The Hammerstein–Wiener model is a nonlinear system with three blocks where a dynamic linear block is sandwiched between two static nonlinear blocks. For parameter learning of the Hammerstein–Wiener model, the synchronous parameter learning methods are proposed to learn the model parameters by constructing hybrid model of the three series block, such as over parameterization method, subspace method and maximum likelihood method. It should be pointed out that the aforementioned methods appeared the product term of model parameters in the process of parameter learning, and parameter separation method is further adopted to separate hybrid parameters, which increases the complexity of parameter learning. To address this issue, a novel three-stage parameter learning method of the neuro-fuzzy based Hammerstein–Wiener model corrupted by process noise using combined signals is developed in this paper. The combined signals are designed to completely separate the parameter learning issues of the static input nonlinear block, the linear dynamic block and the static output nonlinear block, which effectively simplifies the process of parameter learning of the Hammerstein–Wiener model. Parameter learning of the Hammerstein–Wiener model are summarized into the following three aspects: The first one is to learn the output static nonlinear block parameters using two sets of separable signals with different sizes. The second one is to estimate the linear dynamic block parameters by means of the correlation analysis method, the unmeasurable intermediate variable information problem is effectively handled. The final one is to determine the parameters of the static input nonlinear block and the moving average noise model using recursive extended least square scheme. The simulation results are presented to illustrate that the proposed learning approach yields high learning accuracy and good robustness for the Hammerstein–Wiener model corrupted by process noise.

Hammerstein-Wiener模型是一个具有三个模块的非线性系统，其中一个动态线性模块夹在两个静态非线性模块之间。对于Hammerstein-Wiener模型的参数学习，提出了同步参数学习方法，通过构造三个系列块的混合模型来学习模型参数，例如过参数化方法，子空间方法和最大似然方法。需要指出的是，上述方法在参数学习过程中出现了模型参数的乘积项，进一步采用参数分离的方法来分离混合参数，增加了参数学习的复杂度。为了解决这个问题，本文提出了一种基于神经模糊的Hammerstein-Wiener模型的三阶段参数学习方法，该模型由于过程噪声而被组合信号破坏。组合后的信号旨在完全分离静态输入非线性模块，线性动态模块和静态输出非线性模块的参数学习问题，从而有效简化了Hammerstein-Wiener模型的参数学习过程。Hammerstein-Wiener模型的参数学习概括为以下三个方面：第一个方面是使用两组不同大小的可分离信号来学习输出静态非线性块参数。第二个方法是通过相关分析方法估算线性动态块参数，有效地解决了不可测的中间变量信息问题。最后一项是使用递归扩展最小二乘方案确定静态输入非线性块的参数和移动平均噪声模型。仿真结果表明，所提出的学习方法对于被过程噪声破坏的Hammerstein-Wiener模型具有较高的学习准确性和良好的鲁棒性。