Parallel PCA-KPCA for nonlinear process monitoring

Both linear and nonlinear relationships may exist among process variables, and monitoring a process with such complex relationships among variables is imperative. However, individual principal component analysis (PCA) or kernel PCA (KPCA) may not be able to characterize these complex relationships well. This paper proposes a parallel PCA-KPCA (P-PCA-KPCA) modeling and monitoring scheme that incorporates randomized algorithm (RA) and genetic algorithm (GA) for efficient fault detection for a process with linearly correlated and nonlinearly related variables First, to determine the included variables in the parallel PCA (P-PCA) and the parallel KPCA (P-KPCA) models, GA-based optimization is performed, in which RA is used to generate faulty validation data. Second, monitoring statistics are established for the P-PCA and the P-KPCA models, in which the process status is determined. The proposed monitoring scheme discriminates the linear and nonlinear relationships among variables in a process and deals with nonlinear processes efficiently. We provide case studies on a numerical example and the continuous stirred tank reactor process. These case studies demonstrate that the proposed P-PCA-KPCA monitoring scheme is better than conventional PCA- or KPCA-based methods at performing nonlinear process monitoring.