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.

中文翻译：

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分布式参数系统在线建模的二维空间构造

提出了一种二维空间构造方法，用于分布式参数系统（DPS）的在线建模，例如电池热过程。所提出的方法可以结合谱法和Karhunen-Loève分解（KLD）法的优点。首先，连续空间基函数是通过二维空间结构设计的，以保持传感位置之间的信息。通过二维时空分离和递归学习，派生模型可以保持空间维度之间的耦合并随时间更新。径向基函数网络用于识别低维时间动态。经时空综合后，所构建的时空模型可以为DPS提供连续建模，性能令人满意。进行了收敛性分析，这证明了所提出的方法可以保证有界误差。最后，对具有未知偏微分方程的袋式锂离子电池进行仿真和实验，证明了所提方法的有效性。