基于降秩核独立成分分析的故障检测算法

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关键词：核独立成分分析算法；故障检测；降秩；核矩阵；田纳西-伊斯曼过程；统计量中图分类号：TN911.7-34；TP277 文献标识码：A 文章编号：1004-373X（2025）20-0135-07

FaultdetectionalgorithmbasedonRR-KICA

GUOJinyu，FENGChuang，LIYuan （CollegeofInformation Engineering，Shenyang UniversityofChemical Technology，Shenyang11O142，China）

Abstract：Inorder tosolvetheproblemof high computationalcomplexityandlong running timeof traditional kernel independentcomponentanalysis （KICA）algorithmwhenprocessingalargenumberofsamples，afaultdetectionalgorithmbased onreducedrankkernelindependentcomponentanalysis（RR-KICA）isproposed.Thisalgorithmcanimprovetheconstructionof thekernelmatrix，calculatethekernelvectorofeachnewdata，andupdatethekernelmatrixbyaddingrowandcolumnvectors. Basedonwhetherthekernelmatrixisfullrank，thekernelvectorisretainedornotcanbedetermineduntilthecompletepartof thekernelvectoriscalculatedandthekernelmatrix isconstructed，thusestablishing theRR-KICAmodelandcalculatingthe I2 statisticandcontrol limitof thetraining data.The testing dataisprojected ontotheRR-KICA model，and the I2 statistic is calculated and compared with the control limit of the training data.If the Iz statistic exceeds the control limit，it indicates a fault. TheproposedalgorithmisapliedtotheTenessee-Eastan（TE）process，adcompaedwithKCA，KLPP，KECA，KICA， KEICAandRR-KPCAalgorithms.TheresultsshowthatRR-KICAalgorithmhasbeterfaultdetectionperformancethanother algorithmsintermsofdetectionrate，falsealarmrate，detectiondelayandrunningtime.IntheRR-KICAalgorithm，therank reductionmethodisappliedtothecalculationofthekernlmatrix，rducingthedimensionalityoftekerelmatrix，simplifying theKICAmodel，faciliatingtheextractionofmoredatainformationinthefuture，andalsoshorteningthealgorithm'sruing time.

Keywords：kerelindependentcomponentanalysis;faultdetection;reducedrank;kerelmatrix;Tenneee-Eastmanproes; statistic

0 引言

代工业生产过程逐渐向复杂化方向发展，与之相关的故障检测技术变得尤为重要。（剩余8510字）