Multi-class Classification Methods of Enhanced LS-TWSVM for Strip Steel Surface Defects
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FoundationItem : Item SponsoredbyNationalNaturalScienceFoundationofChina ( ６１０５０００６ ) Biography : MaoＧxiangCHU , DoctorCandidate ; EＧmail : chu５２ _ ２００４＠１６３com ; ReceivedDate : September１１ , ２０１２ JOURNALOFIRON ANDSTEELRESEARCH , INTERNATIONAL２０１４ , ２１ ( ２ ): １７４Ｇ１８０ MultiＧclassClassification MethodsofEnhancedLSＧTWSVMfor Stri p SteelSurfaceDefects MaoＧxiangCHU １,２ , AnＧnaWANG １ , RongＧfenGONG １,２ , MoSHA １ ( １．CollegeofInformationScienceandEngineering , NortheasternUniversity , Shenyang１１０８１９ , Liaoning , China ; ２．SchoolofElectronicandInformationEngineering , UniversityofScienceandTechnologyLiaoning , Anshan １１４０５１ , Liaoning , China ) Abstract : Consideringstripsteelsurfacedefectsamples , amultiＧclassclassificationmethodwasproposedbasedon enhancedleastsquarestwinsupportvectormachines ( ELSＧTWSVMs ) andbinarytree．Firstly , pruningregionsamples centermethodwithadjustablepruningscalewasusedtoprunedatasamples．This methodcouldreduceclassifier′s trainingtimeandtestingtime．Secondly , ELSＧTWSVM wasproposedtoclassifythedatasamples．Byintroducing errorvariablecontributionparameterandweightparameter , ELSＧTWSVMcouldrestraintheimpactofnoisesamＧ plesandhavebetterclassificationaccuracy．Finally , multiＧclassclassificationalgorithmsofELSＧTWSVMwereproＧ posedbycombiningELSＧTWSVMandcompletebinarytree．SomeexperimentsweremadeontwoＧdimensionaldataＧ setsandstripsteelsurfacedefectdatasets．TheexperimentsshowedthatthemultiＧclassclassification methodsof ELSＧTWSVM hadhigherclassificationspeedandaccuracyforthedatasetswithlargeＧscale , unbalancedandnoisesamples． Keywords : multiＧclassclassification ; leastsquarestwinsupportvectormachine ; errorvariablecontribution ; weight ; binarytree ; stripsteelsurface Inrecentyears , withfurtherdemandforhigher qualityofstripsteelsurface , theresearch ofstrip steelsurfacedefectsdetectionandrecognitionisbeＧ comingwideanddeep [１－３] ．TheproducedsurfaceofＧ tenhasvarioustypesofdefectssuch asscarring , crack , hole , scratch , wrinkle , scale , andsoon．Itis difficulttoclassifythestripsteelsurfacedefectsamＧ ples．However , beinganewkindofpatternrecogniＧ tionmethod , supportvectormachines ( SVMs ) have beenusedeffectively [４－６] ．Wangetal [４] usedthe improvedversionoftheprogressivelyimmediateinＧ ferenceSVM instripsteelsurfacedefectsrecogniＧ tion．ThismethodcanimprovetheabilityofadaptaＧ bilityandaccuracy．Yangetal [５] improvedtheclasＧ sificationaccuracyforthose defects with similar shapesandsmallsamplesizes by meansofthe weightedhierarchicalSVM usedinthesamefield． Amidetal [６] performedthe multiＧclassclassificaＧ tionbasedontheoneＧagainstＧonemethodandadoptＧ edvariouskernelsintheclassificationofthe menＧ tioneddefects．TheproposedmultiＧclassclassificaＧ tionschemewasmoreaccuratethantheconventionＧ almethods． Inthisstudy , a methodwasputforwardto solvethemultiＧclassclassificationforstripsteelsurＧ facedefectsandtoimproveclassificationspeedand accuracy．Firstly , leastsquarestwinsupportvector machines ( LSＧTWSVMs ) wereusedtoclassifythe stripsteelsurfacedefectsamples．Compared with standardSVM , LSＧTWSVMismoresuitableforthe datasets withlargeＧscaleand unbalancedsamples． Secondly , pruningregion samplescenter ( PRSC ) methodwasusedtoprunestripsteelsurfacedefect samples．Thismethodcanreducetheamountofthe datasamplesbyreplacingtheregion datasamples withthecenterpointoftheregiondatasamplesand improvetheclassificationspeed．Inthemeantime , in ordertoensuretheclassificationaccuracyandreduce influenceofpruned datasampleson classification hyperＧplanes , errorvariablecontributionparameter wasaddedtotheLSＧTWSVM．Also , inordertoreＧ straintheimpactofnoisesamples , weightparameＧ
Transcript of Multi-class Classification Methods of Enhanced LS-TWSVM for Strip Steel Surface Defects
FoundationItemItemSponsoredbyNationalNaturalScienceFoundationofChina(６１０５０００６)BiographyMaoＧxiangCHUDoctorCandidate EＧmailchu５２_２００４１６３1049008com ReceivedDateSeptember１１２０１２
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JOURNALOFIRONANDSTEELRESEARCHINTERNATIONAL1049008２０１４２１(２)１７４Ｇ１８０10512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273105127310512731051273
MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
MaoＧxiangCHU１２ AnＧnaWANG１ RongＧfenGONG１２ MoSHA１
(１CollegeofInformationScienceandEngineeringNortheasternUniversityShenyang１１０８１９LiaoningChina２SchoolofElectronicandInformationEngineeringUniversityofScienceandTechnologyLiaoningAnshan１１４０５１LiaoningChina)
AbstractConsideringstripsteelsurfacedefectsamplesamultiＧclassclassificationmethodwasproposedbasedonenhancedleastsquarestwinsupportvectormachines(ELSＧTWSVMs)andbinarytreeFirstlypruningregionsamplescentermethodwithadjustablepruningscalewasusedtoprunedatasamplesThismethodcouldreduceclassifierprimestrainingtimeandtestingtimeSecondlyELSＧTWSVM wasproposedtoclassifythedatasamplesByintroducingerrorvariablecontributionparameterandweightparameterELSＧTWSVMcouldrestraintheimpactofnoisesamＧplesandhavebetterclassificationaccuracyFinallymultiＧclassclassificationalgorithmsofELSＧTWSVM wereproＧposedbycombiningELSＧTWSVMandcompletebinarytreeSomeexperimentsweremadeontwoＧdimensionaldataＧsetsandstripsteelsurfacedefectdatasetsTheexperimentsshowedthatthemultiＧclassclassificationmethodsofELSＧTWSVMhadhigherclassificationspeedandaccuracyforthedatasetswithlargeＧscaleunbalancedandnoisesamplesKeywordsmultiＧclassclassificationleastsquarestwinsupportvectormachineerrorvariablecontributionweightbinarytreestripsteelsurface
InrecentyearswithfurtherdemandforhigherqualityofstripsteelsurfacetheresearchofstripsteelsurfacedefectsdetectionandrecognitionisbeＧcomingwideanddeep[１－３]TheproducedsurfaceofＧtenhasvarioustypesofdefectssuchasscarringcrackholescratchwrinklescaleandsoonItisdifficulttoclassifythestripsteelsurfacedefectsamＧplesHoweverbeinganewkindofpatternrecogniＧtionmethodsupportvectormachines(SVMs)havebeenusedeffectively[４－６]Wangetal1049008[４]usedtheimprovedversionoftheprogressivelyimmediateinＧferenceSVMinstripsteelsurfacedefectsrecogniＧtionThismethodcanimprovetheabilityofadaptaＧbilityandaccuracyYangetal1049008[５]improvedtheclasＧsificationaccuracyforthosedefects with similarshapesandsmallsamplesizesby meansoftheweightedhierarchicalSVM usedinthesamefieldAmidetal1049008[６]performedthemultiＧclassclassificaＧtionbasedontheoneＧagainstＧonemethodandadoptＧedvariouskernelsintheclassificationofthemenＧtioneddefectsTheproposed multiＧclassclassificaＧ
tionschemewasmoreaccuratethantheconventionＧalmethods Inthisstudya method wasputforwardtosolvethemultiＧclassclassificationforstripsteelsurＧfacedefectsandtoimproveclassificationspeedandaccuracyFirstlyleastsquarestwinsupportvectormachines(LSＧTWSVMs)wereusedtoclassifythestripsteelsurfacedefectsamplesCompared withstandardSVMLSＧTWSVMismoresuitableforthedatasetswithlargeＧscaleandunbalancedsamplesSecondlypruningregionsamplescenter (PRSC)methodwasusedtoprunestripsteelsurfacedefectsamplesThismethodcanreducetheamountofthedatasamplesbyreplacingtheregiondatasampleswiththecenterpointoftheregiondatasamplesandimprovetheclassificationspeedInthemeantimeinordertoensuretheclassificationaccuracyandreduceinfluenceofpruneddatasamplesonclassificationhyperＧplaneserrorvariablecontributionparameterwasaddedtotheLSＧTWSVMAlsoinordertoreＧstraintheimpactofnoisesamplesweightparameＧ
terwasaddedtoerrorvariablesComparingwiththeweightmethodinRef1049008[７]theweightedversionofLSＧTWSVMinthisstudyismoreeffectiveonreＧstrainingtheimpactofnoisesamplesandhasbetterclassificationaccuracyFinallythemultiＧclassclasＧsificationforstripsteelsurfacedefectswasrealizedbycombining the enhanced LSＧTWSVM (ELSＧTWSVM)andthebinarytree
１ LSＧTWSVM
LSＧTWSVM[８]isbasedonregularizationtheorytoimprovetwinsupportvectormachines (TWSVM)[９]ComparedwithTWSVMLSＧTWSVM definestheprimalquadraticprogramming problems (QPPs)withequalityconstraintsinsteadofinequalityconＧstraintsCompared with standard SVM[１０]LSＧTWSVM solvestwosmallersized QPPsratherthanonelargeQPPwhichmakesLSＧTSVM workfasterthanstandardSVMAllthesepropertiesmakesurethattheLSＧTWSVMcannotonlybeusedinlargeＧscalesamplesbutalsoreducetrainingtime LSＧTWSVMisdescribedasthefollowingtwoprimalQPPs
minu１γ１
１２ξ１primeξ１＋
c１
２ξ２primeξ２
s1049008t1049008K(XZprime)u１＋e１γ１＝ξ１
－[K(YZprime)u１＋e２γ１]＝e２－ξ２
(１)
minu２γ２
１２η２primeη２＋
c２
２η１primeη１
s1049008t1049008K(YZprime)u２＋e２γ２＝η２
K(XZprime)u２＋e１γ２＝e１－η１
(２)
whereX isinRn１timesd denotesdatasamples matrixinclass＋１andX＝[X１ X２1049018 Xn１ ]primeYisinRn２timesd deＧnotesdatasamplesmatrixinclass－１andY＝[Y１Y２
1049018Yn２]primeZprime＝[XprimeYprime]Kisanydiscretionarykernele１ande２ arevectorsofonesofappropriatedimenＧsionsc１andc２arethetradeＧoffparametersEqs1049008(１)and(２)aretwosmallersized QPPswithequalityconstraintswhicharedifferentfromthoseinstandＧardSVMandTWSVMAfteraseriesofderivationthesolutionsofEqs1049008(１)and(２)canbeobtained
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝－TprimeT＋
１c１
SprimeSaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Tprimee２ (３)
u２
γ２
eacute
euml
ecircecircecircecirc
ugrave
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uacuteuacuteuacuteuacute＝SprimeS＋
１c２
TprimeTaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Sprimee１ (４)
whereS＝[K (XZprime)e１]T＝[K (YZprime)e２]Eqs1049008(３)and(４)determinetwononparallelkernelＧgenＧeratedsurfacesK(xprimeZprime)u１＋γ１＝０andK(xprimeZprime)u２＋γ２＝０ThetwosurfacesrepresentclassificationhyperＧplanesofthenonlinearLSＧTWSVMInfactthelinearclassificationhyperＧplanesxprimew１＋γ１＝０andxprimew２＋γ２＝
０canbeobtainedbyusinglinearkernelK(xprimeZprime)＝xprimeZprimeanddefiningtwoequationsw１＝Zprimeu１andw２＝Zprimeu２Anewdatasamplexisassignedtoaclass＋１or－１dependingonwhichofthetwohyperＧplanesliesclosertoxintermsofperpendiculardistance
