Failu e mode p edic ion and Ene gy o ecas ing o PV plan s o assis dynamic
Main enance asks by ANN based models 
Oli encia*, J. Fe e o*, J.F. Gómez Fe nández**, A. C espo Má quez**
* Mag el Sys ems. Se ille, Spain
(e-mail: [email p o ec ed], [email p o ec ed])
** Depa men o Indus ial Managemen , Escuela Técnica Supe io de Ingenie os, Se illa
(e-Mail: [email p o ec ed], [email p o ec ed])
ABSTRACT
In he ield o enewable ene gy, eliabili y analysis echniques combining he
ope a ing ime o he sys em wi h he obse a ion o ope a ional and
en i onmen al condi ions, a e gaining impo ance o e ime.
In his pape , eliabili y models a e adap ed o inco po a e moni o ing
da a on ope a ing asse s, as well as in o ma ion on hei en i onmen al
condi ions, in hei calcula ions. To ha end, a logical decision ool based
on wo a i icial neu al ne wo ks models is p esen ed. This ool allows
upda ing asse s eliabili y analysis acco ding o changes in ope a ional
and/o en i onmen al condi ions.
The p oposed ool could easily be au oma ed wi hin a supe iso y con ol
and da a acquisi ion sys em, whe e e e ence alues and co esponding
wa nings and ala ms could be now dynamically gene a ed using he ool.
Thanks o his capabili y, on-line diagnosis and/o po en ial asse
deg ada ion p edic ion can be ce ainly imp o ed.
Reliabili y models in he ool p esen ed a e de eloped acco ding o he
a ailable amoun o ailu e da a and a e used o ea ly de ec ion o
deg ada ion in ene gy p oduc ion due o powe in e e and sola acke s
unc ional ailu es.
Ano he capabili y o he ool p esen ed in he pape is o assess he
economic isk associa ed wi h he sys em unde exis ing condi ions and o
a ce ain pe iod o ime. This in o ma ion can hen also be used o igge
p e en i e main enance ac i i ies.
Keywo ds

