Fault diagnosis and process monitoring through model-based case based reasoning

Transcription

1 Fault dagoss ad pocess motog though model-based case based easog Nelly Olve-Maget a, Stéphae Negy a, Glles Héteux a, Jea-Mac Le La a a Laboatoe de Gée Chmque (CNRS - UMR 5503), Uvesté de Toulouse ; INPT-ENSIACET 118, oute de Naboe F Toulouse Cedex 04, Face, elly.olve@esacet.f Abstact I ths pape, we peset a method fo the fault detecto ad solato based o the esdual geeato coupled wth a case based easog appoach. The ma dea s to ecostuct the outputs of the system fom the measuemet usg the exteded Kalma flte. The estmatos completed wth qualtatve fomato ae cluded a Based Reasog system ode to dscmate the possble faults ad to have a elable dagoss. The efeece model s smulated by the dyamc hybd smulato, PODHyS. The use of ths method s llustated though a applcato the feld of chemcal pocess. Keywods: Fault Detecto ad Isolato, Exteded Kalma Flte, Dyamc Hybd Smulato, Dstace, Based Reasog 1. Itoducto Nowadays, of safety ad pefomace easos, motog ad supevso have a mpotat ole pocess cotol. The complexty ad the sze of dustal systems duce a ceasg umbe of pocess vaables ad make dffcult the wok of opeatos. I ths cotext, a compute decso suppot tool seems to be wse. Nevetheless, the mplemetato of fault detecto ad dagoss fo stochastc system emas a challegg task. Vaous methods have bee poposed dffeet dustal cotexts [1]. They ae geeally classfed as: Methods wthout models such as quattatve pocess hstoy based methods (fo example, eual etwoks), o qualtatve pocess hstoy based methods (expet systems ), Ad model-based methods whch ae composed of quattatve modelbased methods (such as aalytcal edudacy) ad qualtatve modelbased methods (such as causal methods). I ths pape, the poposed appoach to fault detecto ad solato s a modelbased appoach. The fst pat of ths commucato focuses o the poposed dagoss appoach. Ths appoach s llustated though the smulato of the motog of a ddactc example. Ths example puts hghlght the lmt of ths appoach wth a false dagoss. The we popose a evoluto whch ecompasses quattatve ad qualtatve fomato to make the dagoss moe elable. 2. Supevso module The global pcple of ths system s show Fgue 1, whee the sequece of the dffeet opeatos s udeled. Moeove, a dstcto betwee the ole ad off-le opeatos s made. Ou appoach s composed of thee pats: the geeato of the esduals, the geeato of the sgatues ad the geeato of the fault dcatos.

2 2.1. Resdual geeato Refeece Model Pocess Exteded Kalma flte + Adjustmet of the Exteded Kalma flte Resdual Sgatue Rebult Icdece Matx + Geeato of Fault Idcato ON LINE OFF LINE Decso : occuecy of fault(s) Pocess ad/o Faulty smulated system Refeece Model + Resdual Icdece matx: Theoetcal fault sgatues Expeece etu Fgue 1. Supevso Achtectue The fst pat coces the geeato of the esduals (waved patte the Fgue 1). Thus, t s based o the compaso betwee the pedcted behavo obtaed thaks to the smulato of the efeece model (values of state vaables) ad the eal obseved behavo (measuemets fom the pocess coelated thaks to the Exteded Kalma Flte). The ma dea s to ecostuct the outputs of the system fom the measuemet ad to use the esduals fo fault detecto [2-4]. A descpto of the exteded Kalma flte ca be foud [5]. Besdes the esdual s defed accodg to the followg equato: X ( ) X t = ˆ wth { 1, } (Eq. 1.) X whee X s the state vaable, Xˆ s the estmated state vaable wth the exteded Kalma Flte ad s the umbe of state vaables. Note that the geeated esdual s elatve. As a matte of fact, ths allows the compaso of esduals of dffeet vaables, sce the esdual become depedet of the physcal sze of the vaable Sgatue geeato N S = Max ε' ε' ; 0 wth { 1, } ad ε' ε = X Max k k ; 0 k = 1 The secod pat s the geeato of the sgatues (doted patte the Fgue (Eq. 2.) 1). Ths s the detecto stage. It detemates the pesece o ot of a default. Ths s made by a detecto theshold ε. The value of ε s chose accodg to the model eo covaace matx of the Exteded Kalma Flte. The N geeated stuctue S s deoted by Eq Fault dcato geeato The last pat deals wth the dagoss of the fault (hatched patte the Fgue 1). The sgatue obtaed the pevous pat s compaed wth the theoetcal