２ ELSＧTWSVM２1049008１ PRSCmethod SVMisveryappropriateforsmallＧscaledatasamplesSVMrequireslargeRAMandlongtrainingtimewhenittacklesthelargeＧscaledatasamples[１１]TheLSＧTWSVM cansatisfysomelargeＧscaledatasamplesandreducetrainingtimeButitisnotsuitＧableforlargerＧscaledatasamplesInordertosolvethisproblemPRSCmethodisproposedinthepresＧentstudyThescaleofdatasamplescanbedeＧcreasedandtrainingspeedcanbeimprovedbyprunＧingthedatasamplesInthemeantimethepruningextentcanbeadjustedfreelywhichcanmakeabalＧancebetweenthescaleoftrainingsamplesandclasＧsificationaccuracy ThePRSCmethodsetsapruningregionwitharadiusrAllthedatasamplesinthisregionwillbeprunedandreplacedbythecentralpointofthesedaＧtasamplesSupposingthatsamplesmatrixXrepreＧsentsalargerＧscaledatasetandn＝n１thenPRSCmethodstepsareasfollows Step１SelectadatasampleXcfromthedatasetXandcalculateallEuclideandistancesdk＝Xc－Xk|k＝１２1049018nwhere1048944denotestheL２norm Step２Definethepruningregiondk＜randcalＧculatethenumberliofdatasamplesinthisregion Step３CalculatethecenterpointofalldatasamＧ
plesinthepruningregionAi＝１li
sumdk＜r
XkThenalldaＧ
tasamplesinthepruningregionaredeletedfromthedatasetXandnisupdatedThecenterpointisusedastheonlydatasampleinthepruningregion Step４Repeatthesteps１２and３tillalldaＧtasamplesareprunedFinallythedatasetX willbereplacedbythecenterpointsdatasetA＝[A１A２1049018Am１]primewherem１len１ SimilarlythecenterpointsdatasetB＝[B１B２
1049018Bm２]primecanbeobtainedfromthedatasetYaccordＧingtothePRSCmethodwherem２len２ TheradiusrinPRSCisanadjustablescaleThelargertheradiusristhesmallerthetrainingsampleswillbeafterbeingprunedOfcoursethetrainingspeedwillbefasterButtheclassificationaccuracywillbereducedbecausetoomanydatasamＧplesareprunedThesmallertheradiusristhelarＧ
５７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
gerthetrainingsamplewillbeafterbeingprunedSpeciallytheradiusriszerothatistosaythetrainingsamplewillnotbechangedastrainingtimeandclassificationaccuracywillbethesameasbeＧforeSoareasonabler willgetagoodbalancebeＧtweentrainingtimeandclassificationaccuracySohowtodetermineitisprovidedinthispaperFirstＧlyalldikaresortedintoarraydbysizeSecondlytheradiusrisrepresentedbyIthpercentileofarraydTheIthwillbeselectedaccordingtothedistribuＧtionofrealdatasamplesForexampletheIthcanbeset２５thbyapplyingtheinterquartilerange(IQR) LeastsquaremethodisusedtogetthehyperＧplanesinLSＧTWSVMSotheLSＧTWSVMisverysensitivetoallerrorvariablesPRSCmethodisusedtoprunedatasamplesAndtheerrorvariablesofpruneddatasampleswillbelessthanthoseoforigiＧnaldatasampleswhichwillaffectclassificationacＧcuracyInordertosolvethisproblemerrorvariablecontributiontisaddedontheerrorvariablesξandηinEqs1049008(１)and(２)ofLSＧTWSVMtisadiagonalmatrixtheelementtiiisrepresentedbyliTheerＧrorvariableofthedatasampleAiisimprovedaboutlitimesThematrixformoftisgiven
t＝
l１ ０ 1049018 ００ l２ 1049018 ００ ０ 1049018 ００ ０ 1049018 lm１
eacute
euml
ecircecircecircecircecircecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacuteuacuteuacuteuacuteuacuteuacute
(５)
TheerrorvariablecontributiontensuresthatthepruneddatasamplesalsocontributeerrortotheLSＧTWSVM andreduceinfluenceofpruneddatasamplesonclassificationhyperＧplanesHowtousetintheformulasofLSＧTWSVM willbefullydeＧscribedinthefollowingsection
２1049008２ Weight NoisesampleshavemanyeffectsonclassificaＧtionabilityinSVM[１２]ThatistosaytheclassificaＧtionaccuracywillbereducediftherearesomenoisesamplesindatasamplesSotheproblemalsoexistswhenLSＧTWSVMisusedtoclassifystripsteelsurＧfacedefectsamplesThusweightparametervisaddedintheformulaofLSＧTWSVMtorestraintheimpactofnoisesamplesAweightversionedLSＧTWSＧVM (WLSＧTWSVM)wasproposedinRef1049008[７]InWLSＧTWSVMweightparametersareaddedontheξ２andη１Butthe WLSＧTWSVMislesseffectiveforintercrossingnoisesamplesSotheweightpaＧrametervisaddedontheξ１andη２ThischangeismoreeffectiveonrestrainingtheimpactofinterＧcrossingnoisesamplesThiswillbeprovedinthe
followingexperimentalsection ThebettertheweightalgorithmisthemoreeffectivetheimpactofnoisesamplescanberestrainＧedInRef1049008[１３]theweightparameterisobtainedbytrainingleastsquarevectormachinesandgettingerrordisturbanceinformationTheweightalgorithmformulasaredetermined
vii＝
１ if|dis|leE１
E２－|dis|E２－E１
ifE１le|dis|leE２
１０－４ otherwise
igrave
icirc
iacute
iumliumliumliumliuml
iumliumliumliuml
(６)
s＝IQR
２times０1049008６７４５ors＝１1049008４８３MAD(xi) (７)
whereviiisdiagonalelementofmatrixvdiisanerrorvariablegettingfromtheclassifierwhichisnotaddedwithweightparametersisarobustestimateofthestandarddeviationoftheclassifiererrorvariaＧbleE１andE２canbeset２1049008５and３respectivelybeＧcausetherewillbeveryfewresidualslargerthan２1049008５s fora Gaussian distribution[１３]IQR isthedifferencebetweenthe７５thpercentileand２５thperＧcentileandMADisthemedianabsolutedeviationEq1049008(７)providesamethodtoestimatesInthispaＧpertheweightalgorithmwillbeapplied
２1049008３ EnhancedLSＧTWSVM InordertogetbetterclassificationforstripsteelsurfacedefectstheLSＧTWSVMisimprovedasELSＧTWSVMinthispaperFirstlythePRSCmethodisusedtoprunedatasamplesThenerrorcontributionparametertandweightparametervareintroducedintotheLSＧTWSVM formulaswhichcanimprovetheclassificationspeedandaccuracyItissupposedthattwoclassesofsamplesX andYhavebecomeAandBbyusingPRSCmethodt１andv１ representerrorvariablecontributionparameterandweightparameterforArespectivelyt２andv２
representerrorvariablecontributionparameterandweightparameterforBrespectivelyELSＧTWSVMclassifierisobtainedbysolvingthefollowingpairofquadraticprogrammingproblems
minu１γ１
１２sum
m１
i＝１v１iit１iiξ２
１i＋c１
２summ２
j＝１t２jjξ２
２j
s1049008t1049008K(AiprimeCprime)u１＋γ１＝ξ１ii＝１２1049018m１
K(BjprimeCprime)u１＋γ１＋１＝ξ２j j＝１２1049018m２
(８)
minu２γ２
c２
２summ１
j＝１t１iiη２
１i＋１２sum
m２
j＝１v２jjt２jjη２
２j
s1049008t1049008K(BjprimeCprime)u２＋γ２＝η２jj＝１２1049018m２
－[K(AiprimeCprime)u２＋γ２]＋１＝η１i i＝１２1049018m１
(９)
６７１ JournalofIronandSteelResearchInternational Vol1049008２１
whereCprime＝[AprimeBprime]SubstitutingtheequalityconＧstraintsintotheobjectivefunctionofEq1049008(８)andsettingthegradientofEq1049008(８)withrespecttou１andγ１tozerothematrixformofresultisobtained
K(ACprime)primev１t１K(ACprime)K(ACprime)primev１t１e１
e１primev１t１K(ACprime) e１primev１t１e１
eacute
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ecircecircecircecirc
ugrave
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uacuteuacuteuacuteuacute
u１
γ１
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ecircecircecircecirc
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uacuteuacuteuacuteuacute＋
c１K(BCprime)primet２K(BCprime)K(BCprime)primet２e２
e２primet２K(BCprime) e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
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uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝
－c１K(BCprime)primet２e２
e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
(１０)
DefineE＝[p１K(ACprime)p１e１]andF＝[p２K(BCprime)p２e２]wherev１t１＝p１primep１andt２＝p２primep２SpeＧciallyp１ andp２ arerequiredasdiagonalmatrixThenthesolutionofu１andγ１canbegiven
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝－ １
c１EprimeE＋FprimeF
aelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Fprimep２e２ (１１)
SimilarlyafteraseriesofderivationthesoluＧtionofEq1049008(９)canbeobtained
u２
γ２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝GprimeG＋
１c２
HprimeHaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Gprimep３e１ (１２)
whereG＝[p３K(ACprime)p３e１]H＝[p４K(BCprime)p４e２]t１＝p３primep３v２t２＝p４primep４p３andp４arereＧquiredasdiagonalmatrix TwononparallelhyperＧplanesaregottenfromEqs1049008(１１)and(１２) K(xprimeCprime)u１＋γ１＝０K(xprimeCprime)u２＋γ２＝０ (１３) Anewstripsteelsurfacedefectsamplebelongstoaclassdependingon whichofthetwohyperＧplanesinEq1049008(１３)isclosertothesampleintermsofperpendiculardistance
３ MultiＧclassClassificationofELSＧTWSVM TherearemanykindsofsurfacedefectsduringtheproductionandmanufactureofstripsteelSotheclassificationofthestripsteelsurfacedefectsbeＧlongstomultiＧclassclassificationManymultiＧclassclassificationmethodshavebeenused[１４１５]justlikeoneＧagainstＧoneoneＧagainstＧrestdecisiondirectedacyclicgraphandbinarytreeAmongthesemethＧodsthebinarytreeistheoptimalclassificationmethodThebinarytreehastwotypesofcompletebinarytreeandpartialbinarytreeTheyareshowninFig1049008１EverynodeonthepartialbinarytreeisabinarySVMclassifieroftheoneclassandtheothＧersSoaclassisrecognizedoneverynodeThisstructureofpartialbinarytreeenableseverybinarySVMclassifiertoclassifyunbalanceddatasamplesHowevereverynodeonthecompletebinarytreecarriesequalsplitornearlyequalsplitonalldatasamplesThatistosaythenumberofdatasamplesintheleftclassisnearlythesameasthatinthe
rightclasswhichavoidstheunbalanceddatasamＧplesclassificationInordertoavoidtheunbalancethecompletebinarytreeisselectedtoclassifystripsteelsurfacedefects
(a)Completebinarytree (b)PartialbinarytreeFig1049008１ Binarytree
InFig1049008１alldatasamplesofsixclasseswillbedividedintotwoclassesonnodeSVM１oneclassincludesclasses１２and３andtheotherclassinＧcludestheclasses４５and６ItwillbeeasytoclasＧsifyifthedivisiblefactorsareconsideredamongthesixclassesIngeneraltheseclasseswillbedividedintodifferentclassesifthedifferenceamongtheseclassesislargeSotheclasses１２and３willfallintooneclassandtheclasses４５and６willfallintotheotherclassTheeffectivemethodtotestthedifferＧencesamongallclassescanbefoundinRef1049008[１５]FirstlythecenterpointsofsixclassesarecalculatＧedSecondlythedistancebetweeneverytwocenterpointsaretestedFinallythedifferencesaredeterＧminedbythesedistances SupposethattherearenclassesforstripsteelsurfacedefectsamplesThemultiＧclassclassificationmethodsofELSＧTWSVMcanbeobtainedbycomＧbingtheELSＧTWSVMandthecompletebinarytreeThealgorithmsstepsareasfollows Step１Determinethepruningscaleraccordingtothemethodinsection２1049008１prunethedatasamＧplesbyusingPRSCmethodandgetnclassesofallpruneddatasamplesThenparametertisdeterＧminedforpruneddatasamplesaccordingtoEq1049008(５) Step２SplitequallyornearlyequallynclassesofpruneddatasamplesaccordingtothedistancesforthecenterpointsofnclassesThenconstructtrainingsamplesforallthenodesofthecompletebiＧnarytree Step３TrainthepruneddatasamplesforanodeSVM ofthecompletebinarytreebytheLSＧTWSVM withparametertAndgettheweightpaＧrametervbycalculatingEqs1049008(６)and(７)
７７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
Step４Calculatep１p２p３andp４basedontandv Step５Selecttherationalparametersc１c２
andkernelfunctionK Step６DefineEFGandH Step７CalculateparametersofthetwononparＧallelhyperＧplanesbyEqs1049008(１１)and (１２)soastogettheclassifierforthenode Step８Repeatstepsfrom３to７untilgetallclassifiersofthebinarytree Step９Accordingtothecompletebinarytreecalculateeverynodeclassifieruntilanewdefectdatasamplefallsintoaclassofthenclasses
