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.

在系统识别中，尤其是对于参数非线性模型，模型结构和复杂性选择仍然是一个具有挑战性的问题。文献中已经提出了许多基于进化算法（EA）的方法来估计模型的结构和复杂性。在大多数情况下，提出的方法是为估计指定模型类别内的结构和复杂性而设计的，因此，在没有重大更改的情况下，这些方法不会扩展到其他模型结构。在本文中，我们为随机参数模型提出了树邻接语法（TAG）。TAG可以用于在EA框架中生成模型，同时施加所需的结构约束并合并现有知识。在本文中，我们提出了一种TAG，它可以系统地生成从FIR到多项式NARMAX模型的模型。此外，