A novel approach for analog circuit incipient fault diagnosis by using kernel entropy component analysis as a preprocessor

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1 WSEAS RANSACIONS on CIRCUIS and SYSEMS A nove approach for anaog crcut ncpent faut dagnoss by usng kerne entropy component anayss as a preprocessor CHAO-LONG ZHANG Schoo of Physcs and Eectronc Engneerng Anqng Norma Unversty No. 28, Ln Hu Nan Road, Anqng 2460 PEOPLE S REPUBLIC OF CHINA zhangc@aqtc.edu.cn CHAO-LONG ZHANG, YI-GANG HE, LI-FEN YUAN and WEI HE Schoo of Eectrca Engneerng and Automaton Hefe Unversty of echnoogy No. 93, un X Road, Hefe PEOPLE S REPUBLIC OF CHINA Abstract: - In order to dagnose ncpent faut of anaog crcuts effectvey, an anaog crcut ncpent faut approach by usng kerne entropy component anayss (KECA) as a preprocessor s proposed n the paper. me responses are acqured by sampng outputs of the crcuts under test. Raw features wth hgh dmenson are generated by waveet transform. Furthermore, ower dmensona features are produced through KECA as sampes whch are used to construct a cassfcaton mode based on east squares support vector machne. Bandpass fter and eapfrog fter ncpent faut dagnoss smuatons demonstrate the dagnose procedure of the proposed approach, and aso vadate proposed approach by usng KECA as a preprocessor can produce hgher dagnoss accuracy than the commony used methods. Key-Words: - Anaog crcuts, Incpent faut dagnoss, Waveet transform, KECA, Least squares support vector machne Introducton Anaog crcuts are wdey used n many eectronc systems such as home eectroncs, automotve eectroncs, ndustra eectroncs, mtary eectroncs, etc. Meanwhe, anaog crcut faut dagnoss has become an actve area of research n recent years. However, compared to the we nvestgated faut dagnoss of dgta eectronc crcuts, the dagnostcs of anaog crcuts s far fa behnd for the reason of component toerance effects, nsuffcent nformaton, and anaog crcuts nonnearty. Feature extracton s a frst mportant probem n anaog crcut faut dagnoss, whch produces a strong effect on successve cassfer s effcency [-7]. he work n [2] used mpuse responses of anaog crcuts as features, whch ed to a tremendous computng workoad of cassfer. Waveet transform was proposed to dspose mpuse responses and generate hgh dmensona features [3-7]. Meanwhe, prncpa component anayss (PCA) [3-6], kerne prncpa component anayss (KPCA) [7], near dscrmnant anayss (LDA) [8] and kerne near dscrmnant anayss (KLDA) [9] were presented to reduce the dmenson of hgh dmensona features n faut dagnoss, and postve resuts were acqured [3-9]. Cassfer seecton s another crtca probem n anaog crcut faut dagnoss. Artfca neura network has been commony used for t can perform anaog crcut faut dagnoss by usng the extracted performance data [0-2]. However, ow convergence rate, fang oca optma souton, and poor generazaton are dsadvantages of the agorthm. Support vector machne (SVM) s a machne earnng too [8] that accounts for the trade-off between earnng abty and generazng abty by mnmzng structure rsk, and t has been utzed to anaog crcut faut dagnoss [3, 4]. Least squares support vector machne (LSSVM) mproves SVM formuaton by adoptng east-squares near system as the oss functon, whch can sgnfcanty enhance the performance and reduce the computaton compexty [9]. Hence, LSSVM s empoyed to construct cassfcaton mode n many recent works [5-7]. Most of the above works focus on the anaog E-ISSN: X 3 Voume 5, 206