４ Experiments４1049008１ ErrorvariablecontributionandweightsimulaＧtionexperiments BasedontwoＧdimensional(２ＧD)datasetssomesimulationexperimentsaredonetotesttheeffects
oftandvTheexperimentsareimplementedbyusingMATLAB７1049008１１onaPCwithanIntelP４processor(３1049008０GHz)and２GBRAM FirstlysomeexperimentsareusedtotesttheeffectsofparametertConsideringa２ＧDdatasetwithtwoclassesofdatasamplesPRSC methodisusedtoprunethedatasampleswithscalerThentheELSＧTWSVMclassifierwithlinearkernelfunctionisadoptedtoclassifythedatasamplesTheresultsareshowninFig1049008２ItiseasytoseethattheclassifiＧcationhyperＧplanesoforiginaldatasamples(r＝０)aresimilarwiththoseofELSＧTWSVMusingtheerＧrorvariablecontributiont(rne０)butaredifferentfromthoseofnotusingerrorvariablecontributiont(rne０)SotheerrorvariablecontributionparameterreducedthechangeoftheclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamples Thensomeexperimentsareusedtotesttheability
(a)r＝０ (b)rne０t (c)rne０Fig1049008２ ClassificationresultsofELSＧTWSVMin２ＧDspace
ofrestrainingtheimpactofnoisesamplesbyusingparametervConsideringa２ＧDdatasetwithinterＧcrossingnoisesamplesWLSＧTWSVM and ELSＧTWSVMareadoptedforclassificationexperimentsrespectivelyTheresultsareshowninFig1049008３ItiseasytoseethattheclassificationhyperＧplanesofWLSＧTWSVM arenotasgoodasthoseofELSＧTWSVMThisisbecauseweightparameterintheELSＧTWSVMismorereasonablethanthatintheWLSＧTWSVM
４1049008２ Surfacedefectsclassificationapplicationexperiments BasedonthestripsteelsurfacedefectdatasetsofaChineselargesteelplantsomeapplicationexＧ
perimentsaremadetodemonstratetheperformanceofELSＧTWSVMAlargenumberofimagesofthestrip
(a)WLSＧTWSVM (b)ELSＧTWSVMFig1049008３ Classificationresultsoftwoclassifiersin２ＧDspace
８７１ JournalofIronandSteelResearchInternational Vol1049008２１
steelsurfacedefectsarecollectedformthedatasetsSixkindsoftypicaldefectimagesareselectedTheyarescarringcrackholescratchwrinkle andscaleasshowninFig1049008４ Itisimportanttoextractfeaturesfromthestripsteelsurface defectimages before classificationThesefeaturesvectorsmakeupofthedatasampleswhichwillbeclassifiedbySVMInthisstudy４３featuresareextractedfromstripsteelsurfacedefect
imagesThesefeaturesreflectdefectinformationintermsofgreyfeaturesgeometricalfeaturestexturＧalfeaturesand morphologicalfeatures[１６]Inthemeantime４３featuresarereducedbyusingprinciＧpalcomponentanalysis(PCA)[１７]and３３featuresareobtainedFinallythese３３featuresareputtoＧgethertoforma３３ＧdimensionalvectorwhichreＧpresentsastripsteelsurfacedefectsample Inthispaper２３４０imagesareselectedasexperＧ
(a)Scarring (b)Crack (c)Hole (d)Scratch (e)Wrinkle (f)ScaleFig1049008４ Imagesofsixsurfacedefects
imentalsamplesfromwhich３３dimensionsfeaturesareextractedasthesixclassesofdatasamplesThenthedatasamplesarerandomlydividedintotrainingsetandtestingsetInthemeantimethecenterpointsofsixclassesarecalculatedandthedistancebetweeneverytwocenterpointsaretestedAccordingtothedistancetheserialnumberofsixclassesisdeterminedandisshowninTable１Thetrainingsamplesare９０ ofthetotalandare２１０６Thetestingsamplesare１０ofthetotalandare２３４ ThemultiＧclassclassifiersofELSＧTWSVMare
Table１ Differentsurfacedefectdatasamples
Defecttype
Classcode
Numberoftrainingsamples
Numberoftestingsamples
Scarring １ ４０５ ４５Crack ２ ３７８ ４２Hole ３ ３２４ ３６
Scratch ４ ３５１ ３９Wrinkle ５ ３７８ ４２Scale ６ ２７０ ３０
usedtoclassifythestripsteelsurfacedefectsamplesinTable１Radialbasisfunctionisusedaskernelfunctionanditsparametersareobtainedfrom２－２０
to２４Parametersc１andc２arealsoobtainedfrom２－２０to２４ FirstlyaimingatdifferentpruningratiossometestingexperimentsaremadeandtheresultsareshowninTable２ThepruningratioistheratioofthenumberofpruneddatasamplestothatoftheoriginaldatasamplesForexampletheratiois０1049008３０thatistosay３０ ofdatasamplesareprunedfromthe２１０６trainingsamplesItiseasytoseethatthehigherthepruningratioistheshorterthe
Table２ Testingresultswithdifferentpruningratios
Pruningratio Trainingtimes Testingtimes Accuracy
０ ３1049008６１４３ ０1049008３６６７ ９７1049008０１０1049008３０ １1049008６５５５ ０1049008２５５１ ９６1049008１５０1049008５５ ０1049008６７１３ ０1049008１７２０ ８８1049008４６０1049008７５ ０1049008１３４０ ０1049008０８７８ ７５1049008６４０1049008８５ ０1049008０６１８ ０1049008０５６２ ６１1049008９７
９７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
References
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[１０] CCortesVVapnikMachLearn２０(１９９５)２７３Ｇ２９７[１１] Y1049008MWenY1049008NWangB1049008LLuY1049008MChenComputSci３６
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UnivNatSci３３(２０１２)２６７Ｇ２７０[１７] E1049008YHuHWangJ1049008HWangSLuLTianinIEEE
InternationalConferenceonComputerScienceandAutomationEngineeringIEEEShanghai２０１１pp３８８Ｇ３９０
０８１ JournalofIronandSteelResearchInternational Vol1049008２１
terwasaddedtoerrorvariablesComparingwiththeweightmethodinRef1049008[７]theweightedversionofLSＧTWSVMinthisstudyismoreeffectiveonreＧstrainingtheimpactofnoisesamplesandhasbetterclassificationaccuracyFinallythemultiＧclassclasＧsificationforstripsteelsurfacedefectswasrealizedbycombining the enhanced LSＧTWSVM (ELSＧTWSVM)andthebinarytree
１ LSＧTWSVM
LSＧTWSVM[８]isbasedonregularizationtheorytoimprovetwinsupportvectormachines (TWSVM)[９]ComparedwithTWSVMLSＧTWSVM definestheprimalquadraticprogramming problems (QPPs)withequalityconstraintsinsteadofinequalityconＧstraintsCompared with standard SVM[１０]LSＧTWSVM solvestwosmallersized QPPsratherthanonelargeQPPwhichmakesLSＧTSVM workfasterthanstandardSVMAllthesepropertiesmakesurethattheLSＧTWSVMcannotonlybeusedinlargeＧscalesamplesbutalsoreducetrainingtime LSＧTWSVMisdescribedasthefollowingtwoprimalQPPs
minu１γ１
１２ξ１primeξ１＋
c１
２ξ２primeξ２
s1049008t1049008K(XZprime)u１＋e１γ１＝ξ１
－[K(YZprime)u１＋e２γ１]＝e２－ξ２
(１)
minu２γ２
１２η２primeη２＋
c２
２η１primeη１
s1049008t1049008K(YZprime)u２＋e２γ２＝η２
K(XZprime)u２＋e１γ２＝e１－η１
(２)
whereX isinRn１timesd denotesdatasamples matrixinclass＋１andX＝[X１ X２1049018 Xn１ ]primeYisinRn２timesd deＧnotesdatasamplesmatrixinclass－１andY＝[Y１Y２
1049018Yn２]primeZprime＝[XprimeYprime]Kisanydiscretionarykernele１ande２ arevectorsofonesofappropriatedimenＧsionsc１andc２arethetradeＧoffparametersEqs1049008(１)and(２)aretwosmallersized QPPswithequalityconstraintswhicharedifferentfromthoseinstandＧardSVMandTWSVMAfteraseriesofderivationthesolutionsofEqs1049008(１)and(２)canbeobtained
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝－TprimeT＋
１c１
SprimeSaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Tprimee２ (３)
u２
γ２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝SprimeS＋
１c２
TprimeTaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Sprimee１ (４)
whereS＝[K (XZprime)e１]T＝[K (YZprime)e２]Eqs1049008(３)and(４)determinetwononparallelkernelＧgenＧeratedsurfacesK(xprimeZprime)u１＋γ１＝０andK(xprimeZprime)u２＋γ２＝０ThetwosurfacesrepresentclassificationhyperＧplanesofthenonlinearLSＧTWSVMInfactthelinearclassificationhyperＧplanesxprimew１＋γ１＝０andxprimew２＋γ２＝
０canbeobtainedbyusinglinearkernelK(xprimeZprime)＝xprimeZprimeanddefiningtwoequationsw１＝Zprimeu１andw２＝Zprimeu２Anewdatasamplexisassignedtoaclass＋１or－１dependingonwhichofthetwohyperＧplanesliesclosertoxintermsofperpendiculardistance
２ ELSＧTWSVM２1049008１ PRSCmethod SVMisveryappropriateforsmallＧscaledatasamplesSVMrequireslargeRAMandlongtrainingtimewhenittacklesthelargeＧscaledatasamples[１１]TheLSＧTWSVM cansatisfysomelargeＧscaledatasamplesandreducetrainingtimeButitisnotsuitＧableforlargerＧscaledatasamplesInordertosolvethisproblemPRSCmethodisproposedinthepresＧentstudyThescaleofdatasamplescanbedeＧcreasedandtrainingspeedcanbeimprovedbyprunＧingthedatasamplesInthemeantimethepruningextentcanbeadjustedfreelywhichcanmakeabalＧancebetweenthescaleoftrainingsamplesandclasＧsificationaccuracy ThePRSCmethodsetsapruningregionwitharadiusrAllthedatasamplesinthisregionwillbeprunedandreplacedbythecentralpointofthesedaＧtasamplesSupposingthatsamplesmatrixXrepreＧsentsalargerＧscaledatasetandn＝n１thenPRSCmethodstepsareasfollows Step１SelectadatasampleXcfromthedatasetXandcalculateallEuclideandistancesdk＝Xc－Xk|k＝１２1049018nwhere1048944denotestheL２norm Step２Definethepruningregiondk＜randcalＧculatethenumberliofdatasamplesinthisregion Step３CalculatethecenterpointofalldatasamＧ
plesinthepruningregionAi＝１li
sumdk＜r
XkThenalldaＧ
tasamplesinthepruningregionaredeletedfromthedatasetXandnisupdatedThecenterpointisusedastheonlydatasampleinthepruningregion Step４Repeatthesteps１２and３tillalldaＧtasamplesareprunedFinallythedatasetX willbereplacedbythecenterpointsdatasetA＝[A１A２1049018Am１]primewherem１len１ SimilarlythecenterpointsdatasetB＝[B１B２
1049018Bm２]primecanbeobtainedfromthedatasetYaccordＧingtothePRSCmethodwherem２len２ TheradiusrinPRSCisanadjustablescaleThelargertheradiusristhesmallerthetrainingsampleswillbeafterbeingprunedOfcoursethetrainingspeedwillbefasterButtheclassificationaccuracywillbereducedbecausetoomanydatasamＧplesareprunedThesmallertheradiusristhelarＧ
５７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
gerthetrainingsamplewillbeafterbeingprunedSpeciallytheradiusriszerothatistosaythetrainingsamplewillnotbechangedastrainingtimeandclassificationaccuracywillbethesameasbeＧforeSoareasonabler willgetagoodbalancebeＧtweentrainingtimeandclassificationaccuracySohowtodetermineitisprovidedinthispaperFirstＧlyalldikaresortedintoarraydbysizeSecondlytheradiusrisrepresentedbyIthpercentileofarraydTheIthwillbeselectedaccordingtothedistribuＧtionofrealdatasamplesForexampletheIthcanbeset２５thbyapplyingtheinterquartilerange(IQR) LeastsquaremethodisusedtogetthehyperＧplanesinLSＧTWSVMSotheLSＧTWSVMisverysensitivetoallerrorvariablesPRSCmethodisusedtoprunedatasamplesAndtheerrorvariablesofpruneddatasampleswillbelessthanthoseoforigiＧnaldatasampleswhichwillaffectclassificationacＧcuracyInordertosolvethisproblemerrorvariablecontributiontisaddedontheerrorvariablesξandηinEqs1049008(１)and(２)ofLSＧTWSVMtisadiagonalmatrixtheelementtiiisrepresentedbyliTheerＧrorvariableofthedatasampleAiisimprovedaboutlitimesThematrixformoftisgiven
t＝
l１ ０ 1049018 ００ l２ 1049018 ００ ０ 1049018 ００ ０ 1049018 lm１
eacute
euml
ecircecircecircecircecircecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacuteuacuteuacuteuacuteuacuteuacute
