Fault detection in a multivariate process based on kernel PCA and kernel density estimation

Kernel principal component analysis (KPCA) is a method for performing a nonlinear form of principal component analysis (PCA). It involves nonlinear mapping of the input data onto a high dimensional feature space and performing PCA there. Through KPCA, nonlinear relations in the input space are detected as linear relations in the feature space. Furthermore, explicit computation of the mapping is not necessary in KPCA. Only dot products of the mapped data items in the feature space are required which are obtained directly from the input data using a kernel function. Moreover, control limits of traditional statistical process monitoring indices are usually determined under assumption of normal (Gaussian) distribution. Although, it is recognized that this is inappropriate in nonlinear processes, the impact of using kernel density estimation (KDE), which is a nonparametric method, to determine control limits in KPCA-based process monitoring has not been reported. This paper seeks to bridge this gap. The KPCA with KDE approach is applied to the Tennessee Eastman process for the detection of faults. The results confirm that associating KPCA with kernel density estimated control limits provides better monitoring performance than using control limits based on the normal probability density function.