PARAMETRIC FAULT LOCATION OF ELECTRICAL CIRCUIT USING SUPPORT VECTOR MACHINE

Transcription

1 XVIII IMEKO WORLD CONGRESS Metology fo a Sustanable Develoment Setembe, 7 22, 2006, Ro de Janeo, Bazl PARAMETRIC FAULT LOCATION OF ELECTRICAL CIRCUIT USING SUPPORT VECTOR MACHINE S. Osowsk,2, T. Makewcz, R. Salat 3 Wasaw Unvesty of Technology, Wasaw, Poland, sto@em.w.edu.l 2 Mltay Unvesty of Technology,Wasaw, Poland, makewt@em.w.edu.l 3 Agcultue Unvesty, Wasaw, Poland, salat@sggw.edu.l Abstact: The ae s concened wth the alcaton of the Suot Vecto Machne to the dscoveng of the aametc fault n analog electcal ccuts. The ecognton of fault s based on the measuements of the accessble temnal voltage and cuent of the ccut at the set of fequences. The SVM netwok fulflls the ole of the ecognzng system and of the classfe. The numecal esults of ecognton of faulty elements n the LC flte of the ladde netwok stuctue ae esented and dscussed n the ae. Keywods: SVM classfes, aametc fault detecton, dagnoss of ccuts.. INTRODUCTION The ae esents the neual aoach to the detecton of the aametc fault and ts locaton n analog electcal ccuts on the bass of the extenal measuements of the voltages and cuents. It s assumed that the geneal stuctue of the ccut unde nvestgaton s known. The fault of element s undestood as the aametc change of ts value beyond the assumed toleance lmt [,2,6]. Only fault of one element at a tme s consdeed. The detecton of the faulty element s efomed on the bass of the measuements of the temnal sgnals,.e., the temnal voltages and cuents of the ccut, oeatng n the nomal and faulty condtons. The measued sgnals should undego the stage of eocessng to extact the dagnostc featues of the obtaned nfomaton. These featues fom the nut sgnals to the neual netwok, efomng the ole of classfe. The neual netwok of the Suot Vecto Machne (SVM) tye s taned on the examles of the attens belongng to the nomal oeaton of the ccut and to the eesentatves of the tycal faults of the atcula element. The motant advantage of the neual method s ts ablty to teat effcently the aametc changes of the values of the faulty elements. The method s effectve and offes a geat seed and accetable accuacy fo the fault detecton n the lage ange of aamete changes. In comason to the standad neual netwoks, lke the multlaye eceton o self-oganzng Kohonen netwok [,2,8] SVM offes much bette genealzaton ablty at lmted numbe of tanng samles. The esults concenng the ecognton of sngle element faults n the esstvely temnated LC ototye ladde flte ae esented and dscussed. They confm geat effcency of the develoed dagnostc system. 2. PRINCIPLE OF FAULT RECOGNITION AND LOCATION In the ecognton and localzaton of fault n analog electcal ccut t s assumed, that the geneal stuctue of the ccut unde nvestgaton s known [8]. The use s able to measue the extenal voltages and cuents of the ccut, oeatng n the nomal and faulty condtons n the steady state unde snusodal exctaton. We assume the fault of element as the aametc change of ts value above the assumed toleance lmt. The basc obsevaton s that each state of the ccut, ethe nomal o any sngle fault, s assocated wth the secfc fequency chaactestcs of the magntude and hase of the measued vaables. These chaactestcs dffe to some degee at vaous faults. The dffeences between the nomnal and faulty states ae used by us to make the ecognton of the atcula state of the ccut. Ths wll be done by the neual classfe netwok. The classfe s taned on the data eesentng dffeent examles of the nomnal and faulty states of the ccut. Afte tanng, the aametes of the classfe ae fozen and the system s eady fo the on-lne oeaton of the dagnostc task. Let us assume that thee s a suffcent numbe of ndeendent sgnal measuements n the ccut, geate than the numbe of elements n the analog ccut of known toology and nomnal values of ts elements [8,]. The measuements ae concened wth the extenal accessble onts at dffeent fequences. These fequences should be chosen n a way to enhance the dffeences between dffeent states of the ccut. Hence secal ocedue of fequency selecton should be aled. The motant ont s to ovde the hghest senstvty of the system to any changes n the aametes of the ccut element. Hence the natual way to detemne the otmal set of fequences s the alcaton of the senstvty analyss of the ccut []. The senstvty

