Research Article New Strategy for Analog Circuit Performance Evaluation under Disturbance and Fault Value

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1 Mathematca Probems n Engneerng, Artce ID 72821, 8 pages Research Artce New Strategy for Anaog Crcut Performance Evauaton under Dsturbance and Faut Vaue Ahua Zhang, 1 Yongchao Wang, 1 Chen Chen, 1 and Hamd Reza Karm 2 1 Coege of Engneerng, Boha Unversty, Jnzhou 12113, Chna 2 Department of Engneerng, Facuty of Engneerng and Scence, The Unversty of Agder, Grmstad 4898, Norway Correspondence shoud be addressed to Ahua Zhang; jsxnx zah@163.com Receved 23 December 213; Accepted 6 January 214; Pubshed 13 February 214 Academc Edtor: Xudong Zhao Copyrght 214 Ahua Zhang et a. Ths s an open access artce dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgna work s propery cted. Focus on ths ssue of dsturbance and faut vaue s nevtabe n data coecton about anaog crcut. A nove strategy s deveoped for anaog crcut onne performance evauaton based on fuzzy earnng and doube weghted support vector machne (DWMK- FSVM). Frst, the doube weghted support vector regresson machne s empoyed to be the ndrect evauaton means, reed on the coege anaog eectronc technoogy experment to evauate anaog crcut. Second, the superorty of fuzzy earnng aso s addressed to reaze actve suppresson to the faut vaues and dsturbance parameters. Moreover, the mutkerne RBF s empoyed by support vector regresson machne to reaze more fexbty onne such as the bandwdths tunng. Numerca resuts, supported by the coege anaog crcut experments, adopted OTL performance eght ndexes, whch were obtaned va precson nstrument evauaton n two years to construct tranng set and are then to be evauated onne based on DWMK-FSVM. Smuaton resuts presented not ony hghght precson of the evauaton strategy derved here but aso ustrate ts great robustness. 1. Introducton Anaogcrcutsareoneofthefundamentapartsofmodern eectromechanc systems. Much dgta eectronc technoogy has swarmed nto our ves; t seems that a the anaog crcuts are gong to decne, but there st exsts a need to use anaog crcuts [1]. Such as anaog crcut s st used to convert speech sgnas to dgta sgnas, sensor sgnas are nputted to mcroprocessors, and dgta outputs are converted to anaog sgnas. Furthermore, a the dgta systems cannot dvorce from utmatey anaog crcuts [2]. The presence of anaog crcut detecton capabty s vta when focusng on the status dscussed above. Physca damage, manufacturng fauts, agng, radaton, temperature changes, and power surges are possbe reasons; therefore the performance evauaton shoud be done beforehand. If the system has no performance evauaton part, there s a hgh rsk possbty, especay when the anaog crcut s on the status of radca performance degradaton. Even worse, anaog crcuts have been wdey used for the autonomous systems workng wthout the nterventon of human operators n remote and hazardous envronments. The purpose of anaog crcuts performance evauaton s to prevent catastrophc accdents and gve a cauton to the system. In the prevous studes, there have been a ot of works about the automaton of the process, especay wth evoutonary computaton [3 5]. Evoutonary computaton ncudes a set of methodooges mmckng the natura evouton phenomena: neura network [6 9], genetc agorthm [6, 1], fuzzy ogc [11, 12], swtch system [13 16] and data drven [17 2]. Zhang and Yu [2]attemptedtoevoveanaogcrcutsperformance evauaton strategy usng support vector regresson based on data nformaton about norma anaog crcuts such as four ndexes, nput resstance, nput votage, output resstance, and output votage. Ths method has presented some advantages such as we evauaton accuracy, portabty, and ow cost; however, ths desgn has gnored the reaty status that the processng of the data coecton ncudes faut vaue or dsturbancevaue.theowconvergenceratecoudnotmeet theonneevauatonrequrement.lterature[21] focused the snguarty ssue proposed weghted LSSVM agorthm. Based on the dea dscussed n terature [21], fuzzy custerng dea s aso drawn nto LSSVM whch guarantees the robust va weghtng for each sampe [22]. Athough there have been