(５)
TheerrorvariablecontributiontensuresthatthepruneddatasamplesalsocontributeerrortotheLSＧTWSVM andreduceinfluenceofpruneddatasamplesonclassificationhyperＧplanesHowtousetintheformulasofLSＧTWSVM willbefullydeＧscribedinthefollowingsection
２1049008２ Weight NoisesampleshavemanyeffectsonclassificaＧtionabilityinSVM[１２]ThatistosaytheclassificaＧtionaccuracywillbereducediftherearesomenoisesamplesindatasamplesSotheproblemalsoexistswhenLSＧTWSVMisusedtoclassifystripsteelsurＧfacedefectsamplesThusweightparametervisaddedintheformulaofLSＧTWSVMtorestraintheimpactofnoisesamplesAweightversionedLSＧTWSＧVM (WLSＧTWSVM)wasproposedinRef1049008[７]InWLSＧTWSVMweightparametersareaddedontheξ２andη１Butthe WLSＧTWSVMislesseffectiveforintercrossingnoisesamplesSotheweightpaＧrametervisaddedontheξ１andη２ThischangeismoreeffectiveonrestrainingtheimpactofinterＧcrossingnoisesamplesThiswillbeprovedinthe
followingexperimentalsection ThebettertheweightalgorithmisthemoreeffectivetheimpactofnoisesamplescanberestrainＧedInRef1049008[１３]theweightparameterisobtainedbytrainingleastsquarevectormachinesandgettingerrordisturbanceinformationTheweightalgorithmformulasaredetermined
vii＝
１ if|dis|leE１
E２－|dis|E２－E１
ifE１le|dis|leE２
１０－４ otherwise
igrave
icirc
iacute
iumliumliumliumliuml
iumliumliumliuml
(６)
s＝IQR
２times０1049008６７４５ors＝１1049008４８３MAD(xi) (７)
whereviiisdiagonalelementofmatrixvdiisanerrorvariablegettingfromtheclassifierwhichisnotaddedwithweightparametersisarobustestimateofthestandarddeviationoftheclassifiererrorvariaＧbleE１andE２canbeset２1049008５and３respectivelybeＧcausetherewillbeveryfewresidualslargerthan２1049008５s fora Gaussian distribution[１３]IQR isthedifferencebetweenthe７５thpercentileand２５thperＧcentileandMADisthemedianabsolutedeviationEq1049008(７)providesamethodtoestimatesInthispaＧpertheweightalgorithmwillbeapplied
２1049008３ EnhancedLSＧTWSVM InordertogetbetterclassificationforstripsteelsurfacedefectstheLSＧTWSVMisimprovedasELSＧTWSVMinthispaperFirstlythePRSCmethodisusedtoprunedatasamplesThenerrorcontributionparametertandweightparametervareintroducedintotheLSＧTWSVM formulaswhichcanimprovetheclassificationspeedandaccuracyItissupposedthattwoclassesofsamplesX andYhavebecomeAandBbyusingPRSCmethodt１andv１ representerrorvariablecontributionparameterandweightparameterforArespectivelyt２andv２
representerrorvariablecontributionparameterandweightparameterforBrespectivelyELSＧTWSVMclassifierisobtainedbysolvingthefollowingpairofquadraticprogrammingproblems
minu１γ１
１２sum
m１
i＝１v１iit１iiξ２
１i＋c１
２summ２
j＝１t２jjξ２
２j
s1049008t1049008K(AiprimeCprime)u１＋γ１＝ξ１ii＝１２1049018m１
K(BjprimeCprime)u１＋γ１＋１＝ξ２j j＝１２1049018m２
(８)
minu２γ２
c２
２summ１
j＝１t１iiη２
１i＋１２sum
m２
j＝１v２jjt２jjη２
２j
s1049008t1049008K(BjprimeCprime)u２＋γ２＝η２jj＝１２1049018m２
－[K(AiprimeCprime)u２＋γ２]＋１＝η１i i＝１２1049018m１
(９)
６７１ JournalofIronandSteelResearchInternational Vol1049008２１
whereCprime＝[AprimeBprime]SubstitutingtheequalityconＧstraintsintotheobjectivefunctionofEq1049008(８)andsettingthegradientofEq1049008(８)withrespecttou１andγ１tozerothematrixformofresultisobtained
K(ACprime)primev１t１K(ACprime)K(ACprime)primev１t１e１
e１primev１t１K(ACprime) e１primev１t１e１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＋
c１K(BCprime)primet２K(BCprime)K(BCprime)primet２e２
e２primet２K(BCprime) e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝
－c１K(BCprime)primet２e２
e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
(１０)
DefineE＝[p１K(ACprime)p１e１]andF＝[p２K(BCprime)p２e２]wherev１t１＝p１primep１andt２＝p２primep２SpeＧciallyp１ andp２ arerequiredasdiagonalmatrixThenthesolutionofu１andγ１canbegiven
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝－ １
c１EprimeE＋FprimeF
aelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Fprimep２e２ (１１)
SimilarlyafteraseriesofderivationthesoluＧtionofEq1049008(９)canbeobtained
u２
γ２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝GprimeG＋
１c２
HprimeHaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Gprimep３e１ (１２)
whereG＝[p３K(ACprime)p３e１]H＝[p４K(BCprime)p４e２]t１＝p３primep３v２t２＝p４primep４p３andp４arereＧquiredasdiagonalmatrix TwononparallelhyperＧplanesaregottenfromEqs1049008(１１)and(１２) K(xprimeCprime)u１＋γ１＝０K(xprimeCprime)u２＋γ２＝０ (１３) Anewstripsteelsurfacedefectsamplebelongstoaclassdependingon whichofthetwohyperＧplanesinEq1049008(１３)isclosertothesampleintermsofperpendiculardistance
３ MultiＧclassClassificationofELSＧTWSVM TherearemanykindsofsurfacedefectsduringtheproductionandmanufactureofstripsteelSotheclassificationofthestripsteelsurfacedefectsbeＧlongstomultiＧclassclassificationManymultiＧclassclassificationmethodshavebeenused[１４１５]justlikeoneＧagainstＧoneoneＧagainstＧrestdecisiondirectedacyclicgraphandbinarytreeAmongthesemethＧodsthebinarytreeistheoptimalclassificationmethodThebinarytreehastwotypesofcompletebinarytreeandpartialbinarytreeTheyareshowninFig1049008１EverynodeonthepartialbinarytreeisabinarySVMclassifieroftheoneclassandtheothＧersSoaclassisrecognizedoneverynodeThisstructureofpartialbinarytreeenableseverybinarySVMclassifiertoclassifyunbalanceddatasamplesHowevereverynodeonthecompletebinarytreecarriesequalsplitornearlyequalsplitonalldatasamplesThatistosaythenumberofdatasamplesintheleftclassisnearlythesameasthatinthe
rightclasswhichavoidstheunbalanceddatasamＧplesclassificationInordertoavoidtheunbalancethecompletebinarytreeisselectedtoclassifystripsteelsurfacedefects
(a)Completebinarytree (b)PartialbinarytreeFig1049008１ Binarytree
InFig1049008１alldatasamplesofsixclasseswillbedividedintotwoclassesonnodeSVM１oneclassincludesclasses１２and３andtheotherclassinＧcludestheclasses４５and６ItwillbeeasytoclasＧsifyifthedivisiblefactorsareconsideredamongthesixclassesIngeneraltheseclasseswillbedividedintodifferentclassesifthedifferenceamongtheseclassesislargeSotheclasses１２and３willfallintooneclassandtheclasses４５and６willfallintotheotherclassTheeffectivemethodtotestthedifferＧencesamongallclassescanbefoundinRef1049008[１５]FirstlythecenterpointsofsixclassesarecalculatＧedSecondlythedistancebetweeneverytwocenterpointsaretestedFinallythedifferencesaredeterＧminedbythesedistances SupposethattherearenclassesforstripsteelsurfacedefectsamplesThemultiＧclassclassificationmethodsofELSＧTWSVMcanbeobtainedbycomＧbingtheELSＧTWSVMandthecompletebinarytreeThealgorithmsstepsareasfollows Step１Determinethepruningscaleraccordingtothemethodinsection２1049008１prunethedatasamＧplesbyusingPRSCmethodandgetnclassesofallpruneddatasamplesThenparametertisdeterＧminedforpruneddatasamplesaccordingtoEq1049008(５) Step２SplitequallyornearlyequallynclassesofpruneddatasamplesaccordingtothedistancesforthecenterpointsofnclassesThenconstructtrainingsamplesforallthenodesofthecompletebiＧnarytree Step３TrainthepruneddatasamplesforanodeSVM ofthecompletebinarytreebytheLSＧTWSVM withparametertAndgettheweightpaＧrametervbycalculatingEqs1049008(６)and(７)
７７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
Step４Calculatep１p２p３andp４basedontandv Step５Selecttherationalparametersc１c２
andkernelfunctionK Step６DefineEFGandH Step７CalculateparametersofthetwononparＧallelhyperＧplanesbyEqs1049008(１１)and (１２)soastogettheclassifierforthenode Step８Repeatstepsfrom３to７untilgetallclassifiersofthebinarytree Step９Accordingtothecompletebinarytreecalculateeverynodeclassifieruntilanewdefectdatasamplefallsintoaclassofthenclasses
４ Experiments４1049008１ ErrorvariablecontributionandweightsimulaＧtionexperiments BasedontwoＧdimensional(２ＧD)datasetssomesimulationexperimentsaredonetotesttheeffects
oftandvTheexperimentsareimplementedbyusingMATLAB７1049008１１onaPCwithanIntelP４processor(３1049008０GHz)and２GBRAM FirstlysomeexperimentsareusedtotesttheeffectsofparametertConsideringa２ＧDdatasetwithtwoclassesofdatasamplesPRSC methodisusedtoprunethedatasampleswithscalerThentheELSＧTWSVMclassifierwithlinearkernelfunctionisadoptedtoclassifythedatasamplesTheresultsareshowninFig1049008２ItiseasytoseethattheclassifiＧcationhyperＧplanesoforiginaldatasamples(r＝０)aresimilarwiththoseofELSＧTWSVMusingtheerＧrorvariablecontributiont(rne０)butaredifferentfromthoseofnotusingerrorvariablecontributiont(rne０)SotheerrorvariablecontributionparameterreducedthechangeoftheclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamples Thensomeexperimentsareusedtotesttheability
(a)r＝０ (b)rne０t (c)rne０Fig1049008２ ClassificationresultsofELSＧTWSVMin２ＧDspace
ofrestrainingtheimpactofnoisesamplesbyusingparametervConsideringa２ＧDdatasetwithinterＧcrossingnoisesamplesWLSＧTWSVM and ELSＧTWSVMareadoptedforclassificationexperimentsrespectivelyTheresultsareshowninFig1049008３ItiseasytoseethattheclassificationhyperＧplanesofWLSＧTWSVM arenotasgoodasthoseofELSＧTWSVMThisisbecauseweightparameterintheELSＧTWSVMismorereasonablethanthatintheWLSＧTWSVM
４1049008２ Surfacedefectsclassificationapplicationexperiments BasedonthestripsteelsurfacedefectdatasetsofaChineselargesteelplantsomeapplicationexＧ
perimentsaremadetodemonstratetheperformanceofELSＧTWSVMAlargenumberofimagesofthestrip
(a)WLSＧTWSVM (b)ELSＧTWSVMFig1049008３ Classificationresultsoftwoclassifiersin２ＧDspace
８７１ JournalofIronandSteelResearchInternational Vol1049008２１
steelsurfacedefectsarecollectedformthedatasetsSixkindsoftypicaldefectimagesareselectedTheyarescarringcrackholescratchwrinkle andscaleasshowninFig1049008４ Itisimportanttoextractfeaturesfromthestripsteelsurface defectimages before classificationThesefeaturesvectorsmakeupofthedatasampleswhichwillbeclassifiedbySVMInthisstudy４３featuresareextractedfromstripsteelsurfacedefect
imagesThesefeaturesreflectdefectinformationintermsofgreyfeaturesgeometricalfeaturestexturＧalfeaturesand morphologicalfeatures[１６]Inthemeantime４３featuresarereducedbyusingprinciＧpalcomponentanalysis(PCA)[１７]and３３featuresareobtainedFinallythese３３featuresareputtoＧgethertoforma３３ＧdimensionalvectorwhichreＧpresentsastripsteelsurfacedefectsample Inthispaper２３４０imagesareselectedasexperＧ
(a)Scarring (b)Crack (c)Hole (d)Scratch (e)Wrinkle (f)ScaleFig1049008４ Imagesofsixsurfacedefects
imentalsamplesfromwhich３３dimensionsfeaturesareextractedasthesixclassesofdatasamplesThenthedatasamplesarerandomlydividedintotrainingsetandtestingsetInthemeantimethecenterpointsofsixclassesarecalculatedandthedistancebetweeneverytwocenterpointsaretestedAccordingtothedistancetheserialnumberofsixclassesisdeterminedandisshowninTable１Thetrainingsamplesare９０ ofthetotalandare２１０６Thetestingsamplesare１０ofthetotalandare２３４ ThemultiＧclassclassifiersofELSＧTWSVMare
