Robust Spatiotemporal LS-SVM Modeling for Nonlinear Distributed Parameter System With Disturbance

Abstract

Most distributed parameter systems (DPS) have a strongly nonlinear spatiotemporal nature and are affected by disturbance. However, most of the existing DPS modeling methods only consider the linear relation between the spatial positions, but neglect the nonlinear one. Additionally, they also do not account for the influence of disturbance. Thus, in this paper, a robust spatiotemporal least squares support vector machine (LS-SVM) modeling method for DPS with disturbance is proposed. First, a spatial kernel function is constructed in order to describe the nonlinear relation between spatial positions. An optimal fusion method is then developed to derive a robust temporal coefficient, from which the influence of disturbance can be rejected. Through the integration of the spatial kernel function and the robust temporal coefficient, a robust spatiotemporal LS-SVM model is constructed. Since this modeling not only considers the nonlinear nature but also takes the influence of disturbance into account, it has the ability to adapt well to the nonlinear spatiotemporal dynamics, even when disturbance is presented. The analysis and proof show that the proposed robust spatiotemporal LS-SVM modeling method has the better robust performance as compared to the existing ones. Case studies not only demonstrate the effectiveness of the proposed method, but also demonstrate its superior robustness than other conventional modeling methods.