基于主元分析得分重构差分的故障检测策略

Fault detection strategy based on difference of score reconstruction associated with principal component analysis

基于主元分析(PCA)的统计过程控制方法通常假设数据的生成过程是独立同分布的.当数据存在多模态结构或过程变量非线性相关时, PCA方法的故障检测性能将受到影响.针对上述问题,本文提出一种基于PCA得分重构差分的故障检测策略.首先,应用PCA将输入空间分解为主元子空间和残差子空间;接下来,应用k近邻(kNN)规则重构当前样本得分向量并计算样本的得分重构差分向量;最后,计算得分重构差分向量的统计值并进行故障检测.本文方法不仅可以降低数据多模态和变量非线性相关等特征对过程故障检测的影响,同时可以降低统计量的自相关性、提高过程故障检测率.将本文方法在两个模拟例子和田纳西–伊斯曼(TE)过程中进行测试,并与PCA、核主元分析(KPCA)、动态主元分析(DPCA)和k 最近邻故障检测(FD–kNN)方法进行对比分析,测试结果证明了本文方法的有效性.

The statistical process control based on principal component analysis (PCA) usually assumes that the underlying data generation process is independent and identically distributed (I.I.D.). When PCA is applied to detect faults in a process with multimodal structure or nonlinear monitored variables, its fault detection performance will descend. Aiming at the above limitations of PCA, a fault detection strategy based on difference of score reconstruction associated with PCA (Diff–PCA) is proposed in this paper. First, an input space is decomposed into two subspaces: principal component subspace (PCS) and residual subspace (RS) using PCA. Next, the reconstructed score vectors of each score vector are computed respectively through k nearest neighbors (kNN) rule in PCS and RS, and then a difference vector of score reconstruction can be also obtained. At last, the statistic values of the difference vectors are monitored to detect faults. Diff–PCA is capable of not only reducing the influence of multimodal and nonlinear characteristics, but also eliminating the autocorrelation of the statistic and improving the fault detection rate (FDR). The efficiency of the proposed strategy is implemented in two simulated cases and in the Tennessee Eastman (TE) processes. The experimental results indicate that the proposed method outperforms the conventional PCA, Kernel PCA( KPCA), Dynamic PCA (DPCA) and the fault detection method based on k nearest neighbors (FD–kNN).