Fuzzy spatial mapping filter-based spatiotemporal dynamics modeling and uncertainty estimation of nonlinear distributed parameter systems

Many industrial processes, such as transport-reaction processes and battery thermal processes, can be described by distributed parameter systems (DPSs). Due to the internal and external uncertainties, it is difficult for spatiotemporal modeling of DPSs. In this research, a fuzzy spatial mapping filter-based spatiotemporal dynamics modeling method is proposed for DPSs to estimate the distributed state and uncertainty. The fuzzy spatial mapping filter (SMF) is first proposed to overcome the spillover effect of the basic SMF. Based on the fuzzy SMF, the spatiotemporal residual extended state observer (STR-ESO) can achieve the state variable reconstruction and uncertainty estimation with high precision. Besides, an adaptive nominal DPS is constructed to acquire the residual state as the feedback of the STR-ESO. The proposed modeling method is demonstrated to converge in Hilbert space. The feasibility and effectiveness of the proposed method are verified through a benchmark. Additionally, the proposed method is successfully applied to the real-time temperature monitoring of a battery thermal process. © The Author(s), under exclusive licence to Springer Nature B.V. 2026.