2 WSEAS RANSACIONS on CIRCUIS and SYSEMS crcut faut dagnoss, and ncpent faut dagnoss attracts few attentons. However, dentfyng the ncpent faut and mantanng the fauty component tmey s conducve to the heath of anaog crcuts and avod deveopng nto a catastrophc faure of anaog crcuts. Kerne entropy component anayss (KECA) s a spectra approach based on the kerne smarty matrx and t manages to mantan maxmum Reny entropy of the nput space data set [20]. In ths paper, a nove approach for anaog crcut ncpent faut dagnoss by usng KECA as a preprocessor s presented. Waveet transform and KECA are used for feature extracton and dmenson reducton. LSSVM s apped to cassfy dfferent faut casses. he proposed approach s demonstrated by ncpent faut dagnoss smuatons of Saen-Key bandpass fter and eapfrog fter. In addton, KECA s compared wth KPCA n vsuazaton, and aso compared wth PCA, KPCA and KLDA n dagnoss smuatons. hs paper s organzed n the foowng order: Secton 2 ntroduces ncpent faut dagnoss approach used n the work. Secton 3 gves the smuaton resuts and dscussons. Fnay, concusons are drawn n Secton 4. 2 Incpent faut dagnoss approach Faut dagnoss approach s usuay consstng of feature extracton, feature dmenson reducton and cassfcaton mode constructon [2-9,, 2]. In the work, waveet transform s used to produce raw features frsty, and then KECA s utzed to reduce the dmenson of raw features. Fnay, a cassfcaton mode s constructed by usng LSSVM. 2. Waveet transform Waveet transform s an effectve sgna anayss technque, and t can generate suffcent features by usng n-eve waveet decomposton. A mother waveet ψ ( x) s defned frsty ( ) ( x b ψ ) ab, x = ψ () a a where a and b are the scang parameter and transatng parameter, respectvey. Assumng f(x) s a sgna, the waveet transform of f(x) s + x b cab (, ) = f( x), ψab, ( x) = f( x) ψ( ) (2) a a where c(a, b) are the waveet coeffcents of the f(x). he sgna f(x) can be decomposed nto dfferent eves of approxmaton coeffcents and deta coeffcents whch represent the ow-frequency and hgh-frequency components of f(x). For the reason of approxmaton coeffcents can capture the basc structure of the sgna, the frst approxmaton coeffcents of eves to 5 are seected as raw features accordng to the cassc works [3-5]. Haar functon has short duraton n tme doman and dscontnuous character whch can cause dstnct features for dstngushng across faut casses. herefore, Haar waveet s utzed to process the mpuse responses of CUs n the work. 2.2 KECA Kerne entropy component anayss s a nove kerne based data transformaton method. Compared to the wdey used dmenson reducton method KPCA whch s based on top egenvaues and egenvectors of kerne matrx, KECA s on bass of kerne smarty matrx and t manages to mantan the maxmum Reny entropy of the nput space data set. Reny quadratc entropy s defned as 2 H( p) = og p (x) dx (7) where p(x) s probabty densty functon producng data set D= x,x 2,,x N. Snce the ogarthm s a monotonc functon, t can be quantfed as V( p) = p 2 (x) dx. A Parzen wndow densty estmator s defned to estmate V(p) and H(p) pˆ(x) = kσ (x, x u ) (8) N xu D where k σ (x, x u ) s caed Parzen wndow, or kerne functon, and gauss kerne s used n the work. Usng the sampe mean approxmaton of the expectaton operator Vˆ ( p) = pˆ (x u) = kσ (x u, x u ) N xu D N xu D N xu D = A KA 2 N (9) where eement (u,u ) of the N N kerne matrx K equas k σ (x u,x u ) and A s an N vector of ones. Reny entropy estmator can be ustrated n the ght of the egenvaues and egenvectors of the kerne matrx, whch can be egendecomposed as K = EDµ E, where D µ s a dagona matrx consstng of egenvaues µ, µ 2, µ N ; E s a matrx wth coumns are egenvectors e, e 2, en. V ˆ( p ) can be expressed as E-ISSN: X 4 Voume 5, 206

