Strojn{k vestnk 5(24)5,267-276 Journal of Mechancal Engneerng 5(24)5,267-276 ISSN 39-248 ISSN 39-248 UDK 621.313.14:53.88 UDC 621.313.14:53.88 Kratk znanstven prspevek Rakar A., (1.3) Jur~} \.: Modelranje elektromotorjev - Modellng Short scentfc for Fault paper Detecton (1.3) Modelranje elektromotorjev za potrebe zaznavanja napak Modellng for Fault Detecton of Electrc Motors Andrej Rakar - \an Jur~} Prspevek podaja sem-fzkaln model za potrebe zaznavanja zgodnjh napak elektromotorjev. Da b dosegl velko obèutljvost na napake, fzkaln model kombnramo z modelom, k temelj na sstemu mehkega sklepanja na podlag adaptvnh nevronskh mrež (MSSANM - ANFIS). Metodo uporabmo na realnem prmeru elektromotorja sesalne enote. Predstavljena sta zgradba modela n hbrdn postopek uèenja. V prvem koraku najprej dentfcramo parametre fzkalnega modela z osnovno metodo najmanjšh kvadratov. Nato kompenzramo odstopanje modela z uèenjem adaptvne nevronske mreže. Tako lahko ohranmo pomen fzkalnh parametrov. V nadaljevanju so prkazan rezultat zaznavanja elektrènh napak motorja (skrenje šèetk, spremembe v elektrènh parametrh pd.), kjer je odstopanje fzkalnega modela najbolj zrazto. Dagnostèn rezultat kažejo poveèano obèutljvost na napake, kar omogoèa veèjo zanesljvost zaznavanja napak. Posledèno se zmanjša tud števlo lažnh alarmov n spregledanh napak. 24 Strojnšk vestnk. Vse pravce prdržane. (Kljuène besede: zaznavanje napak, modelranje, dentfkacja, elektromotorj unverzaln, mreže adaptvne) A sem-physcal model amed at detecton of ncpent faults n electrc motors s presented. In order to gan hgh senstvty to faults a physcal model s combned wth a black-box model based on an Adaptve- Network-based Fuzzy Inference System (ANFIS) as a correctve term. The method s appled to vacuumcleaner motors. The archtecture and hybrd learnng procedure s presented. In the frst step, the parameters of the physcal model are dentfed by a smple least-squares method. Then, the modellng error s compensated usng an adaptve-network learnng procedure. In ths way, the meanng of the physcal parameters can be preserved. Next, the detecton of the electrcal faults of the motor sparkng of the brushes, changes n electrcal parameters, etc. are presented, where there s the most sgnfcant physcal modellng error. The dagnostc results show a hgher senstvty to faults, whch enables relable fault detecton. Consequently, the false and mssed alarm rato s reduced as well. 24 Journal of Mechancal Engneerng. All rghts reserved. (Keywords: fault detecton, modellng, dentfcatons, unversal motors, adaptve networks) UVOD Konkurenène razmere na trgu sljo prozvajalce v stalno dvgovanje kakovost n zanesljvost zdelkov prozvodnje. Težnje gredo praktèno v smer zagotavljanja 1-odstotne brezhbnost sestavnh delov, s èmer se zmanjšajo strošk servsranja konènh zdelkov. V tem prspevku obravnavamo elektromotor sesalne enote prozvajalca Domel d.d., k je ugleden evropsk zdelovalec. Sesalno enoto sestavlja sklop unverzalnega motorja n zraène turbne. Postopek zdelave je razmeroma vsoko avtomatzran, pr èemer je velko poudarka na zagotavljanju kakovost s posebnm postopk statstène kontrole zdelkov. Želja je, da b bla vsaka sesalna enota po konèan montaž podvržena temeljtemu avtomatskemu testu kakovost, s èmer b zloèl vse enote s pomanjkljvostm oz. napakam. INTRODUCTION Competton on the market s forcng companes to steadly ncrease product qualty and relablty. Ths trend leads to 1% product qualty assurance, whch means to reduced servce costs. Ths paper addresses the modellng of vacuum-cleaner motors produced by Domel, one of Europe s largest manufacturers. The unt conssts of a unversal motor and an ar turbne as a load. The producton lne s hghly automated. Prorty s gven to qualty assurance by means of elaborate statstcal procedures for qualty control of the fnal products. A future modernsaton plan ncludes automatc qualty testng of ndvdual unts at the end of the producton lne, whch would elmnate all defectve unts. stran 267
