An improved support vector machine based on particle swarm optimization in laser ultrasonic defect detection

Transcription

1 A improved support vector machie based o particle swarm optimizatio i laser ultrasoic defect detectio School of Sciece, North Uiversity of Chia, aiyua, Shaxi 35, Chia xut98@63.com,hhp9@63.com,xywag@6.com,43497@qq.com Correspodece should be addressed to Yapig Bai; baiyp666@63.com Abstract: Laser ultrasoic defect detectio ad classificatio has bee widely used i egieerig ad material defect detectio, so detectig ad classifyig the defect targets accurately is sigificat. I order to obtai the higher classificatio accuracy, a improved support vector machie (SVM) based o particle swarm optimizatio algorithm is used as classifier i this paper. o search the optimal parameters of SVM, a ew aget Decreasig Iertia Weight strategy particle swarm optimizatio () algorithm is proposed to determie the optimal parameters for SVM. I additio, to further improve the classificatio accuracy, sparse represetatio is used to extract the target features from the real target echo waveform i experimet. Experimetal results show that the proposed -SVM ca achieve higher classificatio accuracy compared to the commoly -SVM, classical SVM ad BP eural etwork (BPNN) i the laser ultrasoic defect sigals classificatio. Key-words: Laser ultrasoic defect detectio; Classificatio method; Support vector machie; Particle swarm optimizatio; Sparse represetatio. Itroductio Nowadays, with the developmet of moder sciece ad techology, ultrasoic odestructive testig techology has become a multi subect cross egieerig techology. So far, there have bee some researches o the defect detectio ad defect classificatio based o machie learig [-6]. Caoical support vector machie (SVM) ad particle swarm optimizatio optimized support vector machie (-SVM) are applied as classifiers i those studies. Support vector machie proposed by Vapik i 9 [7], is a statistical classificatio method, which based o the structural risk miimizatio approach. It solves the classificatio problem by maximizig the margi of the separatio beside the optimal hyper plae. he kerel fuctio plays a very importat role i the performace of SVM. he iput data is mapped to a higher dimesioal feature space by the kerel fuctio, so that the classificatio problem ca be liearly separable. here are may kids of kerel fuctios, such as liear kerel, polyomial kerel, Gaussia kerel, ad so o. he Gaussia kerel is frequetly used i SVM, due to its excellet oliear classificatio ability. Support vector machies show may uique advatages i solvig small samples, oliear ad high dimesioal patter recogitio, ad to a certai extet, it overcomes the "dimesio disaster" ad "over learig" ad other traditioal difficulties. I additio, today, support vector machies have bee widely cocered, ad have made great progress, due to its solid theoretical foudatio ad a simple ad clear mathematical model. At preset, it has bee successfully applied to solvig patter recogitio, classificatio, approximatio of fuctios, ad time series predictio problems, such as speech recogitio [8], text recogitio [9], target detectio ad recogitio [, ], fault diagosis [], fiacial time series forecast [3], ad so o. However, i those applicatios, the performace of SVM depeds upo the selectio of SVM parameters. I other words, the parameters selectio has great ifluece o the learig ad geeralizatio ability of SVM. herefore, the selectio of the optimal parameters is importat to obtai a excellet performace of SVM. he parameters optimizatio of SVM has gaied great attetios i the past several years. Such as, Shi ad Zhou use grid search method ad geetic algorithm to optimize SVM parameters, ad the study the reliability of blastig vibratio predictio of ope pit miig usig the optimized SVM model, ad achieved good results [4]; Li, Xia, et al, with the combiatio of clusterig method, at coloy algorithm ad support vector machie (SVM) to costruct a efficiet ad reliable classifier, ad the use it to udge whether the etwork access is ormal or ot [5]; E. Avci choose the best subset of features i digital modulatio classificatio with the support vector machie optimized by geetic algorithm [6]. But, grid algorithm method has disadvatages such as E-ISSN: Volume 5, 6

