矿业 矿井 外文翻译 外文文献 英文文献 基于PCA技术核心的打包和变换的矿井提升机失误的发现.docx
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矿业 矿井 外文翻译 外文文献 英文文献 基于PCA技术核心的打包和变换的矿井提升机失误的发现.docx
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矿业矿井外文翻译外文文献英文文献基于PCA技术核心的打包和变换的矿井提升机失误的发现
外文翻译部分:
英文原文
Mine-hoistfault-conditiondetectionbasedon
thewaveletpackettransformandkernelPCA
Abstract:
Anewalgorithmwasdevelopedtocorrectlyidentifyfaultconditionsandaccuratelymonitorfaultdevelopmentinaminehoist.ThenewmethodisbasedontheWaveletPacketTransform(WPT)andkernelPCA(KernelPrincipalComponentAnalysis,KPCA).Fornon-linearmonitoringsystemsthekeytofaultdetectionistheextractingofmainfeatures.Thewaveletpackettransformisanoveltechniqueofsignalprocessingthatpossessesexcellentcharacteristicsoftime-frequencylocalization.Itissuitableforanalysingtime-varyingortransientsignals.KPCAmapstheoriginalinputfeaturesintoahigherdimensionfeaturespacethroughanon-linearmapping.Theprincipalcomponentsarethenfoundinthehigherdimensionfeaturespace.TheKPCAtransformationwasappliedtoextractingthemainnonlinearfeaturesfromexperimentalfaultfeaturedataafterwaveletpackettransformation.Theresultsshowthattheproposedmethodaffordscrediblefaultdetectionandidentification.
Keywords:
kernelmethod;PCA;KPCA;faultconditiondetection
1Introduction
Becauseaminehoistisaverycomplicatedandvariablesystem,thehoistwillinevitablygeneratesomefaultsduringlong-termsofrunningandheavyloading.Thiscanleadtoequipmentbeingdamaged,toworkstoppage,toreducedoperatingefficiencyandmayevenposeathreattothesecurityofminepersonnel.Therefore,theidentificationofrunningfaultshasbecomeanimportantcomponentofthesafetysystem.Thekeytechniqueforhoistconditionmonitoringandfaultidentificationisextractinginformationfromfeaturesofthemonitoringsignalsandthenofferingajudgmentalresult.However,therearemanyvariablestomonitorinaminehoistand,also,therearemanycomplexcorrelationsbetweenthevariablesandtheworkingequipment.Thisintroducesuncertainfactorsandinformationasmanifestedbycomplexformssuchasmultiplefaultsorassociatedfaults,whichintroduceconsiderabledifficultytofaultdiagnosisandidentification[1].Therearecurrentlymanyconventionalmethodsforextractingminehoistfaultfeatures,suchasPrincipalComponentAnalysis(PCA)andPartialLeastSquares(PLS)[2].Thesemethodshavebeenappliedtotheactualprocess.However,thesemethodsareessentiallyalineartransformationapproach.Buttheactualmonitoringprocessincludesnonlinearityindifferentdegrees.Thus,researchershaveproposedaseriesofnonlinearmethodsinvolvingcomplexnonlineartransformations.Furthermore,thesenon-linearmethodsareconfinedtofaultdetection:
Faultvariableseparationandfaultidentificationarestilldifficultproblems.ThispaperdescribesahoistfaultdiagnosisfeatureexactionmethodbasedontheWaveletPacketTransform(WPT)andkernelprincipalcomponentanalysis(KPCA).WeextractthefeaturesbyWPTandthenextractthemainfeaturesusingaKPCAtransform,whichprojectslow-dimensionalmonitoringdatasamplesintoahigh-dimensionalspace.Thenwedoadimensionreductionandreconstructionbacktothesingularkernelmatrix.Afterthat,thetargetfeatureisextractedfromthereconstructednonsingularmatrix.Inthiswaytheexacttargetfeatureisdistinctandstable.Bycomparingtheanalyzeddataweshowthatthemethodproposedinthispaperiseffective.
2FeatureextractionbasedonWPTand
KPCA
2.1Waveletpackettransform
Thewaveletpackettransform(WPT)method[3],whichisageneralizationofwaveletdecomposition,offersarichrangeofpossibilitiesforsignalanalysis.Thefrequencybandsofahoist-motorsignalascollectedbythesensorsystemarewide.Theusefulinformationhideswithinthelargeamountofdata.Ingeneral,somefrequenciesofthesignalareamplifiedandsomearedepressedbytheinformation.Thatistosay,thesebroadbandsignalscontainalargeamountofusefulinformation:
Buttheinformationcannotbedirectlyobtainedfromthedata.TheWPTisafinesignalanalysismethodthatdecomposesthesignalintomanylayersandgivesaetterresolutioninthetime-frequencydomain.Theusefulinformationwithinthedifferentrequencyandswillbeexpressedbydifferentwaveletcoefficientsafterthedecompositionofthesignal.Theonceptof“energyinformation”ispresentedtoidentifynewinformationhiddenthedata.Anenergyigenvectoristhenusedtoquicklymineinformationhidingwithinthelargeamountofdata.Thealgorithmis:
Step1:
Performa3-layerwaveletpacketdecompositionoftheechosignalsandextractthesignalcharacteristicsoftheeightfrequencycomponents,fromlowtohigh,inthe3rdlayer.