Prototp sstema za konèno kontrolo sesalnh enot sestavlja veè funkconalno loèenh modulov [7] (mehansko-elektrèn model, analza vbracj, analza hrupa, analza kakovost komutacje). V nadaljevanju se omejmo na modelranje elektromotorjev sesalnh enot za potrebe zaznavanja napak. V lteratur najdemo kar nekaj prstopov k modelranju za zaznavanje napak elektromotorjev ([1], [2] n [8]). Vendar so le-t navadno omejen na uporabo nomnalnh fzkalnh modelov n razlènh tehnk dentfkacje parametrov. Ko elektromotorje napajamo z zmenèno napetostjo, se pojavjo spremembe v magnetnem polju, k vodjo do nelnearnost, k jh je težko pravlno opsat. Posledca tega je velko odstopanje modela, kar pomen, da lahko zaznamo le veèje napake v delovanju. Obèutljvost na napake lahko poveèamo s hbrdnm matematènm modelom, k ga sestavljata dva dela: fzkaln model n korekcjsk èlen, k predstavlja nemodelrano magnetno karakterstko rotorja n statorja. Identfkacja takega hbrdnega modela je pravzaprav postopek uèenja, k ga poznamo pr adaptvnh mrežah. Struktura modela je navadno doloèena vnaprej, z optmzacjo pa šèemo parametre na podlag vhodno-zhodnh mertev postopka [6]. V danem prmeru smo zbral sstem mehkega sklepanja na podlag adaptvnh nevronskh mrež (MSSANM) [5], k ga je razmeroma preprosto realzrat tud v praks. Prspevek je organzran takole. Prvo poglavje podaja kratek ops metode MSSANM s hbrdnm postopkom uèenja. Drugo poglavje je namenjeno modelranju elektromotorja sesalne enote. Podan je fzkaln model n prncp kompenzacje odstopanja modela. Dagnostèn rezultat so prkazan v tretjem poglavju. Sledjo še glavn sklep. 1 SISTEM MEHKEGA SKLEPANJA NA PODLAGI ADAPTIVNIH NEVRONSKIH MREŽ - MSSANM 1.1 Zgradba MSSANM Vzemmo sstem z dvema vhodoma x n y ter enm zhodom z=f. Opšemo ga lahko z dvema mehkma pravloma tpa Sugeno-Takag prvega reda: The prototype system for the fnal qualty control of vacuum-cleaner motors conssts of several functonally dfferent modules [7]: mechano-electrcal model, vbraton analyss, nose analyss, and commutaton analyss. Next, sem-physcal modellng of vacuum-cleaner motors for dagnostc purposes s dscussed n more detal. Some model-based solutons for the fault detecton of electrc motors are known from the lterature ([1], [2] and [8]). However, they are usually lmted to nomnal physcal models and rely on parameterestmaton technques. But when motors are drven by AC voltage, changes n the magnetc feld mply nonlnear characterstcs that are not consdered correctly, leadng to a large modellng error. Consequently, only larger faults can be relably detected. A way to ncrease the senstvty to faults s to use a mathematcal model made of two parts,.e., a physcal model and a correctve term that accounts for the unmodelled non-lnear magnetc characterstcs of the rotor and the stator. The dentfcaton of such a hybrd model s based on a learnng procedure known from adaptve networks. The structure s usually known n advance, whle the parameters are determned by optmsaton on the nput-output data of the process [6]. In the gven example, the Adaptve-Network-based Fuzzy Inference System (ANFIS) [5] was chosen due to ts relatvely smple mplementaton n practce. The paper s organsed as follows. The frst secton descrbes the ANFIS method wth the hybrd learnng procedure. It s followed by the modellng of the vacuumcleaner motor n the second secton. The physcal model, as well as the prncple of modellng-error compensaton, s gven. The dagnostc results are presented n the thrd secton. The conclusons follow at the end. 1 THE ADAPTIVE NETWORK-BASED FUZZY INFERENCE SYSTEM - ANFIS 1.1 ANFIS Structure Let us assume a