Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming

Abstract

State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based approaches have been proposed for model-structure selection, with special focus on non-linear systems. Recently, an approach for data-driven modelling of non-linear dynamical systems using Genetic Programming (GP) was proposed. The novelty of the method was the modelling of noise and the use of Tree Adjoining Grammar to shape the search-space explored by GP. In this paper, we report results achieved by the proposed method on three case studies. Each of the case studies considered here is based on real physical systems. The case studies pose a variety of challenges. In particular, these challenges range over varying amounts of prior knowledge of the true system, amount of data available, the complexity of the dynamics of the system, and the nature of non-linearities in the system. Based on the results achieved for the case studies, we critically analyse the performance of the proposed method.

A Tree Adjoining Grammar Representation for Models Of Stochastic Dynamical Systems

“…This illustrates that a compact set of elementary trees can be used to express the dynamical relationships across a variety of model classes, thereby enabling the design of TAG-based EA approaches for SI that require minimal user-interaction. The practical soundness of this concept has been demonstrated in Khandelwal et al (2019b), where a TAG-based EA approach was used to identify a non-linear benchmark dataset with minimal user-interaction, and also in Khandelwal et al (2019a), where the same TAG-based EA approach is used to identify multiple real physical systems and benchmark data set with minimal changes in the methodology itself.…”

“…Note that, while the TAG based model set notion developed in this contribution is motivated by its applicability in an EA based identification methodology, the identification approach itself is not in the scope of the present contribution. A preliminary version of such an identification methodology can be found in Khandelwal et al (2019a) and Khandelwal et al (2019b).…”

Deep networks for system identification: a Survey

“…We use the uniformly distributed input signal to learn the dynamics using 60% of the data and validate it on the remaining 40%. This nonlinear dataset was used in previous studies [139,163] and can be modeled by a Wiener-Hammerstein model [342].…”

Automated multi-objective system identification using grammar-based genetic programming

“…A preliminary version of the proposed identification approach was reported in Khandelwal, Schoukens, and Tóth (2019b), and in Khandelwal, Schoukens, and Tóth (2019a), the authors applied the proposed method to multiple physical systems and benchmark case-studies. The main contributions of the present work, as opposed to the previous publications, are:…”

“…The main conclusions are presented in Section 8. While the paper remains self-contained in terms of the developed methodology, the interested reader may refer to the supplementary material in Khandelwal, Schoukens, and Tóth (2021) for additional details regarding implementation and extended results.…”