A temporal–spatiotemporal domain transformation-based modeling method for nonlinear distributed parameter systems

Abstract

Complex nonlinear distributed parameter systems (DPSs) exist widely in advanced industrial thermal processes. The modeling of such highly nonlinear systems is a challenge for traditional time/space-separation-based methods since they employ linear methods for the model reduction and spatiotemporal reconstruction, which may lead to an inefficient application of the nonlinear spatial structure features represented by the spatial basis functions (BFs). To overcome this problem, a novel spatiotemporal modeling framework composed of nonlinear temporal domain transformation and nonlinear spatiotemporal domain reconstruction is proposed in this paper. Firstly, local nonlinear dimension reduction based on the locally linear embedding (LLE) technique is utilized to perform nonlinear temporal domain transformation of the spatiotemporal output of nonlinear DPSs. In this step, the original spatiotemporal data can be directly transformed into low-order time coefficients. Then, the extreme learning machine (ELM) method is utilized to establish a temporal model. Finally, through the spatiotemporal domain reconstruction based on the kernel-based ELM (K-ELM) method, the prediction of the temporal dynamics obtained from the temporal model can be reconstructed back to the spatiotemporal output. The effectiveness and performance of the proposed method are demonstrated in experiments on the thermal processes of a snap curing oven and a lithium-ion battery.