2 cuves of the magntude and hase of the extenal measued vaables wth esect to the ccut elements ae geneated. The fequences coesondng to the maxma of the absolute values of these cuves ae the canddates fo testng fequences. The next ste s to convet the measued vaables nto the dagnostc featues. They should be nomalzed and at the same tme as senstve as ossble to the changes of the aametes of the elements. To dffeentate the featue values coesondng to ndvdual faults we consde hee the elatve dffeences between the faulty and non-faulty modes of the ccut oeaton. Alyng the geneal notaton x fo ethe measued voltage V o cuent I (magntude o hase) we defne the featue as the elatve dffeence of ths vaable at nomnal and actual (esumably faulty) state of the ccut at the fequency f, x( f ) xn ( f ) x ( f ) = () xn ( f ) The vaable x n (f ) means the measued quantty unde non-faulty (nomnal) oeaton of the ccut at the fequency f. The geneated featues x (f ) ae the canddates fo the nut vecto x defnng the nut sgnals fo the classfe. The next ste s the valdaton and selecton of the canddate set of featues. Let us assume that the measuements have been done fo one voltage and cuent of the ccut at the set of fequences, fo whch the dagnostc featues have been geneated fo the magntude and hase accodng to eq. (). As a esult we get fou ossble canddate vectos: V m = abs( V ), V = ag( V ), I m = abs( I ) and I = ag( I ), whee the vecto of V = V f ), V ( f ),..., V ( f ) and cuents voltages [ ( 2 m ] = [ I f ), I ( f ),..., I ( f )] I eesent elatve voltages ( 2 m2 and cuents of the temnals at dffeent fequences f, nomalzed accodng to the elaton (), abs stands fo the magntude and ag fo the hase of the coesondng comlex values. Theefoe the maxmum sze canddate featue vecto x that may be used n leanng, s gven by [ V, V, I I ] x =,. Howeve dffeent canddate vectos m m fomed as the combnatons od V m, I m, V and I may be x = V, V, I, also consdeed, fo examle [ m m ] x = [ V V, I )], x [, ] m, x = I m x = [ V m ], [ ] = V I m m o even n exteme cases, etc. Many dffeent featue assessment methods ae known and aled n actce [3]. To the most oula belong ncal comonent analyss (PCA), coelaton exstng among featues, coelaton between the featues and the classes, statstcal analyss of mean and vaance of the featues o even alcaton of SVM featue ankng. In ths wok we have aled the PCA based assessment of the featues qualty. The PCA [4] s descbed as the lnea tansfomaton y=wx, mang the N-dmensonal ognal vecto x nto L-dmensonal outut vecto y, whee L<N. The vecto y eseves the most motant elements of the ognal nfomaton. The tansfomaton matx W s comosed of the egenvectos assocated wth L lagest egenvalues of the coelaton matx R xx defned fo the set of nut vectos x. Takng the value of L equal two o at most thee we can ma the ognal N-dmensonal vectos x nto the two o thee dmensonal PCA sace, that can be easly eesented n a two- o thee-dmensonal coodnate system. Thanks to ths the vsual nsecton of the tajectoes of onts eesentng the faults of elements can be efomed. Good featue set coesonds to the tajectoes of dffeent faults seaated fom each othe as well as ossble. The set of featues ovdng the best seaaton of tajectoes of dffeent faults should be consdeed as the otental nut vecto x aled to the neual classfe efomng the ecognton of the