Using Supervised Learning Techniques for Diagnosis of Dynamic Systems

Using Supe ised Lea ning Techniques o Diagnosis o Dynamic Sys ems Ped o J. Abad 1, An onio J. Su i ez', Ra ael M. Gasca 2, Juan A. O ega 2 Abs ac . This pape desc ibes an app oach based on supe ised diagnose sys ems aul s a e needed o main ain he sys ems in lea ning echniques o he diagnosis o dynamic sys ems. The le els o secu i y, p oduc ion and eliabili y. me hodology can s a wi h eal sys em da a o wi h a model o Inside he A i icial In elligen communi y he dynamic sys ems he dynamic sys em. In he second case, a se o simula ions o diagnosis ask has been app oached, in mos o he cases, adap ing he sys em is equi ed o ob ain he necessa y da a. In bo h cases, he echniques coming om he s a ic sys ems diagnosis o he ob ained da a will be labelled acco ding o he unning condi ions dynamic beha iou o he sys ems. This way [2] o [3] y o add o he sys em a he ga he ing da a ime. Label indica es he empo a y in o ma ion o GDE [4] unning s a e o sys em: co ec wo king o abno mal unc ioning On he o he hand, quali a i e models ha e also been commonly o any sys em componen . A e being labelled, da a will be used o his pu pose [5] [6]. ea ed o add addi ional in o ma ion abou he unning o sys em. In [7] he undamen s o he based-models diagnosis, applied o The inal goal is o ob ain a se o decision ules by applying a he dynamic sys ems, a e p esen ed, and mo e ecen ly [8] p oposes classi ica ion ool o he se o labelled and ea ed da a. This a consis ency-based app oach wi h quali a i e models. way, any obse a ion on he sys em will be classi ied acco ding O he echniques, coming om he AL, ha e also en e ed in o hose decision ules, ha ing a e u n label indica ing he he diagnosis ield. Following his line, lea ning echniques ies o cu en ly unning s a e o sys em. Re u ned label will be he iden i y he sys em beha iou basing on a p e ious aining. diagnos ic. This en i e lea ning ask is ca ied ou o -line, be o e La ely, some wo ks using lea ning-based echniques ha e been he diagnosing. p esen ed, like s ochas ic me hods [9], neu al ne wo k based lea ning [10] and classi ica ion sys ems [11]. Neu al ne wo k echniques ha e ecen ly been applied in di e se ields, as 1 INTRODUCTION medicine [12] o powe supply [13]. Machine Lea ning echniques, inside he supe ised lea ning Diagnosis de e mines why a sys em, co ec ly designed, doesn' ield, a e au oma ed p ocedu es based on logical ope a ions ha wo k like i was expec ed. Explana ion, o his e oneous lea n a ask s a ing om a sui e o examples. In he classi ica ion beha iou , ep esen s a disc epancy wi h he sys em design. One ield he a en ion has been cen ed, conc e ely, in app oaches wi h diagnosis ask is o de e mine he sys em elemen s ha could cause decision ees [14], whe e classi ica ion is he esul o a se ies o he e oneous beha iou acco ding o he sys em obse a ions. logical s eps. These app oaches a e able o ep esen he mos Moni o ing p ocess is undamen al o a oid non- eal aul s by complex p oblems i hey ha e enough da a. Applied o he small al e a ions in a iables alues. [1] P oposes a knowledge diagnosis, we can ind hese me hods used o he classi ica ion o model o dynamic sys ems moni o ing. empo ay pa e ns [15] o in p e ious wo ks o he cu en one Faul de ec ion consis s on de e mining, s a ing om he [16] [17]. sys em obse a ions, when an inco ec ope a ion o he obse ed The p esen wo k is