The identification of Wiener systems is very difficult because of the output nonlinearity and the parameter product term. To identify the Wiener system, a novel stochastic gradient algorithm based on the multierror and the key term separation is proposed. Firstly, the Wiener system is parameterized as a pseudo-linear model to avoid the products of the parameters. Secondly, a parzen window is used to estimate the probability density function of the error. Thirdly, a stochastic information gradient algorithm with the multierror is adopted to estimate the parameters. The multierror takes the place of the scalar error by the stacked error, which accelerates the algorithm greatly. Fourthly, a variable forgetting factor considering errors is integrated to further speed the algorithm up. Finally, the proposed algorithm is validated by a numerical example and an industrial case. The estimation results indicate that the proposed algorithm can obtain accurate estimates with fast convergence speed.

中文翻译：

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基于可变遗忘因子多误差随机梯度和关键项分离的维纳系统识别

由于输出非线性和参数乘积项，维纳系统的识别非常困难。针对维纳系统的识别问题，提出了一种基于多重误差和关键项分离的随机梯度算法。首先，将维纳系统参数化为伪线性模型，以避免参数的乘积。其次，使用parzen窗口来估​​计误差的概率密度函数。第三，采用具有多误差的随机信息梯度算法进行参数估计。多重误差用叠加误差代替标量误差，大大加快了算法的运行速度。第四，集成了考虑错误的可变遗忘因子以进一步加快算法速度。最后，所提出的算法通过一个数值例子和一个工业案例进行了验证。估计结果表明，该算法能够获得准确的估计值，并且收敛速度快。