Physical-stochastic continuous-time identification of a forced Duffing oscillator

Area of Science:

• Engineering & Applied Sciences
• Nonlinear Dynamics
• System Identification

Background:

• The Duffing oscillator is a fundamental model for rich nonlinear dynamics, applicable to diverse physical systems like stiffening springs and electronic circuits.
• Accurate model identification from input-output data is crucial for understanding and controlling these complex systems.
• Stochastic differential equations (SDEs) offer a powerful framework for grey-box modeling, capturing system physics and uncertainties.

Purpose of the Study:

• To develop an improved method for identifying Duffing oscillator models using SDE-based grey-box approaches.
• To enhance the performance of parameter estimation and long-term prediction for nonlinear systems.
• To validate the proposed identification framework using benchmark experimental data.

Main Methods:

• Utilizing SDEs to define a grey-box model, incorporating drift terms for system dynamics and diffusion terms for process noise.
• Proposing a modified maximum likelihood estimation (MLE) framework for SDE parameter identification.
• Integrating an iterative residual analysis for robust model development and validation.
• Employing data from the Brussels "Silverbox system" for identification and performance evaluation.

Main Results:

• The proposed SDE-based grey-box model identification framework demonstrated improved performance, particularly in long-term predictions.
• The identified model accurately captured the dynamics of the forced Duffing oscillator.
• Simulation errors were quantitatively compared against existing literature results, showing competitive or superior performance.

Conclusions:

• The enhanced MLE framework for SDE grey-box models provides an effective approach for identifying Duffing oscillator dynamics.
• This method offers a robust tool for modeling and predicting the behavior of complex nonlinear systems.
• The study highlights the utility of SDEs in advancing system identification for real-world engineering applications.