2 2 Mathematca Probems n Engneerng severa works on decnng snguarty effect to ths evauaton accuracy wth weght to obtan the robustness the weghted vaue s constant whch s susceptbe to be nfuenced by the parameter seecton. In fact, Kawamura et a. have eaded robust RBF net to robust LSSVR n eary years, yet the seecton and structure determnaton of the weght nta vaue s st the most dffcut probem [23]. In ths paper, we argue that the evoutonary computaton canbeusefutoreazeanaogcrcutonneperformance evauaton under dsturbance and faut vaue based on fuzzy earnng theory and doube weghted support vector machne, and the kerne functon of whch empoys the mutkerne RBF. Numerca resuts, supported by the coege anaog crcut experments, adopted OTL performance eght ndexes, whch were obtaned va precson nstrument evauaton n two years to construct tranng set, and are then to be evauated onne based on DWMK-FSVM. Smuaton resuts presented not ony hghght speed abty of the evauaton strategy derved here but aso ustrate ts great precson and robustness. 2. OTL Technca Index The man technca ndex of OTL ncudes gan, transmsson bands, center frequency, upper/ower cut-off frequency, maxmum output extent, as the mportant technca ndex, nonnear dstorton coeffcent, nput/output resstance, and maxmum output power. In addton, amng at dfferent stuaton, as the other technca ndex, power capacty, antnterference abty, sgna to nose rato, weght, voume, workng temperature, and so forth may be proposed. Durng ths technca ndex, gan embodes the ampfed abty, transmsson bands gve out the response abty to the nput sgna, and upper/ower cut-off frequency gves out the nput/output sgna frequency band threshod. When the quescent pont of OTL s confrmed, the four technca ndexes such as gan, transmsson bands, and upper/ower cut-off frequency are the mportant. 3. Anaog Crcut Performance Evauaton Strategy 3.1. Fuzzy Support Vector Machne (FSVM). The deveopment ofsvmcamefromthebestoptmumhyperpanewhchhas the neary separabe property. For one tranng set wth cassfcaton markers, (x,y ), x R n and y {1, 1}, = 1,...,,f hyperpane ω x b=coud dvde the sampes nto two types correcty; the best optmum hyperpane woud make the sums of the two types to the hyperpane dstance bethemaxmum.thebestoptmumhyperpanemaybe obtaned va sovng the foowng optmzaton probem: mn 1 2 ω C ξ =1 s.t. y [( ω x )b] 1, ξ, =1,...,, where ξ s error expresson and C s penaty factor. (1) Tthe sovng probem of best optmum hyperpane above may be transformed nto dua probem va utzng Lagrange mutper method. Consder max s.t. =1a 1 a 2 a j y y j (x x j ),j=1 =1 a y =, a C, =1,...,, where a s the Lagrange mutper of x.equaton(2) s a typca optma probem of quadratc functon, therefore there w be a guarantee for the exstence of a unque souton.that s a = and the correspondng sampes are support vector. So the decson functon shoud be f(x) = sgn ( =1 (2) a y (x x) b). (3) For the nonseparabe probem, we can soved ths ssue va hgh dmensona mappng φ : R n H,andthenear cassfcaton woud be reazed n the feature space. By defnng the functon k(x,x j ) = φ(x ) φ(x j ),thedua programmng of formua (2)woudbe max s.t. =1a 1 a 2 a j y y j k(x x j ),j=1 =1 a y =, a C, =1,...,. The correspondng decson functon woud be f (x) = sgn ( =1 (4) a y k(x x)b), (5) where k(x,x j ) = φ(x ) φ(x j ) s the kerne