmen and make decisions ela ed wi h he
emaining condi ion o he equipmen . The ins alla ion da e o he equipmen ep esen s he ull
e ec i e li e. As wi h ime and equency o u iliza ion he equipmen will de e io a e, he le wea
36
ma gin will dec ease. E en hough he li e o he equipmen only ends a 0%, a sa e y ma gin o 20%
was de ined by he specialis s, because when he equipmen eaches his le el he p obabili y o ailu e
is e y high. E en i he equipmen does no ail comple ely, he down ime, he cos s o CM and he
high p obabili y o ecu ence make he isk o lea ing he equipmen in ope a ion un il he end o i s
li e a subop imal solu ion.
Figu e 14: Typical Asse De e io a ion Cu e adap ed om CPM Sec ion (2020)
The ou lined s a egy should be ollowed no only o he in eg i y o he bank's ac i i ies bu also by
seeking cos op imiza ion h ough exhaus i e planning o he mos app op ia e ype o main enance
o each piece o equipmen a a gi en s age o he li e cycle. The eplacemen h eshold ies o mee
he exac momen whe e he nega i e sloped equipmen condi ion cu e in e sec s he inc easing
main enance cos s and p obabili y o ailu e cu es, de ining an op imal iming o in e en ion.
Figu e 15: Op imum iming o main enance, e u bishmen and eplacemen as seen in CPM Sec ion,
(2020)
37
The TEFM sec ion has p io i ized he c ea ion o a plan o ac ion, con aining a se o ules used o
p o ide guidance o conduc ing sys ema ic moni o ing and e ec i e measu es agains aging
mechanism and obsolescence (main enance, e u bishmen and/o eplacemen ). The wea ma gin
can indica e he condi ion le el when he asse should be physically inspec ed, epai ed, o eplaced.
The calcula ion concep o he wea ma gin is o p edic he ac ual s a us/ ese e o a
plan /componen .
2.2.4. Applica ions o Fuzzy logics
A signi ican numbe o s udies can be ound whe e Fuzzy echniques ha e been applied con ibu ing
o he esolu ion and op imiza ion o many si ua ions and eal p oblems. Some examples include he
planning o eplacemen o medical equipmen and uzzy heo y applica ions in a ic and
anspo a ion planning (Mummolo e al., 2007; Sa ka , 2012). In he enginee ing sec o , di e en
a eas ha e been po en ialized, unce ain y a ound ma e ials esis ance o s ess, wea he , and use a e
pe ec scena ios o uzzy heo y implemen a ion. In indus ial enginee ing a eas like manu ac u ing,
p ojec managemen , con ol o p ocesses, in en o y and quali y, isk analysis and sa e y ha e been
enhanced by implemen ing echniques de eloped o sol ing p oblems o mechanis ic sys ems wi h
FL. Fuzzy con olle s ha e also been ins alled wi h g ea success in a b oad a ie y o consume
p oduc s, including washing machines, e ige a o s, ideo came as, acuum cleane s, au omobiles’
an iskid b ake sys ems (ABS), au oma ic ansmissions, TV se s, con ol o he ele a o s, spam il e s,
ideo games and many o he s. Many indus ial applica ion p ojec s ha employ uzzy con ol ha e
been comple ed nowadays. A ew examples a e ele a o con ol sys ems, a ic con ol sys ems,
con ol o bulldoze s, con ol sys ems o cemen kilns, and also ai condi ioning sys ems (Reznik,
1997). The las ones a e majo ela ed wi h cen al HVAC sys ems ha a e widely used in la ge
buildings. These complex ins alla ions consis o chille s, wa e dis ibu ion sys ems composed by
pumps and insula ed s eel pipes, ai handling uni s, ai dis ibu ion sys ems consis ing o insula ed
duc s, ans, dampe s and ai e minals, elec ical dis ibu ion sys ems and con ol sys ems (Mo ales
Escoba e al., 2020). Di e en s udies ha e been implemen ing con ol sys ems in hese equipmen s
using FL. The inali y is ypically a con ol me hod o main ain he ambien empe a u e (Hanamane e
al., 2006; Be ouine e al., 2019), o o op imize he high ene ge ic consump ion o he equipmen (Al-
Ali e al., 2012).

