Dual-scale Learning-based Dynamic Spatiotemporal Modeling of Distributed Parameter Systems

Abstract

Distributed Parameter Systems (DPS) widely exist in many industrial process applications, such as the lithium-ion battery heat generation process, liquid flow process, and so on. They are usually described by partial differential equations, which are very difficult to model due to the coupled spatial and temporal dynamics. Accurate modeling of distributed parameter systems is the basis for subsequent fault diagnosis and process control. The time/space separation-based methods have been proven effective for modeling these spatiotemporal dynamic processes. However, the existing traditional static modeling methods may not perform well if the inherent dynamics of DPS change significantly over time due to the time-varying nature of the system. In detail, the challenges in dynamic modeling of distributed parametric systems are as follows:

(1)The temporal and spatial behaviors are coupled with DPS, which complicates the modeling process. Besides, the complex dynamics of the temporal and spatial domains of time-varying DPS are not on the same scale, making it difficult to capture the latest spatiotemporal characteristics.

(2)In the actual industrial system, the processes often work on a large scale varying operating conditions with nonlinearity. The single model may be disabled for this complex situation. How to establish a global model to fit each mode is important.

(3)The dynamic modeling accuracy of DPS deeply relies on a large number of sensors. However, it is difficult to place so many sensors due to the complex industrial scenario, sensor cost, and other constraints. There is an urgent need to establish a spatiotemporal modeling method under sparse sensing.

This report aims to provide systematic research on dynamic spatiotemporal modeling of distributed parameter systems with the help of the incremental learning strategy. To solve the above problems, the following three perspectives are investigated:

(1) A dual-scale incremental learning-based online modeling for distributed parameter systems under time-varying boundary conditions.
To handle dynamics at different scales in the spatial and temporal domains, a dual-scale incremental learning approach is proposed for efficient modeling of the complex time-varying DPS. Under the space/time separation framework, spatial basis functions are first designed and updated incrementally at a slow scale over a long period of time. Under the given Spatial Basis Functions (SBF), the temporal model will be incrementally iterated in real-time (fast scale). An optimal choice of the fast/slow ratio can further improve the modeling performance by better coordinating the dynamics at different scales.

(2) A multi-incremental learning-based dynamic modeling for distributed parameter systems under larger working operation conditions.
A new multi-incremental learning-based predictive modeling approach is proposed to solve the larger working operation conditions problem. First, the larger global working region is adaptively decomposed into multiple subspaces to extract local dynamics hierarchically. Then, a spatiotemporal forgetting-based incremental modeling method is further designed to cope with time-varying dynamics of local subspace. Finally, the global dynamic model is ensembled via multiple locally weighted incremental models to enhance modeling performance.

(3) A sparse information completion learning-based modeling for distributed parameter systems under limited sensing.
A sparse information completion learning approach is proposed for modeling the complex DPS under the sparse sensing environment. First, an incomplete learning module is designed to reconstruct the non-sparse sensor data, which takes spatial coupling effects into account. Then, the spatial incremental basis functions are constructed via recursive learning to capture the systematic spatial variation. Finally, the temporal incremental learning model is developed to track temporal dynamics.

The experiments conducted on industrial processes demonstrated the effectiveness and superiority of all proposed modeling methods.

Date of Award	2 Sept 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Hanxiong LI (Supervisor)