3 WSEAS RANSACIONS on CIRCUIS and SYSEMS N N 2 Vˆ( p ) = ( ) 2 µ ea = 2 ε (0) N = N = where each term ε contrbutes to the entropy estmate n the expresson. he egenvaues and egenvectors whch are the frst v argest contrbuton to the entropy estmate are seected n KECA, then /2 the v dmensona φ eca = Dv E v, thus K eca = φec aφea c can be obtaned n the Mercer kerne space. hs s obvous dfference between KPCA and KECA. 2.3 LSSVM LSSVM s an enhancement of the standard SVM. It uses a near set of equatons nstead of a quadratc programmng probem to obtan support vectors and adopts east-squares near system as oss functon. Consder a mode n the prma weght space of the foowng form y(x) = w ϕ() x + b () N where x R s the nput and y Rs the output; ϕ() maps the nput data to a hgh dmensona N feature space; w s an eement of R. Combnng fttng error and functona compexty, the optmzaton probem of LSSVM s substtuted as 2 mn ww+ c ξ 2 2 (2) wb,, ξ = s.t. : ξ [ φ( x) ], 2,, = y w + b = (3) where c s penaty parameter and ξ s random error. he Lagrangan of probem (2) s gven by 2 Lwb (,, ξ, a) = w w+ c ξ 2 2 = (4) a{ y [ w φ( x ) + b] ξ } = where α are Lagrange mutpers. he equaton s soved by partay dfferentatng wth respect to each varabe L = 0 w= = aφ( x) w L = 0 = a = 0 b (5) L = 0 a = cξ =, 2, ξ L = 0 ξ = y [ w φ( x ) + b] =, 2,. a After emnaton of the varabes w and ξ, the equaton can be rewrtten as a near functon group K + c I a Y = (6) 0 b 0 where Kj = k(x, x j) ; Y = [ y,..., y ] ; α = [ α,..., α ] and = [,...,]. he LSSVM mode can be obtaned as y(x) = ak( x,xj) + b (7) = where a, b are soutons of the near system; k(x,x j ) s a kerne functon whch foows Mercer s theory. RBF kerne has powerfu nonnearty mappng abty, and t s seected as the kerne functon n the work. Because the LSSVM s a bnary cassfer and anaog crcut ncpent faut dagnoss s a mut-cass recognton probem, one-aganst-rest (OAR), one-aganst-one (OAO) and bnary tree method are commony used n the LSSVM mut-cassfcaton. However, for a u-cass probem, OAO method needs to consttute u*(u )/2 LSSVM cassfers whch consumes too many computng resources. Meanwhe, OAR method s somewhat ess accuracy. Bnary tree method ony needs to construct u- LSSVM cassfers, and t has the advantages of effcent computaton of the tree archtecture and hgh cassfcaton accuracy of LSSVMs. Hence, bnary tree method s seected to sove the mut-cass probem n the work. 3 Smuatons and resuts 3. Smuaton procedures and settngs In ths secton, Saen-Key bandpass fter and eapfrog fter are used as exampe crcuts. he nput s a snge puse of heght 0V wth us duraton. oerances of the resstors and capactors are set to 5%. Generay, a component wth 50% devaton from ts nomna vaue s consdered to be a faut [2-7]. Hence, the component wth 25% devaton from ts nomna vaue s regarded as an ncpent faut n the work. me mpuse responses of dfferent faut casses are acqured by sampng the outputs of the CUs frsty, and then waveet transform s empoyed to perform 5-eve Haar waveet decomposton n order to generate approxmaton coeffcents as raw features. hen, the features are normazed. Furthermore, ower dmensona data are obtaned through KECA as sampes. For the sakes of convenence and smpcty n vsuazaton and comparson, the 5 dmensona raw features are reduced to 2 dmensona features. E-ISSN: X 5 Voume 5, 206

4 WSEAS RANSACIONS on CIRCUIS and SYSEMS 00 output sampe data for each faut cass are coected n smuatons. he frst 50 sampe data are used to tran LSSVM n order to set up a cassfcaton mode, and the rest 50 sampe data are apped to test the performance of the mode. he smuaton procedure s shown n Fg.. F3 R3 2kΩ 2.5kΩ F4 R3 2kΩ.5kΩ F5 C 5nF 6.25nF F6 C 5nF 3.75nF F7 C2 5nF 6.25nF F8 C2 5nF 3.75nF Fg. Smuaton procedure Fg. 3 Scatter pots of faut casses characterzed by 2 dmensona features of bandpass fter reduced by KECA 3.2 Exampe Saen Key Bandpass Fter he crcut s shown n Fg. 2. Each component vaue has been abeed n the fgure. R2, R3, C and C2 are seected as experment