functon; the seecton of kerne functon shoud make t to be one of ts feature space nner product. The common kerne functon ncudes poynoma kerne functon (6); Gauss RBF kerne functon (7), and sgmod kerne functon (8), whch are expressed as foows: k(x,x j )=(x x j 1) d, d=1,2,...n; (6) k(x,x j )=exp ( γ x x j 2 ), (7) k(x,x j )=tanh (b (x x j )c), b>, c<. (8) Lke SVM, the am of the FSVM [24] stofndanoptma separatng hyperpane that separates the sampe ponts nto two casses wth the maxma margn. The quadratc optmzaton probem for cassfcaton s consdered as the souton to mn 1 2 ω C s ξ =1 s.t. y [( ω x )b] 1 ξ, ξ, =1,...,. (9)

3 Mathematca Probems n Engneerng 3 For consderng the effect under the feature strong or weak, the weghted dea has been empoyed Doube Weghted Mutkerne FSVM (DWMK-FSVM). Doube weghted FSVM (DW-FSVM) s one method that shoud not ony consder the sampe number dfference and sampe mportance dfference, but aso gve attenton to nfuence above two characterstcs of the feature strong and weak at the same tme. DW-FSVM mproved the cassfcaton precson and conformed FSVM to have better robustness. For ustratve purposes, the DW-FSVM constructed steps [25, 26] are presented as foows. Step 1. Let source dataset be R,whereR={x,x j } j =1, x R n, x j { 1,1}and tranng the FSVMs va R. Step 2. Based on FSVMs tranng resut, we emnated the sampes and obtaned the dataset S, x postve exampe, f(x )>1or f(x )<, (1) x negatve exampe, f(x )< 1or f(x )>. (11) Step 3. We emnated the redundancy sampes of S,obtaned the supportvector dataset P whch ncuded part redundancy sampes: P={x,1} =1 {y j, (12), 1} j=1 where x R n, s the postve exampe number of database P, s the negatve exampe number of database P, x s the postve exampe, and y j s the negatve exampe. Step 4. we cacuated the essentaty weght of P va (13), and the sampe error varance vaue, whch s needed durng the cacuaton, can be obtaned by nta tranng FSVMs m ξ mn =1 ξ max ξ mn ξ ε, m j =1 ξ j mn (13) jξ j max j ξj mn jξj ε, where ε s a tte postve number and category weght may be obtaned va S /S = /. Step 5. The sampes of dataset P were descrbed by feature dataset {cf, uc}, wherecf s the cass abe feature and uc = (u 1,u 2,...,u n ) s the noncass abe feature set. Step 6. We cacuated feature uc (1 n) nformaton gan,constructed feature weght vector ω and nearty transform dagona matrx DM: ω= G =( Gan (uc 1 )),..., Gan (uc n ) where DM kk =ω k δ kk. DM = dag (ω), (14) u C 1 C 5 C 2 C 3 C C H 9 LA412 1 u o C C R R L R F C F C B C D V CC Fgure 1: The OTL Power Ampfer wth Bootstrap Crcut. Step 7. We repaced FSVM kerne functon formuas (6) (8) wth feature weght kerne (15) and seected the approprate mode and tranng arthmetc to construct cassfcaton decson functon for dataset P as foows k p (x,x j )=(x T P xt j P1)d =(x T PPT x j 1) d, k p (x,x j )=exp ( γ xt P xt j P 2 ) d=1,2,..., = exp ( γ(x x j ) T PP T (x x j )), k p (x,x j )=tanh (b (x T P xt j P) c) = tanh (b (x T PPT x j )c), b>, c<. (15) In ths paper, the feature weghted Gauss RBF kerne functon s empoyed. And the mutkerne dea [27] s aso mported n ths part whch can make tsef have more fexbty to the kerne functon onne such as the bandwdths tunng. And the mutkerne RBF s defned by ker (x,x j )= p m=1 k m exp ( d,j /2σ 2 m ) p z=1 k. (16) z 4. Experment Resuts and Anayss ExpermentbasedonthetestcrcutOTL,whchsatypca bootstrap crcut shown n Fgure 1, and the experment data, eght ndexes, are obtaned by precse nstrument evauaton n two years. The sampe number s 4 1 whch s recorded as dataset R. Before verfyng the proposed method n ths paper, the frst thng to be done s estabshng datasets of tranng and testng. However, the dsturbance vaue and faut vaue n the data set whch were caused by ndustry fed nfuence and other noncrcut faut factors w have greateffectsonmodeperformanceofsvm,especaythe dataset, whch ncude the strangeness vaue, are st used for modeng. Hence, a normazaton of the data s requred before presentng the nput patterns to any statstca machne

