Fault estimation of nonlinear processes using kernel principal component analysis

The principal component analysis (PCA) is a well-known technique to detect, isolate and estimate faults affecting a system. However, PCA identifies only linear structures in a given dataset. In this paper, we propose a new technique to estimate the fault affecting nonlinear systems, within the frame of kernel machines. To this end, the kernel methods are combined to the PCA, the so-called kernel PCA (KPCA), to diagnose a nonlinear system. As KPCA is applied in a high dimensional feature space, it is necessary to get back to the input space where the estimation can be interpreted. We derived an iterative pre-image technique that minimizes the square prediction error and the distance between the estimation of a new measure and the one just before it. The relevance of the proposed technique is shown on simulated data.