: Renewable Ene gy; Main enance; Condi ion Based Main enance;
A i icial Neu al Ne wo k; P opo ional Weibull Reliabili y.
1.
In oduc ion
Renewable ene gies p esen a high dependency on he andom condi ion o
clima ological phenomena. This a iabili y may ha e a g ea impac on exis ing
p oduc ion commi men s ul ilmen (as es ablished by he legisla ion in many
coun ies). The e o e, he e is a g ea in e es in en i onmen al condi ions p edic ion
and o ecas ing, ha can be accomplished in di e en ways:
●Including clima ological o ecas ing: using physical models, wi h sola
i adia ion-gene a ed powe cu es, o p edic ing p oduc ion in e ms o
i adia ion.
●Excluding clima ological o ecas ing: using s a is ical models based on
his o ical da a (mon hly-a e aged sola i adia ion). Fo example, he
Minis y o Indus y o Spain p o ides a p edic ion ool wi hou
clima ological calcula ions, including a coe icien able conside ing as
a iables: mon hs, ime o he day and clima ological zones.
Besides abo e men ioned o ecas ing p og ams, g id-connec ed PV sys ems also
equi e ad anced p ocesses moni o ing, h ough a senso dis ibu ed ne wo k, o
ca y ou egula unc ional and pe o mance checks. Fu he mo e, da a ob ained
needs he p ope co esponding ime se ies s a is ical analysis. In ac , au oma ic
ailu e de ec ion in pho o ol aic sys ems is a complex p ocess, needing he logging
o a g ea numbe o elec ical a iables (such as cu en s lowing h ough sola
panels and ol ages on ba e ies), oge he wi h en i onmen al da a (such as
i adiance and empe a u e [1, 2]). As a esul , companies ace a cos ly main enance
p og am, only a o dable o la ge si es and companies wi h he ad an age o ce ain
economies o scale.
In o de o easy he implemen a ion and o educe he complexi y in his ailu e
de ec ion p ocess, some eme ging p oposals a e using ew a iables and mo e
complex s a is ical analyses [3, 4]. This pape ocuses on applying a i icial neu al
ne wo ks o his end.
A i icial neu al ne wo ks (ANNs) a e ma hema ical ools wi h in ensi e
u iliza ion in he esolu ion o many eal-wo ld complex p oblems, especially in
classi ica ion and p edic ion ones. ANNs (A i icial Neu al Ne wo ks) p e end o
emula e biological human neu al ne wo ks lea ning om he expe ience and
gene alizing p e ious beha iou s as cha ac e is ics ime se ies. To do his, he simple
uni is he neu on whose mission is o p ocess he ecei ed da a as an ac i a ing
unc ion ha could be he en y o o he neu on, combining neu ons as a di ec ed
g aph ha can ca y ou in o ma ion p ocessing by means o i s s a e esponse o
con inuous o ini ial inpu [5]. The ANN a chi ec u e consis s on an inpu laye , an
ou pu laye and gene ally, one o mo e hidden laye s. Thei main cha ac e is ic is i s
abili y o p ocess in o ma ion ea u es in non-linea , high-pa allelism, aul and noise
en i onmen s wi h lea ning and gene aliza ion capabili ies [6, 7]. In compa ison o
adi ional model-based me hods, ANNs a e da a-d i en sel -adap i e me hods well
implemen ed in compu e s on eal ime, lea ning om examples and cap u ing sub le
and hidden unc ional ela ionships ha a e unknown o ha d o desc ibe. In addi ion,
ANNs p o ide s ong ole ance be o e noised da a because s o e in o ma ion
edundan ly. Thus, ANNs a e well sui ed o sol ing p oblems whe e explici
knowledge is di icul o speci y o de ine, bu whe e he e a e enough da a. [8-10].
In his sense, [11] ha e shown ha backp opaga ion neu al ne wo k exceeds by an
o de o magni ude o he con en ional lineal and polynomial me hods dealing wi h
chao ic ime se ies o da a. Consequen ly, ou in e es is using ANNs o analyze da a
and dismiss p edic ions e o s conce ning ailu e appea ance.
The applica ion o hese echniques o he enewable ene gies ield, and mo e
speci ically o powe gene a ion o pho o ol aic (PV) sys ems, has been in
con inuous de elopmen du ing he las yea s, including:
●Me eo ological da a o ecas ing [12, 13].
●PV sys ems sizing [14-17].
●PV sys ems modelling, simula ion and con ol [18].
The e a e p e ious wo ks on o ecas ing PV sys ems elec ici y ou pu using
ANNs [19, 20], howe e his pape desc ibes wo new algo i hms o ea ly de ec ion
o ailu es in PV sys ems acco ding o he a ailable amoun o ailu e da a, wi h he
in en ion o be included when desc ibing p edic i e main enance ask esul ing om
RCM p og ams implemen a ion (Reliabili y-Cen ed Main enance).
2. Models E alua ion and Decision Making P ocess
Reliabili y cen ed main enance (RCM) is he mos widesp ead me hodology o
s udy he equi ed main enance p og am o an asse in a gi en ope a ional con ex
[21], quan i ying he isks [22] and e alua ing he emedial measu es o de ec , a oid
o p e en he unc ional ailu es [23]. When conside ing a iable ope a ion and
en i onmen al condi ions, he s udy o ailu es may be complex. A ibu able o
non-op imal ope a ing condi ions, ailu es o en occu in asse s su e ing o changing
en i onmen al (cleanliness, as ening, empe a u e, e c.) and ope a ional
(con igu a ions, p e en i e main enance, undue handling, e c.) condi ions. Mo eo e ,
non-e iden de ec s in he asse s (design impe ec ion, implemen a ion e o s, quali y
o ma e ials, e c.) may also lead o ailu es [24, 25].
Reliabili y analysis o Renewal Ene gy Equipmen , in line wi h he RCM me hod,
is a e y complex ask depending on ope a ing and en i onmen al condi ions. This
analysis conside s he e ec s, in he equipmen unc ion, o he di e en ailu e
modes deg ading he equipmen unc ionali y h ough de ia ions om s anda d
ope a ing condi ions [38]. Based on eal da a as his o ic e en s, his deg ada ion can
be obse ed o p edic ed ollowing a ailu e cu e. Due o i s own complexi y, his
analysis is associa ed o quan i a i e ools and so i ha e o be mainly implemen ed in
dep h in c i ical equipmen o equipmen in which ailu e consequences a e no
admissible (due o en i onmen , heal h and sa e y, e c.).
An example o his is he ‘‘Su i al Da a Analysis’’, ocused on a g oup o
indi iduals and how hey eac o ailu e a e ce ain leng h o ime [29, 30, 31].
Da a and in o ma ion abou hese con ibu ing ac o s could be decisi e o ob ain,
and e en o upda e o e ime, eliabili y es ima ions abou he con ibu ion o some
e en s, ep esen ed h ough explana o y a iables o co a ia es, in o de o ob ain he
ime un il he ailu e (Su i al Time). The e a e se e al echniques o sol e su i al
es ima ions [32, 33], in which ypical ailu e dis ibu ion unc ions a e asymme ical
(censo ed o he igh ). The in luence o hese explana o y ac o s may obey di e en
pa e ns ha could be hen used o wo k ou he eal isk o an asse . These
echniques based on explana o y a iables could be pa ame ic when he haza d
dis ibu ions a e known, semi-pa ame ic in he case o unknown haza d dis ibu ion
bu wi h de ined assump ions o haza d p opo ionali y wi h he ime and
independence be ween he cons an h ough ime co a ia es, o non-pa ame ic when
hese a e no necessa y o be speci ied [34, 35, 36].
In main enance, he decision-making is usually cha ac e ized by condi ions o
unce ain y, an icipa ion in o de o handle non-con olled a iables is equen ly
equi ed and his is done by s udying hei his o ical e olu ion indi idually, o on
hei ela ion o o he a iables. In p ac ice, wi h limi ed knowledge, main enance
echnicians o en eel mo e con iden wi h hei expe ience, and his would in luence
hei decision ha could be conse a i ely based on le els o sa is ac ion ins ead o
being op imal [47]. The e o e, i is ecommended o imp o e decision capaci y using
o malized amewo ks which a e sui able o he le el o in o ma ion equi ed and o
he da a which is a ailable. Quan i a i e ools a e p e e ed o seek g ea e p ecision
in he choice o s a egies, bu his is he choice o wha is "be e ", among wha is
"possible" [48]. Also, he decision p ocess is in e ac i e, no only o p edic
some hing, bu o eplica e eali y; i should be upg adeable as imp o emen
con inues o ob ain and sha e knowledge.
Pa ame ic me hods, as Weibull ac ua ial and g aphical models (EM), a e usually
employed when people ha e enough in o ma ion abou ailu es wi h a egula
pa e n, so hey can be de eloped o model ailu es esul ing, mos o he imes, in a
aylo -made sui pe equipmen . On he o he hand, as p e iously i has al eady
men ioned be o e he u iliza ion o semi-pa ame ic me hods, as he widely applied
P opo ional Haza d Model (PHM) o Cox [37], based on a log-lineal-polynomial
exp ession o he co a ia es unde he assump ions o independency among hem and
cons an wi h he ime. While, in non-pa ame ic me hods s and ou ANN me hods
hanks o be a sel -adap i e and empi ical p ocess e en wi h noised and non-lineal
in o ma ion and/o ime-dependency in co a ia es.
Pa ame ic, semi-pa ame ic and nonpa ame ic echniques a e employed o
es ima e he eliabili y unc ion mainly depending on he knowledge abou he ailu e
ime dis ibu ion ( om majo o mino espec i ely). Howe e , conce ning o he
lexibili y agains o abo e men ioned co a ia es assump ions (independency and
ime-independency), om EM models o ANN models, he lexibili y and e iciency
showing ela ionships among he li e cycles and o he a iables a e inc eased, bu
also he complexi y o implemen a ion and he compu a ional load a e inc eased a
he same ime [39]. Addi ionally, in nume ous pape s [39,40], he PHM and ANN a e
compa ed o i su i al unc ions showing no signi ican di e ences be ween
p edic ions o Cox eg ession and ANN models when complexi y in models is low.
In case o complex models, wi h many co a ia es and any in e ac ion e ms he
di e ences in e ms o ad an ages a e impo an , showing he ollowing esul s:
●ANN p edic ions we e be e han Cox PHM p edic ions wi h high a es o
censo ing (censo ing a e o 60% and highe [46]), educing signi ican
biases.
●ANN p edic ions p o ide be e p edic ions o de ec complex nonlinea
ela ionships be ween independen and dependen a iables.
●ANN p edic ions can inco po a e quan i ied po en ial p ognos ic
ac o s ha may ha e been o e looked in he pas .
As a esul , he main enance decision making in Renewal Ene gy Equipmen s
unde di e en ope a ing en i onmen s can be suppo ed by ANN ul illing he
equi emen s o :
●Sui able o le el o ailu e in o ma ion,
●Implemen able in SCADA sys ems,
●Upg adeable i e a i ely and wi h eali y,
●Flexible and in eg a ed hie a chically.
Acco ding o p e ious pa ag aphs, his wo k main con ibu ion is a logic decision
ool doing PV sys ems elec ici y o ecas ing, which, a he same ime, may se e as
p edic i e main enance ins umen , ha can be linked o p ope RCM p og ams
ou pu s o con ol c i ical ailu e modes. In he sequel, his wo k ocuses on applying
a i icial neu al ne wo ks (ANNs) o model PV sys ems ailu es.
3. P ac ical Case Ma e ials
To suppo his p ac ical esea ch, he ANN models o e case s udies a e now
p esen ed. The idea is, no only building he models, bu also implemen ing hem in a
SCADA sys em.
PV plan s ha e been in p oduc ion o mo e han 25 yea s. Cu en dec ease in
go e nmen incen i es o enewal ene gy sou ces has o ced companies o s udy
use ul li e ex ension possibili ies. Due o his, po en ial plan e-in es men s mus be
also e-e alua ed; inco po a ing u u e ope a ing and en i onmen al condi ions
wi hin equipmen eliabili y analysis is conside ed o be c ucial o a oid u u e
p oduc ion dis up ions.
This ype o pho o ol aic plan was usually buil modula ly, each 100 KW may
ep esen o e 600.000 € o in es men , he e o e he possibili y o eplica e he same
model o di e en modules and egions is also conside ed o g ea in e es . Wi h
ha in mind, his wo k ies o de elop ANN models ha a e easy o ep oduce, and
o upda e, when he mos common pa ame e s ound in a pho o ol aic plan ,
de e mining p oduc ion, su e changes.
Ou p edic ion models ha e inno a i e ea u es compa ed o p e ious wo ks in
he li e a u e. The ANN models use, no only en i onmen a iables as ex e nal
empe a u e o adia ion, bu also asse s’ condi ions a iables as in e nal empe a u e
o he di e en ope a ing imes. Th ough his, an ea ly de ec ion o deg ada ion will
be possible be o e ailu es a ec p oduc ion, and a quan i a i e measu e o isk can
be compu ed. I is impo an o acknowledge how isk o ailu es could e en each
en imes he pu chase equipmen cos [26], he e o e i has o be classi ied, and
modelled p ope ly, he di e en non eliabili y ela ed cos along equipmen

