A novel low-order spatiotemporal modeling method for nonlinear distributed parameter systems

Abstract

Most distributed parameter systems (DPSs) are unknown, including unknown parameter, boundary and even structure, and have a strongly nonlinear spatiotemporal nature. In order to achieve desirable modeling accuracy, the models from the commonly used DPS modeling methods often have a high order, which makes them difficultly used for prediction and control. Here, a novel low-order spatiotemporal least squares support vector machine (LS-SVM) method is proposed for modeling unknown and nonlinear DPSs. Generally, the information of a certain sensor may be represented by information of its neighboring sensors due to the spatial correlation between them. Making use of this feature, a kernel-space based spatial correlation analysis method is developed for deleting redundant spatial kernel functions, from which a low-order model can be achieved and it is without loss of any spatial information. On this basis, a LS-SVM model is constructed to represent the nonlinear temporal dynamics. Integration of the without-redundant spatial kernel functions and the LS-SVM temporal model, a low-order spatiotemporal model is created to reconstruct the spatiotemporal dynamics of the nonlinear DPSs. Additional analysis and proof show that: (1) the proposed method has the same modeling performance with the without-order-reduction spatiotemporal modeling method; and (2) it has better modeling performance than the model with the same order achieved by the without-order-reduction one. Using case studies, the effectiveness of the proposed method and its superior modeling ability compared to several common methods are demonstrated.