Fault Diagnosis in Industrial Processes Using Principal Component Analysis and Hidden Markov Model

Transcription

1 Faul Dagnoss n Indusral Processes Usng Prncpal Componen Analyss and Hdden Markov Model Shaoyuan Zhou, Janmng Zhang, and Shuqng Wang Absrac An approach combnng hdden Markov model (HMM) wh prncpal componen analyss (PCA) for on-lne faul dagnoss s nroduced As a ool for feaure exracon, PCA s used o reduce he large number of correlaed varables o a small number of prncpal componens n an opmal way HMM s appled o classfy varous process operang condons, whch s based on paern recognon prncples and consss of wo phases, ng and esng he movng wndow for rackng dynamc daa s used he mpac of he wndow lengh s suded by smulaon he samplng rae used n ng daa and n es daa s dfferen for correc and quck faul dagnoss Case sudes from he ennessee Easman plan llusrae ha he proposed mehod s effecve W I INODUCION IH he ncreasng negraon and complexy of chemcal processes, s essenal for relably and safey of he plan and for mananng qualy of he producs o denfy fauls correcly and mely Wh he wdespread avalably of dsrbued conrol sysems (DCS), on-lne faul dagnoss of chemcal process s grealy faclaed, and has been suded nensvely n recen years, whch s recognzed as a powerful suppor ool for operaors Much of he prevous work on hs opc s based on mahemacal models and sascal models [8] In he las wo decades many conrbuons have been made usng neural neworks ed by seady-sae daa [],[], whle some researchers ed he neural neworks usng dynamc daa, a number of ses of me seres daa, and qualave process dynamc rend [6],[] here are also some speech recognon approaches developed for faul dagnoss recenly, such as Manuscrp receved Sepember 9, hs work was suppored n par by he Naonal Hgh-ech program of Chna under gran No AA4 Shaoyuan Zhou s wh Naonal Key Lab of Indusral Conrol echnology, Insue of Advanced Process Conrol, Zheang Unversy, Hangzhou, 7, Zheang Provnce, Chna (phone: ; fax: ; e-mal: syzhou@pczueducn) Janmng Zhang s wh Naonal Key Lab of Indusral Conrol echnology, Insue of Advanced Process Conrol, Zheang Unversy, Hangzhou, 7, Chna (e-mal: mzhang@pczueducn) Shuqng Wang s wh Naonal Key Lab of Indusral Conrol echnology, Insue of Advanced Process Conrol, Zheang Unversy, Hangzhou, 7, Chna (e-mal: sqwang@pczueducn) dynamc me warpng (DW) for off-lne dagnoss [], and hdden Markov model (HMM) for deecng abnormal process operaon [9] Mos approaches menoned above conan wo seps, feaure exracon and paern recognon Selecng some mporan measuremen varables va human experence s a crcal sep for faul dagnoss n hese mehods, whch s dffcul n many complex chemcal processes, and he feaure sequences exraced from ng daa and esng daa have he same lengh and samplng rae In hs work, all he measuremen varables of plan are useful for faul dagnoss Snce all he measuremen varables are hghly correlaed wh each oher, prncpal componen analyss (PCA) wll be used o reduce he large number of correlaed varables o a small number of prncpal componens n an opmal way whou losng mporan nformaon hese prncpal componens can be used as he feaure sequences (called observaon sequences n hs work), and ndcae varous knds of process operang condons hen hdden Markov model s used for classfcaon, whch s based on paern recognon prncples and consss of wo seps --Frs, a se of observaon sequences o of ng paerns (ncludng normal and fauls) s exraced va PCA and used o correspondng HMMs --Second, when he paern of an unknown faul s obaned, s compared wh all he reference paerns he movng wndows for rackng dynamc daa are used For correc and quck faul dagnoss, he lengh of observaon sequences o exraced from es paerns, whch s deermned by he movng wndow lengh, can be dfferen from he one of observaon sequences o, and hey also have he dfferen samplng rae he smulaon of ennessee Easman (E) plan wh he decenralzed Proporonal-Inegral-Dfferenal (PID) conrol sysem s used o llusrae he proposed mehod hs paper s organzed as follows: In secon Ⅱ and Ⅲ, PCA and HMM are brefly descrbed In secon Ⅳ, PCA-CHMM based faul dagnoss mehod s developed n deal In secon Ⅴ, a smulaon sudy usng ennessee Easman plan s performed and he resuls are dscussed