li ecycle, such as wa an ies, indemni ies, epa a ions, penal ies, e c.
Addi ionally o be exhaus i e in ailu e p edic ions pe equipmen , he analysis o
ailu es has o be accomplished pe each c i ical ailu e mode because symp oms and
causes could be dissimila among hem and he e ec o equipmen condi ions could
apply in a di e en manne .
In ou case s udy, unc ional analysis and ailu e mode analysis (Failu e Mode
E ec and C i icali y Analysis—FMECA) was ca ied ou in ad ance o c i ical
equipmen o he pho o ol aic plan , unde s anding ha hese e o s in ailu e mode
analysis could add eno mous alue o p o ec ing a p oduc ion o 6,258,966 €/yea in
ou plan . This e o was comple ed iden i ying, a he same ime, pa ame e s
equi ed o p edic ailu e modes (when ha was easible).
Two common sys ems a e selec ed o illus a e he model implemen a ion o e
eal da a and in a SCADA sys em: a powe in e e and a sola acke . Bo h o hem
a e om a 6.1 MW pho o ol aic plan opened up in Sep embe o 2008 (49,640
ope a ion hou s), compound by 37,180 pho o ol aic panels in g oups o 100 Kw o
each in e e . The sola acke s o ien pho o ol aic panels owa d he sun o
maximize collec ed sola ene gy, while he powe in e e ans o ms di ec cu en
(DC) o al e na ing cu en (AC) o m s ings o panels, agg ega ing i s own ene gy
(210,000 KWh/yea ) each i e in e e s join ly in o a ans o me (see con igu a ion
o he selec ed ans o me in Table 1) h ough which ene gy is p o ided o he
dis ibu o a an ini ial p ice o 0.4886 €/KWh (513,030 €/yea o p oduc ion), and
subsequen ly educed due o a legal equi emen . Consequen ly eliabili y aspec s a e
impo an , no only o conside he di ec cos s o ailu es, bu also he indi ec loss o
p o i . An icipa ion o a oid his loss o p o i will be pu sued by he moni o ing
sys em.
The s anda d con igu a ion o one o ans o me is desc ibed in Table 1.
TABLE 1. S anda d Con igu a ion o one T ans o me wi h in e e s and panels.
CT
ID
KW
n
Re .
Module
Nº
S ings
Nº Panels
S ings
CT1
5
A8-
1
100
IS-220
528
12
A8-
2
100
IS-220
528
12
A8-
3
100
IS-220
528
12
A8-
4
100
IS-220
528
12
A8-
5
100
IS-220
528
12
Possible u u e ailu es a e p edic ed using a back-p opaga ion neu al ne wo k ha
is ained wi h in e e s’ his o ical da a o he las i e yea s. This pape ocuses on
ailu es esul ing as a consequence o equipmen de e io a ion and use ul li e
educ ion due o ope a ional and geog aphical (en i onmen al) ea u es ha could
ha e a g ea in luence on he equipmen . In he ollowing pa ag aphs o his Sec ion,
he pape i s desc ibes he back-p opaga ion aining p ocess o he ne wo k, and
hen i concen a es on p esen ing he o e all p edic ion me hodology p esen ed in
he pape , applying i o he case s udy.
Back-p opaga ion is a popula lea ning mechanism o sol ing p edic ions in
mul ilaye pe cep on ne wo ks [27],whe e di e en iabili y is equi ed in he
ac i a ion unc ion (as in he case o sigmoid unc ion o he hype bolic angen
unc ion) in he ou pu laye Z, in which i s alues may a y be ween 0 and 1, when
using no malized a iables in he inpu o he ne wo k. The sigmoid o logis ic
unc ion ha is used is p esen ed in (1).
(1)
Fig.1. De eloped Backp opaga ion Pe cep on Mul i-Laye ANN.
The back-p opaga ion aining consis s in he ollowing wo s eps (see Figu e 1
o a be e unde s anding):
●Fo wa d S eps:
o Selec an inpu alue om he aining se (x1, x2, ..., xQ-1). The
numbe o neu ons in he en y laye is (Q), including he inpu s
a iables (Q-1) and ano he a iable (b) which cha ac e izes a
h eshold used in e nally by he ANN model and acili a es he
con e gence p ope ies. An ANN model is composed by an en y
laye , one o se e al hidden laye s and he ou pu laye .
o Apply his en y se o he ne wo k and calcula es he ou pu (ŷd).
In he hidden laye s, he alue in he nucleus o each neu on is nj, which is calcula ed
using weigh s o each inpu (wj,i), applied o each neu on (j) o he
hidden laye and he co esponden inpu (ai) un il he numbe o
neu ons o he p e ious laye (Q).
(2)
In he i s hidden laye he inpu s o neu ons a e ai=xi. The ou pu o each neu on o
he i s hidden laye (wi h J neu ons) a e he applica ion o he
ac i a ion unc ion is aj:
(3)
In he ollowing hidden ne wo ks, he alue in he nucleus o each neu on is now
based on he pas ou pu s ajusing o he weigh s (wk,j), and p oducing
he ou pu akapplying he ac i a ion unc ion on he nucleus alue;
and a his way o successi e hidden laye s.
Finally, he ou pu o he ANN ( he ou pu laye in he case o one neu on) is ŷd:
(4)
●Backwa d S eps:
o Calcula e he e o s be ween he ob ained ou pu (ŷd) and he eal
ou pu (yd).
o Adjus he weigh s in o de o dec ease he e o in e e se way. Fo
his s age, his wo k has employed a lea ning coe icien equals (μ) o
1 and so is included in he second e m o he sum in equa ions (5) and
(6).
(5)
Equa ion (3) is he weigh s adjus men o he ou pu neu on o he ou pu laye ,
whe e =δŷd. An equa ion (4) is he adjus men on
any neu on o he hidden laye s.
(6)
●Repea o wa d and backwa d s eps abou all he aining se un il he
global e o is accep ably low, o his wo k based on minizing he oo mean
squa e e o o he numbe o obse a ions (n).
(7)
Because o non-linea i y o Z, he lea ning mechanism o mul ilaye pe cep on
ne wo ks equi es a esolu ion heu is ic algo i hm ha gua an ees he bes solu ion o
he global minimum ( his is done using he Quasi-New on esolu ion me hod in he
ee so wa e R o he Le enbe g -Ma qua d Me hod in Ma lab). To a oid
o e -adjus men o he ne wo k epea ing he same employ his ime MSE (Mean
Squa e E o ) wi h penal y cha ac e ized by λ, mainly employed wi h a ba e quan i y
o his o ical da a (o he wise λ end o 0):
(8)
A e desc ibing he p ocess o he back-p opaga ion aining o he ne wo k, le ’s
now concen a e on he Logic Decision Tool based on ANN models ha his pape
p oposes.
4. Logic Decision Tool and ANN models
RCM p esen a gene ic p ocess o he logic selec ion o he main enance ac ions
o co ec o p e en he occu ence o ailu e modes [21], as ex ension o his o he
speci ic on-condi ion main enance ac ions, he p ocess o decision making is
de eloped add essing be o e men ioned equi emen s, see Figu e 2, which includes
he ollowing s eps:
●The wo k low s a s wi h he inspec ion and ailu e da a collec ion o
ex e nal and in e nal ela ionships conside ing he di e ences in he
ope a ional and en i onmen al condi ions.
●Then i con inues, e alua ing i he symp oms o a g adual unc ion loss can
be de ec ed e ec i ely.
●He ea e , he ailu e modes analysis is de eloped, de e mining hei e ec s
in he g adual unc ion loss h ough a se o a iables.
●Nex , a logic decision ee analysis (LTA) is employed o selec among he
di e en p edic ion models (based on e e enced au ho s):
o I he e a e enough o mal s a is ical aining o de elop o wi h lineal
co a ia es, pa ame ic models a e ecommendable.
o I he e a e enough da a abou ailu es bu no as o mal s a is ical
aining, ul il he co a ia es assump ions ( ha is when he
Thanks o his esea ch he “lack o isola ion” ailu e mode associa ed indi ec
cos , as loss o p o i , was educed by 68,591 € pe yea and plan (575 KW/day wi h
MTBF=3 pe yea and o 61 in e e s). Fu he mo e, ex apola ing he po en ial
ad an age o he li e cycle o he plan (5 yea s) he p o i s may ha e eached o he
o al p oduc ion o one in e e du ing i e yea s.
Wi h he aim o ex end he ANN model o o he PV plan s, he ailu e mode
beha io has been analyzed in wo PV plan s in di e en geog aphical p o inces o
Spain, Toledo and Zamo a, whe e he ope a ing en i onmen s a e di e en . In bo h
o hem, he ANN model p edic s he lack o insola ion o he in e e bu in a so en
way e sus in Co doba (sou he n han Toledo and Zamo a), due o he di e ence o
me eo ological a iables, see Figu e 5.
Fig.5. De ec ion om ideal and eal p oduc ion compa ison wi h Zamo a and Toledo.