4 4 Mathematca Probems n Engneerng Tabe 1: Resut of data feature and comparatve experment of regresson probem on experment data. TRSN TESN FN Method Parameter (σ, ε, γ) SVN TRMSE TEMSE CPU/s MKALSSVR (2,.1,.75) e e LSSVR (2,.1, /) e e ε-svr (2,.1, /) e e 4.62 SVN denotes the number of support vector, TRSN denotes the number of tranng support vector, TESN denotes the number of testng support vector, FN denotes the number of the data feature, TEMSE denotes the testng data mean square error, and TDMSE denotes the tranng data mean square error. earnng agorthm. In ths experment, -1 normazaton method, denoted by (17), sutzedto preprocess. x n = xa x mn x max x mn, (17) where x a and x n are the th components of the nput vector before and after normazaton, respectvey, and x max and x mn are the maxmum and mnmum vaues of a the components of the nput vector before the normazaton. After the above data seecton and data normazaton, 25 1 sampes are seected randomy to be the tranng sampes,therestdatasampesaretobeatestsampe.to vadate the superor evauaton performance of the proposed DWMK-FSVM to evauate the anaog crcut performance onne, the dfferent methods such as LSSVR, ε-svr, and the precson nstrument are aso carred out for the comparson purpose whe the anaog crcut performance evauaton s on. Meanwhe severa parameters needs to be ntroduced before appyng the three SVM agorthms. Frst of a, t s requred to denote three parameters namey, error nsenstve zone (ε), penaty factor γ and kerne specfc parameters σ. Probem regardng the choce of ε, γ and σ was studed by severa researchers [28, 29]. The penaty factor γ contros the smoothness or fatness of the approxmaton functon. If we set the vaue γ to be arge, the objectve s ony to mnmze the emprca rsk, whch makes the earnng machne more compex. On the contrary, f we set the vaue γ to be sma, the objectve s to cause the errors to be excessvey toerated yedng a earnng machne wth poor approxmaton [3]. In ths study, SVM modes have been constructed wth γ and ε whch are the emprca vaues gven by [31, 32]. Va some testng, the parameters γ and ε have been vared over a specfc correspondng range n order to obtan better coeffcent of correaton vaue, and the correaton vaue, denoted Re, s determned by (18). The kerne specfc parameters σ srestrctedsncethevaueshownntabe 1 gves the better predcton for these modes. The three vaues foreachmodeareshownnthefoowngtabe.thsstudy adopts RBF (16) whereσ s wdth of RBF, ths s aso known as kerne functon. The adopted γ, ε and σ vaues for the three modes are shown n Tabe 1. Consder n =1 Re = (D a D a )(D p D p ), n (D a D a ) n (D (18) p D p ) where D a and D p are the actua and predcted vaues, respectvey, D a and D p are mean of actua and predcted D vaues correspondng to n patterns. And MSE s defned by MSE = 1 K K =1 (Y Y ) 2, (19) where Y s the rea vaue, Y s the predcted vaue, and K s a testng sampe number. To vadate the superor evauaton performance of the proposed DWMK-FSVM, the other two dfferent methods, LSSVR and ε-svr, are aso empoyed n ths part. The sharp contrast about the tme response of the three methods are presented n Fgure 2. We take one perod of testng tme of LSSVR as comparson, and the other two performance evauaton methods are aso empoyed to reaze comparson n the same testng tme. Va ths testng comparng, we can see ceary that the testng speed s superory greater than the other two methods. In Fgure 2, wecanseethat