38
2.2.5. Resea ch ocus
Wi hin esea ch and a icles o ele ance in he FM sec o ew indica o s o he implemen a ion o FL
o he s a egic bene i o o ganisa ions ha e been iden i ied. The eliance on ine icien and ime-
consuming p ocesses, and he lack o echnological esou ces c ea es eluc ance o change, adop ion,
inno a ion, and con inuous in es men on he esea ch in he ield (Mo amedi, 2013). Combining he
alues o he pa ame e s, assump ions can be made abou he le el o s ess p esen ed o each
componen , bu e en wi h accu a e expe opinions, he esul o en in ol es subjec i i y esul ing in
a quali a i e ague ou come (such as “low”, “medium”, “high”) so he applica ion o FS is a p omising
app oach o o e come hese challenges. In addi ion o ha , in such a complex and la ge building like
he ECB headqua e s, he spec um o equipmen is wide which a a la e s age wi h he ex ension o
he model o o he a eas will become a limi a ion. As he cu en calcula ion lack s uc u e, au oma ed
p ocesses, and compu a ional capabili ies, making i a manual and ime-consuming p ocedu e wi h no
scaling p ospec ions. In ligh o all hese ac o s, he p oposed hesis is ocused on he i s s ep de ined
and al eady unde way in he LTMS and holds as mo i a ion he implemen a ion o a new app oach o
he assessmen o he equipmen s ess le el o he sampled equipmen using a FIS. Taking ad an age
o he compu a ion capabili ies o Py hon, in pa icula he sk uzzy lib a y, his p ojec aims o p esen
an adap i e MF design allowing o speci ically add ess each componen cha ac e is ics and co ec ly
in e p e he pa ame e s c isp alues, au oma e he s ess le el compu a ion and gene a e g aphical
isualiza ions o he inpu and ou pu FS, main ain a knowledge-based c i e ia, based on he Se ice
p o ide s and TEFM’s pe sonal. As FIS, especially he Mamdani ype, can be e icien ly used as a b idge
be ween he domain expe and a CBM sys em, using knowledge bases ha a e in easily
comp ehensible “IF…THEN’’ o ma (Ko hamasu & Huang, 2007).
The implemen a ion o his model also aims o comba he isola ion and one-way in e ac ion be ween
he se ice p o ide and he TEFM sec ion o he bank, hus boos ing coope a ion be ween bo h sides,
s eng hening bonds o us , sha ing esponsibili ies and c ea ing a cul u e o ac i e and con inuous
communica ion a ound he es ablished model. The se ice p o ide 's specialized echnical knowledge
is c ucial o he co ec measu emen o equipmen de e io a ion ma gins and i s in eg a ion keeps
he eams aligned and mo i a ed in he sea ch o he bes esul s, making possible a co ec execu ion
o he decisions aken. This dynamic cycle o syne gies ha in eg a es all he in e ening pa ies and
ul ima ely ein o ces he e ec i eness o he implemen ed s a egy is o en sac i iced in exchange o
igid dis ibu ion o esponsibili ies and lack o inclusion in he de ini ion phase o he p ojec s.
39
3. METHODOLOGY
Whe eas empi ical sciences acqui e knowledge abou he na u al wo ld (physics) o human beha iou
(social sciences), DSR is in e es ed in IT a i ac s, such as algo i hms, me hods and modelling languages,
and he e ec i eness o hei use, i seeks o in en new means o ac ing in he wo ld o change and
imp o e eali y. As a esul , DSR e-c ea es eali y h ough de eloping and e alua ing a e ac s ha
se e human pu poses and sol e human p oblems (Weigand e al., 2021). In his p ojec a new
app oach o assessmen o he le wea ma gin o speci ic equipmen is p esen ed h ough a
ein en ed uzzy con ol sys em suppo ed by applied scien i ic li e a u e and documen a ion o
es ablished models. The de elopmen o his wo k is sus ained on quan i a i e esea ch by s udying a
ep esen a i e sample o he popula ion and co e s bo h ypes o expe imen al and desc ip i e
esea ch.
The expe imen al esea ch es s he accu acy o a heo y by de e mining i he independen a iable(s)
causes an e ec on he dependen a iable ( he a iable being measu ed o change) (Lowho n, 2007).
This will be u he s udied in he an eceden consequen ela ion o he uzzy model. In addi ion,
desc ip i e esea ch is pa o he de eloped model as he sample will be measu ed a a speci ic
momen in ime wi h speci ic cha ac e is ics, his way no aking ull owne ship on u u e e alua ion
condi ions. A six-s ep DSR me hodology (Pe e s e al., 2007) has been selec ed as he guidelines o be
ul illed h oughou his wo k.
