For block-oriented Hammerstein systems with a static nonlinear part and a dynamic linear part, there exists a problem of the parameter coupling in nonlinear part and linear part. Traditional methods are to express its output into a linear or a quasi linear regression equation about parameters. However, a Hammerstein system with a neural network (NN) nonlinear part is difficult to be expressed as a linear regression equation about weights and parameters. This paper decomposes parameter coupling by substituting the nonlinear NN equation into the separated key-term of the linear part through the key-term separation idea, and casts the system model into three fictitious models through the hierarchical decomposition principle. Then a hierarchical gradient algorithm is adopted to alternatively identify parameters of these three models. The advantages of the presented Hammerstein system are of the mapping ability of NNs, and the memory ability of dynamic models.

中文翻译：

---

基于神经网络的 Hammerstein 电池模型的基于关键术语分离的分层梯度方法


对于具有静态非线性部分和动态线性部分的面向块的Hammerstein系统，存在非线性部分和线性部分的参数耦合问题。传统的方法是将其输出表达为关于参数的线性或拟线性回归方程。然而，具有神经网络（NN）非线性部分的Hammerstein系统很难表达为关于权重和参数的线性回归方程。本文通过关键项分离思想，将非线性神经网络方程代入线性部分的分离关键项，从而分解参数耦合，并通过层次分解原理将系统模型转化为三个虚拟模型。然后采用分层梯度算法交替识别这三个模型的参数。所提出的 Hammerstein 系统的优点是神经网络的映射能力和动态模型的记忆能力。