Model structure and complexity selection remains a challenging problem in system identification, especially for parametric non-linear models. Many Evolutionary Algorithm (EA) based methods have been proposed in the literature for estimating model structure and complexity. In most cases, the proposed methods are devised for estimating structure and complexity within a specified model class and hence these methods do not extend to other model structures without significant changes. In this paper, we propose a Tree Adjoining Grammar (TAG) for stochastic parametric models. TAGs can be used to generate models in an EA framework while imposing desirable structural constraints and incorporating prior knowledge. In this paper, we propose a TAG that can systematically generate models ranging from FIRs to polynomial NARMAX models. Furthermore, we demonstrate that TAGs can be easily extended to more general model classes, such as the non-linear Box-Jenkins model class, enabling the realization of flexible and automatic model structure and complexity selection via EA.

中文翻译：

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随机动力系统模型的树邻接语法表示

模型结构和复杂度选择仍然是系统识别中的一个具有挑战性的问题，尤其是对于参数非线性模型。文献中已经提出了许多基于进化算法 (EA) 的方法来估计模型结构和复杂性。在大多数情况下，所提出的方法是为估计特定模型类内的结构和复杂性而设计的，因此这些方法不会在没有重大变化的情况下扩展到其他模型结构。在本文中，我们提出了一种用于随机参数模型的树邻接文法（TAG）。TAG 可用于在 EA 框架中生成模型，同时施加理想的结构约束并结合先验知识。在本文中，我们提出了一个 TAG，它可以系统地生成从 FIR 到多项式 NARMAX 模型的模型。此外，