components. he fauty mpuse responses are measured n order to form 9 faut casses ncudng R2, R2, R3, R3, C, C, C2, C2 and no faut (NF), where and refer to hgher and ower than the nomna vaue, respectvey. Faut codes, faut casses, the nomna and fauty component vaues are shown n abe. R2 3kΩ V n R kω C 5nF C2 5nF R3 2kΩ R4 4kΩ R5 4kΩ V out Fg. 4 Scatter pots of faut casses characterzed by 2 dmensona features of bandpass fter reduced by KPCA Fg. 2 Saen Key bandpass fter crcut abe Faut codes, faut casses, the nomna and fauty component vaues for bandpass fter Faut Faut Fauty Nomna code cass vaue F0 NF - - F R2 3kΩ 3.75kΩ F2 R2 3kΩ 2.25kΩ Subsequenty, the 5 dmensona raw features of a faut casses are reduced to 2 dmensona features whch contrbute more to the Reny entropy by usng KECA. Fg. 3 reveas the scatter pots of faut casses characterzed by the 2 dmensona features reduced by KECA. It s obvousy that a faut casses are dstnct ambguty groups. hs manfests dfferent faut casses are we separated by usng KECA. In order to make a comparson, KPCA s apped to reduce the dmenson of the raw features. he E-ISSN: X 6 Voume 5, 206

5 WSEAS RANSACIONS on CIRCUIS and SYSEMS reduced 2 dmensona features wth the frst 2 arge egenvaues are generated and shown n Fg. 4. he fgure s smar to Fg. 3 because the two approaches are usng the same data to generate ower dmensona features. It s obvousy that F, F2, F3, F4, F5, F6 and F7 faut casses are aso dstnct ambguty groups n the fgure. However, there s overappng for F0 faut cass and F8 faut cass. hs reveas that KECA can generate better extracton performance than KPCA. Fg. 5 Bnary tree structure for bandpass fter he constructed bnary tree s shown n Fg. 5. A faut casses are cassed nto two faut cass groups at the root of the tree by the frst bnary LSSVM. Afterward, the two faut cass groups are cassed nto smaer groups by each bnary LSSVM at the node of the tree n ths fashon. hs s repeated recursvey downward the tree unt reaches a eaf node that represents the cass t has been assgned to. 8 LSSVM cassfers are used n tota. he overa dagnoss accuracy s 00%. 3.3 Exampe 2 Leapfrog Fter Leapfrog fter s shown n Fg. 6, and t s a benchmark crcut of IC97. he crcut s more compex for the reason of t s conssted of 4 capactors, 3 resstors and 6 operatona ampfers. Each component vaue has been abeed n the fgure. R, R2, R4, R5, R6, R7, R9, R2, R3, C and C2 are seected as experment components. 23 faut casses ncudng R, R, R2, R2, R4, R4, R5, R5, R6, R6, R7, R7, R9, R9, R2, R2, R3, R3,C, C, C2, C2 and no faut (NF) are formed. Faut codes, faut casses, the nomna and fauty component vaues are shown n abe 2. abe 2 Faut codes, faut casses, the nomna and fauty component vaues for eapfrog fter Faut Faut Fauty Nomna code cass vaue F0 NF - - F R 0kΩ 2.5kΩ F2 R 0kΩ 7.5kΩ F3 R2 0kΩ 2.5kΩ F4 R2 0kΩ 7.5kΩ F5 R4 0kΩ 2.5kΩ F6 R4 0kΩ 7.5kΩ F7 R5 0kΩ 2.5kΩ F8 R5 0kΩ 7.5kΩ F9 R6 0kΩ 2.5kΩ F0 R6 0kΩ 7.5kΩ F R7 0kΩ 2.5kΩ F2 R7 0kΩ 7.5kΩ F3 R9 0kΩ 2.5kΩ F4 R9 0kΩ 7.5kΩ F5 R2 0kΩ 2.5kΩ F6 R2 0kΩ 7.5kΩ F7 R3 0kΩ 2.5kΩ F8 R3 0kΩ 7.5kΩ F9 C 0nF 2.5nF F20 C 0nF 7.5nF F2 C2 20nF 25nF F22 C2 20nF 5nF R3 0kΩ R2 0kΩ R3 0kΩ V n R 0kΩ C 0nF R4 0kΩ R5 0kΩ R6 0kΩ C2 20nF R7 0kΩ C3 20nF R8 0kΩ R2 0kΩ R9 0kΩ R0 0kΩ R 0kΩ C4 0nF V out Fg. 6 Leapfrog fter crcut E-ISSN: X 7 Voume 5, 206