system wth two nputs, x and y, and one output, z=f. The system can be descrbed by two fuzzy rules of the frst-order Sugeno-Takag type: f x s A 1 and y s B 1 then f 1 =p 1 x+q 1 y+r 1 (1) f x s A 2 and y s B 2 then f 2 =p 2 x+q 2 y+r 2 Ist sstem lahko predstavmo v oblk mehkega sklepanja na podlag adaptvnh nevronskh mrež - MSSANM [5], kakor prkazuje slka 1. Adaptvna vozlšèa vsebujejo parametre n so oznaèena s pravokotnk. V postopku uèenja se vrednost teh parametrov ustrezno spremnjajo. Fksna vozlšèa, k so oznaèena s krog, zvajajo le The same system can be represented as an Adaptve-Network-based Fuzzy Inference System (ANFIS), as shown n Fgure 1 [5]. Adaptve nodes nclude parameters and are denoted as squares. In the learnng procedure, the parameters change accordngly. The fxed nodes are denoted as crcles and have no parameters. Ther stran 268
nvo 1 nvo 2 nvo 3 nvo 4 nvo 5 Sl. 1. Prmer MSSANM Fg. 1. ANFIS example zbrano operacjo n ne vsebujejo parametrov. Adaptvna nevronska mreža je 5-nvojska usmerjenega tpa. Funkcje nvojev n posameznh vozlšè so: Nvo 1: Vsako vozlšèe na tem nvoju je adaptvno s funkcjo: functon s to perform the predefned operaton. The structure s a 5-layer adaptve feed-forward network. The functons of the layers and the partcular nodes are as follows: Layer 1: Each node n ths layer s adaptve wth a membershp functon: O = 1 m A ( x) (2). 1 1 O je stopnja prpadnost spremenljvke x O s a degree of membershp for varable x to jezkovnm vrednostnm A, k jh opsujejo njhove lngustcal terms A, whch are descrbed by ther prpadnostne funkcje. Za prpadnostne funkcje membershp functons. Functons m A (x) are usually m A (x) po navad zberemo funkcjo zvonaste oblke: defned as bell-shaped functons: 1 m A ( x) = b (3), 2 éæ x - c ù ö 1 + ê ç ú ê a ëè ø ú û kjer so {a, b, c } parametr adaptvnega vozlšèa n jh menujemo pogojn parametr. Nvo 2: Vsako vozlšèe na tem nvoju, oznaèeno s P, je fksno vozlšèe, k pomnož vhode O 1 n njhov zmnožek poda na zhodu: where {a, b, c } denote parameters of adaptve nodes and are called premse parameters. Layer 2: Each node n ths layer s a fxed node denoted as P, the output of whch s the product of all the nputs O 1 : w = m ( x) m ( y) A B (4). Izhod w je torej utež odloètvenega pravla. V splošnem lahko namesto zmnožka uporabmo tud opravlo mnmuma. Nvo 3: Vsako vozlšèe na tem nvoju je fksno vozlšèe, oznaèeno z N. Utež odloètvenega pravla w normramo glede na vsoto vseh utež: Izhod w so torej normrane utež odloètvenh pravl. Nvo 4: Vsako vozlšèe na tem novoju je adaptvno s funkcjo: w = The output w represents the weght of the decson rule. In general, the mnmum operator nstead of the product s also possble. Layer 3: Each node n ths layer s a fxed node denoted as N, whch normalses the weght of the decson rule w accordng to the sum of all the weghts: w (5). w The outputs w are normalsed weghts of the decson rules. Layer 4: Each node n ths layer s adaptve wth the functon: å 4 O = w f = w ( p x + q y + r ) (6), stran 269
kjer so parametr {p, q, r } funkcje f adaptvn parametr vozlšèa n jh menujemo posledèn parametr. Nvo 5: Edno vozlšèe na tem novju je fksno vozlšèe, oznaèeno s S, k zraèuna celotn zhod f kot vsoto vseh vhodov O 4 v vozlšèe: O 5 1 = f = å w f where {p, q, r } denote parameters of the adaptve node and are called consequent parameters. Layer 5: The only node n ths layer s a fxed node denoted as S, whch calculates the output f as the sum of all the nputs O 4 : (7). Adaptvna nevronska mreža s tako strukturo je funkcjsko enakovredna klasèn predstavtv sstema mehkega sklepanja [5]. 1.2 Hbrdn postopek uèenja Iz predlagane strukture (en. 6) je razvdno, da je zhod sstema f lnearna kombnacja posledènh parametrov {p, q, r }: The adaptve network wth such a structure s functonally equal to the classcal representaton of the fuzzy nference system [5]. 