Dual Extreme Learning Machines-Based Spatiotemporal Modeling for Nonlinear Distributed Thermal Processes

Abstract

Many industrial thermal processes belong to distributed parameter systems (DPSs), which have two coupled nonlinear blocks. Dual least square support vector machines (LS-SVM) has been proposed to model such systems. However, due to the use of two LS-SVM, this method often leads to heavy computation and long learning time, which does not suit for online application. In this study, a dual extreme learning machine (ELM)-based spatiotemporal modeling method is proposed for such two nonlinearities embedded DPSs. Firstly, the KL method is applied to reduce the dimension of the original system and obtain the spatial basis functions (BFs). Then, dual ELM is designed to match the two nonlinear structures. Finally, through the reconstruction of space–time synthesis, the approximate spatiotemporal distribution model of the original system is obtained. In addition, simulations on a curing process is studied to confirm the effectiveness of the proposed method.