attens assocated wth ethe fault of the element o wth the nomnal state of the ccut. The oosed dagnostc system stuctue s esented n Fg.. Fg. The geneal scheme of the ccut dagnostc system 3. THE NEURAL CLASSIFIER The motant ole n ou dagnostc system fulflls the neual classfe, efomng the fnal ecognton of the ccut state on the bass of the aled nut featue vecto x. In ou soluton we have aled the Suot Vecto Machne (SVM) classfe, egaded now as the most effectve classfcaton tool [0,2]. The dstnct advantage of the SVM netwok soluton s ts good genealzaton ablty. Taned on the lmted numbe of eesentatve examles of each fault, the netwok s able to ecognze the non-deal (aametc) fault n the wde ange of the faulty aamete values assocated wth the assumed toleance of the non-faulty elements. SVM s a lnea system wokng n the hghly dmensonal featue sace fomed by the nonlnea mang of the N-dmensonal nut vecto x nto a K-dmensonal featue sace (K>N) though the use of a mang functon ϕ (x). The SVM netwok ecognzes between two classes, eesented by d = and d =-. In the classfcaton mode the equaton of the seaatng hyelane s gven by the y x = φ b w jϕ j b, whee T elaton ( ) w ( x) + = ( x) + = 0 [ ϕ ( x),..., ϕ ( ] T K ) K j= φ( x) = x s a vecto of mang functons w = w,...,w K s the weght vecto. The aametes of the hyelane y(x) ae adjusted n a way to maxmze the dstance between the closest eesentatves of both classes. The may leanng of hdden unts and [ ] T

3 oblem [0,2] s fomulated as the mnmzaton of the objectve functon φ ( w, ξ) T φ( w, ξ) = w w + C ξ (2) 2 = at the lnea constants defned fo each leanng data samle ( =, 2,..., ) wth ξ - the slack vaable T ( w ϕ( x) + ) d b ξ (3) ξ 0 The fst tem n equaton (2) coesonds to the maxmzaton of the magn of seaaton. The constant C s the egulazaton aamete esonsble fo the mnmzaton of the leanng eos. The hghe s ts value the bgge s the mact of ths tem on the fnal aametes of the hyelane. The most dstnctve fact about SVM s that the leanng task s educed to the quadatc ogammng by ntoducng the so-called Lagange multles α. All oeatons n leanng and testng modes ae done n SVM by usng kenel functons satsfyng Mece condtons [2]. The kenel s defned as T K ( x, x ) = φ ( x ) φ( x) (4) The most often used kenels nclude adal Gaussan, olynomal, slne o lnea functons [0]. The fnal oblem of leanng SVM, fomulated as the task of seaatng leanng vectos x nto two classes of the destnaton values, ethe d = o d =-, wth maxmal seaaton magn, s educed to the dual maxmzaton oblem of the quadatc functon [0] max Q( α) = = wth the lnea constants = j= ( x, x ) α αα jdd jk j (5) 2 = α d = 0, 0 α C. The egulazng aamete C detemnes the balance between the comlexty of the netwok, chaactezed by the weght vecto w and the eo of classfcaton of data. Fo the nomalzed nut sgnals the value of C s usually much hghe than and s adjusted by the coss valdaton ocedue. The soluton of (5) s exessed thougth the Lagange multles, on the bass of whch the otmal weght vecto w ot s detemned ot N = sv = ( ) w α dφ x (6) In ths equaton N sv means the numbe of suot vectos,.e. the leanng vectos x, fo whch the Lagange multles ae nonzeo. The outut sgnal y(x) of the SVM netwok s detemned now as the functon of kenels Nsv = y( x ) α d K( x, x) b (7) = + The sgnal y(x) geate than 0 s assocated wth class and the negatve wth the ooste one. Although SVM seaates the data nto two classes only, the ecognton of moe classes s staghtfowad by alyng ethe one aganst one o one aganst all methods [5]. The moe oweful s one aganst one aoach n whch many SVM netwoks ae taned to ecognze between all combnatons of two classes of data. At M classes we have to tan M(M- )/2 ndvdual SVM netwoks. In the eteval mode the vecto x belongs to the class of the hghest numbe of wnnngs n all combnatons of classes. The motant ont n desgnng SVM classfe