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

The inherent nonlinear and memory-dependent input-output characteristics of piezoelectric actuators pose challenges to the precision of piezoelectric positioning systems. In order to solve this problem, this paper firstly transforms the Jiles-Atherton (JA) model into a neural network structure, designs the Jiles-Atherton neural network (JANN), and combines JANN with nonlinear autoregressive exogenous input (NARX) neural network. A hybrid JA-NARX neural network model is proposed for the first time. This model has the advantages of simple structure, high modeling accuracy, and good interpretability. The effectiveness of the proposed JA-NARX neural network model is validated through a series of experiments, specifically assessing its capacity to accurately capture rate-dependent and asymmetric hysteresis characteristics. The results show that although the proposed neural network model has fewer layers and relatively simple structure, it can realize the high-precision modeling of piezoelectric hysteresis dynamics at a lower computational cost. The experimental data shows that, under the excitation of 60 Hz input signal, the model's PV error only accounts for 0.82% of the full scale range, and the modeling performance is far superior to other models. [Display omitted] • A shallow neural network based on Jiles-Atherton differential-equation model is proposed and constructed for the first time. • An innovative JA-NARX hybrid neural network model is proposed by combining Jiles-Atherton with NARX models. • The JA-NARX hybrid neural network model features simple structure, high modelling accuracy, strong interpretability. • The proposed JA-NARX model was rigorously validated through experiments, effectively describing complex dynamic hysteresis. [ABSTRACT FROM AUTHOR]