Canonical Variate Nonlinear Principal Component Analysis for Monitoring Nonlinear Dynamic Processes

Conventional multivariate statistical process monitoring methods constrained by the assumptions of linear and normal distributions for the measurements, such as principal component analysis and canonical variate analysis, demonstrate significantly higher fault alarm rates and lower fault detection rates in nonlinear dynamic industrial process monitoring. Kernel principal component analysis (KPCA) based on the radial basis function, has already been applied in numerous nonlinear industrial processes. However, an infinite-dimensional nonlinear mapping might be inefficient and redundant. To improve the efficiency of traditional methods, this study proposes the implementation of canonical variate nonlinear principal component analysis for monitoring nonlinear dynamic processes. The training data are first preprocessed by performing canonical variate analysis to reduce the effects of the dynamic characteristics of the data. Then, the state vectors are projected into a high dimension feature space by an explicit second-order polynomial mapping. The first k principal components and the remaining residual vectors are obtained in the feature space via conventional principal component analysis for fault detection. The combined statistic Q(c) is proposed for monitoring the variations in the linear and nonlinear residual spaces; its upper control limits can be estimated by the kernel density function. In comparison to the results of KPCA and nonlinear dynamic principal component analysis, the proposed method yielded significantly higher fault detection rates and relatively lower fault alarm rates in a simulated nonlinear dynamic process and the benchmark Tennessee Eastman process.