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Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems
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 methodolog...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9207537/ https://www.ncbi.nlm.nih.gov/pubmed/35719078 http://dx.doi.org/10.1098/rsta.2021.0194 |
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author | Cenedese, M. Axås, J. Yang, H. Eriten, M. Haller, G. |
author_facet | Cenedese, M. Axås, J. Yang, H. Eriten, M. Haller, G. |
author_sort | Cenedese, M. |
collection | PubMed |
description | 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’. |
format | Online Article Text |
id | pubmed-9207537 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-92075372022-06-26 Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems Cenedese, M. Axås, J. Yang, H. Eriten, M. Haller, G. Philos Trans A Math Phys Eng Sci Articles 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’. The Royal Society 2022-08-08 2022-06-20 /pmc/articles/PMC9207537/ /pubmed/35719078 http://dx.doi.org/10.1098/rsta.2021.0194 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Articles Cenedese, M. Axås, J. Yang, H. Eriten, M. Haller, G. Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
title | Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
title_full | Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
title_fullStr | Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
title_full_unstemmed | Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
title_short | Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
title_sort | data-driven nonlinear model reduction to spectral submanifolds in mechanical systems |
topic | Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9207537/ https://www.ncbi.nlm.nih.gov/pubmed/35719078 http://dx.doi.org/10.1098/rsta.2021.0194 |
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