A Comparative Study of Different Kernel Functions Applied to LW-KPLS Model for Nonlinear Processes

Abstract

Soft sensors are inferential estimators when the employment of hardware sensors is inapplicable, expensive, or difficult in industrial plant processes. Currently, a simple soft sensor, namely locally weighted partial least squares (LW-PLS), which can cope with the nonlinearity of the process, has been developed. However, LW-PLS exhibits the disadvantages of handling strong nonlinear process data. To address this problem, Kernel functions are integrated into LW-PLS to form locally weighted Kernel partial least squares (LW-KPLS). Notice that a minimal study was carried out on the impact of different kernel functions that have not been integrated with the LW-KPLS, in which this model has the potential to be applied to different chemical-related nonlinear processes. Thus, this study investigates the predictive performance of LW-KPLS with several different Kernel functions using three nonlinear case studies. As the results, the predictive performances of LW-KPLS with Polynomial Kernel are better than other Kernel functions. The values of root-mean-square errors (RMSE) and error of approximation (Ea) for the training and testing dataset by utilizing this Kernel function are the lowest in their respective case studies, which are 34.60% to 95.39% lower for RMSEs values and 68.20% to 95.49% smaller for Ea values.