2 computatioally itesive, time cosumig ad low learig accuracy; At coloy algorithm method is iitial pheromoe scarcity, log-time searchig ad local best solutio; Geetic algorithm is operatio complex ad differet issues eed to desig differet crossover or mutatio. So we eed to fid a simpler ad more efficiet optimizatio algorithm to optimize the model parameters. Particle swarm optimizatio () is a ituitive ad easy to implemet algorithm from the swarm itelligece commuity, ad it has bee applied to select the proper parameters of SVM [7-9], but the method is easy to trap ito local optimum ad has a low covergece rate. Focusig o these shortages, the curret focus of improvemet is maily focused o: the update formula of velocity ad particle positio, parameter improvemet, hybrid algorithm ad so o. Differet iertia weight strategies imply differet icremetal chages i velocity per time step which meas exploratio of ew search areas i pursuit of a better solutio. I this paper, a improved iertia weight is proposed. We propose a aget Decreasig Iertia Weight (DIW-) algorithm to get the optimal parameters of SVM. O the other had, feature extractio is a crucial step i laser ultrasoic defect classificatio. I this work, we use sparse represetatio (SR) theory to aalyzig the compoets of received target echo sigals [-], ad describe the characteristics of the target with the sparse coefficiets obtaied. I this paper, the goal is to develop a method of -SVM combied with sparse represetatio-based feature extractio to effective detectio of differet defect categories, i which is used to optimize the parameters of the support vector machie. he structure of the paper is orgaized as follows: Sectio itroduces the basic idea of SVM. I Sectio 3 the basic algorithm ad the improved algorithm based o a taget decreasig iertia weight strategy are itroduced. he optimizatio procedure to the SVM is preseted i Sectio 4. he classificatio model for laser ultrasoic defect is preseted ad the experimetal results are reported i Sectio 5. Fially, the coclusio is preseted i Sectio 6. he classificatio theory of SVM he support vector machie (SVM) is a machie learig method based o statistical learig theory. his ovel learig techique origiated as the priciple of structure risk miimizatio, which performs better tha empirical risk miimizatio utilized by traditioal eural etworks. SVM has bee applicatio as a ew techique for solvig classificatio, approximatio of fuctios, ad time series predictio problems. he aim of SVM is to obtai a optimal hyper plae that ca separate the two class samples as well as maximize the margi of the separatio beside the optimal hyper plae. I order to describe the priciple of SVM, we give a traiig set X x, x, x, Y y, y, y, where x i is the iput of SVM, yi is the output of SVM,the we deote the class A with x i A, yi ad class B with, xi A xi B i.. e yi, xi B I order to get the optimal hyper plae, we ca cosider a equivalet represetatio xi b, if yi xi b, if yi Where is the weight vector adb is the costat, the distace betwee two class is, so maximize is equivalet to miimize Euclidea orm of the weight vector, i.e.to miimize. I additio the decisio fuctio ca be defies as f ( x) sg( w xi b), () his decisio fuctio is used to solve the liear classificatio problem. For the oliear classificatio problem, we ca fid a map that makes the samples x i from low dimesioal space R ito a high dimesioal feature space F, by oliear mappig xi ( xi), the oliear classificatio problem i the low dimesioal space ca be solved as a liear classificatio problem i the high dimesioal feature space. I this method, the decisio fuctio ca be defies as f ( x) sg( ( xi ) b), () Based o the priciple of structural risk miimizatio, the learig process of SVM ca be trasformed ito a covex optimizatio problem. mi( C i ), (3) s. t. ( xi) b i Ad this costraied optimizatio problem ca be trasformed ito a dual problem of as follows max Q( ) i i yi y ( xi ) ( xi ), (4) s. t. y ad C( i,, ) i i i Where i is slack variables, C is a Pealty parameter ad usually it is positive parameter, ad is the i E-ISSN: Volume 5, 6

