Error Compensation-based Time-Space Separation Modeling Method for Complex Distributed Parameter Processes

Abstract

Constructing a model for nonlinear distributed parameter systems (DPSs) is challenging due to their strong nonlinearity and spatiotemporal nature. As a result, most DPS modeling methods have low modeling accuracy for strongly nonlinear DPSs and this inaccuracy is primarily due to truncation errors and neglect of nonlinear dynamics. Here, an error compensation-based time-space separation modeling method is proposed to better resolve these limitations. We first constructed a Karkunen-Loève and least squares support vector machine (KL-LS-SVM) time-space separation model to represent the main dynamic behavior. Simultaneously, we developed a spatiotemporal least squares support vector machine (LS-SVM) to compensate for any modeling errors due to either truncation or unknown nonlinear dynamics. These two models were then integrated to construct a complete spatiotemporal model, which allowed for the reconstruction of the DPSs. Performance analyses and experimental validation further showed that the proposed method can effectively model complex nonlinear DPSs and have better modeling ability than more commonly used DPSs modeling methods.