Online spatiotemporal modeling for time-varying distributed parameter systems using Kernel-based Multilayer Extreme Learning Machine

Many advanced industrial processes are a class of time-varying distributed parameter systems (DPSs). It is not an easy task for traditional spatiotemporal modeling methods to approximate these systems because of the inherent time-varying and strong nonlinear characteristics. To address this problem, a novel online spatiotemporal modeling method using Kernel-based Multilayer Extreme Learning Machine is proposed to model the time-varying DPSs. First, the Kernel-based Multilayer Extreme Learning Machine is designed to create a deep network through stacking multiple Kernel-based Extreme Learning Machine Autoencoders and one original Extreme Learning Machine Autoencoder. In this step, the spatiotemporal output of time-varying DPSs is transformed into low-dimensional time coefficients directly. Then Online Sequential Regularized Extreme Learning Machine is developed to predict temporal dynamics of time-varying DPSs. Finally, based on the temporal dynamics model, Kernel-based Extreme Learning Machine is applied to reconstruct the spatiotemporal dynamics. Simulations on the thermal processes of a lithium-ion battery and a snap curing oven are presented to validate the performance and effectiveness of the proposed modeling method.