Case B) Failu e Mode P edic ion: Sola T acke Blocking.
The selec ed ailu e mode o he sola acke is he “blocking” ailu e, which is
epe i i e in ield due o he huge olume o ins alled uni s. This ailu e mode
eme ges due o co osion and, he en i onmen al condi ions could be de e minan s in
di e en a eas and besides he ope a ing ime. This case, in ou PV plan is
cha ac e ized by enough ailu e da a wi h non-s a is ical o m a ying among plan s
and wi h high censu ed a e. Then, p edic ion can be ealized as Su i al ANN. The
mos ep esen a i e a iables o ope a ion and ex e nal en i onmen condi ions ha e
o be selec ed and es ed o show hei e ec s in he ailu e mode. The selec ed
a iables in ou SCADA in he case o sola acke s a e ela i e o dia y a e age:
ambien humidi y (%), wind speed (m/s), he global ho izon al adia ion (W/m2), he
ope a ion ime o he sola acke (days) (see Table 5). Howe e , o de elop
Su i al Func ion his case has o eo ganize he a ailable da a, because he aining
means adjus s i e a i ely he weigh coe icien s gi en he condi ion in o de o
app oxima e he ou pu o he a ge , which is an inpu o he ANN. In p ac ice,
su i al e en s ha e o be included and depending on he way o include hem,
di e en ANN models a e p oduced [39, 40] in wo manne s, o example:
●Using ANN ins ead o he lineal combina ion o weigh s coe icien s in he
Cox PHM, as Fa agi and Simon [41], being necessa y sol e he PHM wi h
Pa ial Maximum Likelihood Es ima ion (P-MLE).
●Using an inpu wi h he Su i al S a us o e disjoin ime in e als whe e he
co a ia es alues a e eplica ed, wi h a bina y a iable 0 be o e he in e al o
he ailu e and 1 in he e en o a e , as Lies ol e al. [42] and B own e al.
[43] whe e each ime in e al is an inpu wi h Su i al S a us, hen a ec o
o su i al s a us is de ined pe ailu e; o
●Employing he Kaplan-Meie (K-M) es ima o o de ine he ime in e als as
wo addi ional inpu s ins ead o ec o , one is he sequence o he ime
in e als de ined by de K-M su i al s a us, and he o he is he su i al
s a us in each ime o he sequence. This is he case o Ra din and Cla k [44]
o Biganzoli e al. [45] models which a e known as P opo ional
Kaplan-Meie .
Fo simila i y wi h he p e ious case and he in en ion o u ilize he same ANN
a chi ec u e, now his case has o ien ed ou p oposed Su i al ANN model based on
he ideas o Ra din and Cla k, bu wi h some ma hema ical modi ica ions:
●Wi h pe iodic disjoin in e als ( o all he ailu es) o he maximum ime o
ailu e, o be sui able o le el o ailu e in o ma ion, ins ead o employing
Kaplan-Meie es ima o in e als.
●Wi h co a ia es using eal da a ( he a e age) in each disjoin in e al o be
upg adeable i e a i ely and wi h eali y p ope y, ins ead o epea ing he
alue in each in e al.
●Wi h a semi-pa ame ic Weibull es ima ion o he Su i al S a us, ins ead o
employing Kaplan-Meie es ima o , in o de o i ing he cu e be e and
educe he nega i e e ec o non-mono onically dec easing su i al cu e.
Thus, he ANN model would ha e in he inpu laye wi h i e inpu neu ons,
co esponding o ambien humidi y (%), wind speed (m/s), he global ho izon al
adia ion (W/m2), he ope a ion ime o he sola acke (days), he modelled
semi-pa ame ic su i al s a us, and he h eshold neu on. The ou pu laye con ains
a single ou pu neu on co esponding o he es ima ed su i al unc ion wi h alues
om 0 o 1.
The de eloped semi-pa ame ic Weibull model consis s in o c ea e ime in e als
o he maximum ime o ailu e wi h an inc emen o he su i al unc ion ins ead o
o main ain bina y (0 o 1). The e o e, ou p opose esides in:
1. To es ima e in a i s s ep, he su i al unc ion wi h a pa ame ic Weibull
o e g oups o he p oduced ime o ailu es whe e he co a ia es a e he
same. Fo example, i he case has wo PV plan s wi h 8 ailu es each one, i
has o be ealized he Weibull model in wo g oups, one o e he 8 ailu es o
PV plan 1 and o he o e he 8 ailu es o PV plan 2. Then, i will ob ain a
cha ac e is ic α and β in each plan , and wi hou using he co a ia es, only
based on ime o ailu es as shows Table 5. Due o his, an es ima ion o he
su i al cu e shape is ob ained.
2. A e ha , main aining he β in each plan (which ep esen s he slope o he
line), in o de o model an es ima ion o he su i al unc ion o each
speci ic ailu e wi h a g adual inc emen om 0 o 1, i is aken he β and he
speci ic ime o ailu e o eplace in he Weibull Cumula i e Dis ibu ion
Func ion (CDF) in each ime in e al. Consequen ly, he wo addi ional
inpu s a e de eloped, one wi h he ime in e als and o he wi h he Weibull
CDF wi h an inc emen disc e ized in he ime in e als. Al hough, o ma ch
up he CDF cu e wi h a g adual inc emen om 0 a he beginning o he
ime o 1 in he exac ime o he ailu e and la e , he CDF uses he p e ious
β bu α ponde ed by 0,693, simila o he Median Li e (Median Li e = α ·
Ln(2)^ β = 0,693 bu β =1). As a esul o each speci ic ailu e, he
p obabili y o ailu e ascends un o each 1 a he ime o he ailu e and a e ,
using his semi-pa ame ic model, see equa ion 9 wi h Fn as numbe o ailu e
in i s plan , TTFi as speci ics ime o ailu e, i as he ime in e al alue, and
αias ponde ed α. In Table 5, he 16 ailu es (Fn) and hei ime o ailu e
(TTF) a e p esen ed o each plan (PV1 and PV2) wi h he ini ial α and β,
and he modi ied αi wi h he ponde a ion.
(9)
TABLE 5. Semi-pa ame ic Weibull pa ame e s o eo ganiza ion o Su i al Da a.
P 1
Fn
TTFi
Ponde ed
αi
P 2
Fn
TTFi
Ponde ed
αi
1
105.8
2
73.34
1
305.5
8
211.77
2
88.59
61.39
2
119.3
6
82.71
3
84.06
58.25
3
277.8
9
192.57
4
128.0
3
88.73
4
110.3
4
76.47
5
88.28
61.18
5
99.94
69.26
6
167.2
1
115.88
6
134.1
4
92.96
7
188.9
0
130.91
7
170.5
3
118.18
8
181.7
8
125.97
8
375.9
2
260.51
α
144.1
5
α
226.5
8
β
3.47
β
2.19
Consequen ly, he da a o ain and es he ANN a e eo ganized as in Table 6.
TABLE 6. Reo ganized Su i al Da a o ain and es he ANN.
Failu e Numbe (Fn)
1
1
1
1
1
1
1
1
1
1
1
Time In e al
10
20
30
40
50
60
70
80
90
100
11
0
Ambien humidi y
(%)
95
93
99
91
95
92
84
62
40
53
89
Wind Speed (m/s)
11
8.8
6.7
11.3
6.7
11.6
10.9
12.1
8.2
7.3
4.3
G.H.Radia ion (W/m2)
35.4
53.4
43.5
31.9
38.7
51.7
80.1
68.1
54.7
68
86
Weibull CDF
0.00
1
0.01
1
0.04
4
0.11
5
0.23
2
0.39
2
0.57
3
0.74
1
0.86
9
0.94
7
1
Fo ailu e es ima ion, he ou pu o he ANN model o e s an es ima ion o he
CDF o p obabili y o ailu e, lea ning om semi-pa ame ic es ima ion o a Weibull
wi h co a ia es a ec ion, as oughly p opo ional o Weibull Su i al p obabili y.
The ANN analysis, done going h ough he p ocesses o aining, p edic ions and es
p oduces he ollowing esul s (3,200 measu es o wo yea s a e p ocessed, 640
measu es pe a iable dia y, ou inpu s and one ou pu ).
TABLE 7. Da a Se o a iables case B

