Two-Dimensional Spatial Construction for Online Modeling of Distributed Parameter Systems

A 2-D spatial construction method is proposed for the online modeling of distributed parameter systems (DPSs), such as battery thermal process. The proposed method can combine the advantages of spectral method and Karhunen–Loève decomposition (KLD) method. First, the continuous spatial basis functions are designed by the 2-D spatial construction to keep the information between sensing locations. With the 2-D space-time separation and recursive learning, the derived model can preserve the couplings between spatial dimensions and update over time. The radial basis function network is utilized to identify the low-dimensional temporal dynamics. After the space-time synthesis, the constructed spatiotemporal model can provide continuous modeling of the DPS with satisfactory performance. Convergence analysis has been carried out, which proves that the proposed method can guarantee bounded errors. Finally, simulations and experiments on a pouch-type lithium-ion battery with unknown partial differential equations prove the effectiveness of the proposed method.

I. Introduction

Many thermal and fluid processes, such as battery thermal process and catalytic process, can be described by 2-D distributed parameter systems (DPSs). The input, output, and process parameters of DPS vary in space and time [1]. Different from 1-D DPSs, the cross-couplings not only exist between time and space but also between different spatial dimensions in 2-D DPSs. These factors make it extremely difficult to model and control 2-D DPSs [2], [3]. Recently, space-time separation-based methods have been widely applied to the modeling of 2-D DPSs [4]–[6].