2 II PINCIPAL COMPONEN ANALYSIS PCA s an opmal dmensonaly reducon echnque n erms of capurng he varance of he daa Gven n observaons of m measuremen varables sacked no a ng daa marx X, whch can be decomposed va sngular value decomposon (SVD) as follows, X / n = UΣV () where n n m m U and V are unary marces and he n m marx Σ conans he nonnegave real sngular values of deceasng magnude ( σ σ σ m ) he loadng vecors are he orhogonal column vecors n he h marx V, and he varance of he prncpal componen (he proecon of he ng se along he h column of V ), s equal o σ he frs prncpal componen s he drecon n he physcal varables along whch he daa exhb he greaes varably Subsequen prncpal componens explan he remanng varably, whle beng orhogonal o he prevous prncpal componen A small number of prncpal componens, whch sll rean mos of he nformaon, can represen process operang condon In hs sudy, he raw daa from ng paerns and es paerns mus be pre-processed va PCA, and a ceran number of prncpal componens are used as observaon sequences for ng and esng III HIDDEN MAKOV MODEL HMM s a double sochasc model, whch no only can capure he seral correlaons n he daa, bu also can ake no accoun he random facors of process he underlyng backbone of HMM s a Markov process, he saes of whch only can be observed hrough anoher se of sochasc processes represenng a sequence of observaon HMM usually has a chan srucure (shown n Fg ), and can be characerzed by fve parameers ) N : he number of saes n he model he saes are denoed as S = { S, S,, S N } ) M : he number of dsnc observaon symbols per sae he observaon symbols correspond o he physcal oupu of he sysem beng modelled he symbols are denoed as V = { V, V,, V M } ) A = { }: he sae ranson probably dsrbuon, where a 4) B = { b ( k)} : he observaon symbol probably dsrbuon n sae S, where b ( k) = PV ( () q = S ), N, k M () k b ( k ) s he probably of he ha he sae s sae h k observaon symbol gven S and he me s me 5) π = { π }: he nal sae dsrbuon, whch s he probably of beng n he h sae a he nal me, = Where π = Pq ( = S ), N (4) Accordng o characerscs of he observaon symbols, here are wo knds of HMMs, dscree hdden Markov model (DHMM) and connuous hdden Markov model (CHMM) he observaon symbols of DHMM are menoned above he observaon symbols of CHMM are connuous, Gaussan dsrbuon of whch s assumed n each hdden sae In hs sudy, CHMM s used o classfy varous process operang condons here are hree fundamenal problems need o be solved n he HMM applcaon ) Gven he observaon sequence O = { o, o,, o } and a model λ = ( A,B, π ), how o calculae P( O λ )? he soluon provdes a score or measure of smlary beween he observaon sequence and he model ) Gven he observaon sequence O = { o, o,, o } and a model λ = ( A,B, π ), how o deermne he mos lkely sae sequence ha corresponds o he observaon sequence O ) How o refne model parameers λ = ( A,B, π ) o maxmze P( O λ )? he parameer re-esmaon process s carred ou usng a se of observaon sequences from ng daa HMM s formulaed n wo sages, ng and esng he frs wo problems are solved n he es phase, whle he model re-esmaon problem s solved durng ng phase A well-known Bawm-Welch mehod can effcenly solve boh he ng and esng problems menoned above [4] Sae sequence S S k S K N S N a = Pq ( = S q = S ),, N () + a s he probably of gong o sae ha a me, he sae s S S a me +,gven Observaon sequence bo ( ) s b ( O ) s b ( O ) Fg Convenonal HMM chan srucure sk k b ( O ) sn N

