Multivariate Statistical Monitoring of Nonlinear Biological Processes Using Kernel Pca

In this paper, a new nonlinear process monitoring technique based upon kernel principal component analysis (KPCA) is developed. In recent years, KPCA has been emerging to tackle the nonlinear monitoring problem. KPCA can efficiently compute principal components in high dimensional feature spaces by the use of integral operator and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then compute the principal components in that feature space. In comparison to other nonlinear PCA techniques, KPCA requires only the solution of an eigenvalue problem without any nonlinear optimization. Based on T and SPE charts in the feature space, KPCA was applied to fault detection in the simulation benchmark of the biological wastewater treatment process (WWTP). The proposed approach can effectively capture the nonlinear relationship in process variables and its application for process monitoring shows better performance than PCA. Copyright © 2004 IFAC