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双约束非负矩阵分解的复合故障信号分离方法.docx

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双约束非负矩阵分解的复合故障信号分离方法 Title:CompositeFaultSignalSeparationusingBi-constrainedNon-negativeMatrixFactorization Abstract: Inrecentyears,theanalysisandseparationoffaultsignalsfromnoisymeasurementshavegainedsignificantattentioninvariousfields,suchasfaultdiagnosis,signalprocessing,andmachinelearning.Non-negativeMatrixFactorization(NMF)hasbeenwidelyemployedasaneffectivesignalseparationtechnique,particularlyinthecontextoffaultdetectionandidentification.Thispaperproposesanovelcompositefaultsignalseparationmethodusingbi-constrainedNMF,whichcombinesthebenefitsofbothnon-negativityandbi-constrainttoachieveaccurateandrobustfaultsignalseparation. Introduction: Faultsignals,alsoknownasanomalyordisturbancesignals,canoftenbeoverwhelmedbynoiseinpracticalscenarios,makingtheiranalysisandseparationchallenging.Theaccurateseparationoffaultsignalsfromnoisymeasurementsiscrucialforimprovingthereliabilityandefficiencyoffaultdetectionanddiagnosissystems.Non-negativeMatrixFactorization(NMF)hasemergedasapowerfultoolforseparatingmixedsignalsbydecomposingagivenmatrixintotwonon-negativefactors,representingthefaultandnoisecomponents. Methods: 1.Bi-constrainedNMFmodel: Theproposedcompositefaultsignalseparationmethodisbasedonabi-constrainedNMFmodel.TheNMFmodelaimstofactorizetheobservedmixedsignalmatrixMintotwomatrices:HrepresentingthefaultcomponentandWrepresentingthenoisecomponent.Inbi-constrainedNMF,additionalconstraintsareintroducedtoenforcethefactormatricestobenon-negativeandrepresentativeofthefaultandnoisesignatures. 2.Objectivefunction: Theobjectivefunctionofthebi-constrainedNMFmodelconsistsoftwoterms.Thefirsttermmeasuresthereconstructionerror,aimingtominimizethedistancebetweentheobservedmixedsignalmatrixanditsapproximationthroughthefaultandnoisecomponents.Thesecondtermincorporatesthebi-constraints,penalizingnegativeelementsinthefactormatricestoenforcenon-negativity. 3.Optimizationalgorithm: Tosolvethebi-constrainedNMFproblem,anefficientoptimizationalgorithmisdesigned.Thealgorithmiterativelyupdates