Sparse Identification of Nonlinear Duffing Oscillator From Measurement Data

TL;DR

This paper demonstrates the application of a sparse identification technique to accurately model a nonlinear Duffing oscillator with chaotic behavior, highlighting its effectiveness in real-world experimental data.

Contribution

The study adapts sparse identification methods for a Duffing oscillator with cubic feedback, including modifications for optimization and model selection via Pareto analysis.

Findings

Successfully identified the nonlinear model including friction term

Analyzed the effect of regularization on model accuracy

Validated the method on real experimental data

Abstract

In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by nonlinear differential equation which demonstrates chaotic behavior and bifurcations, has received considerable attention in recent years as it arises in many real-world engineering applications. Therefore its identification is of interest for numerous practical problems. To adopt the existing identification method to this application, the optimization process which identifies the most important terms of the model has been modified. In addition, the impact of changing the amount of regularization parameter on the mean square error of the fit has been studied. Selection of the true model is done via balancing complexity and accuracy using Pareto front analysis. This study provides considerable insight into the employment of sparse identification method on the real-world setups and the results show that the developed algorithm is capable of finding the true nonlinear model of the considered application including a nonlinear friction term.