矿井提升机外文翻译

word文档可自由复制编辑word文档可自由复制编辑word文档可自由复制编辑外文翻译部分：英文原文Mine-hoistfault-conditiondetectionbasedonthewaveletpackettransformandkernelPCAAbstract:Anewalgorithmwasdevelopedtocorrectlyidentifyfaultconditionsandaccuratelymonitorfaultdevelopmentinaminehoist.ThenewmethodisbasedontWaveletPacketTransform(WPT)andkernelPCA(KernelPrincipalComponentAnalysis,KPCA).Fornon-linearmonitoringsystemsthekeytofaultdetectionisthextractingofmainfeatures.Thewaveletpackettransformisanoveltechniqueofsignalprocessingthatpossessesexcellentcharacteristicsoftime-frequencylocalization.Itissuitableforanalyzingtime-varyingortransientsignals.KPCAmtheoriginalinputfeaturesintoahigherdimensionfeaturespacethroughanon-linmapping.Theprincipalcomponentsarethenfoundinthehigherdimensionfeaturespace.TheKPCAtransformationwasappliedtoextractingthemainnonlinearfeaturesfromexperimentalfaultfeaturedataafterwaveletpackettransformation.Tresultsshowthattheproposedmethodaffordscrediblefaultdetectionandidentification.Keywords:kernelmethod;PCA;KPCA;faultconditiondetection1IntroductionBecauseaminehoistisaverycomplicatedandvariablesystem,thehoistwillinevitablygeneratesomefaultsduringlong-termsofrunningandheavyloading.Thiscanleadtoequipmentbeingdamaged,toworkstoppage,toreducedoperatingefficiencyandmayevenposeathreattothesecurityofminepersonnel.Thereforetheidentificationofrunningfaultshasbecomeanimportantcomponentofthesafetsystem.Thekeytechniqueforhoistconditionmonitoringandfaultidentificationisextractinginformationfromfeaturesofthemonitoringsignalsandthenofferingajudgmentalresult.However,therearemanyvariablestomonitorinaminehoistand,also,therearemanycomplexcorrelationsbetweenthevariablesandtheworkingequipment.Thisintroducesuncertainfactorsandinformationasmanifestedbycomplexformssuchasmultiplefaultsorassociatedfaults,whichintroduceconsiderabledifficultytofaultdiagnosisandidentification[1].Therearecurrentlymanyconventionalmethodsforextractingminehoistfaultfeatures,suchasPrincipaComponentAnalysis(PCA)andPartialLeastSquares(PLS)[2].Thesemethodshavebeenappliedtotheactualprocess.However,thesemethodsareessentiallyalineartransformationapproach.Butheactualmonitoringprocessincludesnonlinearityindifferentdegrees.Thus,researchershaveproposedaseriesofnonlinearmethodsinvolvingcomplexnonlineartransformations.Furthermore,thesenon-linearmethodsareconfinedtofaultdetection:Faultvariableseparationandfaultidentificationarestilldifficultproblems.ThispaperdescribesahoistfaultdiagnosisfeatureexactionmethodbasedontheWaveletPacketTransform(WPT)andkernelprincipalcomponentanalysis(KPCA).WeextractthefeaturesbyWPTandthenextractthemainfeaturesusingaKPCAtransform,whichprojectslow-dimensionalmonitoringdatasamplesintoahigh-dimensionalspace.Thenwedoadimensionreductionandreconstructionbacktothesingularkernelmatrix.Afterthat,thetargetfeatureisextractedfromthereconstructednonsingularmatrix.Inthiswaytheexacttargetfeatureisdistinctstable.Bycomparingtheanalyzeddataweshowthatthemethodproposedinthispaperiseffective.FeatureextractionbasedonWPTandKPCA2.1WaveletpackettransformThewaveletpackettransform(WPT)method[3],whichisageneralizationofwaveletdecomposition,offersarichrangeofpossibilitiesforsignalanalysis.Thefrequebandsofahoist-motorsignalascollectedbythesensorsystemarewide.Theusefuinformationhideswithinthelargeamountofdata.Ingeneral,somefrequenciesoftsignalareamplifiedandsomearedepressedbytheinformation.Thatistosay,thebroadbandsignalscontainalargeamountofusefulinformation:Buttheinformationcannotbedirectlyobtainedfromthedata.TheWPTisafinesignalanalysismethothatdecomposesthesignalintomanylayersandgivesabetterresolutioninthetime-frequencydomain.Theusefulinformationwithinthedifferentfrequencybandswillbeexpressedbydifferentwaveletcoefficientsafterthedecompositionofthesignal.Theconceptof“energyinformation”ispresentedtoidentifynewinformationhiddenthedata.Anenergyeigenvectoristhenusedtoquicklymineinformationhidingwithinthelargamountofdata.Thealgorithmis:Step1:Performa3-layerwaveletpacketdecompositionoftheechosignalsandextractthesignalcharacteristicsoftheeightfrequencycomponents,fromlowtointhe3rdlayer.Step2:Reconstructthecoefficientsofthewaveletpacketdecomposition.Use3jS(j=0,1,…,7)todenotethereconstructedsignalsofeachfrequencybandrangeinthe3rdlayer.Thetotalsignalcanthenbedenotedas:s7S（1）3jj0Step3:ConstructthefeaturevectorsoftheechosignalsoftheGPR.Whenthecouplingelectromagneticwavesaretransmittedundergroundtheymeetvariousinhomogeneousmedia.Theenergydistributingoftheechosignalsineachfrequencybandwillthenbedifferent.Assumethatthecorrespondingenergyof3jS(j=0,1,…,7)canberepresentedas3jE(j=0,1,…,7).ThemagnitudeofthedisperpointsofedthereconstructedsignaljSis:3jkx(j=0,1,…,7;k=1,2,…,n),wherenisthelengthofthesignal.Thenwecanget:word文档可自由复制编辑word文档可自由复制编辑word文档可自由复制编辑ES(t)2dtnx2（2）3j3jjkk1Considerthatwehavemadeonlya3-layerwaveletpackagedecompositionoftheechosignals.Tomakethechangeofeachfrequencycomponentmoredetailedthe2-rankstatisticalcharacteristicsofthereconstructedsignalisalsoregardedasafeaturevector:1n2D (xx)（3）3jn jk jkk1Step4:The3jEareoftenlargesowenormalizethem.AssumethatE7E3j2,J0thusthederivedfeaturevectorsare,atlast:T=[E/1,E/1,,E/1,E/1]（4） 30 31 36 37Thesignalisdecomposedbyawaveletpackageandthentheusefulcharacteristicinformationfeaturevectorsareextractedthroughtheprocessgivenabove.Comparedtoothertraditionalmethods,liketheHilberttransform,approachesbasedontheWPanalysisaremorewelcomeduetotheagilityoftheprocessanditsscientificdecomposition.2.2KernelprincipalcomponentanalysisThemethodofkernelprincipalcomponentanalysisapplieskernelmethodstoprincipalcomponentanalysis[4–5].LetxRN,k1,2,...,M,Mx0.Theprincipalcomponentistheelementatthek kk11diagonalafterthecovariancematri，CxMMxxThasbeendiagonalized.ijj1Generallyspeaking,thefirstNvaluesalongthediagonal,correspondingtothelargeeigenvalues,aretheusefulinformationintheanalysis.PCAsolvestheeigenvaluesandeigenvectorsofthecovariancematrix.Solvingthecharacteristicequation[6]: 1M(x)x（5）c M j jj1wheretheeigenvalues0andtheeigenvectorsRN\0isessenceofPCA.Letthenonlineartransformations,:RNF,xX,projecttheoriginalspaceintofeaturespace,F.Thenthecovariancematrix,C,oftheoriginalspacehasthefollowingforminthefeaturespace:C1M(x)(x)T（6） M i jJ1NonlinearprincipalcomponentanalysiscanbeconsideredtobeprincipalcomponentanalysisofCinthefeaturespace,F.Obviously,alltheeigenvaluesofC(0)andeigenvectors,VF\{0}satisfyV=CV.Allofthesolutionsareinthesubspacethattransformsfrom(x),i1,2,...,Mj((x)V)(x)CV,k1,2,...,M（7） k kThereisacoefficientLetiVM(x)（8） i ii1FromEqs.(6),(7)and(8)wecanobtain:Ma((x)(x)) i k ji1 （9）1Ma((x)M(x))((x)(x))M i k j k j i1 j1wherek=1,2,…..,M.DefineAasanM×Mrankmatrix.Itselementsare:A(x)(x)（10）ij i jFromEqs.(9)and(10),wecanobtainMAa=A2a.Thisisequivalentto:Ma=Aa.(11)MakeasA’seigenvalues,and,,...,,asthecorresponding1 2 M 1 2 Meigenvector.Weonlyneedtocalculatethetestpoints’projontheeigenvectorsctonsVkthatcorrespondtononzeroeigenvaluesinFtodotheprincipalcomponentextraction.Definingthisasitisgivenby:k(Vk(x))Mk((x)x)(12) i i ki1Principalcomponentweneedtoknowtheexactformofthenon-linearimage.Alsoasthedimensionofthefeaturespaceincreasestheamountofcomputationgoesupexponentially.BecauseEq.(12)involvesaninner-productcomputation,(x)(x)iaccordingtotheprinciplesofHilbert-SchmidtwecanfindakernelfunctionthatsatisfiestheMercerconditionsandmakesK(x,x)(x)(x)ThenEq.