s the choce of the kenel functon. The smlest lnea kenel s usually neffcent due to the lack of lnea seaablty of the data. The olynomal kenel may be also useless, f hgh degee of olynomal s needed, snce n such case the system s becomng badly condtoned. The best esults ae usually obtaned at alcaton of Gaussan kenel and ths kenel has been aled n all futhe exements. On the stage of desgnng the SVM classfe system the choce of the Gaussan sead σ and the egulazaton constant C s vey essental. Esecally motant s the value of C, snce t contols the tadeoff between the comlexty of the machne and the numbe of non-seaable data onts used n leanng. The small value of C esults n the accetaton of moe not seaated leanng onts. At hghe value of C we get the lowe numbe of classfcaton eos of the leanng data onts, but moe comlex netwok stuctue. The otmal value was detemned fo each a of classes ndeendently afte addtonal sees of leanng exements though the use of the valdaton test sets. The ocess of otmzng the values of C and σ was done togethe. Many dffeent values of C and σ combned togethe have been used n the leanng ocess and the otmal values ae those fo whch the classfcaton eo on the valdaton data set was the smallest one. The SVM netwoks wee taned usng Platt algothm [7]. To assess the efomance of ou dagnostc system oely we have comaed t wth the alcaton of MultLaye Peceton (MLP) used as the classfe. MLP s the most known and tycal multlaye neual netwok soluton [4] alyng the sgmodal actvaton functon. It efoms the classfcaton of data n one smle stuctue (no need fo many classfes, as n SVM case). The esults of numecal exements efomed fo the same data sets have confmed the sueoty of the oosed SVM soluton. 4. THE CIRCUIT UNDER TEST The theoetcal consdeatons esented n the evous sectons wll be llustated on the examle of the ototye of the esstvely temnated assve LC ladde flte of 9 th ode esented n Fg. 2 Fg. 2 The RLC ladde flte stuctue

4 It s the nnth ode ccut contanng elements. The elements of the flte have been adjusted to ealze the lowass chaactestcs n the nomalzed ange of fequences. The nomalzed values of the elements used n exements wee as follows: R o =R =, C =0.2, C 2 =0.72, C 3 =.46, C 4 =0.69, C 5 =0.290, L =0.408, L 2 =0.509, L 3 =0.730, L 4 = Only the temnal onts of the ccut ae accessble fo measuements. The dagnostc task s to fnd out f the element value s dffeent fom ts nomnal one by moe than the assumed toleance lmt (0%). Such case s egaded as a fault. We consde the sngle faults of elements (only one faulty element at the same tme). It means that any knd of fault of the element s assocated now wth one class. In such case we have 2 tyes of ccut oeatons. One class eesents the nomal oeaton and classes ae assocated wth the fault of any of ts eleven ccut elements. Two temnal measuements ae avalable n the netwok. At snusodal voltage exctaton and esstve load (R o ) at the outut temnal, the nut cuent I and outut voltage V at dffeent fequences can be detemned. On the bass of these measued values we wll geneate the canddate featues that may fom the nut vecto x fo the SVM netwok, usng equaton (). We may ely hee on the magntude and hase fequency chaactestcs of these two measued vaables. The fequency values used n the analyss of the ccut should be chosen fst. They have been detemned by the senstvty analyss of the ognal ccut. The fequency set s comosed of all fequences fo whch we have obseved the extemes of ethe magntude o hase senstvty chaactestcs of the outut voltage and nut cuent. Fg. 3 esents the exemlay fou senstvty cuves fo the magntude and hase of the outut voltage fequency chaactestcs obtaned by usng NAP ogam [9] wth esect to two caactances (C 3 and C 5 ) and two nductances (L and L 3 ). The onts coesondng to the exteme values of the senstvty functons ae chosen as the