Improved nonlinear fault detection technique and statistical analysis

In this article, first, some drawbacks of original Kernel Principal Component Analysis (KPCA) and Kernel Independent Component Analysis (KICA) are analyzed. Then the KPCA and KICA for multivariate statistical process monitoring (MSPM) are improved. The drawbacks of original KPCA and KICA are as follows: The data mapped into feature space become redundant; linear data introduce errors while the kernel trick is used; computation time increases with the number of samples. To solve the above problems, the original KPCA and KICA for MSPM are improved: similarity factors of the observed data in the input and feature space are defined; similar characteristics are measured; similar data are removed according to the similarity measurements; and k-means clustering in feature space is used to isolate different classes. Specifically, the similarity concept of data in one group is first proposed. Applications of the proposed approach indicate that improved KPCA and KICA effectively capture the nonlinearities. © 2008 American Institute of Chemical Engineers AIChE J, 2008