Abstract
We present a data-driven method based on deep learning for identifying nonlinear normal modes of unknown nonlinear dynamical systems using response data only. We leverage the modeling capacity of deep neural networks to identify the forward and inverse nonlinear modal transformations and the associated modal dynamics evolution. We test the method on Duffing systems with cubic nonlinearity and observe that the identified NNMs with invariant manifolds from response data agree with those analytical or numerical ones using closed-form equations.
Keywords
- Nonlinear normal modes
- Invariant manifolds
- Nonlinear system identification
- Data-driven
- Deep learning
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Reference
Shaw, S., Pierre, C.: Non-linear normal modes and invariant manifolds. J. Sound Vib. 150(1) (1991)
Acknowledgments
This research was partially funded by the Physics of Artificial Intelligence Program of US Defense Advanced Research Projects Agency (DARPA) and the Michigan Technological University faculty startup fund.
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© 2023 The Society for Experimental Mechanics, Inc.
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Li, S., Yang, Y. (2023). Data-Driven Nonlinear Modal Analysis: A Deep Learning Approach. In: Brake, M.R., Renson, L., Kuether, R.J., Tiso, P. (eds) Nonlinear Structures & Systems, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-031-04086-3_31
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DOI: https://doi.org/10.1007/978-3-031-04086-3_31
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Online ISBN: 978-3-031-04086-3
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