Evolutionary-Based Sparse Regression for the Experimental Identification of Duffing Oscillator

TL;DR

This paper introduces an evolutionary-based sparse regression method that automatically constructs a nonlinear function library from data, effectively identifying Coulomb friction in a Duffing oscillator and demonstrating robustness to noise.

Contribution

The novel evolutionary approach automates library construction for sparse identification, reducing the need for prior knowledge and improving system identification accuracy.

Findings

Effective identification of Coulomb friction terms in Duffing oscillator

Robustness of the method under various noise levels

Potential applicability to other nonlinear systems

Abstract

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms as part of the ordinary differential equation of the system. Correct identification of this nonlinear system using sparse identification is hugely dependent on selecting the correct form of nonlinearity included in the function library. Consequently, in this work, the evolutionary-based sparse identification is replacing the need for user knowledge when constructing the library in sparse identification. Constructing the library based on the data-driven evolutionary approach is an effective way to extend the space of nonlinear functions, allowing for the sparse regression to be applied on an extensive space of functions. ,e results show that the method provides an effective algorithm for the purpose of unveiling the physical nature of the Duffing oscillator. In addition, the robustness of the identification algorithm is investigated for various levels of noise in simulation. ,e proposed method has possible applications to other nonlinear dynamic systems in mechatronics, robotics, and electronics.