Table１ Differentsurfacedefectdatasamples
Defecttype
Classcode
Numberoftrainingsamples
Numberoftestingsamples
Scarring １ ４０５ ４５Crack ２ ３７８ ４２Hole ３ ３２４ ３６
Scratch ４ ３５１ ３９Wrinkle ５ ３７８ ４２Scale ６ ２７０ ３０
usedtoclassifythestripsteelsurfacedefectsamplesinTable１Radialbasisfunctionisusedaskernelfunctionanditsparametersareobtainedfrom２－２０
to２４Parametersc１andc２arealsoobtainedfrom２－２０to２４ FirstlyaimingatdifferentpruningratiossometestingexperimentsaremadeandtheresultsareshowninTable２ThepruningratioistheratioofthenumberofpruneddatasamplestothatoftheoriginaldatasamplesForexampletheratiois０1049008３０thatistosay３０ ofdatasamplesareprunedfromthe２１０６trainingsamplesItiseasytoseethatthehigherthepruningratioistheshorterthe
Table２ Testingresultswithdifferentpruningratios
Pruningratio Trainingtimes Testingtimes Accuracy
０ ３1049008６１４３ ０1049008３６６７ ９７1049008０１０1049008３０ １1049008６５５５ ０1049008２５５１ ９６1049008１５０1049008５５ ０1049008６７１３ ０1049008１７２０ ８８1049008４６０1049008７５ ０1049008１３４０ ０1049008０８７８ ７５1049008６４０1049008８５ ０1049008０６１８ ０1049008０５６２ ６１1049008９７
９７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
References
[１] X1049008JDuanF1049008JDuanF1049008FHaninInternationalConferＧenceonControlAutomationandSystemsEngineeringIEEESingapore２０１１pp１Ｇ４
[２] Y1049008HYanK1049008CSongZ1049008TXingX1049008HFenginThirdInＧternationalConferenceon MeasuringTechnologyand MechaＧtronicsAutomationIEEEShanghai２０１１pp９５８Ｇ９６１
[３] L1049008A1049008OMartinsF1049008L1049008CP1048929duaP1049008E1049008MAlmeidain３６thAnnualConferenceonIEEEIndustrialElectronicsSocietyIEEEGlendaleAZ２０１０pp１０８１Ｇ１０８６
[４] C1049008MWangY1049008HYanS1049008LChenY1049008LHanJNortheastUnivNatSci２８(２００７)４１０Ｇ４１３
[５] Q1049008YYangQLiJJinTransNAMRISME３７ (２００９)３７１Ｇ３７８
[６] EAmidS1049008RAghdamHAmindavarProcWorldAcadSciEngTech(２０１２)No1049008６７１３０３Ｇ１３０７
[７] JChenG1049008RJiinThe２ndInternationalConferenceonComＧputerandAutomationEngineeringIEEESingapore２０１０pp２４２Ｇ２４６
[８] M1049008AKumarMGopalExpertSysAppl３６(２００９)７５３５Ｇ７５４３
[９] JayadevaRKhemchandniSChandraIEEETransPatternAnalMachIntell２９(２００７)９０５Ｇ９１０
[１０] CCortesVVapnikMachLearn２０(１９９５)２７３Ｇ２９７[１１] Y1049008MWenY1049008NWangB1049008LLuY1049008MChenComputSci３６
(２００９)No1049008７２０Ｇ２５３１[１２] C1049008FLinS1049008DWangIEEETransNeuralNetw１３(２００２)
４６４Ｇ４７１[１３] J1049008A1049008KSuykensJ1049008DBrabanterLLukasJVandewalle
Neurocomputing４８(２００２)８５Ｇ１０５[１４] B1049008CFanJ1049008YWangY1049008MBoComputEngDes３１(２０１０)
２８２３Ｇ２８２５[１５] L1049008MLiuA1049008NWangMShaF1049008YZhaoJIronSteel
ResInt１８(２０１１)No1049008１０１７Ｇ２３３３[１６] YZhangW1049008WLiuZ1049008TXingY1049008HYanJNortheast
UnivNatSci３３(２０１２)２６７Ｇ２７０[１７] E1049008YHuHWangJ1049008HWangSLuLTianinIEEE
InternationalConferenceonComputerScienceandAutomationEngineeringIEEEShanghai２０１１pp３８８Ｇ３９０
０８１ JournalofIronandSteelResearchInternational Vol1049008２１
gerthetrainingsamplewillbeafterbeingprunedSpeciallytheradiusriszerothatistosaythetrainingsamplewillnotbechangedastrainingtimeandclassificationaccuracywillbethesameasbeＧforeSoareasonabler willgetagoodbalancebeＧtweentrainingtimeandclassificationaccuracySohowtodetermineitisprovidedinthispaperFirstＧlyalldikaresortedintoarraydbysizeSecondlytheradiusrisrepresentedbyIthpercentileofarraydTheIthwillbeselectedaccordingtothedistribuＧtionofrealdatasamplesForexampletheIthcanbeset２５thbyapplyingtheinterquartilerange(IQR) LeastsquaremethodisusedtogetthehyperＧplanesinLSＧTWSVMSotheLSＧTWSVMisverysensitivetoallerrorvariablesPRSCmethodisusedtoprunedatasamplesAndtheerrorvariablesofpruneddatasampleswillbelessthanthoseoforigiＧnaldatasampleswhichwillaffectclassificationacＧcuracyInordertosolvethisproblemerrorvariablecontributiontisaddedontheerrorvariablesξandηinEqs1049008(１)and(２)ofLSＧTWSVMtisadiagonalmatrixtheelementtiiisrepresentedbyliTheerＧrorvariableofthedatasampleAiisimprovedaboutlitimesThematrixformoftisgiven
t＝
l１ ０ 1049018 ００ l２ 1049018 ００ ０ 1049018 ００ ０ 1049018 lm１
eacute
euml
ecircecircecircecircecircecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacuteuacuteuacuteuacuteuacuteuacute
(５)
TheerrorvariablecontributiontensuresthatthepruneddatasamplesalsocontributeerrortotheLSＧTWSVM andreduceinfluenceofpruneddatasamplesonclassificationhyperＧplanesHowtousetintheformulasofLSＧTWSVM willbefullydeＧscribedinthefollowingsection
２1049008２ Weight NoisesampleshavemanyeffectsonclassificaＧtionabilityinSVM[１２]ThatistosaytheclassificaＧtionaccuracywillbereducediftherearesomenoisesamplesindatasamplesSotheproblemalsoexistswhenLSＧTWSVMisusedtoclassifystripsteelsurＧfacedefectsamplesThusweightparametervisaddedintheformulaofLSＧTWSVMtorestraintheimpactofnoisesamplesAweightversionedLSＧTWSＧVM (WLSＧTWSVM)wasproposedinRef1049008[７]InWLSＧTWSVMweightparametersareaddedontheξ２andη１Butthe WLSＧTWSVMislesseffectiveforintercrossingnoisesamplesSotheweightpaＧrametervisaddedontheξ１andη２ThischangeismoreeffectiveonrestrainingtheimpactofinterＧcrossingnoisesamplesThiswillbeprovedinthe
followingexperimentalsection ThebettertheweightalgorithmisthemoreeffectivetheimpactofnoisesamplescanberestrainＧedInRef1049008[１３]theweightparameterisobtainedbytrainingleastsquarevectormachinesandgettingerrordisturbanceinformationTheweightalgorithmformulasaredetermined
vii＝
１ if|dis|leE１
E２－|dis|E２－E１
ifE１le|dis|leE２
１０－４ otherwise
igrave
icirc
iacute
iumliumliumliumliuml
iumliumliumliuml
(６)
s＝IQR
２times０1049008６７４５ors＝１1049008４８３MAD(xi) (７)
whereviiisdiagonalelementofmatrixvdiisanerrorvariablegettingfromtheclassifierwhichisnotaddedwithweightparametersisarobustestimateofthestandarddeviationoftheclassifiererrorvariaＧbleE１andE２canbeset２1049008５and３respectivelybeＧcausetherewillbeveryfewresidualslargerthan２1049008５s fora Gaussian distribution[１３]IQR isthedifferencebetweenthe７５thpercentileand２５thperＧcentileandMADisthemedianabsolutedeviationEq1049008(７)providesamethodtoestimatesInthispaＧpertheweightalgorithmwillbeapplied
２1049008３ EnhancedLSＧTWSVM InordertogetbetterclassificationforstripsteelsurfacedefectstheLSＧTWSVMisimprovedasELSＧTWSVMinthispaperFirstlythePRSCmethodisusedtoprunedatasamplesThenerrorcontributionparametertandweightparametervareintroducedintotheLSＧTWSVM formulaswhichcanimprovetheclassificationspeedandaccuracyItissupposedthattwoclassesofsamplesX andYhavebecomeAandBbyusingPRSCmethodt１andv１ representerrorvariablecontributionparameterandweightparameterforArespectivelyt２andv２
representerrorvariablecontributionparameterandweightparameterforBrespectivelyELSＧTWSVMclassifierisobtainedbysolvingthefollowingpairofquadraticprogrammingproblems
minu１γ１
１２sum
m１
i＝１v１iit１iiξ２
１i＋c１
２summ２
j＝１t２jjξ２
２j
s1049008t1049008K(AiprimeCprime)u１＋γ１＝ξ１ii＝１２1049018m１
K(BjprimeCprime)u１＋γ１＋１＝ξ２j j＝１２1049018m２
(８)
minu２γ２
c２
２summ１
j＝１t１iiη２
１i＋１２sum
m２
j＝１v２jjt２jjη２
２j
s1049008t1049008K(BjprimeCprime)u２＋γ２＝η２jj＝１２1049018m２
－[K(AiprimeCprime)u２＋γ２]＋１＝η１i i＝１２1049018m１
(９)
６７１ JournalofIronandSteelResearchInternational Vol1049008２１
whereCprime＝[AprimeBprime]SubstitutingtheequalityconＧstraintsintotheobjectivefunctionofEq1049008(８)andsettingthegradientofEq1049008(８)withrespecttou１andγ１tozerothematrixformofresultisobtained
K(ACprime)primev１t１K(ACprime)K(ACprime)primev１t１e１
e１primev１t１K(ACprime) e１primev１t１e１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＋
c１K(BCprime)primet２K(BCprime)K(BCprime)primet２e２
e２primet２K(BCprime) e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝
－c１K(BCprime)primet２e２
e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
(１０)
DefineE＝[p１K(ACprime)p１e１]andF＝[p２K(BCprime)p２e２]wherev１t１＝p１primep１andt２＝p２primep２SpeＧciallyp１ andp２ arerequiredasdiagonalmatrixThenthesolutionofu１andγ１canbegiven
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝－ １
c１EprimeE＋FprimeF
aelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Fprimep２e２ (１１)
SimilarlyafteraseriesofderivationthesoluＧtionofEq1049008(９)canbeobtained
u２
γ２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝GprimeG＋
１c２
HprimeHaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Gprimep３e１ (１２)
whereG＝[p３K(ACprime)p３e１]H＝[p４K(BCprime)p４e２]t１＝p３primep３v２t２＝p４primep４p３andp４arereＧquiredasdiagonalmatrix TwononparallelhyperＧplanesaregottenfromEqs1049008(１１)and(１２) K(xprimeCprime)u１＋γ１＝０K(xprimeCprime)u２＋γ２＝０ (１３) Anewstripsteelsurfacedefectsamplebelongstoaclassdependingon whichofthetwohyperＧplanesinEq1049008(１３)isclosertothesampleintermsofperpendiculardistance
３ MultiＧclassClassificationofELSＧTWSVM TherearemanykindsofsurfacedefectsduringtheproductionandmanufactureofstripsteelSotheclassificationofthestripsteelsurfacedefectsbeＧlongstomultiＧclassclassificationManymultiＧclassclassificationmethodshavebeenused[１４１５]justlikeoneＧagainstＧoneoneＧagainstＧrestdecisiondirectedacyclicgraphandbinarytreeAmongthesemethＧodsthebinarytreeistheoptimalclassificationmethodThebinarytreehastwotypesofcompletebinarytreeandpartialbinarytreeTheyareshowninFig1049008１EverynodeonthepartialbinarytreeisabinarySVMclassifieroftheoneclassandtheothＧersSoaclassisrecognizedoneverynodeThisstructureofpartialbinarytreeenableseverybinarySVMclassifiertoclassifyunbalanceddatasamplesHowevereverynodeonthecompletebinarytreecarriesequalsplitornearlyequalsplitonalldatasamplesThatistosaythenumberofdatasamplesintheleftclassisnearlythesameasthatinthe
rightclasswhichavoidstheunbalanceddatasamＧplesclassificationInordertoavoidtheunbalancethecompletebinarytreeisselectedtoclassifystripsteelsurfacedefects
(a)Completebinarytree (b)PartialbinarytreeFig1049008１ Binarytree