cen ed in quan i a i e models. I uses sys em exis s. When ailu e is de ec ed hen diagnosis will ake he supe ised lea ning echniques o ob ain a ules-based model o con ol o ind he easons o ha inco ec beha iou , diagnose dynamic sys ems by ecognizing he co ec beha iou Faul de ec ion and diagnos ic o aul y componen s a e e y models and aul y beha iou models. An app oach o o e se e al impo an om he s a egic poin o iew o he companies, due o aul causes, when he e isn' an only clea cause, is p esen ed. he economic demands and en i onmen conse a ion equi ed o Res o he documen has been o ganized in he ollowing way: emain in compe i i e ma ke s. This is one o he easons causing in he nex sec ion he used me hodology will be exposed and he ha his is a e y ac i e in es iga ion ield. Componen s aul s and o m o ca y ou he diagnosis. Nex a p oblem applica ion p ocess aul s can cause sys ems damages and undesi able hal o example is desc ibed o he de eloped app oach. To illus a e he he sys em. This causes he inc ease o cos s and dec ease o ope a ion o hese echniques a wide se o es s is p esen ed. Las ly p oduc ion. The e o e de eloping mechanisms o de ec and o some imp o emen s ha a e in de elopmen p ocess a e discussed. Dp o de Ingenie ia Elec 6nica, Sis emas In o m n icos y Au omd ica. 2 PROPOSED METHODOLOGY Uni e sidad de Huel a. E-Mail: {abadhe,[email p o ec ed]} 2 Dp o de Lenguaje y Sis emas 1n o md icos. Uni e sidad de Se illa. To ca y ou diagnosis o dynamic sys ems a se o decision ules E- Mail: {gasca,[email p o ec ed]} should be gene a ed. I can be done s a ing om he known ajec o ies o he sys em o he simula ions gene a ed om a 2. Decision ules a e gene a ed using a supe ised lea ning ool. model. Relabelled ajec o ies * Decision ules Be o e s a ing wi h he me hodology some concep s need o be 3. Diagnosis consis s in associa ing an obse a ion as de ined. co esponding o beha iou s amily by using decision ules. Classi ica ion (obse a ion, ules) * Diagnos ic label 2.1 De ini ions and no a ion. De ini ion 1: Beha iou s Family. I is a ini e g oup o 2.2 Me hodology ajec o ies ha ing a simila beha iou om he poin o iew o P oposed me hodology o diagnose is an ampli ica ion o o he one he diagnosis. de eloped in [16]. This basic me hodology may p esen some De ini ion 2: Co ec beha iou . I is he ini e g oup o p oblems when he same sys em beha iou s can be associa ed o ajec o ies belonging o e olu ions o he sys em wi hou any aul di e en aul easons. In o de o don' diagnose inco ec ly hese ype. cases, in his new app oach, hose beha iou s will be associa ed De ini ion 3: Pe ec beha iou . I is he ajec o y desc ibing he wi h all he possible beha iou s amily ha can cause his conc e e sys em when all pa ame e s ake he cen al alues o he anges beha iou . In his way se e al aul causes will be o e ed o de ined as co ec . obse a ions ha can co espond o di e en beha iou s amily. De ini ion 4: Obse a ion. I is a eal ajec o y o he dynamic Basic idea consis s in ob aining a se o classi ica ion ules om sys em con aining alues o he obse a ional a iables in he a sui e o sys em da a in di e en beha iou s modes: he co ec sys em. beha iou and he aul y beha iou s. A e , hose ob ained De ini ion 5: Diagnosis. I is he iden i ica ion o he obse ed classi ica ion ules can be used o associa e an obse a ion wi h beha iou o he sys em as belonging o a ce ain beha iou amily model beha iou . Thus diagnosis o he obse a ion