6 WSEAS RANSACIONS on CIRCUIS and SYSEMS Fg. 8 Scatter pots of faut casses characterzed by 2 dmensona features of eapfrog fter reduced by KPCA Fg. 7 Scatter pots of faut casses characterzed by 2 dmensona features of eapfrog fter reduced by KECA. After acqurng 5 dmensona raw features, KECA s utzed to reduce the dmenson of features from 5 to 2. Fg. 7 reveas the scatter pots of faut casses characterzed by 2 dmensona features. It s obvousy that F0, F, F2, F3, F4, F5, F6, F7, F8, F9, F, F2, F3, F4, F5, F6, F7, F8, F9, F20 and F2 faut casses are dstnct ambguty groups. However, there s partay overappng for F0 faut cass and F22 faut cass. Fg. 8 shows the scatter pots of faut casses characterzed by 2 dmensona features reduced by usng KPCA. F0, F, F2, F3, F4, F5, F6, F7, F8, F9, F, F2, F3, F4, F6, F8, F9, F20 and F2 faut casses are dstnct ambguty groups n the fgure. Nevertheess, there s serousy overappng for F0 faut cass and F22 faut cass, and sghty overappng for F5 faut cass and F7 faut cass. hs exampe aso reveas that KECA can generate better extracton performance than KPCA. abe 3 Accuraces of the dagnoss approach for eapfrog fter Faut code Faut cass Accuracy F0 NF 00% F R 00% F2 R 00% F3 R 2 00% F4 R 2 00% F5 R 4 00% F6 R 4 00% F7 R 5 00% F8 R 5 00% F9 R 6 00% F0 R 6 94% F R 7 00% F2 R 7 00% F3 R 9 00% F4 R 9 00% F5 R 2 00% F6 R 2 00% F7 R 3 00% F8 R 3 00% F9 C 00% F20 C 00% F2 C 2 00% F22 C 2 92% he constructed bnary tree s shown n Fg. 9 and 22 LSSVM cassfers are used. abe 3 demonstrates the accuraces of the dagnoss approach n dentfyng the 23 faut casses. he F0, F, F2, F3, F4, F5, F6, F7, F8, F9, F, F2, F3, F4, F5, F6, F7, F8, F9, F20 and F2 faut casses can be cassfed correcty. Meanwhe, 50 test data of F0 faut cass are cassfed correcty 47 tmes and mscassfed as F22 faut cass 3 tmes; 50 test data of F22 faut cass are cassfed correcty 46 tmes and mscassfed as F0 faut cass 4 tmes. he overa dagnoss accuracy s 99.4%. As can be seen from Fgs. 3, 4, 7 and 8, the separabty of features reduced by usng KECA s further enarged than by usng KPCA, whch represents dfferent faut casses can be better separated by usng KECA. herefore, appyng KECA whch chooses components based on Reny entropy to reduce hgh dmenson of features n anaog crcut ncpent faut dagnoss s more approprate than usng KPCA whch s choosng components based on top egenvaues. E-ISSN: X 8 Voume 5, 206

7 WSEAS RANSACIONS on CIRCUIS and SYSEMS Fg. 9 Bnary tree structure for eapfrog fter abe 4 Dagnoss accuraces of our approach and the referenced approaches Exampe Reference [6] Reference [7] Reference [9] Our work bandpass fter 96.9% 99.% 99.6% 00% eapfrog fter 95.7% 98.2% 99.% 99.4% 3.4 Comparson smuaton For the purpose of vadatng the effectness of KECA presented n the work, the approach s compared wth PCA [6], KPCA [7] and KLDA [9] whch are commony used n anaog crcut faut dagnoss as data transformaton and dmenson reducton approaches. 5 dmensona raw features of exampe and exampe 2 are used, and the ncpent faut dagnoss smuaton steps and condtons are the same wth our work. he dagnoss accuracy of each approach s shown n abe 4. From the resuts of the tabe, t can be seen that performng ncpent faut by usng KECA as a preprocessor can obtan more postve resuts than by usng PCA, KPCA and KLDA, whch represents that KECA can generate better extracton performance than PCA, KPCA and KLDA n dmenson reducton. 4 Concusons In ths work, a nove approach has been presented to perform anaog crcut ncpent faut dagnoss by usng KECA as a preprocessor. Waveet transform on tme responses has produced raw features whch are reated to each of faut casses. KECA has been used to reduce the dmenson of raw features from 5 dmensona to 2 dmensona. Dfferent faut casses have been dentfed by bnary tree LSSVM. hrough comparng the scatter pots of faut casses characterzed by 2 dmensona features reduced by usng KECA and KPCA respectvey, t can be easy concuded that KECA can generate better separabty of features than KPCA. Comparson smuaton resuts have aso verfed that the proposed approach can produce hgher dagnoss accuracy than the commony used methods. Acknowedgements hs work was supported by Natona Natura Scence Foundaton of Chna No , the Natona Defense Advanced Research Project Grant No.C200004, 940A270202DZ502, the Key Grant Project of Chnese Mnstry of Educaton under Grant No.3308, Anhu Provnca Scence and echnoogy Foundaton of Chna under Grant No , Anhu Provnca Natura Scence Foundaton No QF57 and Key projects of Anhu provnce unversty outstandng youth taent support program No. gxyqzd References: E-ISSN: X 9 Voume 5, 206