InFig1049008１alldatasamplesofsixclasseswillbedividedintotwoclassesonnodeSVM１oneclassincludesclasses１２and３andtheotherclassinＧcludestheclasses４５and６ItwillbeeasytoclasＧsifyifthedivisiblefactorsareconsideredamongthesixclassesIngeneraltheseclasseswillbedividedintodifferentclassesifthedifferenceamongtheseclassesislargeSotheclasses１２and３willfallintooneclassandtheclasses４５and６willfallintotheotherclassTheeffectivemethodtotestthedifferＧencesamongallclassescanbefoundinRef1049008[１５]FirstlythecenterpointsofsixclassesarecalculatＧedSecondlythedistancebetweeneverytwocenterpointsaretestedFinallythedifferencesaredeterＧminedbythesedistances SupposethattherearenclassesforstripsteelsurfacedefectsamplesThemultiＧclassclassificationmethodsofELSＧTWSVMcanbeobtainedbycomＧbingtheELSＧTWSVMandthecompletebinarytreeThealgorithmsstepsareasfollows Step１Determinethepruningscaleraccordingtothemethodinsection２1049008１prunethedatasamＧplesbyusingPRSCmethodandgetnclassesofallpruneddatasamplesThenparametertisdeterＧminedforpruneddatasamplesaccordingtoEq1049008(５) Step２SplitequallyornearlyequallynclassesofpruneddatasamplesaccordingtothedistancesforthecenterpointsofnclassesThenconstructtrainingsamplesforallthenodesofthecompletebiＧnarytree Step３TrainthepruneddatasamplesforanodeSVM ofthecompletebinarytreebytheLSＧTWSVM withparametertAndgettheweightpaＧrametervbycalculatingEqs1049008(６)and(７)
７７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
Step４Calculatep１p２p３andp４basedontandv Step５Selecttherationalparametersc１c２
andkernelfunctionK Step６DefineEFGandH Step７CalculateparametersofthetwononparＧallelhyperＧplanesbyEqs1049008(１１)and (１２)soastogettheclassifierforthenode Step８Repeatstepsfrom３to７untilgetallclassifiersofthebinarytree Step９Accordingtothecompletebinarytreecalculateeverynodeclassifieruntilanewdefectdatasamplefallsintoaclassofthenclasses
４ Experiments４1049008１ ErrorvariablecontributionandweightsimulaＧtionexperiments BasedontwoＧdimensional(２ＧD)datasetssomesimulationexperimentsaredonetotesttheeffects
oftandvTheexperimentsareimplementedbyusingMATLAB７1049008１１onaPCwithanIntelP４processor(３1049008０GHz)and２GBRAM FirstlysomeexperimentsareusedtotesttheeffectsofparametertConsideringa２ＧDdatasetwithtwoclassesofdatasamplesPRSC methodisusedtoprunethedatasampleswithscalerThentheELSＧTWSVMclassifierwithlinearkernelfunctionisadoptedtoclassifythedatasamplesTheresultsareshowninFig1049008２ItiseasytoseethattheclassifiＧcationhyperＧplanesoforiginaldatasamples(r＝０)aresimilarwiththoseofELSＧTWSVMusingtheerＧrorvariablecontributiont(rne０)butaredifferentfromthoseofnotusingerrorvariablecontributiont(rne０)SotheerrorvariablecontributionparameterreducedthechangeoftheclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamples Thensomeexperimentsareusedtotesttheability
(a)r＝０ (b)rne０t (c)rne０Fig1049008２ ClassificationresultsofELSＧTWSVMin２ＧDspace
ofrestrainingtheimpactofnoisesamplesbyusingparametervConsideringa２ＧDdatasetwithinterＧcrossingnoisesamplesWLSＧTWSVM and ELSＧTWSVMareadoptedforclassificationexperimentsrespectivelyTheresultsareshowninFig1049008３ItiseasytoseethattheclassificationhyperＧplanesofWLSＧTWSVM arenotasgoodasthoseofELSＧTWSVMThisisbecauseweightparameterintheELSＧTWSVMismorereasonablethanthatintheWLSＧTWSVM
４1049008２ Surfacedefectsclassificationapplicationexperiments BasedonthestripsteelsurfacedefectdatasetsofaChineselargesteelplantsomeapplicationexＧ
perimentsaremadetodemonstratetheperformanceofELSＧTWSVMAlargenumberofimagesofthestrip
(a)WLSＧTWSVM (b)ELSＧTWSVMFig1049008３ Classificationresultsoftwoclassifiersin２ＧDspace
８７１ JournalofIronandSteelResearchInternational Vol1049008２１
steelsurfacedefectsarecollectedformthedatasetsSixkindsoftypicaldefectimagesareselectedTheyarescarringcrackholescratchwrinkle andscaleasshowninFig1049008４ Itisimportanttoextractfeaturesfromthestripsteelsurface defectimages before classificationThesefeaturesvectorsmakeupofthedatasampleswhichwillbeclassifiedbySVMInthisstudy４３featuresareextractedfromstripsteelsurfacedefect
imagesThesefeaturesreflectdefectinformationintermsofgreyfeaturesgeometricalfeaturestexturＧalfeaturesand morphologicalfeatures[１６]Inthemeantime４３featuresarereducedbyusingprinciＧpalcomponentanalysis(PCA)[１７]and３３featuresareobtainedFinallythese３３featuresareputtoＧgethertoforma３３ＧdimensionalvectorwhichreＧpresentsastripsteelsurfacedefectsample Inthispaper２３４０imagesareselectedasexperＧ
(a)Scarring (b)Crack (c)Hole (d)Scratch (e)Wrinkle (f)ScaleFig1049008４ Imagesofsixsurfacedefects
imentalsamplesfromwhich３３dimensionsfeaturesareextractedasthesixclassesofdatasamplesThenthedatasamplesarerandomlydividedintotrainingsetandtestingsetInthemeantimethecenterpointsofsixclassesarecalculatedandthedistancebetweeneverytwocenterpointsaretestedAccordingtothedistancetheserialnumberofsixclassesisdeterminedandisshowninTable１Thetrainingsamplesare９０ ofthetotalandare２１０６Thetestingsamplesare１０ofthetotalandare２３４ ThemultiＧclassclassifiersofELSＧTWSVMare
Table１ Differentsurfacedefectdatasamples
Defecttype
Classcode
Numberoftrainingsamples
Numberoftestingsamples
Scarring １ ４０５ ４５Crack ２ ３７８ ４２Hole ３ ３２４ ３６
Scratch ４ ３５１ ３９Wrinkle ５ ３７８ ４２Scale ６ ２７０ ３０
usedtoclassifythestripsteelsurfacedefectsamplesinTable１Radialbasisfunctionisusedaskernelfunctionanditsparametersareobtainedfrom２－２０
to２４Parametersc１andc２arealsoobtainedfrom２－２０to２４ FirstlyaimingatdifferentpruningratiossometestingexperimentsaremadeandtheresultsareshowninTable２ThepruningratioistheratioofthenumberofpruneddatasamplestothatoftheoriginaldatasamplesForexampletheratiois０1049008３０thatistosay３０ ofdatasamplesareprunedfromthe２１０６trainingsamplesItiseasytoseethatthehigherthepruningratioistheshorterthe
Table２ Testingresultswithdifferentpruningratios
Pruningratio Trainingtimes Testingtimes Accuracy
０ ３1049008６１４３ ０1049008３６６７ ９７1049008０１０1049008３０ １1049008６５５５ ０1049008２５５１ ９６1049008１５０1049008５５ ０1049008６７１３ ０1049008１７２０ ８８1049008４６０1049008７５ ０1049008１３４０ ０1049008０８７８ ７５1049008６４０1049008８５ ０1049008０６１８ ０1049008０５６２ ６１1049008９７
９７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
References
[１] X1049008JDuanF1049008JDuanF1049008FHaninInternationalConferＧenceonControlAutomationandSystemsEngineeringIEEESingapore２０１１pp１Ｇ４
[２] Y1049008HYanK1049008CSongZ1049008TXingX1049008HFenginThirdInＧternationalConferenceon MeasuringTechnologyand MechaＧtronicsAutomationIEEEShanghai２０１１pp９５８Ｇ９６１
[３] L1049008A1049008OMartinsF1049008L1049008CP1048929duaP1049008E1049008MAlmeidain３６thAnnualConferenceonIEEEIndustrialElectronicsSocietyIEEEGlendaleAZ２０１０pp１０８１Ｇ１０８６
[４] C1049008MWangY1049008HYanS1049008LChenY1049008LHanJNortheastUnivNatSci２８(２００７)４１０Ｇ４１３
[５] Q1049008YYangQLiJJinTransNAMRISME３７ (２００９)３７１Ｇ３７８
[６] EAmidS1049008RAghdamHAmindavarProcWorldAcadSciEngTech(２０１２)No1049008６７１３０３Ｇ１３０７
[７] JChenG1049008RJiinThe２ndInternationalConferenceonComＧputerandAutomationEngineeringIEEESingapore２０１０pp２４２Ｇ２４６
[８] M1049008AKumarMGopalExpertSysAppl３６(２００９)７５３５Ｇ７５４３
[９] JayadevaRKhemchandniSChandraIEEETransPatternAnalMachIntell２９(２００７)９０５Ｇ９１０
[１０] CCortesVVapnikMachLearn２０(１９９５)２７３Ｇ２９７[１１] Y1049008MWenY1049008NWangB1049008LLuY1049008MChenComputSci３６
(２００９)No1049008７２０Ｇ２５３１[１２] C1049008FLinS1049008DWangIEEETransNeuralNetw１３(２００２)
４６４Ｇ４７１[１３] J1049008A1049008KSuykensJ1049008DBrabanterLLukasJVandewalle
Neurocomputing４８(２００２)８５Ｇ１０５[１４] B1049008CFanJ1049008YWangY1049008MBoComputEngDes３１(２０１０)
２８２３Ｇ２８２５[１５] L1049008MLiuA1049008NWangMShaF1049008YZhaoJIronSteel
ResInt１８(２０１１)No1049008１０１７Ｇ２３３３[１６] YZhangW1049008WLiuZ1049008TXingY1049008HYanJNortheast
UnivNatSci３３(２０１２)２６７Ｇ２７０[１７] E1049008YHuHWangJ1049008HWangSLuLTianinIEEE
InternationalConferenceonComputerScienceandAutomationEngineeringIEEEShanghai２０１１pp３８８Ｇ３９０
０８１ JournalofIronandSteelResearchInternational Vol1049008２１
whereCprime＝[AprimeBprime]SubstitutingtheequalityconＧstraintsintotheobjectivefunctionofEq1049008(８)andsettingthegradientofEq1049008(８)withrespecttou１andγ１tozerothematrixformofresultisobtained
K(ACprime)primev１t１K(ACprime)K(ACprime)primev１t１e１
e１primev１t１K(ACprime) e１primev１t１e１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＋
c１K(BCprime)primet２K(BCprime)K(BCprime)primet２e２
e２primet２K(BCprime) e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝
－c１K(BCprime)primet２e２
e２primet２e２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute
(１０)
DefineE＝[p１K(ACprime)p１e１]andF＝[p２K(BCprime)p２e２]wherev１t１＝p１primep１andt２＝p２primep２SpeＧciallyp１ andp２ arerequiredasdiagonalmatrixThenthesolutionofu１andγ１canbegiven
u１
γ１
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝－ １
c１EprimeE＋FprimeF
aelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Fprimep２e２ (１１)
SimilarlyafteraseriesofderivationthesoluＧtionofEq1049008(９)canbeobtained
u２
γ２
eacute
euml
ecircecircecircecirc
ugrave
ucirc
uacuteuacuteuacuteuacute＝GprimeG＋
１c２
HprimeHaelig
egrave
ccedilccedilccedil
ouml
oslash
dividedividedivide
－１
Gprimep３e１ (１２)
whereG＝[p３K(ACprime)p３e１]H＝[p４K(BCprime)p４e２]t１＝p３primep３v２t２＝p４primep４p３andp４arereＧquiredasdiagonalmatrix TwononparallelhyperＧplanesaregottenfromEqs1049008(１１)and(１２) K(xprimeCprime)u１＋γ１＝０K(xprimeCprime)u２＋γ２＝０ (１３) Anewstripsteelsurfacedefectsamplebelongstoaclassdependingon whichofthetwohyperＧplanesinEq1049008(１３)isclosertothesampleintermsofperpendiculardistance
３ MultiＧclassClassificationofELSＧTWSVM TherearemanykindsofsurfacedefectsduringtheproductionandmanufactureofstripsteelSotheclassificationofthestripsteelsurfacedefectsbeＧlongstomultiＧclassclassificationManymultiＧclassclassificationmethodshavebeenused[１４１５]justlikeoneＧagainstＧoneoneＧagainstＧrestdecisiondirectedacyclicgraphandbinarytreeAmongthesemethＧodsthebinarytreeistheoptimalclassificationmethodThebinarytreehastwotypesofcompletebinarytreeandpartialbinarytreeTheyareshowninFig1049008１EverynodeonthepartialbinarytreeisabinarySVMclassifieroftheoneclassandtheothＧersSoaclassisrecognizedoneverynodeThisstructureofpartialbinarytreeenableseverybinarySVMclassifiertoclassifyunbalanceddatasamplesHowevereverynodeonthecompletebinarytreecarriesequalsplitornearlyequalsplitonalldatasamplesThatistosaythenumberofdatasamplesintheleftclassisnearlythesameasthatinthe
rightclasswhichavoidstheunbalanceddatasamＧplesclassificationInordertoavoidtheunbalancethecompletebinarytreeisselectedtoclassifystripsteelsurfacedefects
(a)Completebinarytree (b)PartialbinarytreeFig1049008１ Binarytree
