Failure mode prediction and energy forecasting of PV plants to assist dynamic maintenance tasks by ANN based models

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. 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