Kernel-Based Spatiotemporal Multimodeling for Nonlinear Distributed Parameter Industrial Processes

Abstract

Many industrial processes are nonlinear distributed parameter systems (DPS) that have significant spatiotemporal dynamics. Due to different production and working conditions, they often need to work at a large operating range with multiple working points. However, direct global modeling and persistently exciting experiment in a large working region are very costly in many cases. The complex spatiotemporal coupling and infinite-dimensional nature make the problem more difficult. In this study, a kernel-based spatiotemporal multimodeling approach is proposed for the nonlinear DPS with multiple working points. To obtain a reasonable operating space division, an iterative approach is proposed where the operating space division and local modeling are performed iteratively. The working range of the current local model will help to determine the next operating point required for modeling. Utilizing the potential of each local model, the number of regions can be reduced. In the local modeling, the Karhunen–Loève method is used for the space/time separation and dimension reduction, and after that unknown parameters of kernels are estimated. Due to consideration of time-scale properties in the dimension reduction, the modeling approach is particularly suitable for dissipative PDEs, particularly of parabolic type. The multimodeling and space/time separation techniques can largely reduce the complexity of global nonlinear spatiotemporal modeling. Finally, to guarantee a smooth transition between local spatiotemporal models, a scheduling integration method is used to provide a global spatiotemporal model. To design scheduling functions, a two-stage training method is proposed to reduce the design complexity. Compared with direct global modeling, the exciting experiment and modeling for each local region become easier. Compared with one local modeling, the multimodel integration will improve modeling accuracy. The effectiveness of the proposed modeling approach is verified by simulations.