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Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems
M Cenedese1, J Axås1, H Yang2
1Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21 8092, Zürich, Switzerland.
Summary
This study introduces a data-driven method to simplify complex nonlinear systems with multiple states. The technique uses spectral submanifolds to predict system behavior under external forces, validated with structural vibration data.
Area of Science:
- Mechanical Engineering
- Dynamical Systems Theory
- Nonlinear Dynamics
Background:
- Data-driven model reduction is established for linear systems.
- Reducing nonlinearizable systems with multiple steady states lacks general methods.
- Predicting nonlinear system responses requires accurate reduced-order models.
Purpose of the Study:
- To present a data-driven nonlinear model reduction methodology.
- To enable accurate predictions for nonlinearizable systems under external forcing.
- To address the limitations of existing model reduction techniques for complex systems.
Main Methods:
- Utilizing spectral submanifold theory for nonlinear model reduction.
- Constructing normal forms from observed unforced nonlinear oscillations.
- Reducing dynamics to low-dimensional invariant manifolds.
- Capturing amplitude-dependent properties of the system.
Main Results:
- The methodology effectively reduces complex nonlinear dynamics.
- Normal forms accurately represent system behavior, including amplitude dependence.
- Predictions for forced responses show high accuracy.
- Successful application to structural vibration examples using synthetic and experimental data.
Conclusions:
- The spectral submanifold approach provides a general method for data-driven nonlinear model reduction.
- This technique enhances predictive capabilities for complex dynamical systems.
- The approach is applicable to real-world problems in structural dynamics.
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