A Sliding Window Based Dynamic Spatiotemporal Modeling for Distributed Parameter Systems with Time-Dependent Boundary Conditions

Time/space separation based spatiotemporal modeling methods have been proved to be effective and efficient for modeling a class of distributed parameter systems (DPSs). However, these conventional methods may not work satisfactorily for DPSs with time-dependent boundary conditions. A sliding window based dynamic spatiotemporal modeling method is proposed for this kind of DPSs. Firstly, the sliding window is appropriately designed to capture the most recent spatiotemporal data. Then, the conventional Karhunen-Loeve method can be used to construct the analytical model. Besides, a more general sliding window method can be achieved by attaching a forgetting factor by which the influence of the current and previous data can be adjusted. This analytical model can be utilized for online performance prediction. Simulation experiments on a benchmark and a battery with unknown boundary cooling have demonstrated the superior performance of the proposed method on the DPSs with time-dependent boundary conditions.