3 O HMM() PO ( λ ) aw Daa Movng Wndow Feaure Exracon Usng PCA O O HMM() PO ( λ) HMM(N) PO ( λn) Comparaor Faul = ndex (max( P, P,, P )) n Fg Schemac dagram of faul dagnoss sysem IV SUCUE OF PCA-CHMM BASED FAUL DIAGNOSIS MEHOD Same as oher faul dagnoss mehods, PCA-CHMM based faul dagnoss mehod also conans wo manly pars, feaure exracon and paern recognon he parcular aenon of hs sudy s o address, --Frs, reduce many measuremen varables o some prncpal componens usng PCA, and use he prncpal componens as observaon sequences --Second, use he dfferen samplng raes and samplng number n he dfferen knds of observaon sequences: ng and esng, and classfy varous process operang condons va CHMM he PCA-CHMM based faul dagnoss mehod developed n hs sudy has a basc srucure as shown n Fg, where λ represens CHMM for normal operang condon, λ, λ,, λn represen CHMMs for all fauls, and O represens observaon sequence for esng A Feaure Exracon Usng PCA I s almos mpossble o use all he measuremen varables drecly for faul dagnoss n chemcal engneerng In qualave process rend analyss based on Neural Nework, only some mporan varables are seleced from all, and hs mehod s well appled n a connuously well-srred ank reacor (CS) [] and a flud caalyc crackng (FCC) process [6] However many chemcal processes lke E are complex, and s almos mpossble o selec proper varables for faul dagnoss here are a large number of varables and fauls n hese processes And dfferen fauls may affec dfferen varables I s dffcul o fnd a few common varables o explan all knds of he nformaon of process operang condons Snce all he process varables are hghly correlaed, PCA wll be used o reduce he large number of correlaed varables o a small number of prncpal componens n an opmal way whou losng any mporan nformaon hese prncpal componens can be used as he feaure sequences, whch can ndcae varous knds of process operang condons Noe ha PCA wll only be a ool for feaure exracon B Movng Wndows and CHMM Used for On-lne Faul Dagnoss A movng wndow s an ndspensable echnque o rack dynamc daa and wdely used for on-lne faul dagnoss Somemes s mporan o selec he proper me span of he movng wndow for faul dagnoss, whch s he produc of he samplng number (wndow lengh) n each movng wndow and me ncremen (samplng rae) If he wndow s chosen oo small, one may capure process changes quckly, bu he wndow may no conan enough nformaon o suffcenly reflec he curren process operang condon, hus leadng o ambguous classfcaons Large wndow szes can consder more nformaon, bu may lead o large me delays for he classfcaon of varous process operang condons he observaon sequences O for ng can have he dfferen lengh from he observaon sequences for esng, f HMM s used for classfcaon he observaon sequences O are longer for more nformaon of process operang condon, whereas he observaon sequences O are shorer for qucker faul dagnoss he mnmum lengh of he observaon sequences O, whch s deermned by he movng wndow lengh, s found by smulaon he Shannon samplng heorem saes ha for a lmed bandwdh (band-lmed) sgnal wh maxmum frequency f max, he equally spaced samplng frequency f s mus be greaer han wce of he maxmum frequency f max n order o have he sgnal be unquely reconsruced whou alasng Here he samplng rae n ng daa can also be dfferen from he one n es daa, f boh of hem are suffcenly hgh he samplng rae n ng daa s relavely low for more nformaon of process operang condon, whereas he samplng rae n es daa s hgh for mely faul dagnoss Hdden Markov model mehod s manly appled n he feld of sgnal processng, and has been become a prmary echnque for speech recognon In hs sudy, CHMM s appled o classfy varous process operang condons he algorhm conans manly fve seps --Frs, a ceran number of CHMMs are ed o O