1.2 Hybrd learnng procedure It s obvous from the gven structure (Eq. 6), that the output of the system f s a lnear combnaton of the consequent parameters {p, q, r }: f = ( wx) p + ( w y) q + ( w) r + ( w x) p + ( w y) q + ( w ) r 1 1 1 1 1 1 2 2 2 2 2 2 (8). Te parametre lahko torej preprosto doloèmo z metodo najmanjšh kvadratov (MNK - LSE) [5]. Enaèbo lahko v matrèn oblk zapšemo kot: These parameters can easly be dentfed by a smple least-squares method [5]. In matrx form, the equaton can be wrtten as: AX = B (9), kjer je B vektor zhodov, A matrka lnearnh vhodnh enaèb n X vektor neznanh posledènh parametrov. Vektor ocene parametrov dobmo kot: where B stands for the nput vector, A denotes the matrx of the lnear nput equatons, and X represents an unknown vector of the consequent parameters. The estmates are then gven by: ˆ = ( ) T -1 T X A A A B (1). Parametre v nelnearnem pogojnem delu doloèmo z gradentno metodo [5]. Èe a predstavlja pogojn parameter nvoja 1 adaptvne mreže, lahko spremembo zrazmo kot: kjer je E zhodno odstopanje n h htrost uèenja, k jo zrazmo kot: h = Da = - kjer je k velkost koraka (dolžna) posameznega gradentnega pomka v prostoru parametrov n vplva na htrost konvergence. Mala vrednost k natanèno opše gradentno pot, vendar vod k poèasn konvergenc. Po drug stran pa z velko vrednostjo k dosežemo htro konvergenco, vendar vod k osclacjam v okolc optmuma. Problem lahko rešmo s preprostm hevrstènm pravl [5]. Celoten postopek uèenja poteka v dveh korakh [5]. V vsak teracj najprej na podlag vhodnozhodnh podatkov z metodo najmanjšh kvadratov doloèmo posledène parametre. Nato z gradentno å a The parameters of non-lnear condtonal part are dentfed by the gradent method [5]. If a represents a premse parameter n layer 1 of the network, the change s denoted as: E h (11), a where E stands for the output error and h for the learnng rate, whch can be further expressed as: k 2 (12), æ E ö ç è a ø where k s the step sze (length) of each gradent transton n the parameter space, and affects the speed of convergence. A small value of k closely approxmates the gradent path, but leads to slow convergence. On the other hand, a large value of k leads to fast convergence, but causes oscllatons around the optmum. The problem can be solved by smple heurstc rules [5]. The overall learnng procedure s as follows [5]. Frst, at each teraton step, the consequent parameters are dentfed by a least-squares method based on gven nput-output data. Then, the gradent stran 27
metodo na podlag zhodnega odstopanja doloèmo še pogojne parametre, k predstavljajo nelnearn del (vzvratno šrjenje). 2.1 Ops 2 ELEKTROMOTOR SESALNE ENOTE method s used to dentfy the premse parameters n the non-lnear part based on the current output error (back-propagaton). 2 THE VACUUM-CLEANER MOTOR 2.1 Descrpton Elektromotor sesalne enote je enofazn komutacjsk motor, k je po konstrukcj n prncpu delovanja enak enosmernemu motorju. Znan je tud po menu unverzaln motor, ker ga lahko napajamo z zmenèno al enosmerno napetostjo. Ker sta navtj statorja n rotorja zaporedno vezan, tako da teèe st tok skoz obe navtj, dosežemo najveèj možn mehansk vrtln moment. Tak elektromotor ma tud velk startn vrtln moment. Glavno slabost predstavlja komutacja, k je povezana z obrabo šèetk, kar moèno vplva na žvljenjsko dobo naprave. Glavne sestavne dele sesalne enote prkazuje slka 2. Turbnsko kolo, prtrjeno na os motorja, z devetm lopatcam ustvarja zraèn tok skoz odprtno na pokrovu zraène turbne. Vloga dfuzorja je usmert zraèn tok skoz režo med statorjem n rotorjem za potrebe hlajenja motorja. Nazvna vrtlna frekvenca obravnavanh motorjev je 55 s -1. pokrov zraène turbne cover turbnsko kolo fan mpeller The vacuum-cleaner motor s a sngle-phase commutaton motor whose