The identification of black-box nonlinear state-space models requires a flexible representation of the state and output equation. Artificial neural networks have proven to provide such a representation. However, as in many identification problems, a nonlinear optimization problem needs to be solved to obtain the model parameters (layer weights and biases). A well-thought initialization of these model parameters can often avoid that the nonlinear optimization algorithm converges to a poorly performing local minimum of the considered cost function. This paper introduces an improved initialization approach for nonlinear state-space models represented as a recurrent artificial neural network and emphasizes the importance of including an explicit linear term in the model structure. Some of the neural network weights are initialized starting from a linear approximation of the nonlinear system, while others are initialized using random values or zeros. The effectiveness of the proposed initialization approach over previously proposed methods is illustrated on two benchmark examples.
翻译:确定黑盒非线性国家-空间模型需要灵活地代表状态和输出方程式。人工神经网络已证明可以提供这种代表。然而,正如许多识别问题一样,需要解决非线性优化问题才能获得模型参数(层权重和偏向 ) 。这些模型参数经过深思熟虑的初始化往往可以避免非线性优化算法与当地最低成本功能的不良表现相融合。本文介绍了对作为经常性人工神经网络代表的非线性国家-空间模型的改进初始化方法,并强调了在模型结构中列入明确的线性术语的重要性。有些神经网络加权数是从非线性系统线性近似开始的初始化,而另一些则使用随机值或零进行初始化。两个基准示例说明了拟议的初始化方法相对于先前提议方法的有效性。