40
Table 3: Design Science Resea ch Me hodology (DSRM) adap ed om Venable e al. (2017)
Resea ch S ep
Conce ns
Ou pu o nex s ep
En y Poin
1. Iden i y P oblem
& Mo i a e
• De ine P oblem
• Show Impo ance
In e ence
P oblem-cen ed Ini ia ion
2. De ine Objec i es
o a solu ion
• Wha would a
be e a i ac
accomplish?
Theo y
Objec i e-cen ed
Ini ia ion
3. Design and
De elopmen
• A i ac
How- o Knowledge
Design & De elopmen -
cen ed Ini ia ion
4. Demons a ion
• Find Sui able
con ex
• Use a i ac o
sol e p oblem
Me ics, Analysis
Knowledge
Clien / Con ex Ini ia ed
5. E alua ion
• Obse e how
e ec i e and
e icien
• I e a e back o
design
Disciplina y Knowledge
N/A
6. Communica ion
• Schola ly
Publica ions
• P o essional
Publica ions
N/A
N/A
The i s wo s eps ha e been closely sc u inized in he p e ious chap e . In his one, he cen al opic
will be a ound he hi d s ep, and i will include de ailed elabo a ion o he a ious componen s o he
a e ac , as well as he p ocess ollowed. The con ex o he p oblem and i s applica ion as pa o he
solu ion and he e alua ion o he esul s a e also cen al opics on his chap e . The me hodology o
he de elopmen o his a i ac can be di ided in h ee dis inc phases:
41
1. Selec ion o equipmen Sample
2. Da a collec ion and p ocessing
3. De elopmen o he Fuzzy Model.
Figu e 16: Th ee s ep app oach o he a i ac de elopmen
3.1. SELECTION OF EQUIPMENT SAMPLE
The sample conside ed o his p ojec comp ises 14 componen s - all pa o he oom ai echnology
iden i ica ion block, also labelled TL. Wi hin his g oup we can segmen he equipmen as belonging o
he Pilla TLC, Ai -Condi ioning Sys em. The equipmen chosen include a Ro o Con olle Hea
Exchange (RCHE) - a o a o y wheel wi h small duc s made o aluminium esponsible o ans e ing
hea om one place o ano he . Hea e and P ehea e Pump (HP,PP) a e esponsible o mo e hea
om low- empe a u e sou ces o high empe a u e demand en i onmen s. P ehea e , Rehea e and
Cooling Val e (PV,RV,CV) a e used o con ol he low o ho and cold ai in he pipes. F equency
Con e e Supply and Exhaus Fan (FCSF,FCEF) a e esponsible o he speed con ol in he an’s elec ic
mo o . Humidi ie Con ol (HC) egula es he wa e supply in he humidi ie ; he e o e, le elling he
ai humidi y p o ided by he HVAC sys em. Also ou side, Supply, Exhaus and Reci cula ion dampe
(OAD, SAD,EAD,RAD) egula e ai low and edi ec s i o speci ic a eas. These equipmen a e pa o
he Main Building Ai Condi ioning Sys em and belong o he sample conside ed in he Ini ial Pilo , as
shown in Table 1. The selec ion c i e ia was based on a “c i icali y” assessmen speci ying which a e
he “so e eign” asse s and which do no ha e a ele an impac on he ope a ional side. The selec ed
48
Table 7: Membe ship Func ions Ranges o Inpu Linguis ic Te ms.
Inpu
Linguis ic
Va iables
Linguis ic
Te m
Membe ship
Func ion Fo ma
Membe ship Func ion Domain
Inpu A
Small
T apezoidal
[0, 0, Min(SC), Mean(SC)]
No mal
T iangula
[Min(SC), Mean(SC), Max(SC)]
Big
T apezoidal
[Mean(SC), Max(SC), Max(SC)] + 50, Max(AC)]+50]
Inpu B
New
T apezoidal
Midli e
T iangula
Old
T apezoidal
To illus a e he cons uc ion o he inpu s MFs and be e unde s and he de ined domains o all e m
domains, wo equipmen ha e been selec ed: PV and SAD. Obse ing Fig.19, he h ee MFs ep esen
he e ms o each o he inpu s linguis ic a iables. In blue o he Inpu A, he FS “Small” is
ep esen ed in a apezoidal o ma , ollowed by a iangula shaped FS in yellow o “No mal”, and a
apezoidal unc ion ep esen ing he “Big” e m in g een.
