FoundationItemItemSponsoredbyNationalNaturalScienceFoundationofChina(61050006)BiographyMaoGxiangCHUDoctorCandidate EGmailchu52_20041631049008com ReceivedDateSeptember112012
1051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271105127110512711051271
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
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
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
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