基于稀疏动态主元分析的故障检测方法

Fault detection based on sparse dynamic principal component analysis

摘要:

本文将动态主元分析(Dynamic Principal Component Analysis, DPCA)和稀疏主元分析(Sparse Principal Component Analysis, SPCA)两种方法结合起来，提出一种新的稀疏动态主元分析方法，并将其用于工业过程的故障检测。所提出的稀疏动态主元分析方法通过对过程数据的动态增广矩阵进行稀疏主元的求解，获取稀疏的负荷向量，该方法既考虑到了过程数据的动态特性，又降低了过程数据的冗余度，同时降低了计算负荷，非常适合工业过程的实时故障检测。此外，本文还提出了一种前向选择算法，用于确定稀疏主元中的非零负荷数目。最后，将所提出方法应用于数值例子和田纳西-伊斯曼过程，并将与主元分析、动态主元分析和稀疏主元分析等三种方法相比较，表明所提方法可以获得更好的故障检测效果。

Abstract:

In this paper, a new sparse dynamic principal component analysis (SDPCA) technique is proposed, which combines two popular monitoring methods, dynamic principal component analysis (DPCA) and sparse principal component analysis (SPCA). The proposed SDPCA is used for fault detection for industrial process. In the proposed SDPCA method, the sparse loading vectors are derived by solving an optimization problem through the dynamic augmented matrix of process data. SDPCA technique not only considers the temporal correlation of process data, but also reduces redundancy of the process data, meantime reduces the computation load. Moreover, we will discuss a new forward selection algorithm for determining the number of non-zero loadings. The proposed SDPCA method is assessed through a numerical example and Tennessee Eastman benchmark process. Results show that the SDPCA based fault detection method could obtain a better performance compared with PCA, DPCA and SPCA based methods. Key words：principal component analysis; sparse principal component analysis; dynamic principal component analysis; non-zero loading; Fault detection