InFig1049008１alldatasamplesofsixclasseswillbedividedintotwoclassesonnodeSVM１oneclassincludesclasses１２and３andtheotherclassinＧcludestheclasses４５and６ItwillbeeasytoclasＧsifyifthedivisiblefactorsareconsideredamongthesixclassesIngeneraltheseclasseswillbedividedintodifferentclassesifthedifferenceamongtheseclassesislargeSotheclasses１２and３willfallintooneclassandtheclasses４５and６willfallintotheotherclassTheeffectivemethodtotestthedifferＧencesamongallclassescanbefoundinRef1049008[１５]FirstlythecenterpointsofsixclassesarecalculatＧedSecondlythedistancebetweeneverytwocenterpointsaretestedFinallythedifferencesaredeterＧminedbythesedistances SupposethattherearenclassesforstripsteelsurfacedefectsamplesThemultiＧclassclassificationmethodsofELSＧTWSVMcanbeobtainedbycomＧbingtheELSＧTWSVMandthecompletebinarytreeThealgorithmsstepsareasfollows Step１Determinethepruningscaleraccordingtothemethodinsection２1049008１prunethedatasamＧplesbyusingPRSCmethodandgetnclassesofallpruneddatasamplesThenparametertisdeterＧminedforpruneddatasamplesaccordingtoEq1049008(５) Step２SplitequallyornearlyequallynclassesofpruneddatasamplesaccordingtothedistancesforthecenterpointsofnclassesThenconstructtrainingsamplesforallthenodesofthecompletebiＧnarytree Step３TrainthepruneddatasamplesforanodeSVM ofthecompletebinarytreebytheLSＧTWSVM withparametertAndgettheweightpaＧrametervbycalculatingEqs1049008(６)and(７)
７７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
Step４Calculatep１p２p３andp４basedontandv Step５Selecttherationalparametersc１c２
andkernelfunctionK Step６DefineEFGandH Step７CalculateparametersofthetwononparＧallelhyperＧplanesbyEqs1049008(１１)and (１２)soastogettheclassifierforthenode Step８Repeatstepsfrom３to７untilgetallclassifiersofthebinarytree Step９Accordingtothecompletebinarytreecalculateeverynodeclassifieruntilanewdefectdatasamplefallsintoaclassofthenclasses
４ Experiments４1049008１ ErrorvariablecontributionandweightsimulaＧtionexperiments BasedontwoＧdimensional(２ＧD)datasetssomesimulationexperimentsaredonetotesttheeffects
oftandvTheexperimentsareimplementedbyusingMATLAB７1049008１１onaPCwithanIntelP４processor(３1049008０GHz)and２GBRAM FirstlysomeexperimentsareusedtotesttheeffectsofparametertConsideringa２ＧDdatasetwithtwoclassesofdatasamplesPRSC methodisusedtoprunethedatasampleswithscalerThentheELSＧTWSVMclassifierwithlinearkernelfunctionisadoptedtoclassifythedatasamplesTheresultsareshowninFig1049008２ItiseasytoseethattheclassifiＧcationhyperＧplanesoforiginaldatasamples(r＝０)aresimilarwiththoseofELSＧTWSVMusingtheerＧrorvariablecontributiont(rne０)butaredifferentfromthoseofnotusingerrorvariablecontributiont(rne０)SotheerrorvariablecontributionparameterreducedthechangeoftheclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamples Thensomeexperimentsareusedtotesttheability
(a)r＝０ (b)rne０t (c)rne０Fig1049008２ ClassificationresultsofELSＧTWSVMin２ＧDspace
ofrestrainingtheimpactofnoisesamplesbyusingparametervConsideringa２ＧDdatasetwithinterＧcrossingnoisesamplesWLSＧTWSVM and ELSＧTWSVMareadoptedforclassificationexperimentsrespectivelyTheresultsareshowninFig1049008３ItiseasytoseethattheclassificationhyperＧplanesofWLSＧTWSVM arenotasgoodasthoseofELSＧTWSVMThisisbecauseweightparameterintheELSＧTWSVMismorereasonablethanthatintheWLSＧTWSVM
４1049008２ Surfacedefectsclassificationapplicationexperiments BasedonthestripsteelsurfacedefectdatasetsofaChineselargesteelplantsomeapplicationexＧ
perimentsaremadetodemonstratetheperformanceofELSＧTWSVMAlargenumberofimagesofthestrip
(a)WLSＧTWSVM (b)ELSＧTWSVMFig1049008３ Classificationresultsoftwoclassifiersin２ＧDspace
８７１ JournalofIronandSteelResearchInternational Vol1049008２１
steelsurfacedefectsarecollectedformthedatasetsSixkindsoftypicaldefectimagesareselectedTheyarescarringcrackholescratchwrinkle andscaleasshowninFig1049008４ Itisimportanttoextractfeaturesfromthestripsteelsurface defectimages before classificationThesefeaturesvectorsmakeupofthedatasampleswhichwillbeclassifiedbySVMInthisstudy４３featuresareextractedfromstripsteelsurfacedefect
imagesThesefeaturesreflectdefectinformationintermsofgreyfeaturesgeometricalfeaturestexturＧalfeaturesand morphologicalfeatures[１６]Inthemeantime４３featuresarereducedbyusingprinciＧpalcomponentanalysis(PCA)[１７]and３３featuresareobtainedFinallythese３３featuresareputtoＧgethertoforma３３ＧdimensionalvectorwhichreＧpresentsastripsteelsurfacedefectsample Inthispaper２３４０imagesareselectedasexperＧ
(a)Scarring (b)Crack (c)Hole (d)Scratch (e)Wrinkle (f)ScaleFig1049008４ Imagesofsixsurfacedefects
imentalsamplesfromwhich３３dimensionsfeaturesareextractedasthesixclassesofdatasamplesThenthedatasamplesarerandomlydividedintotrainingsetandtestingsetInthemeantimethecenterpointsofsixclassesarecalculatedandthedistancebetweeneverytwocenterpointsaretestedAccordingtothedistancetheserialnumberofsixclassesisdeterminedandisshowninTable１Thetrainingsamplesare９０ ofthetotalandare２１０６Thetestingsamplesare１０ofthetotalandare２３４ ThemultiＧclassclassifiersofELSＧTWSVMare
Table１ Differentsurfacedefectdatasamples
Defecttype
Classcode
Numberoftrainingsamples
Numberoftestingsamples
Scarring １ ４０５ ４５Crack ２ ３７８ ４２Hole ３ ３２４ ３６
Scratch ４ ３５１ ３９Wrinkle ５ ３７８ ４２Scale ６ ２７０ ３０
usedtoclassifythestripsteelsurfacedefectsamplesinTable１Radialbasisfunctionisusedaskernelfunctionanditsparametersareobtainedfrom２－２０
to２４Parametersc１andc２arealsoobtainedfrom２－２０to２４ FirstlyaimingatdifferentpruningratiossometestingexperimentsaremadeandtheresultsareshowninTable２ThepruningratioistheratioofthenumberofpruneddatasamplestothatoftheoriginaldatasamplesForexampletheratiois０1049008３０thatistosay３０ ofdatasamplesareprunedfromthe２１０６trainingsamplesItiseasytoseethatthehigherthepruningratioistheshorterthe
Table２ Testingresultswithdifferentpruningratios
Pruningratio Trainingtimes Testingtimes Accuracy
０ ３1049008６１４３ ０1049008３６６７ ９７1049008０１０1049008３０ １1049008６５５５ ０1049008２５５１ ９６1049008１５０1049008５５ ０1049008６７１３ ０1049008１７２０ ８８1049008４６０1049008７５ ０1049008１３４０ ０1049008０８７８ ７５1049008６４０1049008８５ ０1049008０６１８ ０1049008０５６２ ６１1049008９７
９７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
References
[１] X1049008JDuanF1049008JDuanF1049008FHaninInternationalConferＧenceonControlAutomationandSystemsEngineeringIEEESingapore２０１１pp１Ｇ４
[２] Y1049008HYanK1049008CSongZ1049008TXingX1049008HFenginThirdInＧternationalConferenceon MeasuringTechnologyand MechaＧtronicsAutomationIEEEShanghai２０１１pp９５８Ｇ９６１
[３] L1049008A1049008OMartinsF1049008L1049008CP1048929duaP1049008E1049008MAlmeidain３６thAnnualConferenceonIEEEIndustrialElectronicsSocietyIEEEGlendaleAZ２０１０pp１０８１Ｇ１０８６
[４] C1049008MWangY1049008HYanS1049008LChenY1049008LHanJNortheastUnivNatSci２８(２００７)４１０Ｇ４１３
[５] Q1049008YYangQLiJJinTransNAMRISME３７ (２００９)３７１Ｇ３７８
[６] EAmidS1049008RAghdamHAmindavarProcWorldAcadSciEngTech(２０１２)No1049008６７１３０３Ｇ１３０７
[７] JChenG1049008RJiinThe２ndInternationalConferenceonComＧputerandAutomationEngineeringIEEESingapore２０１０pp２４２Ｇ２４６
[８] M1049008AKumarMGopalExpertSysAppl３６(２００９)７５３５Ｇ７５４３
[９] JayadevaRKhemchandniSChandraIEEETransPatternAnalMachIntell２９(２００７)９０５Ｇ９１０
[１０] CCortesVVapnikMachLearn２０(１９９５)２７３Ｇ２９７[１１] Y1049008MWenY1049008NWangB1049008LLuY1049008MChenComputSci３６
(２００９)No1049008７２０Ｇ２５３１[１２] C1049008FLinS1049008DWangIEEETransNeuralNetw１３(２００２)
４６４Ｇ４７１[１３] J1049008A1049008KSuykensJ1049008DBrabanterLLukasJVandewalle
Neurocomputing４８(２００２)８５Ｇ１０５[１４] B1049008CFanJ1049008YWangY1049008MBoComputEngDes３１(２０１０)
２８２３Ｇ２８２５[１５] L1049008MLiuA1049008NWangMShaF1049008YZhaoJIronSteel
ResInt１８(２０１１)No1049008１０１７Ｇ２３３３[１６] YZhangW1049008WLiuZ1049008TXingY1049008HYanJNortheast
UnivNatSci３３(２０１２)２６７Ｇ２７０[１７] E1049008YHuHWangJ1049008HWangSLuLTianinIEEE
InternationalConferenceonComputerScienceandAutomationEngineeringIEEEShanghai２０１１pp３８８Ｇ３９０
０８１ JournalofIronandSteelResearchInternational Vol1049008２１
Step４Calculatep１p２p３andp４basedontandv Step５Selecttherationalparametersc１c２
andkernelfunctionK Step６DefineEFGandH Step７CalculateparametersofthetwononparＧallelhyperＧplanesbyEqs1049008(１１)and (１２)soastogettheclassifierforthenode Step８Repeatstepsfrom３to７untilgetallclassifiersofthebinarytree Step９Accordingtothecompletebinarytreecalculateeverynodeclassifieruntilanewdefectdatasamplefallsintoaclassofthenclasses
４ Experiments４1049008１ ErrorvariablecontributionandweightsimulaＧtionexperiments BasedontwoＧdimensional(２ＧD)datasetssomesimulationexperimentsaredonetotesttheeffects
oftandvTheexperimentsareimplementedbyusingMATLAB７1049008１１onaPCwithanIntelP４processor(３1049008０GHz)and２GBRAM FirstlysomeexperimentsareusedtotesttheeffectsofparametertConsideringa２ＧDdatasetwithtwoclassesofdatasamplesPRSC methodisusedtoprunethedatasampleswithscalerThentheELSＧTWSVMclassifierwithlinearkernelfunctionisadoptedtoclassifythedatasamplesTheresultsareshowninFig1049008２ItiseasytoseethattheclassifiＧcationhyperＧplanesoforiginaldatasamples(r＝０)aresimilarwiththoseofELSＧTWSVMusingtheerＧrorvariablecontributiont(rne０)butaredifferentfromthoseofnotusingerrorvariablecontributiont(rne０)SotheerrorvariablecontributionparameterreducedthechangeoftheclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamples Thensomeexperimentsareusedtotesttheability
(a)r＝０ (b)rne０t (c)rne０Fig1049008２ ClassificationresultsofELSＧTWSVMin２ＧDspace
ofrestrainingtheimpactofnoisesamplesbyusingparametervConsideringa２ＧDdatasetwithinterＧcrossingnoisesamplesWLSＧTWSVM and ELSＧTWSVMareadoptedforclassificationexperimentsrespectivelyTheresultsareshowninFig1049008３ItiseasytoseethattheclassificationhyperＧplanesofWLSＧTWSVM arenotasgoodasthoseofELSＧTWSVMThisisbecauseweightparameterintheELSＧTWSVMismorereasonablethanthatintheWLSＧTWSVM
４1049008２ Surfacedefectsclassificationapplicationexperiments BasedonthestripsteelsurfacedefectdatasetsofaChineselargesteelplantsomeapplicationexＧ
perimentsaremadetodemonstratetheperformanceofELSＧTWSVMAlargenumberofimagesofthestrip
(a)WLSＧTWSVM (b)ELSＧTWSVMFig1049008３ Classificationresultsoftwoclassifiersin２ＧDspace
８７１ JournalofIronandSteelResearchInternational Vol1049008２１
steelsurfacedefectsarecollectedformthedatasetsSixkindsoftypicaldefectimagesareselectedTheyarescarringcrackholescratchwrinkle andscaleasshowninFig1049008４ Itisimportanttoextractfeaturesfromthestripsteelsurface defectimages before classificationThesefeaturesvectorsmakeupofthedatasampleswhichwillbeclassifiedbySVMInthisstudy４３featuresareextractedfromstripsteelsurfacedefect
imagesThesefeaturesreflectdefectinformationintermsofgreyfeaturesgeometricalfeaturestexturＧalfeaturesand morphologicalfeatures[１６]Inthemeantime４３featuresarereducedbyusingprinciＧpalcomponentanalysis(PCA)[１７]and３３featuresareobtainedFinallythese３３featuresareputtoＧgethertoforma３３ＧdimensionalvectorwhichreＧpresentsastripsteelsurfacedefectsample Inthispaper２３４０imagesareselectedasexperＧ