is ob ained. (diagnosis label) and acco ding o decision ules. P ocess can s a wi h eal sys em da a o wi h a model o he P oposed app oach can be gene a ed om wo di e en ways: dynamic sys em. In he second case, a se o simula ions o he "* Rules a e gene a ed s a ing om a g oup o di e en sys em is equi ed o ob ain he necessa y da a. In bo h cases, beha iou models. ob ained da a will be labelled acco ding o he unning condi ions Model (beha iou ) * labelled ajec o ies o he sys em a he ga he ing da a ime. Label indica es he "* Rules a e gene a ed s a ing om a g oup o expe imen al unning sys em s a e: co ec wo king o abno mal unc ion o any ajec o ies o dynamic sys em o he co ec beha iou and sys em componen . Final esul consis s in a da abase con aining all possible aul beha iou . labelled ajec o ies. T ajec o ies (beha iou ) * labelled ajec o ies. Ob ained da abase con ains e y simila ajec o ies Lea ing o one o hese si ua ions he p ocess can con inue like co esponding o di e en beha iou amily and he e o e wi h ha : di e en labels. To sol e his p oblem he se o all simila 1. Simila ajec o ies belonging o di e en beha iou s amily a e ajec o ies will be elabelled wi h new labels. This new labels will iden i ied. These ajec o ies a e labelled again as belonging o be composed as a mix o he olde labels. Thus, elabelled bo h beha iou s amily. ajec o ies will be associa ed wi h anyone o he o iginal Simila T ajec o ies (di e en beha iou amily) • beha iou s amily. The p oblem is o de ine when wo o mo e elabelled ajec o ies, ajec o ies a e simila . Decision aken is ha se e al ajec o ies P oblem Simula ing Desc ip ion M14ln Moe iuaig D bae LbligLble Sys em Real Sys em Obse a ion DecisionRc ble Rules ClassiFica ion Labelled & Da a Da abase T ea ed T ea men D M hbdasoe E alua ion DIAGNOSIS Figu e 1. P oposed Me hodology a e simila when dis ance be ween hem is lowe han a magni ude. Sys em can be modelled by he ollowing equa ions, which Tha magni ude should be speci ied o each ea ed sys em. Used include a cons an o each componen ha is used o model also dis ance is Euclidean dis ance, he aul y beha iou o he componen : A e being labelled and elabelled, ajec o ies da a will be ea ed o add addi ional in o ma ion abou unning o he sys em. dw This addi ional in o ma ion will be e y use ul when classi ica ion d (1) ool ies o ind decision ules, because a ailable in o ma ion will be g ea e . This addi ional in o ma ion should cha ac e ize he d sys em u he han ga he ing da a and i is speci ied o each I - Con olle : -- = c, (d - w.) (2) ea ed sys ems. d A new da abase, which con ains o iginal ajec o ies plus new a ibu es and he co esponding label, is ob ained. Senso : w,, = c, * w (3) Final s ep, o ob ain decision ules, is o use a classi ica ion ool wi h he labelled and ea ed da abase. Whe e T is he ine ia o he mo o , c., is he cons an o he An aspec o highligh is ha all p ocess, un il his momen , mo o ; c, is he cons an o he con olle and c, is he cons an o ha e been de elopmen o -line, and ime needed o his p ocess is he e olu ion coun e . no impo an o he diagnosis p ocess. Componen anomalous ope a ion is caused, mainly, by he Diagnosis p ocess consis s on e alua ing an obse a ion wi h de ia ion o he componen cons an nominal alue. These he ob ained decision ules. Time spending o diagnose is only he cons an s s ay o he conside ed co ec alues ange ime o e alua ing ob ained decision ules. Decision ules e