Reduced kernel PCA based approach for fault detection in complex systems

Abstract

Multivariate statistical methods have been widely applied to complex systems for fault detection. While methods based on principal component analysis (PCA) are popular, more recently kernel PCA (KPCA) has been utilized to better model nonlinear process data. This report proposes a new method for fault detection using a reduced kernel principal component analysis (RKPCA) to cope with the computational problem introduced by KPCA. The proposed RKPCA method consists on reducing the number of observations in a data matrix using the dissimilarities between the pairs of its observations. PCA, KPCA and the suggested approach RKPCA are carried out using the cement rotary kiln system. The Hotelling’s T², Q in addition to the new proposed index called the combined statistic φ are used as fault indicators. The two methods PCA and KPCA are compared to the proposed approach in terms of False Alarms Rate (FAR), Missed Alarms Rate (MDR), Detection Time Delay (DTD), the cost function (J) and the Execution Time (ET). The obtained results demonstrate the effectiveness of the proposed technique in reducing the computational time from 1h37min when KPCA is used to 9min30s.Moreover, it has effectively detected the different types of faults when using the φ index.