Evolutionary sparse data-driven discovery of complex multibody system dynamics

TL;DR

This paper presents an evolutionary symbolic sparse regression method using genetic programming to discover governing equations and parameters of complex multibody systems directly from time-series data, improving system identification accuracy.

Contribution

It introduces a novel evolutionary symbolic regression approach that simultaneously identifies equations, parameters, and system modes for multibody dynamics from data.

Findings

Method accurately discovers equations of motion in simulations.

Approach effectively estimates system parameters.

Demonstrates efficiency and robustness on various multibody systems.

Abstract

The value of unknown parameters of multibody systems is crucial for prediction, monitoring, and control, sometimes estimated using a biased physics-based model leading to incorrect outcomes. Discovering motion equations of multibody systems from time-series data is challenging as they consist of complex rational functions, constants as function arguments, and diverse function terms, which are not trivial to guess. This study aims at developing an evolutionary symbolic sparse regression approach for the system identification of multibody systems. The procedure discovers equations of motion and system parameters appearing as either constant values in function arguments or coefficients of function expressions. A genetic programming algorithm is written to generate symbolic function expressions, in which a hard-thresholding regression method is embedded. In an evolutionary manner, the complex functional forms, constant arguments, and unknown coefficients are identified to eventually discover the governing equation of a given system. A fitness measure is presented to promote parsimony in distilled equations and reduction in fit-to-data error. Hybrid discrete-continuous dynamical systems are also investigated, for which an approach is suggested to determine both mode number and system submodels. The performance and efficiency of the suggested evolutionary symbolic sparse regression methodology are evaluated in a simulation environment. The capability of the developed approach is also demonstrated by studying several multibody systems. The procedure is efficient and gives the possibility to estimate system parameters and distill respective governing equations. This technique reduces the risk that the function dictionary does not cover all functionality required to unravel hidden physical laws and the need for prior knowledge of the mechanism of interest.