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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...

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Detalles Bibliográficos
Autores principales: Cenedese, M., Axås, J., Yang, H., Eriten, M., Haller, G.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
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’.
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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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