u ns Some aul s ep esen ha cons an s ake alues abo e he he label associa ed o he beha iou by co espondence be ween co ec ones and o he s aul s ep esen ha cons an s ake alues aining da a and obse ed da a. This e u ned label is o e ed as below he co ec ones. Diagnosis esul should indica e, in diagnosis. addi ion o he aul y componen , i aken alues o he componen Nex a case s udy will be p esen ed o de elop his cons an a e below co ec alues o abo e hem. me hodology. Possible aul easons ha we wan o iden i y a e he e o e: 'CmHigh' when alues o Cm a e abo e he co ec ones; M 4 'CmLow' when alues o Cm a e below he co ec ones; 'CsHigh' when alues o Cs a e abo e he co ec ones; 'CsLow' when alues o Cs a e below he co ec ones; 'CcHigh' when alues o Cc a e abo e he co ec ones and 'CcLow' when alues o Cc a e below he co ec ones. To desc ibe he sys em co ec beha iou , i is conside ed ha alues o all cons an s don' ha e only one co ec alue, bu a he hey can ake alues inside an in e al ha will be conside ed as c _ co ec . This way, ope a ion lexibili y is allowed and sys em eal beha iou is be e simula ed, whe e he e is no a co ec alue bu d a he co ec ion ma gins a e lexible. This p oduces ha sys em doesn' ha e an only co ec beha iou , bu a he a co ec beha iou s amily. I ep esen s all possible combina ions o he Figu e 2. The example sys em cons an s alues ha a e inside o he de ined ole ance limi . A co ec beha iou s amily does he diagnosis mo e di icul , 3 CASE STUDY because i is necessa y o ecognize di e en beha iou s as co ec , bu on he con a y i p o ides a mo e ealis ic ision o he sys em. As i has been commen ed p e iously, me hodology can be used In ou model he cons an alues conside ed as co ec a e: wi h eal sys em da a o wi h ob ained da a o a model simula ion. In ou case, he me hodology will be applied o a model, which is Table I. Values o OK beha iou s an idealized si ua ion, bu i o e s us a clea idea o he way o ac . Cm [0.98-1.02] In case o applica ion on a eal sys em, many di icul aspec s, no Cc [0.98-1.02] men ioned he e (as moni o ing o small phase shi ), need o be aken in accoun , bu wi h he model we a e only ying o p esen he app oach. As example o dynamic sys em o diagnose we conside he O he conside ed cha ac e is ics in ou sys em a e: con olle elec ic mo o in [18] and [19]. Figu e 2 ep esen s 1. Faul is p esen om he beginning and i doesn' e ol e in he ea ed sys em. The mo o 'M', whose o a ional speed is 'w', is ime. d i en h ough a ol age ' ' by he con olle 'C' which ac s based 2. Beha iou change occu s ins an ly and s a ing om he e i on he desi ed speed 'd' and he speed 'w,,' measu ed by he doesn change again. e olu ion coun e 'S'. Con olle 'C' is conside ed as an I- con olle . 3. Once he wan ed angula speed has been indica ed, i doesn' change un il his angula speed is eached. This way, diagnosis will be ca ied ou when he desi ed angula classi ica ion ool o ob ain a se o decision ules, and i we ha e speed (d) is changed. The way o diagnose is by checking he simila ajec o ies wi h di e en labels hen classi ie can' e olu ion o each he inal speed. I is necessa y o keep in mind co ec ly wo k; ha is o say, hose simila ajec o ies will be ha in spi e o exis ence o a ailu e in some componen , I- inco ec ly classi ied. Figu e 7 shows an example o his. con olle is able o ac on he mo o o each he equi ed inal speed. O cou se e olu ion o he sys em o each he desi ed inal speed will