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.

中文翻译：

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通过改进的 Newton-Raphson 优化器进行神经增强分数滞后建模和识别


磁滞系统的建模和参数识别仍然是一项艰巨的任务。本文旨在通过结合分数级 Backlash 模型和级联前向神经网络来开发滞后模型，并提出了一种改进的基于 Newton-Raphson 的优化器参数识别方法，以精确捕获压电平台的非线性行为。本文有三篇文章。首先，利用分数阶演算的定义，提出了一种类似分数阶 Backlash 的模型，并从理论上证明了其速率依赖性。其次，通过将分数级 Backlash-like 模型与级联前向神经网络相结合，建立混合分数级 Backlash-like 模型，以增强模型的拟合和泛化能力;再次，改进的基于 Newton-Raphson 的优化器通过结合动态反向学习策略、Q 学习策略、新的自适应系数和基于 Levy 飞行的局部开发，增强了原始的基于 Newton-Raphson 的优化器，理论分析表明收敛性、多样性和准确性都有所提高。消融试验结果表明，所提建模方法的精度比经典 Backlash-like 模型获得的均方根误差低 40% 以上。此外，与传统的基于Newton-Raphson的优化器、蒲公英优化器、粒子群优化和非洲秃鹫优化算法相比，改进后的算法在所有测试频率下在精度、收敛速度和鲁棒性方面均表现出显著优势。获得的均方根误差减少了 20% 以上。 这些结果表明，所提方法为高效、准确的磁滞系统建模和参数辨识提供了有力的研究思路。