  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.