fequences fo the analyss of the flte. They wee used fo the geneaton of the leanng and testng data. Afte efomng the senstvty analyss we have found 2 and 20 dffeent fequency onts coesondng to the extemes of the magntude and hase of the outut voltage, esectvely, as well as 24 and 25 fequency onts coesondng to the extemes of the magntude and hase chaactestcs of the nut cuent. At such numbe of fequency onts the vecto of magntude voltage chaactestcs V m s comosed of 2 elements, the hase voltage chaactestcs V 20 elements, the magntude of the nut cuent vecto I m 24 elements and the hase of the nut cuent vecto I 25 elements. Hence the maxmal dmenson of the featue vecto x s 90. We have consdeed hee the aametc faults of the ccut elements. As the faults we undestand all changes of the nomnal values of esstances, nductances and caactances beyond the assumed toleance lmt (0% n exements). Each fault has been assocated wth the toleance of the emanng non-faulty elements, changng andomly n the exements fom 0 to 5%. 5. THE RESULTS OF NUMERICAL EXPERIMENTS The fst motant queston s of the otmal featue eesentaton of the measued data. All combnatons of the magntude and hase nfomaton contaned n the nomalzed outut voltage and nut cuent (vectos V m, V, I m, I ) may fom the featue vecto x. The same numbe of each case (ethe aoate fault o nomal oeaton) was used n exements. The ncal comonent analyss of the nomalzed data at dffeent aangement of the featue vectos has been efomed. Afte assessng all esults by vsual nsecton we have come to the concluson that the full length vecto x s not the best one snce the combnaton of the magntudes of the outut voltage and nut cuent, x=[v m I m ] has ovded a bt bette seaaton of dffeent fault tajectoes. Fg. 4 esents the PCA eesentaton of the leanng data coesondng to the best aangement (the educed dmenson vecto comosed only of the magntude nfomaton x=[v m I m ]). Fg. 3 The senstvty of the magntude and hase of the outut voltage of the tested ccut Fg. 4 The PCA eesentaton of the measued data fo the best featue vecto x=[v m I m]

5 Even n ths fgue the unque nteetaton of the esults s not easy snce the dstbuton of the onts belongng to 2 classes ( faults of element lus the nomal oeaton of the ccut) s extemely comlex, esecally vey close to the cente (nomal oeaton of the ccut). The next exements have been dected to check the effcency of dffeent eesentatons of the featue vecto x fo the fault ecognton by the SVM netwok. We have used dffeent ossble combnatons of magntude and hase nfomaton to fom featue vecto x, begnnng fom the sngle ndvdual vectos and endng on all of them combned togethe (x=[v m V I m I ]). The numecal exements of classfcaton by usng Gaussan kenel SVM wokng n one aganst one mode, have been efomed fo the data samles evenly slt fo leanng and testng sets (420 samles fo each faulty element and fo the nomal state of the ccut). All dffeent sets of featues fomng the vecto x have been ted n exements. The testng data have been aled only n the testng mode of the taned SVM netwok. Hee we wll show the esults coesondng to 5% toleance of the non-faulty elements. To deal wth 2 classes we have aled one aganst one stategy [4], esultng n leanng 66 ndvdual SVM classfes, ecognzng two classes at a tme. Table esents the cumulatve comason of the aveage testng msclassfcaton ate n ecentage, coesondng to dffeent eesentatons of the featue vecto x. The esults ae gven fo the nomal oeaton of the ccut (all element values wthn the toleance lmt) and fo the faulty mode of oeaton. The faults of elements have been dstbuted n the wde consdeed egon, fo whch the atcula element value dffes moe than allowed by the toleance (0%). The faulty elements changed fom 0.05 to 0.9 and fom. to 0 of the nomnal values. In the case of faulty mode oeaton the mean values of the msclassfcaton ate wthn all classes have been calculated and esented n the table. Table Summay of the msclassfcaton ate of the testng data at dffeent eesentatons of the featue vecto x Reesentaton Total msclassfcaton ate of featue vecto Nomal Faulty Mean oeaton mode x=[v m I m V I ] 3.