Quality-Driven Principal Component Analysis Combined With Kernel Least Squares for Multivariate Statistical Process Monitoring

This brief discusses a novel quality-driven principal component analysis method for statistical process monitoring. Through a nonlinear mapping, the original measurement space is mapped to another high-dimensional space, and then the relevant information between the high-dimensional space and the process quality can be obtained with the help of the kernel least squares. Based on this, the high-dimensional space will be further projected onto two mutually orthogonal high-dimensional subspaces representing quality-related part and quality-unrelated part, respectively. The traditional method is difficult to achieve this type of projection because the mapping from the original space to a high-dimensional space is hard to calculate explicitly. The main contribution is to derive the projection matrix using the knowledge of matrix theory. For each subspace, some meaningful statistical indicators are constructed to give more targeted fault information. Case studies on a numerical instance and the Tennessee Eastman process indicate that the proposed approach outperforms some of the current research results. The reliability of quality monitoring is improved through a proper space decomposition, and the fault detection rate turns to be higher due to reasonable monitoring indicators.