Step2:
Reconstructthecoefficientsofthewaveletpacketdecomposition.Use3jS(j=0,1,…,7)todenotethereconstructedsignalsofeachfrequencybandrangeinthe3rdlayer.Thetotalsignalcanthenbedenotedas:
(1)
Step3:
ConstructthefeaturevectorsoftheechosignalsoftheGPR.Whenthecouplingelectromagneticwavesaretransmittedundergroundtheymeetvariousinhomogeneousmedia.Theenergydistributingoftheechosignalsineachfrequencybandwillthenbedifferent.Assumethatthecorrespondingenergyof3jS(j=0,1,…,7)canberepresentedas3jE(j=0,1,…,7).Themagnitudeofthedispersedpointsofthereconstructedsignal3jSis:
jkx(j=0,1,…,7;k=1,2,…,n),wherenisthelengthofthesignal.Thenwecanget:
(2)
Considerthatwehavemadeonlya3-layerwaveletpackagedecompositionoftheechosignals.Tomakethechangeofeachfrequencycomponentmoredetailedthe2-rankstatisticalcharacteristicsofthereconstructedsignalisalsoregardedasafeaturevector:
(3)
Step4:
The3jEareoftenlargesowenormalizethem.Assumethat
thusthederivedfeaturevectorsare,atlast:
T=[
](4)
Thesignalisdecomposedbyawaveletpackageandthentheusefulcharacteristicinformationfeaturevectorsareextractedthroughtheprocessgivenabove.Comparedtoothertraditionalmethods,liketheHilberttransform,approachesbasedontheWPTanalysisaremorewelcomeduetotheagilityoftheprocessanditsscientificdecomposition.
2.2Kernelprincipalcomponentanalysis
Themethodofkernelprincipalcomponentanalysisapplieskernelmethodstoprincipalcomponentanalysis[4–5].
Theprincipalcomponentistheelementatthediagonalafterthecovariancematrix,
hasbeendiagonalized.Generallyspeaking,thefirstNvaluesalongthediagonal,correspondingtothelargeeigenvalues,aretheusefulinformationintheanalysis.PCAsolvestheeigenvaluesandeigenvectorsofthecovariancematrix.Solvingthecharacteristicequation[6]:
(5)
wheretheeigenvalues
andtheeigenvectors,
isessenceofPCA.
Letthenonlineartransformations,⎫:
RN
F,x
X,projecttheoriginalspaceintofeaturespace,F.Thenthecovariancematrix,C,oftheoriginalspacehasthefollowingforminthefeaturespace:
(6)
Nonlinearprincipalcomponentanalysiscanbe
consideredtobeprincipalcomponentanalysisof
inthefeaturespace,F.Obviously,alltheigenvaluesofC
andeigenvectors,V
F\{0}satisfy
V=
V.Allofthesolutionsareinthesubspace
thattransformsfrom
(7)
Thereisacoefficient
Let
(8)
FromEqs.(6),(7)and(8)wecanobtain:
(9)
wherek=1,2,…..,M.DefineAasanM×Mrank
matrix.Itselementsare:
FromEqs.(9)and(10),wecanobtain
M
Aa=A2a.Thisisequivalentto:
M
Aa=Aa.
Make
asA’seigenvalues,and
asthecorrespondingeigenvector.
Weonlyneedtocalculatethetestpoints’projections
ontheeigenvectors
thatcorrespondto
nonzeroeigenvaluesinFtodotheprincipalcomponent
extraction.Definingthisas
itisgivenby:
(12)
principal
componentweneedtoknowtheexactformofthenon-linearimage.Alsoasthedimensionofthefeaturespaceincreasestheamountofcomputationgoesupexponentially.BecauseEq.(12)involvesaninner-productcomputation,
accordingtotheprinciplesofHilbert-SchmidtwecanfindakernelfunctionthatsatisfiestheMercerconditionsandmakes
ThenEq.(12)can
bewritten:
Here
istheeigenvectorofK.Inthiswaythedotproductmustbedoneintheoriginalspacebutthespecificformof
(x)neednotbeknown.Themapping,
(x),andthefeaturespace,F,areallcompletelydeterminedbythechoiceofkernelfunction[7–8].
2.3Descriptionofthealgorithm
Thealgorithmforextractingtargetfeaturesinrecognitionoffaultdiagnosisis:
Step1:
ExtractthefeaturesbyWPT;
Step2:
Calculatethenuclearmatrix,K,foreachsample,
intheoriginalinputspace,and
Step3:
Calculatethenuclearmatrixafterzero-meanprocessingofthemappingdatainfeaturespace;
Step4:
SolvethecharacteristicequationM
a=Aa;
Step5:
ExtractthekmajorcomponentsusingEq.(13)toderiveanewvector.BecausethekernelfunctionusedinKPCAmettheMercerconditionsitcanbeusedinsteadoftheinnerproductinfeaturespace.Itisnotnecessarytoconsiderthepreciseformofthenonlineartransformation.Themappingfunctioncanbenon-linearandthedimensionsofthefeaturespacecanbeveryhighbutitispossibletogetthemainfeaturecomponentseffectivelybychoosingasuitablekernelfunctionand
kernelparameters[9].
3Resultsanddiscussion
Thecharacterofthemostcommonfaultofaminehoistwasinthefrequencyoftheequipmentvibrationsignals.Theexperimentusedthevibrationsignalsof
aminehoistastestdata.Thecollectedvibrationsignalswerefirstprocessedbywaveletpacket.Thenthroughtheobservationofdifferenttime-frequency
energydistributionsinalevelofthewaveletpacketweobtainedtheoriginaldatasheetshowninTable1byextractingthefeaturesoftherunningm
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