desgn and workng prncple are the same as n DC motors. It s also referred to as unversal motor because t can be run by an AC or a DC voltage supply. Owng to the fact that the stator and rotor wndngs are connected n seres and the load current flows through the exctaton wndngs, the largest motor torque s acheved. Ths electrc motor also has a bg start-up torque. The man weak pont s the commutaton,.e., problems of sparkng and brush wear, whch serously affect the devce s lfetme. The man parts of the vacuum-cleaner motor are shown n Fgure 2. The fan mpeller wth nne shovels mounted on the motor s shaft generates the arflow through the hole n the cover. The dffuser then drects the arflow through the orfce between the stator n order to cool the motor. The nomnal rotatonal speed of such motors s 55 s -1. usmernk zraka dffuser unverzaln elektromotor unversal electrc motor Sl. 2. Sestavn del sesalne enote Fg. 2. Components of the vacuum-cleaner motor 2.2 Fzkaln model 2.2 Physcal model Strukturo analtènega modela na podlag fzkalnh zakontost podajajo naslednje enaèbe: elektrèn del: mehansk del: Pomen parametrov je naslednj: R v n R a predstavljata upornost navtj statorja n rotorja, L v n L a sta nduktvnost statorja n rotorja, K pomen d() t ut () = t ()( Rv + Ra) + K t () w() t + ( Lv + La) dt mechancal part: dw() t 2 2 J = K () t -m -mw 1 () t -m2w (), t w> dt The physcal laws governng the motor are gven by the followng equatons: electrcal part: (13), (14). The meanng of the parameters s as follows: R v and R a stand for the stator and rotor resstances, L v and L a are the stator and rotor nductances, K stran 271
Sl. 3. Vezava motorja Fg. 3. Motor wrng koefcent magnetnega fluksa ter J konstanto vztrajnost. Zraèno turbno kot breme opšemo s koefcent suhega m, vskoznega m 1 n turbulentnega m 2 trenja. Vhod v sstem predstavlja napajalna napetost u(t). Dvoje stanj: tok (t) n vrtlna frekvenca w(t) sta merljva n predstavljata zhoda sstema. Vezavo motorja prkazuje slka 3. Ker sta navtj statorja n rotorja vezan zaporedno, lahko dentfcramo le skupno upornost R n nduktvnost L navtja. Motor napajamo z zmenèno napetostjo po htrostnem proflu, k vzbud celotno dnamèno obmoèje sstema. Nato vse parametre dentfcramo z metodo najmanjšh kvadratov v zveznem èasovnem prostoru. Mertve zajemamo s frekvenco vzorèenja 1 khz, podatke pa nato še fltrramo z nzkoprepustnm Butterworth-ovm fltrom z mejno frekvenco 25 Hz. Ujemanje dobljenega fzkalnega modela z dejanskm motorjem prkazuje slka 4. Prkazana je efektvna vrednost toka (t) n vrtlna frekvenca w(t). Odstopanje modela defnramo kot razlko med ocenjeno n zmerjeno vrednostjo zhoda sstema: represents the magnetc-flux coeffcent, and J s the nerta constant. The ar turbne as a load s charactersed by the dry frcton m, the vscous frcton m 1, and the turbulent frcton m 2 coeffcents. The supply voltage u(t) represents the process nput. The two states, current (t) and rotatonal speed w(t), are measurable and represent the system outputs. The electrcal wrng s gven n Fgure 3. As the stator and rotor wndngs are connected n seres, only the jont resstance R and the nductance L can be dentfed. The motor s drven by AC voltage wth a profle sutable for stmulatng all the dynamcal modes of the system. Then, all the parameters are dentfed by a least-squares method n the contnuous tme doman. The measurements are sampled at 1 khz and fltered by a low-pass Butterworth flter wth a cut-off frequency of 25 Hz. The comparson between the obtaned physcal model and the actual motor s gven n Fgure 4. Here, the RMS value of the current (t) and the rotatonal speed w(t) are shown. The modellng error s defned as the dfference between the estmated and the measured output of the system: e electrcal = m (t) - (t) n / and e mechancal = w m (t) - w(t) (15). 8 35 3 SKV / RMS, m [A] 6 4 2 w, wm [rad/s] 25 2 15 1 5 2 4 6 8 èas / tme [s] a),... m 2 4 6 8 èas / tme [s] b) w,... w m Sl 4. Ujemanje fzkalnega modela za a) elektrèn n b) mehansk del Fg.4. Physcal model valdaton for a) electrcal and b) mechancal part stran 272