4 consruc a daabase, ncludng one CHMM correspondng o normal operang condon and oher CHMMs correspondng o fauls --Second, a me, a lmed number of daa pons are go from he raw daa usng movng wndow, and observaon sequence O (prncpal componens) s exraced va PCA --hrd, he probables P( O λ )( =,, N) are calculaed, whch are he probables of he observaon sequence O, gven all CHMMs λ n he daabase --Fourh, he maxmum probably P( O λ ) s found by comparng hese probables, whch ndcaes ha he plan s runnng wh faul ( =,, N) --Ffh, wh me gong on, he seps from second o fourh are repeaed unl we can make a correc faul classfcaon V APPLICAION he ennessee Easman process smulaor was creaed by he Easman Chemcal Company o provde a realsc ndusral process for evaluang process conrol and monorng mehods As a sandard model, he ennessee Easman process smulaor has been wdely used by he process monorng and dagnoss communy as a source of daa o esmae varous faul deecon and dagnoss mehods [] he process consss of fve maor un operaons: a reacor, a produc condenser, a vapor-lqud separaor, a recycle compressor, and a produc srpper wo producs are produced by wo smulaneous gas-lqud exohermc reacons, and a byproduc s generaed by wo addonal exohermc reacons he conrol sysem used for dynamc smulaons s he decenralzed PID conrol sysem desgned by McAvoy and Ye [7], whch s shown n Fg he process has manpulaed varables, connuous process measuremens, and 9 composon measuremens of reacor feed, purge gas and produc In hs sudy, he reference se consss of four paerns,,,, and he frs paern corresponds o he normal operang condon, whereas he oher hree paerns correspond o hree maor deermnsc upses, IDV(), IDV(), and IDV(7) [] A oal of 4 varables s recorded every 6 mnues, and he deals are shown n able he paerns n he reference se n our case sudes conan 4 measuremen varables However, no all 4 varables carry equally process nformaon of varance for faul dagnoss purposes Snce he 4 varables are hghly correlaed wh one anoher, PCA s used o reduce he dmenson of he paerns n an opmal way ABLE I PAENS IN HE EFEENCE SE Paern Faul ype Sep sze Smulaon me(mnue) Normal 48 IDV() Sep + 48 IDV() Sep + 48 IDV(7) Sep + 48 Afer PCA, he frs four prncpal componens, whch can explan mos nformaon of process operang condon, are used as he observaon sequence for ng correspondng CHMM hus he observaon sequence of each paern n he reference se consss of four vecors wh lengh of 8 Fg 4a, 4b, 4c, and 4d show he frs four prncpal componens for,,, and respecvely Feed A Feed D LIC 7 8 Compressor Condenser JIC Coolng Condenser IC LIC 5 PI Separaor PI I Purge 9 Analyzer X B Fg 4a Four prncpal componens of PIC Feed E eacor Coolng LIC Srpper IC X F Feed C 4 Analyzer 6 FI eacor IC IC FC FI sream FC Analyzer G H Produc Fg A dagram of ennessee Easman smulaor Fg 4b Four prncpal componens of

5 faul afer 48 mnues A oal of 4 varables s recorded every mnue (mn) he deals are shown n able he movng wndow s used for rackng dynamc daa n he es se, and he wndow lengh should be as shor as possble for qucker faul dagnoss Here four wndows wh dfferen lengh,,, 4 and 8, are used o es he effec of he wndow lengh on delay of dagnoss Fg 6a, 6b, 6c, and 6d Fg 4c Four prncpal componens of Fg 4d Four prncpal componens of here are four CHMMs need o be ed n hs sudy, one for normal operaon and oher hree for correspondng faul operaons For each reference paern ( =,,,), he correspondng observaon sequence s used o he connuous hdden Markov model λ ( =,,,) va Baum-Welch mehod Fg 5 shows he resuls of ng From Fg 5, we can see ha he wo ng processes, and, are que smlar, whch ndcaes ha he dynamc response characersc of paern s close o normal, whereas he wo oher paerns, and, are que dfferen from normal operang condon here are also four paerns n he es se All fauls n he es se are dencal o he fauls of he reference se, and each es paern begns wh normal operaon and nroduces a Paern Faul ype ABLE II PAENS IN HE ES SE Sep sze Faul occurs from/o (mnue) Normal IDV() Sep + 48/96 IDV() Sep + 48/96 4 IDV(7) Sep + 48/96 show he resuls of four paerns n he es se wh he wndow lengh of he vercal coordnaes represen log( P( O λ )( =,,)), he log probables of he observaon