Diagnosis of uncertain nonlinear systems using interval kernel principal components analysis: Application to a weather station

Abstract

The Principal Component Analysis (PCA) is one of the most known and used linear statistical methods for process monitoring. However, the PCA algorithm is not designed to handle the uncertainty of the sensor measurements that is represented by an interval type data. Including uncertainty of the sensors measurements in the analysis requires extending the PCA methodology to the Symbolic Data Analysis (SDA). The SDA refers to a paradigm where statistical units are described by interval-valued variables. In this regard, Symbolic Principal Component Analysis (SPCA), particularly Midpoints-Radii PCA (MRPCA) technique, is investigated for modeling and diagnosis of uncertain data. The aim of the present paper is to propose an extended version of the linear SPCA technique, based on midpoints and radii, to the nonlinear case of kernel PCA method (MR-KPCA). The basic idea is to construct a robust KPCA model from midpoints and radii of the nonlinear uncertain process data. Then, the robust KPCA model is used for diagnosis (FDI) purpose. In fact, the FDI decisions are improved by taking in to account the uncertainties on the nonlinear data. The MR-KPCA algorithm is applied for sensor fault detection and isolation of an automatic weather station. The results of applying this algorithm show its feasibility and advantageous performances.