3 Lagrage multiplier. Here, the decisio fuctio ca be defies as: f ( x) sg( i yi ( xi ) ( xi ) b), (5) By defiig a kerel matrix K such that: K( x, x ) ( x ) ( x ) ( x ) ( x ), (6) i i i rasform ito the followig form: max Q( ) i i yi y K( xi, x ) he decisio fuctio ca be expressed as:, (7) f ( x) sg( i yik( xi, x ) b). (8) Ad the ier product ca be computed by a kerel fuctio i the low dimesioal space without kowig the oliear mappig explicitly. Ay fuctio that meets Mercer s coditio (Vapik 9) ca be used as the kerel fuctio. here are several commo types of kerel fuctio: Liear kerel: K( x, x ) x x ; i i d Polyomial kerel: K( x, x ) ( x x ), where d is a positive iteger; i i Gaussia kerel: K( x, x ) exp( x x ) i i where is the width of the Gaussia kerel. Research idicates that the Gaussia kerel fuctio shows good performace i oliear classificatio problems. herefore, we selected it as the kerel fuctio for SVM i this study. I additio, the parameters selectio has great ifluece o the learig ad geeralizatio ability of SVM. For SVM with Gaussia kerel fuctio, the parameters iclude kerel fuctio parameter ad Pealty parameter C. he value of is relevat to the rage ad width of the iput data space, C is the compromise betwee the structure risk ad the samples, ad its value is closely related to the tolerated error. As algorithm ot oly has strog global search ability ad but also helps to search for the optimum parameters quickly. herefore, we use the proposed DIW- algorithm to optimize parameter ad C i this study, which we call -SVM. of particles, also kow as a swarm, are flow through the D-dimesioal search space of the optimizatio problem. Each particle alters its ow velocity ad positio based o the experieces of the particle itself ad those of other particles i the swarm. I the searchig process, every particle is coected to ad able to share iformatio with every other particle i the swarm ad the swarm commuicatio topology is kow as a global eighborhood described i [4]. his sharig iformatio mechaism keeps the overall cosistecy to get the global solutio for the overall swarm. he swarm cosists of particles; each particle has a velocity vector vi ( vi, vi,, vid ) ad a positio vector xi ( xi, xi,, xid ), where i,,, ;each particle is represeted as a potetial solutio to a problem i a D-dimesioal search space, respectively ld ad u d are the lower ad upper bouds of the dth dimesio of the search space, x [ l, u ], id d d d,,, D. Durig each geeratio,the particles are accelerated toward the particles previous best positio ad the global best positio. Where, the persoal best positio of the ith particle deotes as p ( p, p,, p ), the global best positio of the i i i id swarm deotes as pg ( pg, pg,, pgd ). he ew velocity value is used to calculate the ext positio of the particle i the search space. his process will keep the iteratio util settig the maximum umber of iteratio or a optimal fitess degree is obtaied. he updatig of velocity ad particle positio ca be obtaied by usig the followig formula: t t t t t t v v c ( p x ) c ( p x ), (9) id id id id gd id x x v. () t t t id id id where c ad c are Learig Factor (also amed as the Acceleratio Coefficiet) ad they re positive costats, ad are radom umbers ragig from to, t is the iteratio couter, is the iertia weight o the iterval keepig the memory of the old velocity vector of the same particle. Whe is a costat [3], it ca lead to a static, ad whe is varyig iteratively, it leads to a dyamic. 3 Particle swarm optimizatio algorithm 3. Caoical particle swarm optimizatio algorithm Particle swarm optimizatio () developed by Keedy ad Eberhart i 9 [3], is a evolutioary computatio algorithm. I algorithm, each potetial solutio to the optimizatio problem is treated as a bird, which is also called a particle. he set 3. Proposed iertia weight variat As we kow, i the operatio of the itelliget optimizatio method, the exploratio ability ad the exploitatio ability of the balaced is very importat. I algorithm, the balace of these two kids of ability is realized by the iertia weight. he larger iertia weight is that the particle has a greater speed i their origial directio which ca further i the origial E-ISSN: Volume 5, 6