Figu e 19: G aphical ep esen a ion o MFs o Inpu A.

49
In bo h se s, he i s wo e ices ha e he alue 0, ollowed by he alue Min(F) which means ha in
his in e al he membe ship will be equal o 1. In he case o PV, we can say ha in he in e al [0,4],
he c isp alue ob ained has a 100% p obabili y o belonging o he FS "small". The opposi e happens
when he unc ion and he x-axis mee which can be e i ied when he Inpu alue A is 17, he Mean
(SC) o he speci ic equipmen . Fo he second Equipmen , SAD, he blue FS ep esen ing he lowe
equency le el has a much la ge ex ension, as seen in he pic u e, i only d ops on 100% membe ship
close o 100 ac i a ions. Since he alue ha ep esen s he membe ship o one o mo e unc ions
canno be g ea e han 1, he lines o he di e en membe ships end o in e sec in he middle o he
y-axis, which quan i ies he pe cen age o belonging o each o he se s. This numbe always a ies
be ween 0 and 1. Using he second image as an example, i he inpu A alue is 150 he e is a 50/50
chance o belonging o “small” and “no mal”, his is he poin o iew ha he use o FL adds.
Whene e one o he unc ions has he alue o 1, he emaining ha e he alue 0. The yellow MF
ep esen s he ange o he linguis ic e m "no mal”, and i has a T iangula shape, as i can be
o e se ed i only has h ee e ices, he las apezoidal MF in g een ep esen s he "big" e m.
Compa ing he wo g aphs we can see ha he alues p esen ed in able A, in luence he MF o ma .
A simila p ojec ion has been conduc ed o Inpu B, as i can be seen in Figu e 20, he ange o he c isp
alues a ies acco dingly o he expec ed li e ime in hou s o he equipmen . The wo selec ed
equipmen a e a good example o ha . The midli e e m has i s ully membe ship exac ly a he middle
o he use ul li e. He e, he e a e conside ed wo pe iods whe e he equipmen is conside ed o ally
new, a he beginning o he blue 'new' unc ion, and one wi h he same in e al a he end o he li e
cycle whe e he s a e o de e io a ion o he equipmen is high and i is conside ed "old", highligh ed
in g een.
Figu e 20: G aphical ep esen a ion o MFs o Inpu B.
50
A e de ining he MFs o he h ee e ms o each o he wo linguis ic inpu a iables, we mus now
de ine he linguis ic ou pu a iable, S ess Le el. I is composed by 5 linguis ics e ms: “Ve y Low”,
“Low”, “Medium”, “High” and “Ve y High” he same logic is ollowed.
Table 8: MFs Ranges o Ou pu Linguis ic Te ms.
The i s ou MF ha e a iangula shape while he las one is apezoidal. This is due o he ac ha
he esul s ob ained h ough he in e ence o he equipmen can p esen a alue highe han 200 %. I
is c ucial o no e ha he highes poin o he g een MF "medium" indica es he c isp alue 100;
he e o e, he neu al alue assigned o he s ess le el is ep esen ed a 100%.
Ou pu Linguis ic
Va iable
Linguis ic
Te m
Membe ship Func ion
Shape
Membe ship Func ion
Domain
S ess Le el
Ve y Low
T iangula
[0,0,50]
Low
T iangula
[0,50,100]
Medium
T iangula
[50,100,150]
High
T iangula
[100,150,200]
Ve y High
T apezoidal
[150,200,250,250]
Figu e 21: G aphical ep esen a ion o MF o Ou pu S ess Le el
51
3.3.3. Fuzzi ica ion
The uzzi ica ion p ocess ans o ms he nume ical measu emen s in o uzzy a iables. In o he wo ds,
i con e s c isp inpu in o a uzzy alue. Fo he sake o simplici y, he p e iously exe cised
componen s (PV and SAD) a e used as examples and he esul s o uzzi ica ion o all he equipmen
a e a ailable in he appendix. As men ioned, he mon hly alues o Janua y and Feb ua y 2021 we e
collec ed and ans o med o p esen he ele an c isp alues o he model. The ollowing able (see
Table 9) p esen s he esul s o bo h mon hs.
Table 9: Mon hly C isp Values o Inpu A and B.