(a)Scarring (b)Crack (c)Hole (d)Scratch (e)Wrinkle (f)ScaleFig1049008４ Imagesofsixsurfacedefects
imentalsamplesfromwhich３３dimensionsfeaturesareextractedasthesixclassesofdatasamplesThenthedatasamplesarerandomlydividedintotrainingsetandtestingsetInthemeantimethecenterpointsofsixclassesarecalculatedandthedistancebetweeneverytwocenterpointsaretestedAccordingtothedistancetheserialnumberofsixclassesisdeterminedandisshowninTable１Thetrainingsamplesare９０ ofthetotalandare２１０６Thetestingsamplesare１０ofthetotalandare２３４ ThemultiＧclassclassifiersofELSＧTWSVMare
Table１ Differentsurfacedefectdatasamples
Defecttype
Classcode
Numberoftrainingsamples
Numberoftestingsamples
Scarring １ ４０５ ４５Crack ２ ３７８ ４２Hole ３ ３２４ ３６
Scratch ４ ３５１ ３９Wrinkle ５ ３７８ ４２Scale ６ ２７０ ３０
usedtoclassifythestripsteelsurfacedefectsamplesinTable１Radialbasisfunctionisusedaskernelfunctionanditsparametersareobtainedfrom２－２０
to２４Parametersc１andc２arealsoobtainedfrom２－２０to２４ FirstlyaimingatdifferentpruningratiossometestingexperimentsaremadeandtheresultsareshowninTable２ThepruningratioistheratioofthenumberofpruneddatasamplestothatoftheoriginaldatasamplesForexampletheratiois０1049008３０thatistosay３０ ofdatasamplesareprunedfromthe２１０６trainingsamplesItiseasytoseethatthehigherthepruningratioistheshorterthe
Table２ Testingresultswithdifferentpruningratios
Pruningratio Trainingtimes Testingtimes Accuracy
０ ３1049008６１４３ ０1049008３６６７ ９７1049008０１０1049008３０ １1049008６５５５ ０1049008２５５１ ９６1049008１５０1049008５５ ０1049008６７１３ ０1049008１７２０ ８８1049008４６０1049008７５ ０1049008１３４０ ０1049008０８７８ ７５1049008６４０1049008８５ ０1049008０６１８ ０1049008０５６２ ６１1049008９７
９７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
References
[１] X1049008JDuanF1049008JDuanF1049008FHaninInternationalConferＧenceonControlAutomationandSystemsEngineeringIEEESingapore２０１１pp１Ｇ４
[２] Y1049008HYanK1049008CSongZ1049008TXingX1049008HFenginThirdInＧternationalConferenceon MeasuringTechnologyand MechaＧtronicsAutomationIEEEShanghai２０１１pp９５８Ｇ９６１
[３] L1049008A1049008OMartinsF1049008L1049008CP1048929duaP1049008E1049008MAlmeidain３６thAnnualConferenceonIEEEIndustrialElectronicsSocietyIEEEGlendaleAZ２０１０pp１０８１Ｇ１０８６
[４] C1049008MWangY1049008HYanS1049008LChenY1049008LHanJNortheastUnivNatSci２８(２００７)４１０Ｇ４１３
[５] Q1049008YYangQLiJJinTransNAMRISME３７ (２００９)３７１Ｇ３７８
[６] EAmidS1049008RAghdamHAmindavarProcWorldAcadSciEngTech(２０１２)No1049008６７１３０３Ｇ１３０７
[７] JChenG1049008RJiinThe２ndInternationalConferenceonComＧputerandAutomationEngineeringIEEESingapore２０１０pp２４２Ｇ２４６
[８] M1049008AKumarMGopalExpertSysAppl３６(２００９)７５３５Ｇ７５４３
[９] JayadevaRKhemchandniSChandraIEEETransPatternAnalMachIntell２９(２００７)９０５Ｇ９１０
[１０] CCortesVVapnikMachLearn２０(１９９５)２７３Ｇ２９７[１１] Y1049008MWenY1049008NWangB1049008LLuY1049008MChenComputSci３６
(２００９)No1049008７２０Ｇ２５３１[１２] C1049008FLinS1049008DWangIEEETransNeuralNetw１３(２００２)
４６４Ｇ４７１[１３] J1049008A1049008KSuykensJ1049008DBrabanterLLukasJVandewalle
Neurocomputing４８(２００２)８５Ｇ１０５[１４] B1049008CFanJ1049008YWangY1049008MBoComputEngDes３１(２０１０)
２８２３Ｇ２８２５[１５] L1049008MLiuA1049008NWangMShaF1049008YZhaoJIronSteel
ResInt１８(２０１１)No1049008１０１７Ｇ２３３３[１６] YZhangW1049008WLiuZ1049008TXingY1049008HYanJNortheast
UnivNatSci３３(２０１２)２６７Ｇ２７０[１７] E1049008YHuHWangJ1049008HWangSLuLTianinIEEE
InternationalConferenceonComputerScienceandAutomationEngineeringIEEEShanghai２０１１pp３８８Ｇ３９０
０８１ JournalofIronandSteelResearchInternational Vol1049008２１
steelsurfacedefectsarecollectedformthedatasetsSixkindsoftypicaldefectimagesareselectedTheyarescarringcrackholescratchwrinkle andscaleasshowninFig1049008４ Itisimportanttoextractfeaturesfromthestripsteelsurface defectimages before classificationThesefeaturesvectorsmakeupofthedatasampleswhichwillbeclassifiedbySVMInthisstudy４３featuresareextractedfromstripsteelsurfacedefect
imagesThesefeaturesreflectdefectinformationintermsofgreyfeaturesgeometricalfeaturestexturＧalfeaturesand morphologicalfeatures[１６]Inthemeantime４３featuresarereducedbyusingprinciＧpalcomponentanalysis(PCA)[１７]and３３featuresareobtainedFinallythese３３featuresareputtoＧgethertoforma３３ＧdimensionalvectorwhichreＧpresentsastripsteelsurfacedefectsample Inthispaper２３４０imagesareselectedasexperＧ
(a)Scarring (b)Crack (c)Hole (d)Scratch (e)Wrinkle (f)ScaleFig1049008４ Imagesofsixsurfacedefects
imentalsamplesfromwhich３３dimensionsfeaturesareextractedasthesixclassesofdatasamplesThenthedatasamplesarerandomlydividedintotrainingsetandtestingsetInthemeantimethecenterpointsofsixclassesarecalculatedandthedistancebetweeneverytwocenterpointsaretestedAccordingtothedistancetheserialnumberofsixclassesisdeterminedandisshowninTable１Thetrainingsamplesare９０ ofthetotalandare２１０６Thetestingsamplesare１０ofthetotalandare２３４ ThemultiＧclassclassifiersofELSＧTWSVMare
Table１ Differentsurfacedefectdatasamples
Defecttype
Classcode
Numberoftrainingsamples
Numberoftestingsamples
Scarring １ ４０５ ４５Crack ２ ３７８ ４２Hole ３ ３２４ ３６
Scratch ４ ３５１ ３９Wrinkle ５ ３７８ ４２Scale ６ ２７０ ３０
usedtoclassifythestripsteelsurfacedefectsamplesinTable１Radialbasisfunctionisusedaskernelfunctionanditsparametersareobtainedfrom２－２０
to２４Parametersc１andc２arealsoobtainedfrom２－２０to２４ FirstlyaimingatdifferentpruningratiossometestingexperimentsaremadeandtheresultsareshowninTable２ThepruningratioistheratioofthenumberofpruneddatasamplestothatoftheoriginaldatasamplesForexampletheratiois０1049008３０thatistosay３０ ofdatasamplesareprunedfromthe２１０６trainingsamplesItiseasytoseethatthehigherthepruningratioistheshorterthe
Table２ Testingresultswithdifferentpruningratios
Pruningratio Trainingtimes Testingtimes Accuracy
０ ３1049008６１４３ ０1049008３６６７ ９７1049008０１０1049008３０ １1049008６５５５ ０1049008２５５１ ９６1049008１５０1049008５５ ０1049008６７１３ ０1049008１７２０ ８８1049008４６０1049008７５ ０1049008１３４０ ０1049008０８７８ ７５1049008６４０1049008８５ ０1049008０６１８ ０1049008０５６２ ６１1049008９７
９７１Issue２ MultiＧclassClassificationMethodsofEnhancedLSＧTWSVMforStripSteelSurfaceDefects
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
References
[１] X1049008JDuanF1049008JDuanF1049008FHaninInternationalConferＧenceonControlAutomationandSystemsEngineeringIEEESingapore２０１１pp１Ｇ４
[２] Y1049008HYanK1049008CSongZ1049008TXingX1049008HFenginThirdInＧternationalConferenceon MeasuringTechnologyand MechaＧtronicsAutomationIEEEShanghai２０１１pp９５８Ｇ９６１
[３] L1049008A1049008OMartinsF1049008L1049008CP1048929duaP1049008E1049008MAlmeidain３６thAnnualConferenceonIEEEIndustrialElectronicsSocietyIEEEGlendaleAZ２０１０pp１０８１Ｇ１０８６
[４] C1049008MWangY1049008HYanS1049008LChenY1049008LHanJNortheastUnivNatSci２８(２００７)４１０Ｇ４１３
[５] Q1049008YYangQLiJJinTransNAMRISME３７ (２００９)３７１Ｇ３７８
[６] EAmidS1049008RAghdamHAmindavarProcWorldAcadSciEngTech(２０１２)No1049008６７１３０３Ｇ１３０７
[７] JChenG1049008RJiinThe２ndInternationalConferenceonComＧputerandAutomationEngineeringIEEESingapore２０１０pp２４２Ｇ２４６
[８] M1049008AKumarMGopalExpertSysAppl３６(２００９)７５３５Ｇ７５４３
[９] JayadevaRKhemchandniSChandraIEEETransPatternAnalMachIntell２９(２００７)９０５Ｇ９１０
[１０] CCortesVVapnikMachLearn２０(１９９５)２７３Ｇ２９７[１１] Y1049008MWenY1049008NWangB1049008LLuY1049008MChenComputSci３６
(２００９)No1049008７２０Ｇ２５３１[１２] C1049008FLinS1049008DWangIEEETransNeuralNetw１３(２００２)
４６４Ｇ４７１[１３] J1049008A1049008KSuykensJ1049008DBrabanterLLukasJVandewalle
Neurocomputing４８(２００２)８５Ｇ１０５[１４] B1049008CFanJ1049008YWangY1049008MBoComputEngDes３１(２０１０)
２８２３Ｇ２８２５[１５] L1049008MLiuA1049008NWangMShaF1049008YZhaoJIronSteel
ResInt１８(２０１１)No1049008１０１７Ｇ２３３３[１６] YZhangW1049008WLiuZ1049008TXingY1049008HYanJNortheast
UnivNatSci３３(２０１２)２６７Ｇ２７０[１７] E1049008YHuHWangJ1049008HWangSLuLTianinIEEE
InternationalConferenceonComputerScienceandAutomationEngineeringIEEEShanghai２０１１pp３８８Ｇ３９０
０８１ JournalofIronandSteelResearchInternational Vol1049008２１
trainingtimeandtestingtimeareButtheaverageclassificationaccuracyforsixclassesoftestingsamＧplesislowerSoinrealclassificationproblemtheidealpruningratioshouldbeconsideredbasedontrainingtimeandclassificationaccuracy Secondlyclassificationaccuracyistestedintermsofusingerrorvariablecontributionparameterandnotusingerrorvariablecontributionparameterwherepruningratiois０1049008４ThefinalresultsareshowninTable３FromtheresultsitcanbeseenthaterrorvariablecontributionparametertinELSＧTWSVMhascontributedtoclassificationaccuracy
Table３ Classificationaccuracyofdifferentdefects
DefecttypeAccuracy
Notusingt Usingt
Scarring ８６1049008６７ ９３1049008３３Crack ９２1049008８６ ９７1049008６２Hole ８６1049008１１ ９４1049008４４
Scratch ８２1049008０５ ９４1049008８７Wrinkle ８８1049008１０ ９５1049008２４Scale ８６1049008６７ ９６1049008２７
FinallymultiＧclassclassifierofELSＧTWSVMandmultiＧclassclassifierofLSＧTWSVMareusedtoclassifythesixclassesofstripsteelsurfacedefectsamplesbyusingarationalpruningratio (０1049008４)TrainingtimetestingtimeandclassificationaccuＧracyareshowninTable４ItindicatesthattrainingtimeandtestingtimeofthemultiＧclassclassifierofELSＧTWSVMareshorterthanthoseofthemultiＧclassclassifierofLSＧTWSVMandclassificationacＧcuraciesarebothhigh
Table４ Testingresultsoftwoclassifiers
ClassifierTrainingtimes
Testingtimes
Accuracy
LSＧTWSVM ３1049008０１７２ ０1049008３６６１ ９６1049008１５ELSＧTWSVM １1049008１２０１ ０1049008２１１８ ９５1049008３０
５ Conclusions
ThemultiＧclassclassifierofELSＧTWSVM hasbeenusedinthefieldofstripsteelsurfacedefectsrecognitionTheresearchhasbeenmadeonsixclasＧsesofstripsteelsurfacedefectsincludingscarringcrackholescratchwrinkleandscaleThePRSCmethodhasbeenimplemented withanadjustable
scalerBothtrainingtimeandtestingtimehavebeenreducedErrorvariablecontributionparametertreducesthechangeofclassificationhyperＧplaneswhichiscausedbyerrorvariablesofpruneddatasamplesandensuresclassificationaccuracytothelargestextentTheweightparameterviseffectivetorestraintheimpactofnoisesamplesThemultiＧclassclassifierbycombingtheELSＧTWSVM andthecomplete binarytreeis effectiveto classifymultiＧclassdatasamplesTheexperimentsshowthatmultiＧclassclassifierofELSＧTWSVMismoresuitabletoclassifystripsteelsurfacedefectsamplesintermsofclassificationspeedandaccuracyMoreoＧverthemethodismoresuitableforlargerＧscaleunbalancedandnoisesamples
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０８１ JournalofIronandSteelResearchInternational Vol1049008２１