4 directio, therefore larger iertia weight is advatageous to fid the global best solutio as soo as possible i the early iterative steps, but may lead to miss the global best solutio easily i later iterative steps. I cotrast, the smaller the iertia weight makes the particles iherit a few of the origial directio, so as to fly closer, with better exploitatio capabilities, so smaller iertia weight meas loger time to provide slower updatig for fie tuig a local exploratio. Appropriate iertia weight is helpful to fid the best solutio with the least umber of iterative steps. herefore, how to adust the iertia weight i order to balace the global exploratio ad local exploitatio better has become a problem. o solve this problem, we usually use the followig approach: i the early iterative steps, larger iertia weight is eeded for coarse global exploratio, but i later iteratios iertia weight should decrease for fie tuig the local exploratio. A larger iertia weight facilitates global exploratio ad a smaller iertia weight teds to facilitates local exploratio to fie tue the curret search area. I order to balace the global exploratio ad local exploratio, we preset a ew aget Decreasig Iertia Weight strategy, hereiafter referred to as DIW strategy. I this strategy, the iertia weight is with the icrease of iterative step t accordig to taget decreasig. he proposed iertia weight is determied based o the followig equatio: t ( t) start ( start ed )*ta * 4. () 4 Optimize the parameters of SVM by I this paper, the Gaussia kerel fuctio is used to costruct SVM classificatio model, the the width of the Gaussia kerel ad pealizatio parameter C eed to be determied. he proposed DIW- algorithm is applied to determie the parameters of SVM. he positio vector x of each particle is eeded to be optimized, which represets the width of the Gaussia kerel ad pealizatio parameter C.he k -fold cross validatio (where k 5) method is used to evaluate fitess i this study, ad average classificatio accuracy (CV) is adopted as the fitess fuctio. he fitess fuctio is deoted by formula: k CV acc(), () k t acc( ) (,,, k). (3) I k -fold cross validatio, the traiig set is roughly divided ito k groups, trai (), trai (), trai() k, acc() is the accuracy whe trai( ) as testig set ad other groups as traiig set. is the sample umber of trai( ), t is the correct classificatio umber of trai( ). he iteratio process of the improved -SVM learig algorithm ca be described clearly as follows. Step:Read sample data, ad we use sparse represetatio theory (SR) for feature extractio, the the feature data is divided ito two subsets: oe subset is traiig set; the other subset is testig set. Step: Iitialize : Iitialize the relative parameters, icludig the size of swarm, the boudary of velocity vmax, v mi ad positio x max, x mi, the acceleratio factors c ad c, ad max umber of iterative max. r ad r are the two radom umbers with the rage from to. Iitialize t ; for each particle, select two D -dimesioal vectors radomly to iitialize the velocity ad positio of this particle. Step3: Calculate the fitess value of each particle accordig to formula ()(3).Set the curret positio of each particle as the persoal best fitess p i. he fid the maximum fitess value as the global best fitess p of the whole swarm. g Step4: Update the iertia weight accordig to formula (). Modify the particle velocity v i ad positio x i accordig to formula (9) (). Step5: Recalculate the fitess values of each particle ad modify p i ad p g.for each particle, if the curret fitess value is better tha the previous local best, the set the curret fitess value to be the local