be di e en . This di e ence in he beha iou will allow 20 he diagnosis. T 10 / % • - VW INTEG(F2) W = INTE G(/ Cm Wm'•--- -- cs F2 = Cc*(d-W.g) F2 / F = (•.y-YV/T Cc 0 6 12 18 24 30 Time (Second) Figu e 4. OK Beha iou P2O Figu e 3. Fo es e diag am Fi s s ep, he e o e, is pe o ming sys em simula ions in 15 di e en beha iou s modes. In ou case, sys em has been modelled as a Fo es e diag am [20], o be able o simula e using he 7 - simula ion ool VEMSIM&. Fo es e diag am gene a ed o he 10 .... - -j -. sys em is p esen ed in igu e 3. J Simula ed beha iou s will be hose ha we wan o diagnose. / They will be: OK o co ec beha iou and CmHigh, CmLow, CsHigh, CsLow, CcHigh, CcLow o each componen aul abo e men ioned. 0 A beha iou amily will ep esen each one o hese beha iou s. 0 6 12 1i 24 30 Simula ions alues a e shown in able 2. Time (Second) Table 2. Sys em alues o simula ion Figu e 5. CmHigh Beha iou T 3 D 10 20 W 5 Time S ep 0.1 15 Fo he co ec beha iou he cons an alues a e in o [0.98- 10 ------- -- 1.02]. Values o simula e beha iou s abo e he co ec one a e in o -J [1.02-5]. Values o simula e beha iou s bellow he co ec one a e in o [0-0.98]. 5 7 _ Cons an s alues o simula ed beha iou s ha e been elec ed by andom wi h he Mon e Ca lo me hod ollowing a uni o m 0 dis ibu ion. Numbe o simula ions pe beha iou will be 100. 0 6 12 18 24 30 Label co esponding o beha iou is placed o each one o he Time (Second) ajec o ies. This way, a da abase con aining 700 labelled ajec o ies is ob ained. Figu e 6. CcLow Beha iou T ajec o ies a e composed wi h alues o he a iable 'w,,' in each ime s ep. Reason o selec a iable 'w,,' and no 'w' is ha 'w,,,' is he only obse able a iable in he eal sys em. To sol e his p oblem a new label will be assigned o e y In igu es 4, 5 and 6 di e en sys em beha iou s a e shown, simila ajec o ies. A mix u e o labels o all simila ajec o ies Ob ained da abase has simila ajec o ies belong o di e en will compose he new label. This way, nex s ep is o ind all beha iou s. This way se e al e y simila ajec o ies ha e simila ajec o ies in o he da abase and assigning a new label. di e en labels. This is a p oblem, because ou inal goal is o use a I is necessa y o de ine when wo o mo e ajec o ies a e .Max speed ime (MST). I is he momen in which he highes simila . Two ajec o ies a e conside ed simila when dis ance e olu ion speed is eached. be ween hem is smalle han a magni ude. Dis ance be ween This way a new da abase con aining ajec o ies plus new ajec o ies is measu ed as Euclidean Dis ance and magni ude a ibu es is gene a ed. chosen is 10% o he Euclidean dis ance be ween he wo u he Da a in new da abase ha e he ollowing o m: away ajec o ies o he co ec beha iou . This magni ude in ou RT, SS, MS, MST, Win[1], DP[ 1, 111], ....... Win[n], DP[n], I[n], example is 0.45. LABEL Final s ep is pe o ming supe ised lea ning wi h he ob ained da abase. Classi ica ion ool selec ed o pe o m he supe ised 20 lea ning is C4.5 [21]. Wha is go en wi h his ool is o cha ac e ize each one o he beha iou amilies acco ding o he 15-- alues o he a ibu es ha ha e been p o ided. Resul is a decision ee and an equi alen se o decision ules. These ules / will be he way o do he diagnosis. In ou example classi ie 10 ------ - -- ob ains 27 ules wi h an e o a e o 1.2%. This mean ha 1.2% o ýT " ajec o ies a e no co ec ly classi ied wi h hose ules. 3.1 Diagnosis 0 The way o do he diagnosis is e alua e he obse ed da