Sparse Kernel Principal Component Analysis via Sequential Approach for Nonlinear Process Monitoring

Abstract

Kernel principal component analysis (KPCA) has been widely used for nonlinear process monitoring. However, since the principal components are linear combinations of all kernel functions, traditional KPCA suffers from poor interpretation and high-computation cost. To address this problem, obtaining sparse coefficients in KPCA is of paramount importance, particularly for real-time process monitoring and large-scale processes. In this paper, a new sparse kernel principal component analysis via sequential approach, named SSKPCA is proposed for nonlinear process monitoring. We first incorporate elastic net regularization into the framework of KPCA to establish a modified optimization problem. Then, a sequential approach is employed to derive the solution. Different from the existing sparse KPCA method based on elastic net regularization, the extra computations associated with the kernel matrix, such as matrix inversion and matrix square root are avoided in the optimizing procedure for solving the modified optimization problem. Therefore, the proposed SSKPCA method is more efficient in numerical implementation. The SSKPCA-based T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and squared prediction error (Q) statistics are constructed for fault detection. Furthermore, the sensitivity analysis principle is adopted for fault identification. A comparative study of Tennessee Eastman Process (TEP) is carried out to illustrate the ability and efficiency of the proposed SSKPCA-based nonlinear process monitoring method.