Efficient recursive kernel principal component analysis for nonlinear time-varying processes monitoring

Due to the nonlinear time-varying characteristics of industrial processes, the kernel principal component analysis (KPCA) without updating statistics would result in a much higher false alarm rate. To monitor nonlinear time-varying processes more effectively, an efficient recursive kernel principal component analysis (ERKPCA) is proposed based on recursive eigenvalue decomposition with less complexity. First, the new observations data are projected into a high-dimensional linear feature space using a nonlinear mapping method. In the linear feature space, the first order perturbation theory is introduced to update the eigenvalues and eigenvectors directly, which can reduce the computational cost to (O(m
²
)) compared with that of the traditional eigenvalue decomposition ((O(m
³
))). The distribution of the kernel principal components and residual in the feature space are non-Gaussian, thus upper control limits of statistics can be derived by kernel density estimation. With the simulation of the Tennessee Eastman chemical process, the monitoring results illustrate the validity of the proposed approach. It can not only accommodate the slow process drift under normal operation, but also identify the three types of process faults in nonlinear time-varying processes.