Development of data-driven modeling method for nonlinear coupling components.

Area of Science:

• Engineering
• Dynamical Systems Analysis
• Computational Mechanics

Background:

• Many engineering components exhibit complex nonlinear behaviors that are challenging to model accurately.
• Traditional modeling approaches may struggle to capture the intricate dynamics of such systems.
• Data-driven methods offer a promising alternative for system identification.

Purpose of the Study:

• To develop and validate a novel data-driven regression modeling methodology for nonlinear dynamic systems.
• To extend the sparse identification of nonlinear dynamics (SINDy) method for component modeling.
• To ensure the resulting models are both accurate and possess physically interpretable solutions.

Main Methods:

• Utilized the sparse identification of nonlinear dynamics (SINDy) method for regression modeling.
• Extended SINDy to formulate models for interconnected nonlinear components.
• Employed linear term weights and an error histogram for model optimization and selection.
• Focused on achieving a balance between model accuracy and sparsity.

Main Results:

• Successfully generated a comprehensive regression model for a nonlinear component (sponge gasket).
• Validated the model's reliability by comparing its predictions against experimental responses.
• Demonstrated the methodology's capability to create accurate dynamical system models under realistic conditions.

Conclusions:

• The proposed data-driven methodology effectively models nonlinear dynamic systems.
• The SINDy-based approach yields physically interpretable and accurate governing equations.
• This technique provides a reliable tool for system identification in engineering applications.