a wi h he 0 6 12 18 24 0 ob ained ules. Because in ules appea a ibu es ha ha e been calcula ed and Time (Second) no appea in obse ed da a, same a ibu es should be calcula ed o obse ed da a in o de o be able o classi y wi h hose ules. Figu e 7. Beha iou CcHigh s CmHigh This way in he momen ha one obse ed da a is ga he ed all possible a ibu es should be calcula ed. A e ha , decision ules A e his p ocess we ob ain a new da abase wi h all simila a e e alua ed wi h wo possible esul s: a label is e u ned o ajec o ies e-labelled as co esponding wi h all beha iou s o he in o ma ion is insu icien o e alua e all ules. In he i s case he simila ajec o ies. e u ned label is he esul o he diagnosis. In he second one we Nex s ep is o calcula e new a ibu es o each ajec o y wi h need o wai mo e in o ma ion in u he momen s. he goal ha classi ie has mo e in o ma ion o gene a e decision I we wan o diagnose he sys em wi h ano he unning ules. These new a ibu es mus be ep esen a i e o each condi ions, we should ha e p epa ed he decision ules se o hose ajec o y. speci ic condi ions. I. e. i we wan o diagnose his sys em when Fo each ajec o y poin nex a ibu es ha e been calcula ed: cu en o a ional speed is 12 ad/sec and desi ed o a ional speed " Dis ance o pe ec beha iou . I indica es how a away is is 7 ad/sec, we should ha e gene a ed a se o decision ules o cu en ajec o y om pe ec beha iou (abo e de ined). I hose condi ions and we will use hem in he diagnosis momen . is calcula ed as: DP(i) = Wm[i]- Wmp [i] (4) 4 RESULTS ON THE EXAMPLE SYSTEM To e alua e he p oposed me hodology a se o es s ha e been Whe e Wm[i] is he ea ed poin in he cu en ajec o y and done. Wmpj[i] is he co esponden poin in he pe ec beha iou . Obse a ional da a ha e been ob ained by simula ing he sys em " In eg al. I is he magni ude e u ned by nume ical in eg a ion wi h speci ic condi ions o he es . This way a es ajec o y is be ween cu en poin and he p eceden one. I ep esen s he ob ained and he diagnosis co ec esul is known, because i mus closed a ea be ween hem. I is calcula ed by app oxima ing be he co esponding o he simula ed condi ions. as ollow: Condi ions o he es a e he same abo e men ioned. We emembe hem in able 3: p[ijj- pi~i-1](5 l(i) = T's x _____ 5 2 Table 3. Tes s condi ions T 3 Whe e Ts is he ime s ep in he simula ion, p[i] is he cu en D 10 ea ed poin and p[i-1] he p eceden one. W ini ial 5 In addi ion nex a ibu es will be calcula ed o each ajec o y: Time S ep 0.1 "* Rise Time (RT). I is he momen in which desi ed e olu ion Values o OK [0.98 - 1.02] speed is eached o i s ime. Values o HIGH [1.02 -5] "* S eady s a e (SS). I is he momen in which desi ed Values o LOW [0 - 0.98] e olu ion speed is eached de ini i ely. "• Max speed (MS). I is he alue o he highes e olu ion In able 4 we can see esul s o he es s: eached speed. Table 4. Tes s esul s imes, me hodology e u ns an inco ec diagnosis, bu in gene al VALUE OF THE DIAGNOSIS DIAGNOSIS o e ed esul s a e accep able. CORRECT WITH SIMPLE WITH This occu s because he e a e e y simila ajec o ies belonging Cm Cc Cs DIAG S LABELLED LEL o di e en beha iou s, and classi ie canno co ec ly selec he LABELLED ules o di e ence hem. 1 1 1.03 CS HIGH CS HIGH CS HIGH To sol e his p oblem he new me hodology p oposes he e- 1 1 1.07 CS HIGH CS HIGH CS HIGH labelled o all simila ajec o ies as ha e been abo e men ioned. I 1 1.1 CS HIGH CS HIGH CS HIGH Ob ained esul s show ha he new me