best; or keep the previous local best. For the global swarm, if the best value of all curret local best is better tha the previous global best, the update the value of global best; or keep the previous global best. Step6: Check stop coditio. If t, the stop the iteratio ad pg max is the optimal solutio which represets the best parameters for SVM, ad go to. Step7; Otherwise, let t t go to Step4. Step8: Use the optimal SVM to perform classificatio problem. Apply the above- 7 steps util the obtaied optimal solutio, get the optimized parameters, ad the perform classificatio problem. he flow char is as i Figure. E-ISSN: Volume 5, 6

5 I the part of the feature extractio, we use the method of sparse represetatio to extract features which the defect sigals obtaied from the above experimets. he defect sigal waveform after sparse represetatio was as show i Figure 4. Waveform of trasmissio wave Waveform of reflected wave Fig.. Classificatio model based o -SVM 5 Example of applicatio 5. Laser ultrasoic surface acoustic wave defect detectio experimet Laser ultrasoic defect detectio techology is based o the theory of soud ad light effect. Laser irradiatio o the surface of the sample, the ultrasoic sigal cotaiig the measured surface iformatio is geerated by the thermal elastic effect, ad the the defect iformatio is extracted ad detected by detectig the ultrasoic sigal modulated by the defect. 8mm mm mm (a)waveform of trasmissio wave (b) Waveform of reflectio wave Fig.3. he defect sigal waveform Waveform of trasmissio wave (a)waveform of trasmissio wave (b) Waveform of reflectio wave Fig.4. he defect sigal waveform after sparse represetatio Waveform of reflected wave mm 8mm Laser poit probe mm (a)schematic diagram of reflected wave measuremet m m 8 m m 5 m m L a s e P r o b e p o i 8 m m m (b) Schematic diagram of trasmissio wave measuremet Fig.. Experimetal schematic diagram I the experimet, as show i Figure, test sample is *5*8mm alumium plate, we use M ultrasoic probe i the detectio distace of laser poit mm get reflectio wave, detectio distace of laser poit mm get trasmitted wave, samplig frequecy is MHz, samplig poits is. Five groups of experimets were carried out, each of which was repeated five times. he defect sizes were.*.3mm,.*mm,.*.7mm,.*.9mm ad odestructive. his experimet was doe two times, ad two groups of trasmissio wave (tdata ad data) ad two groups of reflected waves (fdata ad fdata) were obtaied. he obtaied waveforms were as show i Figure3. 5. Feature extractio 5.3 Performace aalysis for the proposed model I this sectio, we evaluate the performace of the previously proposed method for laser ultrasoic surface acoustic wave defect sigal classificatio. he features of the received sigals are extracted based o sparse represetatio. he, the sparse represetatio based features are used as the iput of the classifiers. Fially, the proposed -SVM classifier is used to classify ad forecast the target types. We obtaied five kids of defect sigals by experimet, with 5 i each group. herefore, a dataset icludig 5 samples for all defect types is established. All samples i the dataset are divided ito two sets, i which the testig sets icludig 5 samples (Radomly select sample for each defect types) are used to test the accuracy of the classificatio for each model, ad the trai sets icludig samples are used to trai the classificatio model. o maitai a more realistic ivestigatio of this classificatio techique, the traiig ad testig sets do ot iclude ay overlap i data. I the cotext of optimizatio of the parameters of SVM, i this experimet, we first provide the performace compariso betwee the ad the classical as well as other improvemets (L, N, ad E are i the literature [5-7]). he populatio size N for all is, ad the maximum E-ISSN: Volume 5, 6

