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M Cenedese1, J Axås1, H Yang2

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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.

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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.