矿井提升机 外文翻译.docx
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矿井提升机 外文翻译.docx
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矿井提升机外文翻译
外文翻译部分:
英文原文
Mine-hoistfault-conditiondetectionbasedonthewaveletpackettransformandkernelPCA
Abstract:
Anewalgorithmwasdevelopedtocorrectlyidentifyfaultconditionsandaccuratelymonitorfaultdevelopmentinaminehoist.ThenewmethodisbasedontheWaveletPacketTransform(WPT)andkernelPCA(KernelPrincipalComponentAnalysis,KPCA).Fornon-linearmonitoringsystemsthekeytofaultdetectionistheextractingofmainfeatures.Thewaveletpackettransformisanoveltechniqueofsignalprocessingthatpossessesexcellentcharacteristicsoftime-frequencylocalization.Itissuitableforanalyzingtime-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.
2FeatureextractionbasedonWPTandKPCA
2.1Waveletpackettransform
Thewaveletpackettransform(WPT)method[3],whichisageneralizationofwaveletdecomposition,offersarichrangeofpossibilitiesforsignalanalysis.Thefrequencybandsofahoist-motorsignalascollectedbythesensorsystemarewide.Theusefulinformationhideswithinthelargeamountofdata.Ingeneral,somefrequenciesofthesignalareamplifiedandsomearedepressedbytheinformation.Thatistosay,thesebroadbandsignalscontainalargeamountofusefulinformation:
Buttheinformationcannotbedirectlyobtainedfromthedata.TheWPTisafinesignalanalysismethodthatdecomposesthesignalintomanylayersandgivesabetterresolutioninthetime-frequencydomain.
Theusefulinformationwithinthedifferentfrequencybandswillbeexpressedbydifferentwaveletcoefficientsafterthedecompositionofthesignal.Theconceptof“energyinformation”ispresentedtoidentifynewinformationhiddenthedata.Anenergyeigenvectoristhenusedtoquicklymineinformationhidingwithinthelargeamountofdata.
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)
Nonlinearprincipalcomponentanalysiscanbeconsideredtobeprincipalcomponentanalysisof
inthefeaturespace,F.Obviously,alltheeigenvaluesofC
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:
(10)
FromEqs.(9)and(10),wecanobtainM
Aa=
a.Thisisequivalentto:
M
a=Aa.(11)
Make
asA’seigenvalues,and
asthecorrespondingeigenvector.
Weonlyneedtocalculatethetestpoints’projectionsontheeigenvectors
thatcorrespondtononzeroeigenvaluesinFtodotheprincipalcomponentextraction.Definingthisas
itisgivenby:
(12)
Principalcomponentweneedtoknowtheexactformofthenon-linearimage.Alsoasthedimensionofthefeaturespaceincreasestheamountofcomputationgoesupexponentially.BecauseEq.(12)involvesaninner-productcomputation,
accordingtotheprinciplesofHilbert-SchmidtwecanfindakernelfunctionthatsatisfiestheMercerconditionsandmakes
ThenEq.(12)can
bewritten:
(13)
Here
istheeigenvectorofK.Inthiswaythedotproductmustbedoneintheoriginalspacebutthespecificformof
neednotbeknown.Themapping,
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.Theexperimentusedthevibrationsignalsofaminehoistastestdata.Thecollectedvibrationsignalswerefirstprocessedbywaveletpacket.Thenthroughtheobservationofdifferenttime-frequencyenergydistributionsinalevelofthewaveletpacketweobtainedtheoriginaldatasheetshowninTable1byextract
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