6 evolutio geeratio is set to. Figure 5 shows the average fitess curve of ad other for fidig the optimal parameters of SVM. From the fitess performaces that are show i Figure 5, it is clearly see that he average fitess curve of is better tha that of other, It idicates that is superior to other i SVM parameters optimizatio. I the optimized SVM, pealty parameter C ad the width of RBF kerel fuctio are optimized by the proposed ad classical ad other improvemets, the adusted parameters with maximal classificatio accuracy rate are selected as the most appropriate parameters. he, the optimal parameters are utilized to trai SVM model. I the caoical SVM model, the parameter C ad are radomly selected to costruct the classificatio model. he, all the samples gaied from experimetal measuremets are adopted to verify the superior classificatio performace of the proposed method compared with that of -optimized support vector machie model (-SVM), caoical SVM model, the back propagatio eural etworks (BPNN) model. Each experimet is carried out times. he experimetal results are showed i ables ad 9 Average Fitess L N E Number of geeratio Average Fitess L N E Number of geeratio E Number of geeratio (a) tdata (b) tdata (c) fdata (d) fdata Fig.5. Fitess performace for the proposed ad others able: Classificatio results compariso of four sets data data Average classificatio accuracy rate (%) -SVM -SVM L-SVM N-SVM E-SVM SVM BPNN tdata tdata fdata fdata able: Classificatio average computig time compariso of four sets data data Average computig time(s) -SVM -SVM L-SVM N-SVM E-SVM SVM BPNN tdata tdata fdata fdata Average Fitess 8 7 L N Average Fitess 9 8 L N E Number of geeratio From ables ad, we ca see that, the -optimized support vector machie model has higher average classificatio accuracy rate tha caoical SVM ad BPNN classificatio algorithmic to laser ultrasoic surface acoustic wave defect sigal classificatio. he average classificatio accuracy rate of the improvemet SVM by is more tha 98.9%. Amog the several -SVM models metioed i this paper, we proposed that -SVM model ot oly has higher classificatio accuracy, but also the computatioal complexity is ot icreased.herefore, the proposed method has more excellet classificatio performace tha these traditioal classificatio algorithmic to laser ultrasoic surface acoustic wave defect sigal classificatio. 6 Coclusio I this paper, a improved support vector machie (SVM) based o particle swarm optimizatio algorithm is used as classifier for laser ultrasoic surface acoustic wave defect sigal classificatio. Ad the classificatio performace of this model is demostrated o four group defect sigals. I the preseted method, a ew aget Decreasig Iertia Weight strategy particle swarm optimizatio () algorithm is proposed to determie the optimal parameters of SVM, ad sparse represetatio is used to extract the target features from the real target echo waveform i experimet. he experimetal data sets are used to evaluate its feasibility ad performace i the classificatio of defect. Experimetal results show that the proposed -SVM has more excellet classificatio compared to the commoly -SVM, E-ISSN: Volume 5, 6

7 classical SVM ad BP eural etwork (BPNN) i the laser ultrasoic defect sigals classificatio. I future research, the proposed method will be made toward a higher efficiet model beyod curret level, ad more attetio should paid to ivestigate the classificatio performace of models o large size of traiig sets oce eough samples are obtaied. Coflict of Iterests he authors declare that there is o coflict of iterests regardig the publicatio of this paper. Ackowledgmet his work is fully supported by the Natioal Natural Sciece Foudatio Grat o.6 of Chia. Refereces [] Y. Wag, Applicatio of Support Vector Machie i Weld Defect Detectio ad Recogitio of X-ray Images, Computer Aided Draftig Desig & Maufacturig, Vol.3,No.3,4,pp.