Desc ip ion
Inpu A
Inpu B
01-21
02-21
01-21
02-21
PV
1
7
52608
54024
SAD
194
56
54288
55704
In Janua y 2021 o PV only one ac i a ion has been egis e ed. The numbe o hou s o use was
calcula ed by accoun ing o he di e ence be ween he ins alla ion da e and he las day o he mon h
o he yea being analysed. The alue o ha is 5260 which gi es us he c isp alue o inpu B. In Figu e
22, below, he c isp alue o he wo inpu s is ep esen ed by a black e ical line. In he case o Inpu
A o Janua y, he alue 1, ac i a es wo MFs wi h di e en weigh s. The "small" MF c osses he
ep esen a ion line, when y=0.67 while he "no mal" MF p esen s he alue y = 0.33, also named le els
o an eceden u h. In Feb ua y, he numbe o ac i a ions was 7, ac i a ing only he "big" MF wi h
he alue y=1. Since he c isp alues o he inpu B ha e a cumula i e na u e, he a ia ion will be
p og essi e and expec ed, con a y o he unp edic abili y o he numbe o ac i a ions. In Janua y,
he linguis ic e m "New" is ep esen ed a 60% and in Feb ua y a 57.5%. None heless, he e m
"Midli e" ises om 40% o 42.5%. This beha iou is logical since as ime goes by he equipmen will
ind alues ha a e mo e s ongly ep esen ed by he Midli e and Old e ms. SAD is a highly demanded
componen when looking a he s anda d alues ob ained in 2020, especially when compa ed PV’s
esul s. The F equency o Ac i a ions om he 2 i s mon hs o 2021, 194 and 56 espec i ely, in ol e
he 3 MF in di e en ways, he i s esul ge ing 0.82 o he "no mal" e m and only 0.18 o he
"big", he second ela ing only o he "Small" unc ion. Rega ding he age componen , he logic emains
he same, wi h he only di e ence being a g ea e ac i a ion o he "new" MF since he SAD has an
expec ed li e o 30 yea s. In he images he colou ed a eas a e de ine a he op by he alue a which
he unc ion in e sec s he c isp alue and hey ep esen he DoM o he MF.
52
Figu e 22: Fuzzi ica ion esul o Equipmen PV and SAD - Janua y 2021
Figu e 23: Fuzzi ica ion esul o Equipmen PV and SAD - Feb ua y 2021.
53
3.3.4. Rules
Fuzzy ules a e used wi hin FL sys ems o in e an ou pu based on inpu a iables in his s ep i is
desc ibed he ule se o he model. To ensu e co e age o he comple e space, we mus conside he
wo linguis ic a iables, each wi h i s h ee e ms (MFs), and hei possible combina ions (3 * 3), which
would amoun o 9 possible ules. The uzzy ules c ea ed a e as ollows:
• Rule 1: IF Inpu A is Small AND Inpu B is New THEN S ess Le el is Ve y Low
• Rule 2: IF Inpu A is Small AND Inpu B is Midli e THEN S ess Le el is Low
• Rule 3: IF Inpu A is Small AND Inpu B is Old THEN S ess Le el is Medium
• Rule 4: IF Inpu A is No mal AND Inpu B is New THEN S ess Le el is Low
• Rule 5: IF Inpu A is No mal AND Inpu B is Midli e THEN S ess Le el is Medium
• Rule 6: IF Inpu A is No mal AND Inpu B is Old THEN S ess Le el is High
• Rule 7: IF Inpu A is Big AND Inpu B is New THEN S ess Le el is Medium
• Rule 8: IF Inpu A is Big AND Inpu B is Midli e THEN S ess Le el is High
• Rule 9: IF Inpu A is Big AND Inpu B is Old THEN S ess Le el is Ve y High
Di e en combina ions o an eceden s can gene a e he same ou pu as in he pe spec i e o eal use,
equipmen in di e en phases o i s li e cycle and wi h unequal le els o use, can ha e alues o s ess
le el wi hin he same linguis ic e m. Looking a he able 10, he combina ions "Big and New", "No mal
and Midli e", "Small and Old" ac i a e he in e media e le el o s ess le el, no meaning ha he 3
combina ions necessa ily ha e he same de uzzi ied nume ical c isp alue assigned.
Table 10: Rules - An eceden and Consequen Combina ion
New
Midli e
Old
Small
Ve y Low
Low
Medium
No mal
Low
Medium
High
Big
Medium
High
Ve y High
Inpu B
Inpu A

54
3.3.5. In e ence and de uzzi ica ion
.
