On Grey-Box System Identification Using Bayesian Tree-Adjoining Grammars: An Experimental Case Study

A promising development in Nonlinear System Identification (NLSI) has been the introduction of Tree-Adjoining Grammars (TAGs). The approach provides a powerful and versatile means of estimating system models, based on a model class encoded as a set of grammatical rules. In this paper, the model structures are estimated with a Bayesian methodology. By combining the TAG framework with Bayesian inference, distributions over models in terms of both parameters and the tree structure are fitted simultaneously. The proposed algorithm is applied and validated on a challenging case study involving wave-loading data from the Christchurch Bay Tower experiments, demonstrating that TAGs are also well-suited to fitting grey-box/physics-informed models.