Mixed Kernel Functions for Multivariate Statistical Monitoring of Nonlinear Processes

Machine learning techniques have now become pervasive in the field of process condition monitoring. In particular, kernel methods are those that use kernel functions to allow for the efficient nonlinear analysis of process data by projecting them onto high-dimensional spaces. A widely used kernel machine in multivariate process monitoring is kernel principal components analysis (KPCA). Many choices of kernel functions were used in previous KPCA studies. However, the use of single kernels alone was recently shown to give only limited expressive ability. In this work, we explored the impact of combining various kernel functions to the performance of KPCA for condition monitoring. Fault detection performance is defined by percent correct detection of faulty states and non-detection of normal states. Optimal kernel parameters were obtained using the genetic algorithm (GA). Visualizations of the boundary between normal and faulty states are provided for demonstration in a chemical process case study. This work can inform the development of mixed kernels for nonlinear process monitoring, not only in KPCA, but also in other kernel machines.