Observation and Detection for a Class of Industrial Systems

Abstract

For a non-Gaussian process, a kernel principal component analysis that is applied to handle a Gaussian process is used to calculate a whitening matrix using the conventional kernel independent component analysis (KICA). Some errors exist as the orthogonal matrix is calculated by negentropy, which is an approximate method. In this paper, a kernel-independence-criterion-based independent component analysis algorithm for fault monitoring is proposed. The main contributions are as follows: 1) kernel independence criterion in regeneration Hilbert space is given. Based on which, an exact objective function is given. Compared with the conventional KICA, the accuracy of calculation is enhanced, and the proposed method is applied to any twice differentiable kernel function. 2) High computational efficiency is achieved by the quasi-Newton method that has a rapid convergence on the objective function. 3) The proposed method provides more stability to the local minimum value when the initialization data are far away from independent. The performance of the proposed method is illustrated by a numerical example and the penicillin fermentation process. Compared to the conventional KICA method, the experimental results show the advantages and effectiveness of the proposed approach.