De uzzi ica ion, which is he las s ep o implemen ing he FS heo y, is he opposi e o he p ocess o
uzzi ica ion, by his s age he inpu s ha e i s membe ship deg ee calcula ed and a e in he o m o a
ully linguis ic s a emen , in o de o ge a c isp nume ical alue as an ou pu i mus be e e ed back
h ough de uzzi ica ion.
As seen, ou model has wo an eceden s (Inpu s) and one consequen (Ou pu ), 9 ules wi h he
ope a o “AND” ha e been se and he ou pu o each ule is a FS; he e o e, a Mamdani sys em using
he minimum DoT o each ule membe ship alue is ans e ed o he ou pu membe ship deg ees.
To be e unde s and his p ocedu e, once again, he PV ou pu in e ence in Janua y 2021 is illus a ed
in Figu e 24, al hough he MFs a e p e iously de ined. The DoT in each o he unc ions a e a ained
h ough he conjuga ion o he sys em ules and he DoT o he inpu s ob ained in he uzzi ica ion.
The low c isp alue o inpu A igge s bo h “small and no mal” MF as o inpu B “new and midli e”
ha e membe ship highe hen 0, he e o e ules 1, 2,4,5 a e applied. The "and" ope a o assigns he
smalles membe ship alue wi hin each ule o he s ess le el MF ha is co espondingly ac i a ed.
By in e p e a ing he ou ac i a ed ules:
• Rule 1 – small (0.67) and new (0.6) – Ve y Low (0.6)
• Rule 2 – small (0.67) and midli e (0.4) – Low (0.4)
• Rule 4 – no mal (0.33) and new (0.6) - Low (0.33)
• Rule 5 – no mal (0.33) and midli e (0.4) – Medium (0.33)
The Ve y Low MF inhe i s he lowes DoM om he wo inpu esul s, in a p ocess named clipping
whe e he consequen MF is cu a he le el o he an eceden u h. The same logic is ollowed o he
o he h ee ela ed ules. In o de o de uzzi y, he ou pu s a e combined in one single se , i wo ules
a e associa ed wi h he same ou pu MF only he highe alue is conside ed. The e o e, ule 4 has no
impac on he ou pu accumula ed se as i s a ea is ully wi hin he cumula i e a ea o he o he h ee
ules.
55
Figu e 24: De uzzi ica ion P ocess o Equipmen PV, Janua y 2021
Figu e 25 shows he esul s MF o S ess Le el o he o he h ee scena ios being used as p o e o
concep . We can obse e ha he di e en FS a e being shaped as a consequence o he s eng h o
he ules and he weigh o he membe ships de ined by he c isp alues. The black e ical line In he
S ess Le el g aphs slices he accumula e ou pu in o wo equals masses. This exac poin ep esen s
he De uzzi ied c isp alue and i is compu ed h ough he p inciple o he COG. This me hod e u ns
a p ecise alue depending on he FS ‘s CoG. In Figu e 26, he esul s ob ained o all equipmen a e
displayed, wi h special emphasis o he wo equipmen s desc ibed. As a esul , c isp alues o 63.03%
and 121.98% we e calcula ed o PV in Janua y and Feb ua y 2021. The SAD he alues o bo h mon hs
we e 71.96% and 28.79% espec i ely.
PV-Feb ua y 2021
SAD- Janua y 2021
Sad- Feb ua y 2021
Figu e 25: De uzzi ica ion esul s o equipmen PV, Feb ua y 2021 and SAD, Janua y and Feb ua y 2021
56
Figu e 26: De uzzi ied C isp Values o he sample o equipmen , Janua y and Feb ua y 2021.
The S ess le el esul s will consequen ly impac he condi ion assessmen o he equipmen . I is
impo an o keep in mind ha he 24 hou s o he day a e being conside ed in he equipmen li e
span, hence he pe cen age o SL will be mul iplied by he ha he o al numbe o mon hly hou s and
e lec ing di ec ly he o e o unde -s ess on which he asse was subjec ed. In he p esen ed able-
11, h ee alues epo unde -s ess alues. In o he wo ds, s ess pe cen ages o less han 100%,
esul ing in less wea and ea ep esen ed by a dec ease in he numbe o hou s consumed in he
mon h. In Feb ua y 2021, an o e -s essed alue esul ed in a highe han expec ed numbe o mon hly
hou s, as i can be seen in he second ow o he column Adjus ed Mon hly Hou s. The highe esis ance
o S age 1 equipmen means ha he pe cen ages end o be lowe compa ed o he esul s ob ained
a S age 3. The s ipula ed ules show exac ly ha endency, equipmen ha is a a mo e ad anced
s age o i s li e cycle is subjec o highe le els o s ess, e en i he numbe o swi ching commands
does no inc ease. Consequen ly, he numbe o hou s consumed will ha e a p opensi y o be highe .
