This paper deals with the identification of the fractional order Hammerstein model by using proposed adaptive differential evolution with the Local search strategy (ADELS) algorithm with the steepest descent method and the overparameterization based auxiliary model recursive least squares (OAMRLS) algorithm. The parameters of the static nonlinear block and the dynamic linear block of the model are all unknown, including the fractional order. The initial value of the parameter is obtained by the proposed ADELS algorithm. The main innovation of ADELS is to adaptively generate the next generation based on the fitness function value within the population through scoring rules and introduce Chebyshev mapping into the newly generated population for local search. Based on the steepest descent method, the fractional order identification using initial values is derived. The remaining parameters are derived through the OAMRLS algorithm. With the initial value obtained by ADELS, the identification result of the algorithm is more accurate. The simulation results illustrate the significance of the proposed algorithm.

中文翻译：

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基于ADELS的分数阶Hammerstein模型的递归辨识

本文采用分数阶汉默斯坦模型的识别方法，该方法采用拟议的自适应差分进化，具有最速下降法的局部搜索策略（ADELS）算法和基于超参数化的辅助模型递归最小二乘（OAMRLS）算法。模型的静态非线性模块和动态线性模块的参数都是未知的，包括分数阶。参数的初始值通过提出的ADELS算法获得。ADELS的主要创新在于通过计分规则根据总体中的适应度函数值自适应生成下一代，并将Chebyshev映射引入到新生成的总体中以进行本地搜索。根据最速下降法，得出使用初始值的分数阶识别。其余参数是通过OAMRLS算法得出的。利用ADELS获得的初始值，该算法的识别结果更加准确。仿真结果说明了该算法的重要性。