Improved nonlinear process monitoring using KPCA with sample vector selection and combined index

Abstract

AbstractKernel principal component analysis (KPCA) has been found to be one of the promising methods for nonlinear process monitoring in recent years. It effectively captures the data nonlinearities by transforming the original data using nonlinear kernel functions and then performs linear PCA in high‐dimensional feature space F. However, KPCA is computationally intense, as it needs the solution of the eigenvalue decomposition problem involving a high‐dimensional kernel matrix. The present work addresses this issue by adopting a sample vector selection (SVS) scheme that facilitates the analysis in a lower dimensional kernel space formed by a set of optimally selected transformed samples in F. These sample vectors are selected through an iterative sequential forward selection procedure based on a geometric consideration. Furthermore, the efficiency of the KPCA methodology is improved by proposing a combined index‐based process monitoring in the reduced kernel space. The performance of the proposed methodology is evaluated by applying it to a complex nonlinear Tennessee Eastman process. The results demonstrate the better fault detection ability of the proposed methodology in terms of lower computational effort and reduced false alarm and missed detection rates. Copyright © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.