.
Va iable
Max.
Re .
Min.
Uni
Tiempo
400
205
10
h
Humedad ela i a
100
74.5
27.3
%
Velocidad Media Vien o
17.2
4.59
0.6
m/s
Radiación Global
379.5
106.64
1.4
W/m2
Supe i encia
1
0.5
0
Now, he lea ning algo i hm pa ame e s a e as ollows: a) maximum numbe o
cycles = 1000, b) maximum alida ion ailu es = 40, c) min_g ad = 1.0e-10, d) goal
= 0, e) μ = 0.005, ) μ _dec = 0.1, g) μ _inc = 10, h) λ = 0, i) min E o = 0.00001833.
The ob ained esul s in his case gua an ee a good op imiza ion model, as shown in
Table 8.
TABLE 8. Resul s o T aining case B in de eloped model.
Resul s
Value
MSE aining
0.01551932
MSE es
0.01641588
R2 aining
0.8681797
R2 es
0.8540106
While, i he Ra din and Cla k model had been employed di ec ly, he esul s had
been wi h less accu acy (as Table 9 shows).
TABLE 9. Resul s o T aining case B wi h Ra din and Cla k.
Resul s
Value
MSE aining
0.08595152
MSE es
0.08493271
R2 aining
0.6371432
R2 es
0.6520446
In his de eloped model, R2explained 85.4% o he su i al da a. Figu es 6 is he
ep esen a ion o deduced p edic ions, ema king a s aigh line o indica e he bes
app oxima ion o e o minimiza ion.
Fig.6. ANN p edic ions case B.
As a esul , o quick con e gence and i ing o he cu e, he ini ial alues o
ain he ANN his case has u ilized he semi-pa ame ic es ima ion o Weibull CDF
as an inpu o ob ain he ou pu as close as possible. Then, his case is esea ching a
p opo ional semi-Weibull ANN model.
These wo de eloped ANN models p e end o explo e he capaci y o ANN o
ob ain knowledge abou co a ia es upda ing i based on expe ience wi h new alid
da a. Al hough, weigh ed sum o he inpu s o he ANN nodes could no be di ec ly
in e p e ed as he coe icien s o he co a ia es. The aim is o es ima e ailu es wi h
one ANN a chi ec u e, ei he as i s app oxima ion o he co a ia es coe icien s, o
o be employed as inpu o o he model, o o upda e he ob ained coe icien s wi h
o he echniques, o o inco po a ing new inpu s, o o compa e he quali y e sus
ailu es in di e en PV plan s o di e en equipmen s.
5. Conclusions
PV Plan s manage s wan o ensu e longe p o i abili y pe iods wi h mo e eliable
plan s. To ensu e p o i abili y along he li e cycle o he plan main enance
depa men s mus ensu e c i ical equipmen eliabili y and maximum ex ension o
hei li e cycle, o he wise ailu e cos s will penalize he expec ed p o i .
Th oughou his documen , his pape sugges s o apply an ANN model pe ailu e
mode and os e a p ac ical implemen a ion in SCADA sys ems o di e en plan s.