the support vector densty s cosey bound up the curvature. If the curvature s bgger, the support vector densty s aso bgger; on the contrary, whe n the poston of the reatvey smooth, the support vector densty s reatvey sma. For further anayss, the maxmum absoute error s presented by MAE = max Y Y. (2) From the expermenta data gven n Tabes 2 and 3, wecan fnd the exceent capacty of the proposed DWMK-FSVM to dea wth the dsturbance and faut vaues. And Tabe 4 shows the further proof that the proposed method has better evauaton performance than the other two methods. To vadate the superor evauaton performance of the proposed DWMK-FSVM, we aso gve out the oca regresson effect comparson curve of wth/wthout faut vaues and dsturbances under DWMK-FSVM, LSSVR, and ε-svr. The sharp contrast about the tme responses of the three methods are presented n Fgures 2 and 3. Theproposed methodhastheweabtytodeawththedsturbancevaue and faut vaue, and the other ones do not. At the same tme, the proposed method aso has the same evauaton precson as the other two methods. For the same purpose, the regresson effect comparson curves of A u wth/wthout faut vaues and dsturbances under DWMK-FSVM, LSSVR, and ε-svr are presented n Fgures 4 and 5. Fromthefour fgures, we can see that the regresson effect of the proposed

5 Mathematca Probems n Engneerng ε-svr LSSVR Tme (s) Tme (s) (a) (b) DWMK-FSVM Tme (s) (c) Fgure 2: The oca regresson effect comparson curve of wthout faut vaues and dsturbances under three agorthms. ε-svr Tme (s) LSSVR 1 Dsturbance Faut vaue Tme (s) (a) (b) DWMK-FSVM Tme (s) (c) Fgure 3: The oca regresson effect comparson curve of wth faut vaues and dsturbances under three agorthms. Tabe 2: Resut of data feature and comparatve error of tranng sampe. TRSN Method Tranng MAE Tranng MSE A u U om U s U N A u U om U s U N 25 1 DWMK-FSVM LSSVR ε-svr

6 6 Mathematca Probems n Engneerng ε-svr A 15 u 1 5 Dsturbance Faut vaue LSSVR A 15 u (a) (b) DWMK-FSVM A u (c) Fgure 4: The regresson effect comparson curve of A u wth faut vaues and dsturbances under three agorthms. A u 5 A u 5 ε-svr LSSVR (a) (b) DWMK-FSVM A u (c) Fgure 5: The regresson effect comparson curve of A u wthout faut vaues and dsturbances under three agorthms. Tabe 3: Resut of data feature and comparatve error of testng sampe. TSSN Method Test MAE Test MSE A u U om U s U N A u U om U s U N 1 1 DWMK-FSVM LSSVR ε-svr

7 Mathematca Probems n Engneerng 7 Tabe4:Resutofcomparatveassessment. Method A u f BW (MHz) f L (Hz) f H (MHz) U om (V) P om (mw) U s (mv) U N (pv) CPU/s DWMK-FSVM LSSVR ε-svr Test theory vaue method s obvous better than the others, and the abty of deangwthdsturbanceandfautvauessmoreremarkabe than the other ones. 5. Concuson For the shortcomngs of tradtona anaog crcut performance evauaton method for processng the wrong vaues, ths paper presents an evauaton method based on anaog crcut performance of DWMK-FSVM. Usng standard SVM, combne fuzzy earnng advantages wth doube weghted SVM to effcenty dea wth the dataset that contans the wrong vaue. Moreover, takng nto account the tradtona offne evauaton strategy resuts n the ssues that the mode cannot adjust tmey when the data sampe of the sampe group s ncreased or decreased; then the mut-kerne desgnsempoyedwhchhastheabtytochangetherbf wdthtmey.andthsmakestheevauatonhavetheonne processng abty. In engneerng practce, consderng the ow-cost deveopment, exceent accuracy evauaton, hgh operaton speed, easy mpementaton and other features of evauaton methods n DWMK-FSVM, the evauaton strategy deserves deveopment and mpementaton. Confct of Interests The authors decare that there s no confct of nterests regardng the pubcaton of ths paper. Acknowedgments Ths