sequence O, gven all four CHMMs n he daabase, and he horzonal coordnaes represen me From hese fgures, we can see ha varous process operang condons can be recalled correcly usng he proposed faul dagnoss mehod log( P( O λ ) and log( P( O λ ) are close n each fgure, because he process operang condons beween and are que smlar, whch menoned above For paern 4, when faul IDV(7) s nroduced a 48 mn, he dagnosc performance s no so sasfyng a he begnnng (see Fg 6d) Some random dsurbance of process may worsen such performance Wh me gong on, he faul feaure can be more dscrmnable, whch s avalable of correc faul denfcaon able gves he dagnoss delay of dfferen es paerns wh he wndows of dfferen lengh, whch shows ha for he same es paern wh dfferen lengh wndows, he shorer of he wndow, he qucker of faul dagnoss And for he same lengh wndow used for dfferen paerns, he delay of dagnoss s shorer f he es paern s closer o normal operaon In hs sudy, f he wndow lengh s less han, he es paerns wll no be recognzed correcly Fg 5 Ieraon process for ng four CHMMs Fg 6a esul of dagnoss for

6 Fg 6b esul of dagnoss for paerns and resuls n large mprovemen n he dscrmnaory power of he classfer he CHMM, whch no only can capure he seral correlaons n he feaure sequences of he paerns, bu also can ake no accoun he process random facors, s used o classfy varous process operang condons I s very mporan o a ceran number of CHMMs accuraely hese CHMMs consruc a daabase, ncludng one CHMM correspondng o normal operang condon and oher CHMMs correspondng o all fauls he samplng rae and he samplng number of paerns n he reference se, are relavely low and more so ha he observaon sequences of paerns can conan suffcen process operang nformaon and be used o more accurae CHMMs he movng wndow s used o rackng dynamc daa for on-lne faul dagnoss he movng wndows wh shorer lengh and he hgh samplng rae of he es paerns are seleced for qucker faul dagnoss he proposed faul dagnoss mehod s demonsraed n ennessee Easman smulaor, and resuls show ha can recall sngle fauls correcly Fg 6c esul of dagnoss for Fg 6d esul of dagnoss for 4 ABLE III DIAGNOSIS DELAY ACCODING O WINDOW LENGH Wndow lengh dagnoss me n (mnue) dagnoss me n (mnue) dagnoss me n 4 (mnue) VI CONCLUSION An approach combng PCA wh HMM for on-lne faul dagnoss has been descrbed he use of PCA as a ool for feaure exracon grealy reduces he dmensons of he EFEENCES [] A Kassdas, P A aylor, and J F MacGregor, Off-lne dagnoss of deermnsc fauls n connuous dynamc mulvarable processes usng speech recognon mehods, J Proc Con, vol 8, no 5, pp 8-9, 998 [] A Vemur, and M M Polycarpou, Neural-nework-based robus faul dagnoss n roboc sysems, IEEE ransacon on Neural Neworks, vol 8, no 6, pp 4-4, 997 [] E L ussell, L H Chang, and D Braaz, Faul deecon n ndusral processes usng canoncal varae analyss and dynamc prncple componen analyss, Chemomercs and Inellgen Laboraory Sysems, vol 5, pp 8-9, [4] L abner, A uoral on hdden Markov models and seleced applcaons n speech recognon, Proceedngs of he IEEE, vol 77, no, pp 57-86, 989 [5] L, J H Olson, and D L Cheser, Dynamc faul deecon and dagnoss usng neural neworks, Inellgen Conrol, vol, pp 69-74, 99 [6] S H Yang, B H Chen, and X Z Wang, Neural nework based faul dagnoss usng unmeasurable npus, Engneerng Applcaons of Arfcal Inellgence, vol, pp 45-56, [7] J McAvoy, and NYe, Base conrol for he ennessee Easman problem, Compuers and Chemcal Engneerng, vol 8, no 5, pp 8-4, 994 [8] V Venkaasubramanan, engaswamy, and K Yn, A revew of process faul deecon and dagnoss (Par I), Compuers and Chemcal Engneerng, vol 7, pp 9-, [9] W Sun, A Palazoglu, and J A omagnol, Deecng abnormal process rends by wavele-doman hdden Markov models, AIChE J, vol 49, no, pp 4-5, [] Y Mak, and K A Loparo, A neural-nework approach o faul deecon and dagnoss n ndusral process, IEEE rans on conrol sysems echnology, vol 5, no 6, pp 59-54, 997