(12)can i ibewritten:(Vk(x))Mk(K(x,x))(13) i i ki1HereistheeigenvectorofK.Inthiswaythedotproductmustbedoneintheoriginalspacebutthespecificformofxneednotbeknown.Themapping,x,andthefeaturespace,F,areallcompletelydeterminedbythechoiceofkernelfunction[7–8].2.3DescriptionofthealgorithmThealgorithmforextractingtargetfeaturesinrecognitionoffaultdiagnosisis:Step1:ExtractthefeaturesbyWPT;Step2:Calculatethenuclearmatrix,K,foreachsample,xRN(i1,2,...,N)intheioriginalinputspace,andK((x)(x)) ij iStep3:Calculatethenuclearmatrixafterzero-meanprocessingofthemappingdatainfeaturespace;Step4:SolvethecharacteristicequationMa=Aa;Step5:ExtractthekmajorcomponentsusingEq.(13)toderiveanewvector.BecausethekernelfunctionusedinKPCAmettheMercerconditionsitcanbeusedinsteadoftheinnerproductinfeaturespace.Itisnotnecessarytoconsiderthepreciseformthenonlineartransformation.Themappingfunctioncanbenon-linearandthedimensionsofthefeaturespacecanbeveryhighbutitispossibletogetthemainfeaturecomponentseffectivelybychoosingasuitablekernelfunctionandkernelparameters[9].3ResultsanddiscussionThecharacterofthemostcommonfaultofaminehoistwasinthefrequencyoftheequipmentvibrationsignals.Theexperimentusedthevibrationsignalsofaminehoisastestdata.Thecollectedvibrationsignalswerefirstprocessedbywaveletpacket.Thenthroughtheobservationofdifferenttime-frequencyenergydistributionsinalevelofthewaveletpacketweobtainedtheoriginaldatasheetshowninTable1byextractingthefeaturesoftherunningmotor.Thefaultdiagnosismodelisusedforfaultidentificationorclassification.Experimentaltestingwasconductedintwoparts:ThefirstpartwascomparingtheperformanceofKPCAandPCAforfeatureextractionfromtheoriginaldata,namely:ThedistributionoftheprojectionofthemaincomponentsofthetestedfaultsamplesThesecondpartwascomparingtheperformanceoftheclassifiers,whichwereconstructedafterextractingfeaturesbyKPCAorPCA.Theminimumdistanceandnearest-neighborcriteriawereusedforclassificationcomparison,whichcanalsotestheKPCAandPCAperformance.Inthefirstpartoftheexperiment,300faultsampleswereusedforcomparingbetweenKPCAandPCAforfeatureextraction.TosimplifythecalculationsaGaussiankernelfunctionwasused:xy2K(x,y)(x),(y)exp()1022Thevalueofthekernelparameter,,isbetween0.8and3,andtheintervalis0.4whenthenumberofreduceddimensionsisascertained.Sothebestcorrectclassificationrateatthisdimensionistheaccuracyoftheclassifierhavingthebestclassificationresults.Inthesecondpartoftheexperiment,theclassifiers’recognitirateafterfeatureextractionwasexamined.Comparisonsweredonetwoways:theminimumdistanceorthenearest-neighbor.80%ofthedatawereselectedfortrainingandtheother20%wereusedfortesting.TheresultsareshowninTables2and3.FromTables2and3,itcanbeconcludedfromTables2and3thatKPCAtakeslesstimeandhasrelativelyhigherrecognitionaccuracythanPCA.4ConclusionsAprincipalcomponentanalysisusingthekernelfaultextractionmethodwasdescribed.Theproblemisfirsttransformedfromanonlinearspaceintoalinearhigherdimensionspace.Thenthehigherdimensionfeaturespaceisoperatedonbytakingtheinnerproductwithakernelfunction.Thistherebycleverlysolvescomplexcomputingproblemsandovercomesthedifficultiesofhighdimensionsandlocalminimization.Ascanbeseenfromtheexperimentaldata,comparedtothetraditionalPCAtheKPCAanalysishasgreatlyimprovedfeatureextractionandefficiencyinrecognitionfaultstates.word文档可自由复制编辑word文档可自由复制编辑word文档可自由复制编辑ReferencesRibeiroRL.Faultdetectionofopen-switchdamageinvoltage-fedPWMmotordrivesystems.IEEETransPowerElectron,2003,18(2):587–593.SottileJ.Anoverviewoffaultmonitoringanddiagnosisinminingequipment.IEEETransIndAppl,1994,30(5):1326–1332.PengZK,ChuFL.Applicationofwavelettransforminmachineconditionmonitoringandfaultdiagnostics:areviewwithbibliography.MechanicalSystemsandSignalProcessing,2003(17):199–221.RothV,SteinhageV.Nonlineardiscriminantanalysisusingkernelfunction.In:AdvancesinNeuralInformationProceedingSystems.MA:MITPress,2000:568–574.TwiningC,TaylorC.Theuseofkernelprincipalcomponentanalysistomodeldatadistributions.PatternRecognition,2003,36(1):217–227.MullerKR,MikaS,RatschS,etal.Anintroductiontokernel-basedlearningalgorithms.IEEETransonNeuralNetwork,2001,12(2):181.XiaoJH,FanKQ,WuJP.AstudyonSVMforfaultdiagnosis.JournalofVibration,Measurement&Diagnosis,2001,21(4):258–262.ZhaoLJ,WangG,LiY.StudyofanonlinearPCAfaultdetectionanddiagnosismethod.InformationandControl,2001,30(4):359–364.XiaoJH,WuJP.Theoryandapplicationstudyoffeatureextractionbasedonkernel.ComputerEngineering,2002,28(10):–386.中文译文基于小波包变换和核主元分析技术的矿井提升机的自我故障检测摘要：这是一种新的运算法，它能正确识别矿井提升机的故障并且准确地监测矿井提升机故障的发展过程。这种方法是基于小波包变换（WPT）和核主成份分析（KPCA，核主成份分析）技术。对于非线性监听系统，故障检测的关键是提取主要特征。小波包变换是时间频率的局部化分析，尤其适合于非平稳信号。KPCA就是将最初输入的数据特征透过非线性映射映射到高维特征空间，然后在高维特征空间发现其主要组成部分。KPCA变换适用于从经过小波包变换的实验故障特征数据中提取主要的非线性特征。结果表示，该方法能提供可靠的故障检测和鉴定。关键词：核心方法;主成分分析;核主元分析;故障检测1介绍因为矿井提升机是一种复杂的可变性比较大的系统，提升机在长期运行和重载情况下难免会产生一些故障。这些都有可能损坏设备，停工，降低工作效率，甚至对我们员工的安全带来威胁。因此，运行中故障的检测已经变成安全系统的一个重要组成部分。提升机状态监测与故障识别的关键技术是从监测信号特征中提取的信息和提供一个判断的结果。但是，在矿井提升机的检测中有很多不同的情况，而且在各种各样的工作设备之间有许多复杂的相互关系。这里不确定因素和数据由复杂的形式所表现，如多个故障或相关故障，这些故障的诊断和鉴定是相当困难的。目前有许多传统的方法可以提取矿井提升机故障特征，如主成分分析（PCA）和偏最小二乘法（PLS）。这些方法已经被熟练的运用于我们的实际生产中来。然而，这些方法基本上是一个线性变换方法。