This me hodology may ease and may imp o e decision-making p ocessed in
condi ion-based main enance and isk modelling, enabling educ ions o co ec i e
main enance di ec and indi ec cos s o allowing o show esidual li e un il o al
equipmen ailu e.
In cases when enough da a o signi ican aining is a ailable, a be e
implemen a ion o ou me hodology will help o educe he cos s and will imp o e
he knowledge o he li e cycle o he plan when su e ing non-homogeneous
ope a ional and en i onmen al condi ions.
ANN capaci y o au o-lea ning among sou ces o da a (some imes noised o
dep i ed o communica ion) hanks o ei e a i e memo y is impo an . In ou case
s udy, a as quan i y o da a om di e en emo e plan s was a ailable, al hough
some imes his da a was a ec ed by p oblems o senso s eadings o
communica ions. Back-p opaga ion pe cep on ANN is ecommend o au oma ion
de elopmen s wi h eal- ime u iliza ion. Fu he mo e, ad anced ANN models could
be applied suppo ing addi ional a iables.
I is impo an o know he ailu e mode beha io in o de o p e ea men
his o ical da a, elimina ing abno mal da a ha may dis o he esul s.
Values ha e o be no malized i i is used di e en iabili y ac i a ion unc ions,
and wi h he same scale o all he inpu alues o simpli y calcula ions and analysis.
A e he no malized alues ha e o be des-no malized be o e compa ison.
Acknowledgmen s
Pa o he unding o his esea ch was p o ided by he SMARTSOLAR p ojec
(OPN – INNPACTO -Re IPT-2011-1282-920000).
Re e ences
[1] A. O ioli and A. Di Gangi, "A p ocedu e o calcula e he i e-pa ame e model o
c ys alline silicon pho o ol aic modules on he basis o he abula pe o mance da a,"
Applied Ene gy,