V danem prmeru mamo 2-odstotno odstopanje pr elektrènem delu n 5-odstotno odstopanje pr mehanskem delu. Medtem ko je toènost mehanskega modela zadovoljva, pa toènost elektrènega modela n sprejemljva za potrebe zaznavanja napak [4]. Sklepamo, da je tako velko odstopanje posledca nemodelrane nelnearne magnetne karakterstke (npr. hstereza, nasèenje jedra), k je posledca zmenènega napajanja motorja. Razlago v nadaljevanju poenostavmo tako, da obravnavamo le elektrèn model motorja. 2.3 Kompenzacja odstopanja modela Veèjo obèutljvost na napake lahko dosežemo s kompenzacjo odstopanja modela ([3] n [4]). Tu fzkaln model kombnramo s sstemom mehkega sklepanja na podlag adaptvnh nevronskh mrež NSSANM, opsanega v prejšnjem poglavju. Tako hkrat ohranmo pomen osnovnh parametrov fzkalnega modela, k so potrebn pr morebtn zolacj napak [4]. Glavn problem pr zaznavanju napak predstavljajo t.. nestrukturrana odstopanja modela z neznanm parametr, za katere ne poznamo fzkalnega ozadja. V tem prmeru je za sprotno kompenzacjo v realnem èasu najprmernejš vzporedn hbrdn model [9]. Prncp kompenzacje odstopanja modela prkazuje slka 5. Potrebn vhod v adaptvno mrežo so vstop procesa, zstop modela n odstopanje modela (ostanek). Med fazo uèenja uporabmo dejansko odstopanje, med sprotno rabo pa uporabmo oceno odstopanja. V nasprotnem prmeru b se lahko znèlo tud odstopanje zarad napak v delovanju motorja, k jh tako ne b blo mogoèe zaznat. 2.4 Hbrdn model V danem prmeru zberemo kot vhod v nevronsko mrežo vrednost napetost u(t), toka (t) ter vrtlne frekvence w(t), zhod pa predstavlja odstopanje modela toka. Pr prvh poskush The results show an error-to-sgnal rato of roughly 2% for the electrcal part and 5% for the mechancal part. Whle the accuracy of the mechancal model s acceptable, the obtaned electrcal model s unacceptable for detecton purposes [4]. It s assumed that such a bg error s caused by the unmodelled non-lnear magnetc characterstc (.e., hysteress, magnetc saturaton) as the motor s drven by an AC voltage. For smplcty, only the electrcal model wll be elaborated. 2.3 Compensaton of the modellng error To acheve a hgher fault senstvty, the compensaton of the modellng error can be employed ([3] and [4]). Ths s done by combnng the physcal model wth a black-box model based on ANFIS ntroduced n the prevous secton. By keepng the nomnal model descrpton, the physcal parameters that are necessary for possble fault solaton are preserved [4]. The man problem of fault detecton s caused by a non-structured modellng error wth unknown parameters and an unfamlar theoretcal background. In ths case, a parallel hybrd model seems sutable for onlne compensaton n real tme [9]. The prncple of compensaton of the modellng error s shown n Fgure 5. The necessary nputs to the adaptve network are the process nput, the model output, and the modellng error (resdual). Durng the learnng stage, the actual error s used, whle durng the onlne usage, the estmated error s utlsed. Otherwse, the error caused by faulty operaton of the motor could also be compensated, whch would make t undetectable. 2.4 Hybrd model In the gven case, the supply voltage u(t), the current (t) and the rotatonal speed w(t) were chosen as nputs to the adaptve network, whle the modellng error of the current was chosen as the u Process Uèenje Learnng y u Process Uporaba Usage y Model ŷ - e Model ŷ - e w h n,1 w h n,2 w h n,m n=1,,n? w o n? NN ê - w h n,1 w h n,2 w h n,m n=1,,n? w o n? NN ê - ecomp Sl. 5. Prncp kompenzacje napake modela Fg. 5. Prncple of modellng-error compensaton stran 273
