Time/Space-Separation-Based SVM Modeling for Nonlinear Distributed Parameter Processes

Modeling of distributed parameter systems (DPSs) is difficult because of their infinite-dimensional spatiotemporal nature and complex nonlinearities. Data-based modeling is necessary because there are usually some unknown uncertainties in first-principles modeling. In practice, a low-dimensional spatiotemporal model is often required for real-time implementations. In this study, a time/space-separation-based support-vector-machine (SVM) model identification approach is proposed for unknown nonlinear DPSs. The spatiotemporal output of the system is measured at a finite number of spatial locations, and for easy implementation, the input is assumed to be a finite-dimensional temporal variable. First, Karhunen−Loève (KL) decomposition is used for time/space separation and dimension reduction. Subsequently, the spatiotemporal output is expanded onto a low-dimensional Karhunen−Loève space with temporal coefficients. Finally, the least-squares support-vector-machine (LS-SVM) approach is used to model the system dynamics in a low-dimensional temporal domain. After the time/space synthesis, the nonlinear spatiotemporal dynamics can be reconstructed. Simulations are presented to demonstrate the effectiveness of this spatiotemporal modeling method.