% 0.4% 0.63% x=[v m I m V ] 5.0% 0.4% 0.69% x=[v m I m I ] 0.72% 0.58% 0.60% x=[v m V I ] 4.7% 0.39% 0.65% x=[i m V I ] 5.0% 0.45% 0.73% x=[v m I m ] 0.24% 0.54% 0.52% x=[v m I ].7% 0.76% 0.8% x=[v m V ] 5% 0.58% 0.85% x=[i m I ] 2.67%.9%.28% x=[i m V ] 4.7% 0.39% 0.66% x=[i V ] 2.9% 0.87%.04% x=v m 6.7%.7% 2.0% x=v 4.67%.04%.26% x=i m 3%.34%.44% x=i.33%.60%.59% The mean eo (last column of the table) s comuted as the ato of the total numbe of msclassfcatons to the numbe of samles used n the exements (at faults and equal eesentaton of classes the faults have edomnant mact on the mean esults). The summay esults esented n Table ont out that many dffeent eesentatons, ovdng smla level of msclassfcaton ato ae ossble. If we take nto account the mean value of the total eo, the best seems to be the educed eesentaton of the featue vecto x=[v m I m ]. It s nteestng that some atal eesentatons of the featues, fo examle x=[v m I m I ] o x=[v m V I ] ae also vey good fo ecognton of the faults of elements and even bette than full set of featues. Table 2 esents the detaled esults of faulty element ecognton at testng mode of the taned SVM netwok usng testng set (not takng at n leanng) fo the best selected eesentaton of the featues, x=[v m I m ]. The fst column shows whch element s faulty and the second one the aveage msclassfcaton ate (n ecentage) coesondng to the atcula fault. Table 2 The esults of testng the SVM classfe on the data samles coesondng to dffeent faults at the featue vecto x=[v m m] Faulty Msclassfcaton ate element No fault 0.24% R 0 C 0.7% C 2 0 C % C 4 0.7% C % L 0 L 2 0 L 3 0 L % R o 0.48% Mean 0.52% As t s seen the oveall accuacy of the fault ecognton at the unfom dstbuton of data n the whole egon of the consdeed fault s satsfactoy fom the actcal ont of vew. In the wost case (the fault of element C 5 ) the aveage msclassfcaton ate was 2.86%. The msclassfcaton ato of the sngle fault of most elements has been educed to the nsgnfcant o even zeo values. The total aveage eo of the fault ecognton, calculated as the odnay mean of all eos, has been educed to the value of 0.52%. The detaled obsevaton of eo dstbuton has evealed that most eos wee commtted fo the data laced vey close to the bode of the nomal oeaton (the element values vaaton slghtly below o above the toleance lmt of 5% and at the bode of the faulty state (slght cossng of the assumed 0% toleance lmt egaded as a fault). To check n detals how the classfe system s able to deal wth ths knd of data we have geneated addtonal set of data coesondng to the nomnal element values laced

6 close to the toleance lmt ( 5 % ± 2%) and the faults laced on the bode of the assumed toleance 0 % ± 2%). Once agan the non-faulty elements have been dstubed andomly wthn the toleance lmt ± 3%. In ths exement half of the data geneated n ths way has been added to the aleady exstng leanng set and the othe half was left fo testng only. So n the exement the testng data set contaned only these most dffcult cases. The testng has been efomed fo the SVM netwok etaned usng the extended leanng data set contanng also the addtonal data eesentng the egon vey close to the toleance lmt. The efomed test was extemely dffcult snce the testng set contaned only the data most dffcult fo the ecognton. Howeve, even n ths vey demandng test the esults ae faly accetable. Fo most elements the fault ecognton eo was below 6%, although the ecognton of some faults has been done wth lage eo eachng n wost case even 40% (the caacto C 5 ). The aveage msclassfcaton ate calculated as the