Spatiotemporal prediction for nonlinear parabolic distributed parameter system using an artificial neural network trained by group search optimization

Abstract

A spatiotemporal variable of distributed parameter systems (DPSs) can be expressed by an infinite number of spatial basis functions and the corresponding temporal coefficients. For parabolic type DPSs, the first finite basis functions can provide a good approximation because of their slow/fast separation properties. This paper proposes an artificial neural network (ANN) based time/space separation modeling approach to predict nonlinear parabolic DPSs. First, the spatial-temporal output is divided into a few dominant spatial basis functions and low-dimensional time series by PCA method. Then an ANN is identified by low-dimensional time series, where the group search optimization (GSO) is proposed to optimize the connection weights and thresholds to solve the problem of falling into the local optima. Finally, the nonlinear spatiotemporal dynamics is determined after the time/space reconstruction. Simulations are presented to demonstrate the accuracies and effectiveness of the proposed methodologies.