3 fault sgatues by meas of dstace. A theoetcal sgatue T,j of a patcula default j s obtaed by expeece o ou case, by smulatos of the pocess wth dffeet occuecy dates of ths fault. The, a fault dcato s geeated. Fo ths, two dstaces ae defed: the elatve Mahatta dstace ad the mpoved Mahatta dstace. The fst dstace s deoted by the followg expesso: N S t = 1 j = M D ( ) T j (Eq. 3.) The secod dstace, whch allows the dagoss of may smultaeous faults, s deoted by the followg expesso: Ma D N S m Tj Tj =1 j = (Eq. 4.) whee s the umbe of o-zeo elemets of the theoetcal default sgatue N T,j ad m s the umbe of o-zeo elemets of the default sgatue S. 3. Applcato: the addg-evapoato ut opeato 3.1. Descpto U lmax U lm F B T eacto A+B Fgue 2. The studed pocess x B Table 1. The opeatg codtos T (K) P (atm) x A=eau x B=méthaol U l (mol) Flow ate (mol/m) Reacto Mateal Feed The pocess of addg-evapoato s geeally used to chage solvets. Its ecpe descbes a successo of evapoatos ad addg of the ew solvet (methaol). Ths pocess s studed hee (Fgue 2). The opeato codtos ae lsted the Table 1. The values of the mmum ad maxmum holdups U l ae espectvely 200 ad 800 moles. The steps of ths pocess ae the followg: a feedg step dug 500 secods, a step of heatg ad feedg, utl the holdup has eached the maxmum theshold, ad a heatg step utl the mmum holdup theshold. The pessue s supposed to be costat dug ths opeato. The goal of ths pocess s to have a mola composto of methaol the eacto at Results The behavo of ths pocess s goveed by themal pheomea. A default of the eacto themal system ca damage the success of ths opeato. That s why, t s mpotat to detect t as soo as possble Icdece matx To pefom a motog of a pocess, some off-le adjustmets must be made. I oe had, we eed to deteme the covaace matces of the model ad

4 . measuemet dstubaces. Whle the measuemet oses ae supposed to be well-kow by expemets o by the seso maufactue, the model dstubaces s estmated by a esemble method. Numeous smulatos have bee pefomed dug whch a model paamete has bee dstubed. Ths allowed the estmato of statstc dstbuto of the model mstakes. The, f the behavo of the system goes beyod ths dstbuto, ts behavo s abomal. So, the detecto thesholds ae detemed accodg to the model dstubaces. O the othe had, the secod adjustmet s the leag of the cdece matx. It s based o the same esemble theoy. Fo ths, we pefom a set of smulatos, dug whch a fault s toduced at dffeet occuecy dates, fo each potetal state of the hybd dyamc system. Fo ths study, we cosde seve faults: Fault 1: The eegy system povdes o moe powe; Fault 2: The eegy system povdes a powe lowe tha the omal oe; Fault 3: The eegy system povdes a powe hghe tha the omal oe; Fault 4: The feedg povdes o moe mateal; Fault 5: The feedg povdes mateal wth a flow ate lowe tha the omal oe; Fault 6: The feedg povdes mateal wth a flow ate hghe tha the omal oe; Fault 7: The holdup detecto detects a damaged value. The obtaed cdece matx s the followg: Table 2. Icdece matx Sgatue Faults Eegy Powe 0, , , Flow Rate , , , Tempeatue 0, , Holdup 0, , , , , , x Wate x Methaol We ca otce that all the faults have a affect o the holdup of the mxtue. The faults ae dffeetated thaks to the tempeatue, eegy powe o feedg flow ate fomato Detecto esults A default of the eacto heatg eegy feed s toduced at t = secods. Ths eegy feed povdes a heat quatty lowe tha the omal oe (fault 2). We suggest that we have oly a holdup seso. So, we do t have ay fomato about the tempeatue, the flow ate ad the powe. I ths case, the exteded Kalma flte ca ot coect the estmated state thaks to the measuemets. It oly cosdes the holdup devato. Fgue 3 shows the detecto stage. It llustates the evoluto of the esduals lked to the holdup of the mxtue. Fom t = 80 secods, the values of both esduals udele the abomal behavo of the pocess. The dagoss s lauched at t = secods.

