期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2021.0194
关键词
nonlinear dynamics; mechanical vibrations; reduced-order modelling; normal form; machine learning
资金
- US National Science Foundation CMMI-CAREER [1554146]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1554146] Funding Source: National Science Foundation
This paper reviews a data-driven nonlinear model reduction methodology based on spectral submanifolds, which can be used to reduce the dimensionality of nonlinear systems and provide accurate predictions.
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing nonlinearizable systems with multiple coexisting steady states have been unavailable. In this paper, we review such a data-driven nonlinear model reduction methodology based on spectral submanifolds. As input, this approach takes observations of unforced nonlinear oscillations to construct normal forms of the dynamics reduced to very low-dimensional invariant manifolds. These normal forms capture amplitude-dependent properties and are accurate enough to provide predictions for nonlinearizable system response under the additions of external forcing. We illustrate these results on examples from structural vibrations, featuring both synthetic and experimental data.This article is part of the theme issue 'Data-driven prediction in dynamical systems'.
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