结构振动信号盲源分离的快速复杂度追踪算法

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关键词：盲源分离；模态参数识别；复杂度追踪；梯度下降；子空间搜索 中图分类号：TB123；TN911.6 文献标志码：A DOI：10.16385/j.cnki.issn.1004-4523.202310029

Fast complexity pursuit algorithm for blind source separation ofstructural vibration signals

HU Zhixiang，HUANGLei，HE Wenyu （College of Civil Engineering，HefeiUniversityof Technology，Hefei 23OoO9，China）

Abstract：Blindsourceseparation（BSS）canbeused toextractmodalcoordinatevibrationsfromstructuralvibrationsignals.Complexitypursuit（CP）isoneof theclasicalmethodsforsolvingtheBSS problem.Toimprove thecomputationaleficiencyof the CPalgorithm，thispaperproposestwoenhancements：ituses thenegativelogfunctionofaGausiandistributionasanonlinear functiontoestimatesignalcomplexityandderivesformulasforrapidlycomputingsignalcomplexityanditsgradient;itemploysa subspacesearch-based gradientdescentalgorithm tocalculate theoptimalmixing vectorinthereduced subspace.Thenew formulas onlyrequire thecovariance matrixofmixed signalsandthecovariance matrixoftimedelayswhencomputingcomplexityanditsgradient，without using allsignaldata.Numerical examples and structural vibrationdataareemployed to evaluatethe proposed method.Theresultsdemonstrate thatthefastcomplexitypursuitalgorithmoutperforstraditionalmethodsintermsofcomputationalefficiency and accurately separates structural modal coordinate vibrations.

Keywords：blind source separation;modalparameter identification;complexity pursuit;gradientdescent;subspace search

结构模态参数（振型、频率和阻尼比）是结构的固有属性，在地震、风荷载等作用下，结构出现损伤时模态参数会发生变化，可以在一定程度上反映结构的健康状态，因此，结构模态参数的识别是结构健康监测的重要内容[1-2]

盲源分离（blindsource separation，BSS）是一种新型的信号处理技术，该技术在语音处理、生物医学工程、数据挖掘以及振动信号处理等多个领域显现出了重要的应用价值[3]。（剩余12317字）