5 Fault detecto ad solato based o the model-based appoach Holdup esdual (mol) Maxmum theshold Occuecy date of the fault Detecto date of the fault Holdup esdual (mol) Dagoss esults Table 3. The stataeous fault sgatues Sgatue Eegy Powe 0 Flow Rate 0 Tempeatue 0 Holdup 1 x Wate 0 0 x Methaol 0 Cofdece ego Tme (secods) Fgue 3. The evoluto of the holdup esdual The esdual s the estmated ad we obta the coespodg stataeous default sgatue (Table 3). We compae the stataeous fault sgatue (Table 3) wth the theoetcal fault sgatues (Table 2), by calculatg the elatve ad mpoved Mahatta dstaces (Eq. 3. ad 4.). The, the fault dcatos ae geeated (Table 4). They coespod to the complemet to 1 of these dstaces. The Mahatta elatve ad mpoved dcatos detect the pesece of the fault 7 wth a pobablty of 100%. The fault 7 s a false dagosed. So, wth oly the holdup measuemets, a fault dagoss s establshed. We must complete the system fomato wth qualtatve fomato ode to be moe pecse ad elevat dug the dagoss step. Table 4. The default dcatos of the example Faults Mahatta elatve dcato 0,688 0,802 0,832 0,719 0,753 0,676 1 Mahatta mpoved dcato 0,121 0,611 0,666 0,235 0,387 0, Impoved Appoach To ovecome ths dawback, the pevous appoach s coupled wth the Based Reasog (CBR) method. Ths method ams to captalze ad euse pas expeeces ad kowledge fo solvg poblem. I ou case the couplg of both methods allows to have a same poblem descpto qualtatve ad quattatve fomato. I the CBR, llustated o fgue 4 (ad detaled [6]), the poblem s descbed (Repeset Step) wth the ma ad most elevat chaactestcs, o matte the type of fomato. The, the poblem s compaed wth othe oes stoed a case based ad the most smla oe ad ts assocated soluto ae extacted to popose a soluto to the tal poblem (Reuse). I the pevous example, the poblem descpto s composed of the attbutes gve Table 3. The model based appoach allows the fllg of the

6 quattatve attbutes lke holdup, ad the qualtatve attbutes lke tempeatue, complete ad detal the poblem descpto. The qualtatve fomato comes fom detecto thesholds fo example. Wth ths addtoal fomato, the fault 2 s detfed, thus the dagoss efed ad moe elable. Taget poblem Repeset New Reteve Leaed case New Reteved Reta Valdated soluto Revsed ad tested base Revse Solved Reuse Fgue 4. CBR Cycle 4. Cocluso I ths eseach wok, the feasblty of couplg qualtatve methods ad model based oe s demostated fo fault detecto ad dagoss fo chemcal egeeg pocess motog. These two complemetay appoaches mpove the dagoss phase thaks to smultaeous teatmet of both qualtatve ad quattatve fomato. Ufotuately, the motog task s ot lmted to the dagoss, afte ths step the opeato has to take decsos ode to epa the fault ude costats: poductvty, ecoomc, secuty, evometal Cosequetly, a elevat decso suppot tool must help the opeato ths dffcult task. Cuetly, ou tool, the soluto to the poblem ecompasses oly the dagoss but t ca be exteded to the poposto of ways to stop (o stad by) the pocess utl the epa, ad afte ways to estat t. I these codtos, these poposed ways could be easly tested ad the valdated by smulato (Revse step of Fgue 4) because the model of the pocess aleady exsts (eeded fo the geeato of the esduals). Oly, the ew opeatg codtos must be gve. 5. Refeeces [1] V. Vekatasubamaa, R. Regaswamy, K. Y ad S. N. Kavu Comp. & Chem. Eg., 27 (2003) 293 [2] R.K. Meha ad J. Pescho, Automatca, 5 (1971) 637 [3] G. Welch ad G. Bshop, Techcal Repot TR , Uv. of Noth Caola, 1995 [4] S. Sma ad C. Fatuzz, Mechatocs, 16 (2006) 341 [5] N. Olve-Maget, G. Héteux, J.M. LeLa ad M.V. LeLa, Chem. Eg. & Poc., (2008) 1942 [6] S. Negy ad J.M. Le La, Chem. Eg. Reseach & Desg, 86 (2008) 646