NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes

Abstract

This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of general fuzzy systems when facing high dimensional data. For relieving the curse of dimensionality, as well as improving approximation performance of fuzzy models, we propose combining the NARX with the DCFS to provide a good approximation of the complex nonlinear dynamic behavior and a fast-training algorithm with ensured convergence. There are three NARX DCFS structures proposed, and the appropriate training algorithm is adapted. Evaluations were performed on a popular benchmark—Box and Jenkin’s gas furnace data set and the four nonlinear dynamic test systems. The experiments show that the proposed NARX DCFS method can be successfully used to identify nonlinear dynamic systems based on external dynamics structures and nonlinear static approximators.

An explainable neural network integrating Jiles-Atherton and nonlinear auto-regressive exogenous models for modeling universal hysteresis

“…is the delayed output; f is a nonlinear approximation function which can be replaced by a neural network. The NARX model ( 34) is a simplified version of the NARMAX model developed by Billings [48] and has been widely used in the literature [49][50][51]. As a type of recurrent neural network, the nonlinear auto-regressive with exogenous inputs (NARX) neural network is analogous to a back-propagation network with a delayed feedback connection between the output and input [52].…”