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−Loeve 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.

A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

“…The comparison with the multi-modeling approach in the previous paper (see [35] for more details) is also performed. The prediction errors SNAT(t) of two models are shown in Fig.…”

“…Recently, a kernel-based spatio-temporal multi-modeling approach is proposed [35] for nonlinear DPS. Note that the operating space division is mainly based on the experiment data and no process knowledge is utilized.…”

“…Compared with the previous paper [35], the main contributions of this study are that a fuzzy-based spatio-temporal multi-modeling approach is proposed for the nonlinear distributed parameter system (DPS).…”

Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

“…Thus, model reduction for nonlinear STSs at a reasonable cost and accuracy has a great significance in practical engineering applications. Empirical eigenfunctions (EEFs) identified by proper orthogonal decomposition (POD) [1] are widely used as global spatial basis functions in advanced methods for model reduction of nonlinear STSs [2][3][4][5][6][7][8]. Modes obtained from POD can be calculated quite easily as the solutions of an eigenvalue problem involving second-order correlation tensors.…”

Operation-Region-Decomposition-Based Singular Value Decomposition/Neural Network Modeling Method for Complex Hydraulic Press Machines

“…Singular value decomposition (SVD) has found many successful applications, such as the modeling of distribution parameter systems, since it can factorize time-space variables into time variable and space variable. − It is also used to model system for design because it can factorize output into parameter-space and time-space. − Moreover, the SVD can produce a low-dimension model from high-dimensional data . It has also been used in feature identification .…”