Table 11: S ess Le el impac on Mon hly Equipmen Li e Hou s.
Equipmen
Mon hly
Hou s
Fuzzy Model
S ess Le el
Adjus ed Mon hly Hou s
PV
Jan-21
744
63.03%
469
Feb-21
672
121.99%
820
SAD
Jan-21
744
71.97%
535
Feb-21
672
28.79%
193
57
4. DISCUSSION
In he me hodology chap e , he building s eps o he a i ac we e desc ibed. As p esen ed, he way
he inpu anges a y acco dingly o he speci ica ion o he equipmen is one o he mos impo an
s eps o he model as i di e en ia es his a i ac om he esea ched spec um. The MF o each inpu
a e ailo -made acco ding o he cha ac e is ics o he equipmen . This echnique no only allows
scalabili y on he p ocess since much ime is sa ed in c ea ing and adap ing he limi s o each FS and
in calcula ing he s ess le el o indi idual componen s, bu also and mos impo an ly allows he
c ea ion o a new app oach in he assessmen o equipmen wea ma gins. The s anda dized asse ’s
de e io a ion es ima ion is ixed and o eseeable, as he s ess le el o he machine is no conside ed,
only he emaining li e ime is aken in o accoun . None heless, he new model’s le wea ma gin is
de e mined by he in ensi y o he wo k o which i is submi ed and he empo al condi ions ha i
p esen s in a ce ain phase o i s use ul li e. The e o e, i is conside ing he ageing p ocess o he
machine. The di e ences be ween he wo app oaches can be be e unde s ood when compa ing he
wea ma gins o e ime. As shown in able 12, i s line o each componen has he accumula ed hou s
and he espec i e le wea ma gin o each elemen ollowing he s anda dized me hod o asse
de e io a ion. The mon h o Decembe was conside ed as a s a ing poin , looking a he PV wi h a
o al used hou s o 52608 a he gi en da e. The numbe o hou s co esponding o Janua y 744 a e
added o a o al o 53352 and Feb ua y 244 wi h an accumula ed alue o 54024. The decline e i ied
in he las h ee columns e e ing o he emaining use is guided only by he a iable ime. In he
second ow he mon hly hou s we e used and hey we e calcula ed h ough he ela ion wi h he s ess
le el. Ye , as p e iously explained, al hough in Decembe he pe cen age o wea le ma gin is equal,
we can e i y a lowe decline han he expec ed in he ollowing mon hs. I is impo an o e e ha
al hough in Feb ua y he s ess le el is highe han 100%, he mean o he wo mon hs is s ill lowe
han 100%, explaining he highe alue a he end. The same beha io is e i ied a SAD. Despi e he
longe use ul li e o he equipmen , co esponding o 30 yea s, we conclude ha he lowe s ess le els
led o a lowe wea o he equipmen .
64
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7. ANNEXES
In his sec ion, wo annexes will be included. The i s , Annex A, shows he code ha was
de eloped in Py hon language o de elop he a e ac . The second, Annex B, aims o eco d all
he g aphical demons a ions ob ained o he mon hs Janua y and Feb ua y o he Inpu s and
Ou pu s o he o he equipmen componen s o he sample.
7.1. ANNEX A – FUZZY CONTROL SYSTEM DESIGN
Fig 6.1.2: Sciki - uzzy Ins alla ion, impo packages and sub packages
Fig 6.1.2: Impo da a o Equipmen Uni e se o disclosu e and mon hly c isp alues
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Fig.6.1.3: An eceden s and Consequen anges
Figu e 6.1.4: MFs o Inpu A, B and Ou pu
Fig 6.1.5: IF-Then Rules wi h ope a o and (&)
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Fig 6.1.6: In e ence and De uzzi ica ion
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7.2. ANNEX B – INPUTS AND OUTPUTS RESULTS
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