In this article, a stochastic gradient algorithm based on the minimum Shannon entropy is proposed to identify a type of Hammerstein system with random noise. Firstly, the probability density function is estimated by a parzen window based on the Gaussian kernel. Then, the traditional stochastic gradient algorithm is adopted to estimate the parameters. However, the traditional stochastic gradient algorithm converges quite slowly. To fasten the algorithm, a multierror method is integrated into the algorithm. In this multierror gradient algorithm, the scalar error is replaced by a vector error. This vector error can accelerate the algorithm greatly and give a more accurate estimate by using the same data set. Finally, the proposed algorithm is validated by a numerical example and an industrial process. The estimation results indicate that the proposed algorithm can obtain more accurate estimates than the traditional gradient algorithm and has a faster convergence speed.

中文翻译：

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具有随机噪声的 Hammerstein 系统识别的多误差随机梯度算法及其在连续搅拌釜反应器建模中的应用

本文提出了一种基于最小香农熵的随机梯度算法来识别一类具有随机噪声的Hammerstein系统。首先，通过基于高斯核的parzen窗估计概率密度函数。然后，采用传统的随机梯度算法来估计参数。然而，传统的随机梯度算法收敛速度相当慢。为了加强算法，将多错误方法集成到算法中。在这个多误差梯度算法中，标量误差被矢量误差代替。这种矢量误差可以大大加快算法速度，并通过使用相同的数据集给出更准确的估计。最后，所提出的算法通过一个数值例子和一个工业过程进行了验证。