ol. 102, pp. 1160-1177, Feb 2013.
[2] V. Kos yle and A. Pa lo ski, "Sola powe o ecas ing pe o mance– owa ds indus y
s anda ds," in 1s In e na ional Wo kshop on he In eg a ion o Sola Powe in o Powe
Sys ems, Aa hus, Denma k

, 2011.
[3] D. Guasch, S. Sil es e, and R. Cala ayud, "Au oma ic ailu e de ec ion in pho o ol aic
sys ems," P oceedings o 3 d Wo ld Con e ence on Pho o ol aic Ene gy Con e sion,
Vols a-C,

pp. 2269-2271, 2003.
[4] F. Oli encia Polo, J. Alonso del Rosa io, and G. Ce uela Ga cía, "Supe iso y con ol
and au oma ic ailu e de ec ion in g id-connec ed pho o ol aic sys ems," T ends in
Applied In elligen Sys ems,

pp. 458-467, 2010.
[5] W. T. Mille III, F. H. Glanz, and L. G. K a III, "Cmas: An associa i e neu al ne wo k
al e na i e o backp opaga ion," P oceedings o he IEEE,

ol. 78, pp. 1561-1567, 1990.
[6] I. A. Bashee and M. Hajmee , "A i icial neu al ne wo ks: undamen als, compu ing,
design, and applica ion," Jou nal o Mic obiological Me hods,

ol. 43, pp. 3-31, Dec 1
2000.
[7] G. Q. Zhang, B. E. Pa uwo, and M. Y. Hu, "Fo ecas ing wi h a i icial neu al ne wo ks:
The s a e o he a ," In e na ional Jou nal o Fo ecas ing,

ol. 14, pp. 35-62, Ma 1998.
[8] B. CURRY, P. MORGAN, and M. BEYNON, "Neu al ne wo ks and lexible
app oxima ions," IMA Jou nal o Managemen Ma hema ics,

ol. 11, pp. 19-35, 2000.
[9] B. MALCOLM, C. BRUCE, and P. MORGAN, "Neu al ne wo ks and ini e-o de
app oxima ions," IMA Jou nal o Managemen Ma hema ics,

ol. 10, pp. 225-244,
1999.
[10] C. Kuo, "Cos e iciency es ima ions and he equi y e u ns o he US public sola
ene gy i ms in 1990–2008," IMA Jou nal o Managemen Ma hema ics,

ol. 22, pp.
307-321, 2011.
[11] A. Lapedes and R. Fa be , "Nonlinea signal p ocessing using neu al ne wo ks," 1987.
[12] A. Melli , M. Benghanem, M. Bendekhis, and Ieee, "A i icial neu al ne wo k model o
p edic ion sola adia ion da a: Applica ion o sizing, s and-alone pho o ol aic powe
sys em," in 2005 Ieee Powe Enginee ing Socie y Gene al Mee ing, Vols, 1-3

, ed, 2005,
pp. 40-44.
[13] R. Yace , M. Benghanem, and A. Melli , "P edic ion o daily global sola i adia ion da a
using Bayesian neu al ne wo k: A compa a i e s udy," Renewable Ene gy,

ol. 48, pp.
146-154, Dec 2012.
[14] M. Benghanem and A. Melli , "Radial Basis Func ion Ne wo k-based p edic ion o
global sola adia ion da a: Applica ion o sizing o a s and-alone pho o ol aic sys em
a Al-Madinah, Saudi A abia," Ene gy,

ol. 35, pp. 3751-3762, Sep 2010.
[15] A. Melli , M. Benghanem, A. H. A ab, A. Guessoum, and Ieee, Modelling o sizing he
pho o ol aic sys em pa ame e s using a i icial neu al ne wo k

, 2003.
[16] A. Melli , M. Benghanem, A. H. A ab, A. Guessoum, and K. Moulai, Neu al ne wo k
adap i e wa ele s o sizing o s and-alone pho o ol aic sys ems

