HSIC-based kernel independent component analysis for fault monitoring

For nonlinear and non-Gaussian industrial processes, KICA is a mature and successful method for fault monitoring. However, a fixed-point ICA algorithm uses a negative entropy method, which has relatively high requirements for non-quadratic function and initial point; accuracy is unsatisfactory. The calculation of control limits of Hotelling's T2 statistic is based on a kernel density estimation, which is difficult to calculate and implement and sometimes cannot guarantee accuracy. In this paper, the kernel independent component analysis method based on the Hibert-Schmidt independence criterion (HSIC) is used instead of the fixed-point ICA algorithm for fault monitoring to improve the accuracy of the independent element. We obtain the independent element directly from the objective function, rather than through the combination of KPCA and ICA. At the same time, we use the direct binomial expansion theorem to obtain the control limit, which reduces computational complexity and implementation difficulty and improves accuracy. The control limit is improved to obtain multi-fault diagnosis. Gray-level information and color information of each frame of the video are respectively read through the information entropy and HSV spatial color histogram. Experimental results show the advantage and effectiveness of the proposed approach. Meanwhile, shadow variables are introduced to smooth the statistics. The contributions of this paper are as follows. 1) Using the kernel independent component method based on HSIC for fault monitoring improves speed and accuracy. 2) The binomial expansion theorem is used instead of traditional kernel density estimation to calculate the control limit, which improves the results of fault monitoring. 3) A method of fault detection using information entropy, HSV color histogram and multivariate statistical analysis is presented.