Sparse Information Completion-Based Incremental Learning for Modeling of Complex Distributed Parameter Systems

Distributed parameter systems (DPS) are widely presented in various industrial fields. Time/space separation-based methods have proven to be effective modeling schemes for DPS. However, the sparse sensing environments in practical industrial scenarios inevitably result in incomplete data, posing significant challenges to the implementation of traditional modeling methods. In addition, the nonstationary spatiotemporal dynamics of the system pose another challenge for modeling. In this article, a sparse information completion-based incremental learning approach is proposed for modeling the complex DPS. First, a sparse information completion module is designed to reconstruct the nonsensor data, which takes spatial coupling effects into account. Then, the spatial basis functions are incrementally constructed to capture the systematic spatial variation. Finally, the temporal learning model is also incrementally developed to track temporal dynamics. Two case studies of sparse sensing in industrial processes demonstrate the superiority of the proposed modeling approach. © 2025 IEEE.