Weeger, Oliver ; Wever, Utz ; Simeon, Bernd (2021)
On the use of modal derivatives for nonlinear model order reduction.
In: International Journal for Numerical Methods in Engineering, 2016, 108 (13)
doi: 10.26083/tuprints-00019820
Artikel, Zweitveröffentlichung, Postprint
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Kurzbeschreibung (Abstract)
Modal derivative is an approach to compute a reduced basis for model order reduction of large-scale nonlinear systems that typically stem from the discretization of partial differential equations. In this way, a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller, based on the resulting small-scale state-space model. We investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction, which has been missing so far. Concentrating on the application field of structural mechanics and structural dynamics, we show that the concept of modal derivatives can also be applied as nonlinear extension of the Craig–Bampton family of methods for substructuring. We furthermore generalize the approach from a pure projection scheme to a novel reduced-order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables. This complexity reduction leads to a frequency-preserving nonlinear quadratic state-space model. Numerical examples with carefully chosen nonlinear model problems and three-dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods, along with the current limitations.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Weeger, Oliver ; Wever, Utz ; Simeon, Bernd |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | On the use of modal derivatives for nonlinear model order reduction |
| Sprache: | Englisch |
| Publikationsjahr: | 2021 |
| Publikationsdatum der Erstveröffentlichung: | 2016 |
| Verlag: | Wiley |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | International Journal for Numerical Methods in Engineering |
| Jahrgang/Volume einer Zeitschrift: | 108 |
| (Heft-)Nummer: | 13 |
| Kollation: | 25 Seiten |
| DOI: | 10.26083/tuprints-00019820 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/19820 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichungsservice |
| Kurzbeschreibung (Abstract): | Modal derivative is an approach to compute a reduced basis for model order reduction of large-scale nonlinear systems that typically stem from the discretization of partial differential equations. In this way, a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller, based on the resulting small-scale state-space model. We investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction, which has been missing so far. Concentrating on the application field of structural mechanics and structural dynamics, we show that the concept of modal derivatives can also be applied as nonlinear extension of the Craig–Bampton family of methods for substructuring. We furthermore generalize the approach from a pure projection scheme to a novel reduced-order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables. This complexity reduction leads to a frequency-preserving nonlinear quadratic state-space model. Numerical examples with carefully chosen nonlinear model problems and three-dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods, along with the current limitations. |
| Status: | Postprint |
| URN: | urn:nbn:de:tuda-tuprints-198209 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet Cyber-Physische Simulation (CPS) |
| Hinterlegungsdatum: | 15 Dez 2021 10:47 |
| Letzte Änderung: | 16 Dez 2021 06:49 |
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| Suche nach Titel in: | TUfind oder in Google |
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- On the use of modal derivatives for nonlinear model order reduction. (deposited 15 Dez 2021 10:47) [Gegenwärtig angezeigt]
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