-6. [] D. A. Karras, Improved defect detectio usig support vector machies ad wavelet feature extractio based o vector quatizatio ad SVD techiques, i: Proceedigs of IEEE Iteratioal Coferece o Neural Networks, Vol.3, No.3, 3,pp [3] K. Kurokawa, M. Morimoto, K. Fuii, Heterogeeous Defect Detectio of Metal Surface usig SVM, Ieice echical Report Sigal Processig, Vol.9,No.9,9,pp [4] A. Widodo, B. S. Yag, Applicatio of oliear feature extractio ad support vector machies for fault diagosis of iductio motors, Expert Systems with Applicatios, Vol.33,No.,7,pp.4-5. [5] X.W. Zhag, Y. Q. Dig, Y. Y. Lv, et al. A visio ispectio system for the surface defects of strogly reflected metal based o multi-class SVM, Expert Systems with Applicatios,Vol.38,No.5,, pp [6] F.Y. Zhag, R. J. Liu, Study o the Parts Surface Defect Detectio Method Based o Modifed SVM Algorithm, Applied Mechaics & Materials, Vol.54-54,4, pp [7] V. N. Vapik, he Nature of Statistical Learig heory, Spriger -Verlag, New York, 9. [8] V. Wa, W.M.Campbell, Support vector machies for speaker verificatio ad idetificatio, Neural Networks for Sigal Processig X, IEEE Sigal Processig Society Workshop, Vol.,No.,, pp [9]. Joachims, Learig to Classify ext Usig Support Vector Machies, Methods, heory ad Algorithms, Spriger Berli, Vol.9,No.4,,pp [] P. Lei, J. Wag, P. Guo, et al., Automatic classificatio of radar targets with micro-motios usig etropy segmetatio ad time-frequecy features, AEU - Iteratioal Joural of Electroics ad Commuicatios, Vol.65,No.,, pp [] A. Eryildirim, I. Oara, Pulse Doppler Radar arget Recogitio usig a wo-stage SVM Procedure, IEEE rasactios o Aerospace & Electroics Systems, Vol.47,No.,,pp [] Q. Qi, Z. N. Jiag, K.Feg, et al., A ovel scheme for fault detectio of reciprocatig compressor valves based o basis pursuit, wave matchig ad support vector machie, Measuremet, Vol.45,No.5,,pp [3]C. Huag, L. L. Huag,.. Ha. Fiacial time series forecastig based o wavelet kerel support vector machie, IEEE, Vol.,,pp [4] X. Shi, J. Zhou, Predictio Residetial House's Damage Effect Near Opepit Agaist Blastig Vibratio Based o SVM with Grid Searchig Method/Geetic Algorithm, Joural of Computatioal & heoretical Naosciece, Vol.,No.,, pp [5] Y. Li, J. Xia, S. Zhag, et al., A efficiet itrusio detectio system based o support vector machies ad gradually feature removal method, Expert Systems with Applicatios, Vol.39,No.,,pp [6] E. Avci, Selectig of the optimal feature subset ad kerel parameters i digital modulatio classificatio by usig hybrid geetic algorithm support vector machies: HGASVM, Expert Systems with Applicatios, Vol.36,No.,9, pp [7] X. Wag, J. We J, Y. Zhag, et al., Real estate price forecastig based o SVM optimized by, Optik - Iteratioal Joural for Light ad Electro Optics, Vol.5,No.5,4,pp [8] W.C. Hog, Chaotic particle swarm optimizatio algorithm i a support vector regressio electric load forecastig model, Eergy Coversio ad Maagemet, Vol.5,No.,9,pp.5-7. [9] M. H. Abdulameer, S. N. H. Sheikh Abdullah, Z. A. Othma, Support Vector Machie Based o Adaptive Acceleratio Particle Swarm Optimizatio, Scietific World Joural, Vol.4,No.,4,pp.-4. [] H. Liu, C. Liu, Y. Huag, Adaptive feature extractio usig sparse codig for machiery fault diagosis, Mechaical Systems & Sigal Processig, Vol.5,No.,,pp [] N. Yu,. Qiu, F. Bi, et al., Image Features Extractio ad Fusio Based o Joit Sparse Represetatio, Selected opics i Sigal Processig IEEE Joural of, Vol.5,No.5,,pp []. Guha, Learig Sparse Represetatios for Huma Actio Recogitio, IEEE rasactios o Patter Aalysis & Machie Itelligece, Vol.34,No.8,, pp [3] R. C. Eberhart, J. Keedy, A ew optimizer usig particle swarm theory, i Proceedigs of the 6th iteratioal symposium o micro machie ad huma sciece, Vol.,No.9,9,pp [4] R. M.Che, C. M. Wag, Proect schedulig heuristics-based stadard for task-resource assigmet i heterogeeous grid, Abstract ad Applied Aalysis, Hidawi Publishig Corporatio, Vol.,. [5] Y. Shi, R. Eberhart, A modified particle swarm optimizer, i: Proceedigs of the 998 IEEE Iteratioal Coferece o Evolutioary Computatio(ICEC 98,998,pp [6] A. Chatteree, P. Siarry, Noliear iertia weight variatio for dyamic adaptatio i particle swarm optimizatio, Computers & Operatios Research, Vol.33,No.3,6,pp [7] J. Lu, H. Hu, Y. Bai, Radial Basis Fuctio Neural Network Based o a Improved Expoetial Decreasig Iertia Weight-Particle Swarm Optimizatio Algorithm for AQI Predictio, Abstract ad Applied Aalysis, 4. E-ISSN: Volume 5, 6