present work was supported partay by the Natona Natura Scence Foundaton of Chna (Project no ), the Natura Scence Foundaton of Laonng, Chna (Project no ), and the Posh-Norwegan Research Programme (Project no. Po-Nor/2957/47/213). The authors hghy apprecate the above fnanca supports. References [1] P. Kabsatpathy, A. Barua, and S. Snha, Faut Dagnoss of Anaog Integrated Crcuts, vo.3,sprnger,newyork,ny, USA, 25. [2] J. R. Koza, F. H. Bennett III, D. Andre, M. A. Keane, and F. Dunap, Automated synthess of anaog eectrca crcuts by means of genetc programmng, IEEE Transactons on Evoutonary Computaton,vo.1,no.2,pp ,1997. [3] A. E. Akad, A. Amne, A. E. Ouardgh, and D. Aboutajdne, A two-stage gene seecton scheme utzng MRMR fter and GA wrapper, Knowedge and Informaton Systems,vo.26,no.3,pp , 211. [4]W.SongandS.C.Park, Latentsemantcanayssforvector space expanson and fuzzy ogc-based genetc custerng, Knowedge and Informaton Systems,vo.22,no.3,pp , 21. [5] J. Martnez-G and J. F. Adana-Montes, Evauaton of two heurstc approaches to sove the ontoogy meta-matchng probem, Knowedge and Informaton Systems,vo.26,no.2,pp , 211. [6] C.-W. Chen, P.-C. Chen, and W.-L. Chang, Modfed ntegent genetc agorthm-based adaptve neura network contro for uncertan structura systems, Journa of Vbraton and Contro,vo.19,no.9,pp ,213. [7] S. K. Shevade, S. S. Keerth, C. Bhattacharyya, and K. R. K. Murthy, Improvements to the SMO agorthm for SVM regresson, IEEE Transactons on Neura Networks, vo. 11, no. 5, pp , 2. [8] B. Xao, Q. L. Hu, and Y. M. Zhang, Adaptve sdng mode faut toerant atttude trackng contro for fexbe spacecraft under actuator saturaton, IEEE Transactons on Contro Systems Technoogy,vo.2,no.6,pp ,211. [9] B. Xao, Q. L. Hu, and G. Ma, Adaptve sdng mode backsteppng contro for atttude trackng of fexbe spacecraft under nput saturaton and snguarty, Proceedngs of the Insttuton of Mechanca Engneers G,vo.224,no.2,pp ,21. [1] S. Sra, S. Nowozn, and S. J. Wrght, Optmzaton for Machne Learnng, 211. [11] S. Abdua and M. Tokh, Fuzzy ogc based FES drven cycng by stmuatng snge musce group, n Convergng Cnca and Engneerng Research on Neurorehabtaton, pp , Sprnger,NewYork,NY,USA,213. [12] S. Yn, H. Luo, and S. Dng, Rea-tme mpementaton of fauttoerant contro systems wth performance optmzaton, IEEE Transactons on Industra Eectroncs, vo.61,no.5,pp , 213. [13] X. Zhao, L. Zhang, P. Sh, and H. Karm, Robust contro of contnuous-tme systems wth state-dependent uncertantes and ts appcaton to eectronc crcuts, IEEE Transactons on Industra Eectroncs,213. [14]X.Zhao,L.Zhang,P.Sh,andM.Lu, Stabtyofswtched postve near systems wth average dwe tme swtchng, Automatca, vo. 48, no. 6, pp , 212. [15] X. Zhao, X. Lu, S. Yn, and H. L, Improved resuts on stabty of contnuous-tme swtched postve near systems, Automatca,213. [16] X.Zhao,L.Zhang,P.Sh,andM.Lu, Stabtyandstabzaton of swtched near systems wth mode-dependent average dwe tme, IEEE Transactons on Automatc Contro,vo.57,no.7,pp , 212. [17]S.Yn,S.X.Dng,A.H.A.Sar,andH.Hao, Data-drven montorng for stochastc systems and ts appcaton on batch

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9 Advances n Operatons Research Advances n Decson Scences Journa of Apped Mathematcs Agebra Journa of Probabty and Statstcs The Scentfc Word Journa Internatona Journa of Dfferenta Equatons Submt your manuscrpts at Internatona Journa of Advances n Combnatorcs Mathematca Physcs Journa of Compex Anayss Internatona Journa of Mathematcs and Mathematca Scences Mathematca Probems n Engneerng Journa of Mathematcs Dscrete Mathematcs Journa of Dscrete Dynamcs n Nature and Socety Journa of Functon Spaces Abstract and Apped Anayss Internatona Journa of Journa of Stochastc Anayss Optmzaton