Probabilistic PCA-Based Spatiotemporal Multimodeling for Nonlinear Distributed Parameter Processes

Abstract

Many industrial processes are nonlinear distributed parameter systems (DPSs). Data-based spatiotemporal modeling is required for analysis and control when the first-principles model is unknown. Because a DPS is infinite-dimensional and time–space coupled, a low-order model is necessary for prediction and control in practice. For low-order modeling, traditional principal component analysis (PCA) is often used for dimension reduction and time–space separation. However, it is a linear method and leads to only one set of fixed spatial basis functions. Therefore, it might not be always effective for nonlinear systems. In this study, a spatiotemporal multimodeling approach is proposed for unknown nonlinear DPSs. First, multimodel decomposition is performed, where probabilistic PCA (PPCA) is used to obtain multiple sets of spatial basis functions from the experimental data by maximizing a likelihood function. Using these multiple sets of PCA spatial bases for time–space separation, the high-dimensionality spatiotemporal data can be reduced to multiple sets of low-dimensionality temporal series. Then, multiple low-order neural models can be easily established to model these local dynamics. Finally, the original spatiotemporal dynamics can be reconstructed by multimodel synthesis. Because the proposed spatiotemporal modeling approach involves a multimodeling mechanism, it can achieve better performance than the traditional PCA-based single-modeling for nonlinear DPSs, which is demonstrated by numerical simulations.