Finite Gaussian Mixture Model based Multi-modeling for Nonlinear Distributed Parameter Systems

Complex nonlinear distributed parameter systems (DPSs) widely exist in real industrial thermal processes. Modeling of such systems often leads to the following challenges: strong nonlinearities, time-varying dynamics, and large operating range with multiple working points. Therefore, traditional single spatiotemporal model will become ill suited. Motivated by the idea of multimodeling, integration of finite Gaussian mixture model (FGMM) and principle component regression (PCR) based multiple spatiotemporal modeling is proposed in this paper for complex nonlinear DPSs. The main idea of the proposed method can be summarized as the following three parts: FGMM-based operating space separation, Karhunen–Loeve based local spatiotemporal modeling, and PCR-based local spatiotemporal models integration. To evaluate the generalization bound of the proposed method, the Rademacher complexity is also developed here theoretically. Since multimodeling can reduce the nonlinear complexity, the proposed model has strong ability to track and handle the complex nonlinear dynamics. Simulations on a two-dimensional curing thermal process demonstrated the superior model performance of the proposed model.