但实际监测过程包括不同程度的非线性。因此我们的研究员已经提出了一系列涉及复杂的非线性变换非线性方法。此外，这些非线性方法只限于故障检测，故障变量分离和故障识别仍然是难以解决的问题。这篇论文是介绍了一种基于小波包变换（WPT）和核主成份分（KPCA）的矿井提升机故障诊断的特征提取方法。我们用WPT提取特征数据然后用核主成分分析变换提取主要数据特征，这种变换将低维的监测数据样本映射到高维的特征空间。然后我们做了降维和重建并备份到奇异核矩阵。在这之后，目标特征从重构的非奇异矩阵提取出来。用这样的方法我们得到清楚又稳定的目标特征。通过比较分析数据，我们得出本文提出的方法是有效的。2基于小波包变换和主成分分析技术的特征提取2.1小波包变换小波包变换（小波包变换）方法[3]，这是一种小波的分解的概括，为信号分析提供了很多可能。传感器系统收集到的升降器的信号频带是非常广泛的。有用的信息隐藏在大量的数据中。一般情况下，某些频率的信号被放大，某些频率的信号被抑制。这就是说，这些宽带信号包含大量有用的信息：但是从这些信息中不能直接获得有用数据。小波包变换是一个很好的信号分析方法，它把信号分解成很多层的信号并在时频域给出了一个更好的分辨率，不同频段内的有用信息在信号分解后将被不同的小波系数表达。该信号的提出，是以确定新的信息隐藏在数据的中新信息。然后一种能量特征向量快速挖掘隐藏在大量的数据中的有用信息。该算法是：第1步：将回波信号执行3层小波包分解，并提取8个频率成分的信号特征在第三层，从低到高。第2步：重构小波包分解的系数。利用3jS(j=0,1,…,7)指每个重建信号的频带范围内的第3层。总的信号就可以被命名为：s7S（1）3jj0第3步：构建的探地雷达回波信号的特征向量。当电磁波的耦合传输他们满足各种地下非均匀介质。能源分布的回波信号在每个频带然后将不同：承担相应的能量3jS(j=0,1,…,7)可以代表3jE(j=0,1,…,7).的规模分散点的重建信号3jS是jkx(j=0,1,…,7;k=1,2,…,n),word文档可自由复制编辑word文档可自由复制编辑word文档可自由复制编辑其中n是长度的信号。然后，我们可以得到：ES(t)2dtnx2（2）3j3jjkk1考虑到我们做的只有3层的回波信号的小波包分解。为了使每个频率成分的变化更详细，重构信号的2级的统计特性也被视为一个特征向量：1n2D (xx)（3）3jn jk jkk1(4)第4步3jE往往大，所以我们将他们标准化。假设E7E3j2，从而得J0出的特征向量是，最后：T=[E/1,E/1,,E/1,E/1] 30 31 36 37信号通过小波包变换分解，然后提取有用的特征信息的特征向量通过上述过程。相对于其他传统方法，像希尔伯特变换，基于小波包变换分析方法更受欢迎，这是由于它敏捷的过程和它的科学分解。2.2核主成份分析核主成分份析方法就是将核心方法应用在主成分分析法中[4-5]。使xRN,k1,2,...,M,Mx0.主要组成部分是在对角线元素后，协方差矩阵，k kk11MCxxT已是结尾。一般而言，第一次N值山对角线长，相应的大特征值，M ijj1是有用的信息在数据分析.PCA解决了特征值和特征向量的协方差矩阵。求解特征方程[6]：c1M(x)xM j jj1如果特征值和特征向量0，RN/0是属于PCA的。使非线性变换，RNF,xX项目原始空间到特征空间，楼然后，协方差矩阵，中，原来的空间具有下列表格中的功能空间：C1M(x)(x)T(6) M i jJ1非线性主成分分析可被认为是主成分分析的功能空间，楼显然，所有的C(0)抗原值和特征向量，VF\{0}满足VCV。所有的解决方案是在子这一转变从(x),i1,2,...,M j ((x)V)(x)CV,k1,2,...,M（7） k k使系数i可以得到VM(x)（8） i ii1从678式我们可以得到Ma((x)(x)) i k ji1 (9)1Ma((x)M(x))((x)(x))M i k j k j i1 j1使k=1,2,…,M定义A是M×M的矩阵，它的要点是A(x)(x)（10）ij i j从9和10式我们可以得到MAa=A2a这就相当于Ma=Aa.（11）使作为A的特征值，以及,...,相应的特征向量。我们只需 1 2 M 1 2 M要计算测试点的预测的特征向量对应的非零特征值的F这样做主要成分的提取。界定这种因为它是由：(Vk(x))Mk((x)x)(12) i i ki1主要组成部分，我们需要知道确切形式的非线性图像。还为层面的特征空间增加了计算量随之呈指数。由于均衡器。由于式（12）涉及内积计算，(x)(x)i根据希尔伯特-施密特的原则，我们可以找到一个内积函数，满足的默瑟条件下，方程（12）K(x,x)(x)(x)可以改写成(Vk(x))Mk(K(x,x))i i i i ki1这里是K的一个变量。这样，点积必须在原来的空间，但(x)的具体形式没必要知道。特征空间F，完全取决于选择的核心特征[7-8]。2.3说明算法在故障诊断的识别中提取目标特征的算法是：第1步：用小波包变换提取特征;第2步：计算每个样本的核矩阵，KxRN(i1,2,...,N)在原始的空间输入，和K((x)(x))i ij i第3步：在特征空间进行测绘数据的均值处理，然后计算核矩阵;第4步：求解特征方程Ma=Aa;第5步：利用方程提取的K式的重要组成部分(13)，制定出一个新的载体。由于核函数在核主成分分析要满足Mercer的条件，可用于代替内积的特征空间。没有必要考虑的具体形式的非线性变换。映射功能可以非线性和特征空间的尺寸可以很高，但有它可能得到有效的主要成分通过选择合适的核函数和内核参数[9]。3结果与讨论矿井提升机的最常见的故障特征可以在设备振动信号的频率中提取出来。实验中使用矿井提升机的振动信号作为测试数据，将收集到的振动信号首先进行小波包处