modelranja smo uporabl tud veè zakasnjenh vhodov zarad prèakovane nelnearnost s spomnom (hstereza). Vendar smo dobl zadovoljvo toènost modela že s preprosto statèno relacjo. Za vsak vhod smo zbral tr prpadnostne funkcje, kar nam da model NSSANM z naslednjm lastnostm: - števlo vozlšè: 91 - števlo lnearnh parametrov: 18 - števlo nelnearnh parametrov: 27 - števlo mehkh odloètvenh pravl: 27 Dobljen hbrdn model dentfcramo v dveh korakh. Najprej dentfcramo parametre fzkalnega modela z metodo najmanjšh kvadratov. Nato zvedemo postopek uèenja adaptvnh mrež (poglavje 1.2), da kompenzramo odstopanje nomnalnega modela (en. 13). 3.1 Vrednotenje 3 DIAGNOSTIÈNI REZULTATI Vrednotenje modela je potekalo na množc 1 motorjev. Slka 6 prkazuje potek zhoda elektrènega dela enega zmed dobrh motorjev n ocene hbrdnega modela ter prpadajoèe odstopanje e. output. Prelmnarly, several delayed nputs were also consdered due to the expected nonlnearty wth memory (.e., hysteress). However, acceptable model accuracy was acheved wth a smple statc relaton. Three membershp functons were chosen for each nput, resultng n the followng ANFIS model structure: - number of nodes: 91 - number of consequent parameters: 18 - number of premse parameters: 27 - number of fuzzy decson rules: 27 The resultng hybrd model s dentfed n two steps. Frstly, parameters of the physcal model are estmated by a smple least-squares method. Then, a learnng procedure for adaptve networks (Secton 1.2) s appled n order to compensate the errors resultng from the nomnal model (Eq. 13). 3.1 Valdaton 3 DIAGNOSTIC RESULTS The valdaton was performed on a seres of 1 motors. Fgure 6 shows the tme plots of the electrcal part for one of the fault-free motors wth ts estmated hybrd model output and the resultng resdual e..2 8 RMS, m [A] 6 4 e=- m [A].1 SKV / 2 -.1 2 4 6 8 tme [s] a),... m èas / èas / Sl. 6. Ujemanje hbrdnega modela Fg. 6. Valdaton of the hybrd model -.2 2 4 6 8 tme [s] b) erms=.54 Vdmo, da dosežemo odlèno ujemanje modela z dejanskm motorjem, saj je efektvno odstopanje manj kot 1% n je na slk 6 a) praktèno nevdno. Poudart je treba, da dentfcramo parametre modela le enkrat za zbran tp motorja, zaznavanje napak pa poteka na osnov ocene modela. 3.2 Zaznavanje napak V nadaljevanju st hbrdn model uporabmo na prmeru motorja z okvaro na elektrènem delu (skrenje šèetk). Obravnavamo le nenadne napake, saj je bl namen dagnostènega sstema zaznavanje The results show that the error-to-sgnal rato reduces to roughly less than 1% and s therefore practcally nvsble n Fgure 6 a). It s mportant to note that the model parameters are dentfed only for each type of motor and that the estmated model s then used n fault detecton. 3.2 Fault detecton The same hybrd model s further appled to the motor wth a fault n the electrcal part (sparkng of the brushes). Only abrupt faults are consdered, as the purpose of the dagnostc system was to detect stran 274
.2 8 RMS, m [A] 6 4 e=- m [A].1 SKV / 2 -.1 2 4 6 8 tme [s] Sl. 7. Ujemanje modela na motorju z okvaro Fg. 7. Hybrd model appled to faulty motor -.2 2 4 6 8 tme [s] èas / èas / a),... m b) erms=.81 prrojenh napak na koncu prozvodne lnje. Slka 7 prkazuje ujemanje modela z dejanskm motorjem. Vdmo, da se efektvno odstopanje poveèa veè kot 1-krat, kar omogoèa zanesljvo zaznavanje napake motorja. 