, 2004.
[17] A. Melli , M. Benghanem, A. H. A ab, and A. Guessoum, "An adap i e a i icial neu al
ne wo k model o sizing s and-alone pho o ol aic sys ems: applica ion o isola ed
si es in Alge ia," Renewable Ene gy,

ol. 30, pp. 1501-1524, Aug 2005.
[18] T. Hiyama, "Neu al ne wo k based es ima ion o maximum powe gene a ion om PV
module using en i onmen al in o ma ion - Discussion," Ieee T ansac ions on Ene gy
Con e sion,

ol. 12, pp. 247-247, Sep 1997.
[19] I. Ash a and A. Chand a, "A i icial neu al ne wo k based models o o ecas ing
elec ici y gene a ion o g id connec ed sola PV powe plan ," In e na ional jou nal o
global ene gy issues,

ol. 21, pp. 119-130, 2004.
[20] A. Melli and S. Shaa i, "Recu en neu al ne wo k-based o ecas ing o he daily
elec ici y gene a ion o a Pho o ol aic powe sys em," Ecological Vehicle and
Renewable Ene gy (EVER), Monaco, Ma ch,

pp. 26-29, 2009.
[21] J. Moub ay, Reliabili y-cen e ed main enance

: Indus ial P ess Inc., 1997.
[22] M. Rausand and A. Høyland, Sys em eliabili y heo y: models, s a is ical me hods, and
applica ions

ol. 396: John Wiley & Sons, 2004.
[23] J. Campbell and A. Ja dine, "Main enance Excellence: Op imising Equipmen Li e-cycle
Decisions, 2001," ed: Ma cel Dekke : New Yo k, NY.
[24] A. C espo Má quez, The main enance managemen amewo k: models and me hods
o complex sys ems main enance

: Sp inge Ve lag, London, 2007.
[25] H. Pham and H. Wang, "Impe ec main enance," Eu opean jou nal o ope a ional
esea ch,

ol. 94, pp. 425-438, 1996.
[26] R. L. Wilson, "Ope a ions and suppo cos model o new p oduc concep
de elopmen ," Compu e s & Indus ial Enginee ing,

ol. 11, pp. 128-131, 1986.
[27] J. L. McClelland, D. E. Rumelha , and P. R. G oup, "Pa allel dis ibu ed p ocessing,"
Explo a ions in he mic os uc u e o cogni ion,

ol. 2, 1986.
[28] K. Ho nik, M. S inchcombe, and H. Whi e, "Mul ilaye eed o wa d ne wo ks a e
uni e sal app oxima o s," Neu al ne wo ks, ol. 2, pp. 359-366, 1989.
[29] D.R. Cox, D. Oakes, "Analysis o su i al da a". Chapman and Hall

, London, 1984.
[30] J. Klein, M. Moeschbe gue , "Su i al analysis echniques o censo ed and unca ed
da a". Sp inge

, New Yo k Inc, 1997
[31] A.M. Law, W.D. Kel on, "Simula ion modeling and analysis". McG aw-Hill, New Yo k.
1991.
[32] J.K. Lindsey, "The s a is ical analysis o s ochas ic p ocesses in ime". Camb idge Uni
P ess

. 2001.
[33] P.J. Smi h, "Analysis o ailu e and su i al da a". Chapman-Hall

, New Yo k. 2002.
[34] P. Hougaa d, "Analysis o mul i a ia e su i al da a". Sp inge

, New Yo k. 2000.
[35] E.T. Lee, "S a is ical me hods o su i al da a analysis". Wiley

. 1992.
[36] W.R. Blischke, D.N.P. Mu hy, "Reliabili y modelling, p edic ion and op imiza ion".
Wiley

, New Yo k. 2000.
[37] D.R. Cox, "Reg ession models and li e- ables". Jou nal o he Royal S a is ical Socie y
Se ies

34:187–220. 1972.
[38] K. Mobley, "An in oduc ion o p edic i e main enance". Else ie ,

Ams e dam. 2002.
[39] L. Ohno-Machado, "Modeling Medical P ognosis: Su i al Analysis Techniques".
Jou nal o Biomedical In o ma ics

34, 428–439 (2001).
[40] A. Xianga, P. Lapue a, A. Ryu o a, J. Buckley, S . Azena, “Compa ison o he
pe o mance o neu al ne wo k me hods and Cox eg ession o censo ed su i al
da a,” Compu a ional S a is ics & Da a Analysis

, ol. 34, no. 2, pp. 243–257, 2000.
[41] D. Fa aggi, R. Simon, "A neu al ne wo k model o su i al da a". S a Med

, 14:73–82.
1995.
[42] K. Lies ol, P. K. Ande sen, U. Ande sen. "Su i al analysis and neu al ne s", S a is ics in
Medicine

, 13, 1189-1200, 1994.
[43] S.F. B own, A. B an o d, W. Mo an, "On he use o a i icial neu al ne wo ks o he
analysis o su i al da a". IEEE T ansac ion o Neu al Ne wo ks

, 8:1071-1077. 1997.
[44] P.M. Ra din, G.M. Cla k, "A p ac ical applica ion o neu al ne wo k analysis o
p edic ing ou come o indi idual b eas cance pa ien s". B eas Cance Res T ea
22:285-293. 1992.
[45] E. Biganzoli, P. Bo acchi, L. Ma iani, E. Ma ubini, "Feed o wa d neu al ne wo ks o he
analysis o censo ed su i al da a: a pa ial logis ic eg ession app oach". S a Med

,
17:1169-1186. 1998.
[46] A. Bigla ian, E. Bakhshi, A.R. Baghes ani, M.R. Goha i, M. Rahgoza , M. Ka imloo, "
Nonlinea Su i al Reg ession Using A i icial Neu al Ne wo k". Hindawi Publishing
Co po a ion. Jou nal o P obabili y and S a is ics

, Volume 2013, A icle ID 753930.
[47] E. Mi chell, A. Robson, VB. P abhu, "The impac o main enance p ac ices on
ope a ional and business pe o mance". Manag Audi ing J

11(1):25–39. 2002.
[48] T. S ewa T, "A c i ical su ey on he s a us o mul iple c i e ia decision-making heo y
and p ac ice". OMEGA, In J Manag Sci

20(5/6):569–586. 1992.
[49] J. M. Blanes, F. J. Toledo, S. Mon e o, and A. Ga igos, "In-Si e Real-Time Pho o ol aic
I-V Cu es and Maximum Powe Poin Es ima o ," IEEE T ansac ions on Powe
Elec onics

, ol. 28, pp. 1234-1240, Ma 2013.