hodology o e s a mul iple I 1 1.5 CS HIGH CS HIGH CS HIGH diagnosis when he p e ious one can' ind he co ec aul . I 1 3 CS HIGH CS HIGH CS HIGH Among he mul iple o e ed diagnoses, nea o all es s e u n he 1 1.03 1 CCGH CS OK OK co ec one. CC HIGH C I is impo an o highligh ha , in es s whe e beha iou is a 1 1.07 1 CC HIGH CM HIGH CM HIGH o he co ec one, o e ed diagnosis is he co ec one. CC HIGH In he se o p esen ed es s he diagnosis is co ec in 58.33 % CM HIGH o he cases. Co ec diagnosis is o e ed, among o he s, in 30.55 % 1 1.5 1 CC HIGH CC HIGH CC HIGH o he cases. An inco ec diagnosis is o e ed in 2.7 % o he cases. 1 2 1 CC HIGH CC HIGH CC HIGH The aul is no de ec ed in 8.33 % o he cases. O he wise, ne e 1 3 1 CC HIGH CC HIGH CC HIGH de ec ailu e when ailu e doesn' exis . 1.03 1 1 CM HIGH OK OKCI CS LOW 1.07 1 1 CM HIGH CM HIGH CC HIGH 5 CONCLUSIONS AND FURTHER CM HIGH CC HIGHI O K 1.1 1 1 CM HIGH CM HIGH CCHGWO K CM HIGH P esen ed me hodology is able o pe o m diagnosis o dynamic 1.5 1 1 CM HIGH CM HIGH CM HIGH 2 1 1 CM HIGH CM HIGH CM HIGH sys ems and i is independen o he sys em ype. In ac , one o 3_ 1 1 CM HIGH CM HIGH CM HIGH u he wo ks is o apply his me hodology o a non-linea dynamic 3 1 1 CM HIGH CM HIGH CM HIGHsy m 1 1 .97 S LO OKCS LOW j sys em. 1 1 0.97 CS LOW OK OK This capaci y is due o he ac ha he me hodology is only 1 1 0.93 CS LOW CS LOW CS LOW cen ed in he e olu ion cha ac e is ics o he sys em o he co ec 1 1 0.89 CS LOW CS LOW CS LOW beha iou o aul y beha iou s. 1 1 0.85 CS LOW CS LOW CS LOW Ano he cha ac e is ic o he me hodology is ha he diagnosis 1 1 0.5 CS LOW CS LOW CS LOW can be pe o med in a e y simple way, and a e y li le 1 1 0.1 CS LOW CS LOW CS LOW compu a ional ime is equi ed. 1 0.97 1 CC LOW OK OK Ce ain sys ems, as he p esen ed in he example, can p oduce 1 0.93 1 CC LOW CC LOW CC LOW j simila beha iou s o di e en aul easons. This is due o CM LOW ela ionship among a iables ha go e n he sys em beha iou . 1 0.89 1 CC LOW CC LOW CC LOW j This ela ionship, among sys em a iables, can p oduce ha an 1 0.89 1 CCLM CCLW I_ CM LOW al e a ion o a a iable would be compensa ed by he al e a ion o 1 0.85 1 CC LOW CC LOW CC LOW ano he a iable in con a y sense. To sol e his p oblem, ____ CM LOW 1 0.5 1 CC LOW CC LOW CC LOW me hodology assigns mul iple aul easons o sys em beha iou s 1 0.1 1 CC LOW CC LOW CC LOW ha could be p oduced by di e en aul easons. This way a 0.97 1 1 CM LOW OK OK mul iple diagnosis is o e ed in hose si ua ions. 0.93 1 1 CMLOW CCLow CC LOW j Ano he u he wo k is o be able o diagnose dynamic sys em CM LOW when mul iple aul occu s a he same ime, is o say, iden i ying CM LOW CM LOW CC LOW j sys em beha iou s when mo e han one componen is aul y. 0.89 1 CMC LOLOWLO CM LOW CC LOW 0.85 1 1 CM LOW CM LOW CM LOW CM LOW ACKNOWLEDGMENTS 0.5 1 1 CM LOW CM LOW CM LOW 0.1 1 1 CM LOW CM LOW CM LOW This wo k has been pa iali y inanced by he Comisi6n 0.99 0.98 1.02 OK OK OK In e minis e ial de Ciencia y Tecnologia (DP12000-0666-C02-02) 1 1.02 1.02 OK OK OK and he Modelizaci6n Ma emdi ica Redes y Mul imedia 0.98 1 0.98 OK OK OK in es iga ion g oup o he Uni e si y o Huel a. 0.98 1.02 1.02 OK OK OK 0.99 1.01 1.01 OK OK OK 1.01 1 0.99 OK OK OK REFERENCES We can see ha diagnosis me hodology wi h simple labelled doen' o aco ec digno icin es a e e yea o he [1] C. J. Alonso, J. A. Maes o, J. B. Pulido y C. 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