smle mean of all aveage eos was equal n ths test 4.5%. To check the mact of fequences on the accuacy of the dagnostc system we have made addtonal exements by alyng the andom choce of fequency values n the analyss of the flte. The numbe of fequency onts of the analyss of the ccut was changng fom 0 to 23. The dstbuton was also changng. The SVM system has been taned and then tested usng the same numbe of testng data. The total msclassfcaton ato on the testng data was ths tme hghe and deendent on the numbe and dstbuton of the fequency analyss onts. At 0 fequences and the andom dstbuton wthn the nomalzed ange fom 0 to 2 the aveage classfcaton eo was close to.5% (the actual values deend on the actually geneated andom values of elements). At 23 fequency onts dstbuted andomly n the same ange the aveage classfcaton eo has doed to the value of 0.78%. The esults of ths test confm the motance of the senstvty analyss aled fo choosng the numbe of fequency onts used n the eaaton of the data and the selecton of the atcula values. In the last exements we have comaed the accuacy of ou SVM based dagnostc system wth the one alyng the MLP classfe. The otmal MLP netwok contanng 90 nuts, 20 hdden and 2 outut sgmodal neuons was leaned usng the same data set as n the evous exements and then tested on the testng data. The obtaned esults ae nfeo n comason to the SVM. The mean classfcaton eo fo the testng data was equal 5.43%, whch s much hghe than 0.52% obtaned by the SVM classfe. Besdes ths the tanng of the MLP classfe was extemely tme consumng n comason to SVM one. At the same numbe of data (420 samles of each of 2 classes) and alcaton of LM algothm t lasted at least 50 tmes longe. 6. CONCLUSION The ae has esented the new aoach to the fault detecton and locaton n an analog ccut, based on the alcaton of Suot Vecto Machne. The most dffcult case of the aametc faults of ccut elements has been consdeed. The numecal exements conducted fo the 9 th ode RLC ladde flte have confmed that the develoed dagnostc system woks well and s able to locate the sngle faults wth the accetable accuacy fo the whole ange of aamete values fom the toleance lmt to the shot ccut o oen ccut of the element. The motant featue of the oosed soluton s ts hgh effcency and geat seed of oeaton. The tanng of the SVM netwok system, efomed usng Platt algothm [7] was vey quck. At 5040 data as and 2 classes t lasted no longe than 3 mnutes on the PC comute of 2.4GHz and 52M RAM. Moeove, once the netwok was taned, the ecognton of fault was acheved mmedately, esectve of the sze of the ccut. Thus the soluton s suted fo the eal tme alcatons fo fault detecton and locaton n any lnea ccut. The dstnct advantage of the SVM netwok soluton ove the standad MLP case s ts good genealzaton ablty. Taned on the lmted numbe of eesentatve examles of each fault, the netwok s able to ecognze the non-deal (aametc) fault n the wde ange of changed aamete values and at some assumed toleance of the nonfaulty elements. REFERENCES [] C. Al, M. Catelan, A. Fot, Automatc selecton of test fequences fo the dagnoss of faults n analog ccuts, Poc. IMTC., Anchoage, 2002, [2] A. Fann, M. Gua, A. Maches, A. Montsc, A neual netwok dagnoss aoach fo analog ccuts, Jounal of Aled Intellgence, 999, vol.,. -20 [3] I. Guyon, A. Elsseeff, An ntoducton to vaable and featue selecton. J. Machne Lean., 2003, [4] S. Haykn, Neual netwoks, comehensve foundaton, Pentce Hall, 999, New Jesey [5] W. Hsu and C. J. Ln. A comason of methods fo mult-class suot vecto machnes, IEEE Tans. NN, 3, 2002, [6] R. Lu, Testng and dagnoss of analog ccuts and systems, Van Nostand Renhold, New Yok, 99 [7] L. Platt, Fast tanng of SVM usng sequental otmzaton, (n B. Scholkof, et.al. Eds., Advances n kenel methods. MIT Pess), 998, [8] R. 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