4 SKLEP Predstavl smo zaznavanje napak elektromotorjev sesalnh enot z matematènm modelom. Zaznavanje napak poteka na osnov zakonov o ohrantv energjske blance sstema. Vsako odstopanje med zmerjenm n ocenjenm vrednostm pomen prsotnost napake. Zato vsako odstopanje modela neposredno vplva na obèutljvost na napake. Da b znèl vplv nemodelranh nelnearnost, uporabmo prncp kompenzacje odstopanja modela s pomoèjo adaptvnh nevronskh mrež (NSSANM). Dagnostèn rezultat na realnh napravah potrjujejo bstveno zmanjšanje odstopanja modela, kar omogoèa veèjo obèutljvost na napake. Posledèno se zmanjša tud števlo lažnh alarmov n spregledanh napak. Ob vsak zamenjav tpa motorja pa je treba poskrbet za ustrezno vzbujanje, k zajame celotno dnamèno obmoèje delovanja. Tud sposobnost osamtve napak je omejena le na elektrèn oz. mehansk del. Do doloèene mere lahko dosežemo veèjo loèljvost z dodatno uporabo klasènh metod ocenjevanja parametrov. 5 ZAHVALA Avtorj se skreno zahvaljujejo podpor podjetja Domel d.d. n slovenskemu Mnstrstvu za šolstvo, znanost n šport v okvru programa P2-1. nherent faults at the end of the producton lne. The output s shown n Fgure 7. The results show that the model dscrepancy ncreases more than 1 tmes and can therefore be used as a relable feature for fault detecton. 4 CONCLUSION A model-based fault detecton of vacuumcleaner motors s presented. The fault detecton reles on energy balance conservaton laws. The dscrepancy between the measured and the predcted values reflects the presence of a fault. Any modellng error drectly affects the senstvty to faults. To account for unmodelled non-lnear characterstcs, the prncple of compensatng the modellng error by ANFIS s chosen. The dagnostc results on real devces show a sgnfcant reducton of the modellng error, whch enables hgher fault senstvty. Consequently, the false and mssed alarm rato s reduced as well. However, good exctaton durng the learnng phase for each motor type s requred, whch stmulates all the dynamcal modes of the system. Also, the solaton ablty s lmted to ether the electrcal or the mechancal part. To some extent, dfferentaton s possble by further employng classcal parameter-estmaton technques. 5 ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of the company Domel Ltd. and the Slovenan Mnstry of Educaton, Scence and Sport wthn the programme P2-1. stran 275
6 LITERATURA 6 REFERENCES [1] Albas E., T. Durakbasa and D. Eroglu (2) Applcaton of a new fault detecton technology for qualty mprovement of applance motors, http://www.artess.com/products/mqm/atc_2_artess_paper.pdf [2] Höflng, T., R. Isermann (1996) Adaptve party equatons and advanced parameter estmaton for fault detecton and dagnoss. Prepr. 13th IFAC World Congress, San Francsco, N, 55-6. [3] Klanèar, G., Ð. Jurèæ, R. Karba (22) Robust fault detecton based on compensaton of the modellng error. Int. J. Syst. Sc., Vol. 33, 2, 97-15. [4] Rakar, A. (2) Fault dagnoss of techncal systems by means of approxmate reasonng, PhD Thess, Unversty of Ljubljana. [5] Shng, J., R. Jang (1993) ANFIS: Adaptve-network-based fuzzy nference system. IEEE Trans. Syst. Man Cybern, Vol. 23, 3, 665-685. [6] Takag, T., M. Sugeno (1985) Fuzzy dentfcaton of systems and ts applcatons to modelng and control. IEEE Trans. Syst. Man Cybern, Vol. 15, 1, 116-132. [7] Tnta, D., J. Petrovèæ,, U. Benko, Ð. Jurèæ, A. Rakar, M. Žele, J. Tavèar, J. Rejec, A. Stefanovska (23) A dagnostc system for vacuum cleaner motors, Prepr. SAFEPROCESS 23, Washngton, 921-926. [8] Vetter Th., H. Weber, J. Grossehelweg (1994) Vollautomatsche Fehlerdagnose n der Serenfertgung von Elektromotoren, VDI-Tagung: Überwachtung und Fehlerdagnose, Darmstadt. [9] Patton, R.J., J. Chen (1997) On-lne resdual compensaton n robust fault dagnoss of dynamc systems, Prepr. SAFEPROCESS 97, Hull, 371-377, 1997. Naslov avtorjev: doc.dr. Andrej Rakar doc.dr. Ðan Jurèæ Odsek za ssteme n vodenje Insttut Jožef Stefan Jamova 39 1 Ljubljana andrej.rakar@js.s Authors Address: Doc.Dr. Andrej Rakar Doc.Dr. Ðan Jurèæ Dept. of Systems and Control Jožef Stefan Insttute Jamova 39 1 Ljubljana, Slovena andrej.rakar@js.s Prejeto: Sprejeto: Odprto za dskusjo: 1 leto Receved: 21.8.23 Accepted: 8.4.24 Open for dscusson: 1 year stran 276