8 WSEAS RANSACIONS on CIRCUIS and SYSEMS [] A. Pułka, wo heurstc agorthms for test pont seecton n anaog crcut dagnoses, Metroogy and Measurement Systems, Vo.8, No., 20, pp [2] R. Spna, S. Upadhyaya, Lnear crcut faut dagnoss usng neuromorphc anayzers, IEEE ransactons on Crcuts and Systems II: Anaog and Dgta Sgna Processng, Vo.44, No.3, 997, pp [3] F. Amnan, M. Amnan, Jr. H. W. Cons, Anaog faut dagnoss of actua crcuts usng neura networks, IEEE ransactons on Instrumentaton and Measurement, Vo.5, No.3, 2002, pp [4] M. Amnan, F. Amnan. A, moduar faut-dagnostc system for anaog eectronc crcuts usng neura networks wth waveet transform as a pre-processor, IEEE ransactons on Instrumentaton and Measurement, Vo.56, No.5, 2007, pp [5] F. Amnan, M. Amnan, Faut dagnoss of anaog crcuts usng Bayesan neura networks wth waveet transform as pre-processor, Journa of eectronc testng, Vo.7, No., 200, pp [6] Y. Xao, Y. He, A near rdgeet network approach for faut dagnoss of anaog crcut, Scence Chna Informaton Scences, Vo.53, No., 200, pp [7] Y. Xao, L. Feng, A nove near rdgeet network approach for anaog faut dagnoss usng waveet-based fracta anayss and kerne PCA as preprocessors, Measurement, Vo.45, No.3, 202, pp [8] L. Xu, J. Huang, H. Wang, et a. A nove method for the dagnoss of the ncpent fauts n anaog crcuts based on LDA and HMM, Crcuts, Systems and Sgna Processng, Vo.29, No.4, 200, pp [9] Y. Xao, L. Feng, A nove neura-network approach of anaog faut dagnoss based on kerne dscrmnant anayss and partce swarm optmzaton, Apped Soft Computng, Vo.2, No.2, 202, pp [0] L. Yuan, Y. He, J. Huang, et a. A new neura-network-based faut dagnoss approach for anaog crcuts by usng kurtoss and entropy as a pre-processor, IEEE ransactons on Instrumentaton and Measurement, Vo.59, No.3, 200, pp [] Y. He, Y. an, Y. Sun, Waveet neura network approach for faut dagnoss of anaogue crcuts, IEE Proceedngs-Crcuts, Devces and Systems, Vo.5, No.4, 2004, pp [2] Y. an, Y. He, C. Cu, et a. A nove method for anaog faut dagnoss based on neura networks and genetc agorthms, IEEE ransactons on Instrumentaton and Measurement, Vo.57, No., 2008, pp [3] D. Grzechca, J. Rutkowsk, Faut dagnoss n anaog eectronc crcuts-the SVM approach, Metroogy and Measurement Systems, Vo.6, No.4, 2009, pp [4] J. Cu, Y. Wang, A nove approach of anaog crcut faut dagnoss usng support vector machnes cassfer, Measurement, Vo.44, No., 20, pp [5] A. S. S. Vasan, B. Long, Pecht M. Dagnostcs and prognostcs method for anaog eectronc crcuts, IEEE ransactons on Industra Eectroncs, Vo.60, No., 203, pp [6] B. Long, S. an, H. Wang, Dagnostcs of ftered anaog crcuts wth toerance based on LS-SVM usng frequency features, Journa of Eectronc estng, Vo.28, No.3, 202, pp [7] B. Long, S. an, H. Wang, Feature vector seecton method usng Mahaanobs dstance for dagnostcs of anaog crcuts based on LS-SVM, Journa of Eectronc estng, Vo.28, No.5, 202, pp [8] C. Cortes, V. Vapnk, Support-vector networks, Machne earnng, Vo.20, No.3, 995, pp [9] J. A. K. Suykens, J. Vandewae, Least squares support vector machne cassfers, Neura processng etters, Vo.9, No.3, 999, pp [20] R. Jenssen, Kerne entropy component anayss, IEEE ransactons on Pattern Anayss and Machne Integence, Vo.32, No.5, 200, pp E-ISSN: X 20 Voume 5, 206