聚类奇异谱分解方法及其在机械复合故障诊断中的应用

Clustering Singular Spectrum Decomposition Method and its Application in Mechanical Compound Fault Diagnosis

针对奇异谱分解(Singular Spectrum Decomposition,简称SSD)方法在重构奇异谱分量(Singular Spectrum Compo-nent,简称SSC)时的不足,结合聚类理论,提出了聚类奇异谱分解(Clustering Singular Spectrum Decomposition,简称CSSD)方法。该方法首先对时间序列数据构造轨迹矩阵;然后通过奇异值分解获得若干奇异值向量矩阵和特征值矩阵;接着利用对角平均化得到初始单分量;最后采用层次聚类方法计算任意两个初始单分量之间的相似度,并完成单分量的重构获得聚类奇异谱分量(Clustering Singular Spectrum Component,简称CSSC)。通过仿真信号和机械复合故障信号的分析结果表明,相比较于SSD方法,CSSD方法具有优越的分解性能并可以有效地提取出机械复合故障的特征。

In view of the deficiencies of the singular spectrum decomposition(SSD)method in reconstructing singular spectrum components(SSC),a clustering singular spectrum decomposition(CSSD)method is proposed combined with clustering theory.Firstly,the trajectory matrix is constructed for time series data.Secondly,several singular value vector matrices and feature matrices are obtained by singular value decomposition.Thirdly,the initial single components are obtained by diagonal averaging.Finally,the hierarchical clustering method is used to calculate the similarity between any two initial single components,and the clustering singular spectrum components(CSSCs)are obtained by reconstructing initial single compon-ents.The analysis results of the simulated signal and the mechanical compound fault signal show that compared with the SSD method,the CSSD method has superior decomposition performance and can effectively extract the characteristics of mechan-ical compound faults.