Randomized Kernel Principal Component Analysis for Modeling and Monitoring of Nonlinear Industrial Processes with Massive Data

Kernel principal component analysis (KPCA) has shown excellent performance in monitoring nonlinear industrial processes. However, model building, updating, and online monitoring using KPCA are generally time-consuming when massive data are obtained under the normal operation decomposition of a high-dimensional kernel matrix constructed from massive NOC samples is computationally complex. Many studies have been devoted to solving this problem through reducing the NOC samples, but a KPCA model constructed from the reduced sample set cannot ensure good performance in monitoring nonlinear industrial processes. The performance of a KPCA model depends on whether the results of the eigen-decomposition of the reduced kernel matrix can well approximate that of the original kernel matrix. To improve the efficiency of KPCA-based process monitoring, this paper proposes randomized KPCA for monitoring nonlinear industrial processes with massive data. The proposed method uses random sampling to compress a kernel matrix into a subspace which maintains most of the useful information about process monitoring. Then, the reduced kernel matrix is operated to obtain desired eigen-decomposition results. On the basis of these approximated eigen-decomposition results, the proposed randomized KPCA can enhance the performance in monitoring nonlinear industrial processes. This is because the commonly used monitoring statistics are related to the eigenvalues and eigenvectors of the kernel matrix. Finally, numerical simulation and the benchmark TE chemical process are used to demonstrate the effectiveness of the proposed method.