Neuro-enhanced fractional hysteresis modeling and identification by modified Newton-Raphson optimizer

Abstract

The modeling and parameter identification of a system with hysteresis remains a difficult task. This paper aims to develop a hysteretic model by combining with a fractional Backlash-like model and cascade forward neural network, and proposed a modified Newton-Raphson-based optimizer parameter identification method to precisely capture the nonlinear behavior of piezoelectric platform. There are three contributions in this paper. Firstly, leveraging the definition of fractional calculus, a fractional Backlash-like model is proposed, whose rate dependence is proved theoretically. Secondly, a hybrid fractional Backlash-like model is established by combining fractional Backlash-like model with cascade forward neural network to enhance the fitting and generalization ability of the model. Thirdly, a modified Newton-Raphson-based optimizer enhances the original Newton-Raphson-based optimizer by incorporating a dynamic reverse learning strategy, a Q-learning strategy, a new adaptive coefficient, and local exploitation based on Levy flight, with theoretical analysis demonstrating improvements in convergence, diversity, and accuracy. The ablation test results show that the accuracy of the proposed modeling method is more than 40% less than that of the root mean square error obtained by the classic Backlash-like model. In addition, compared with the traditional Newton-Raphson-based optimizer, dandelion optimizer, particle swarm optimization and african vultures optimization algorithm, the modified algorithm shows significant advantages in accuracy, convergence speed and robustness under all test frequencies. The root mean square error obtained was reduced by more than 20%. These results show that the proposed method provides a powerful research idea for efficient and accurate hysteresis system modeling and parameter identification.