Data-driven models for crashworthiness optimisation: intrusive and non-intrusive model order reduction techniques
To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly...
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| Veröffentlicht in: | Structural and multidisciplinary optimization Jg. 65; H. 7 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2022
Springer Nature B.V |
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| ISSN: | 1615-147X, 1615-1488 |
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| Abstract | To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly reducing the computational cost. MOR methods for crashworthiness became only available in recent years; a detailed and comparative assessment of their potential is still lacking. Hence, this work evaluates the advantages and drawbacks of intrusive and non-intrusive projection based MOR methods in the framework of non-linear structural transient analysis. Both schemes rely on the collection of full-order training simulations and a subsequent subspace construction via Singular Value Decomposition. The intrusive MOR is based on a Galerkin projection and a consecutive hyper-reduction step. In this work, its inter-and extrapolation abilities are compared to the non-intrusive technique, which combines the subspace approach with machine learning methods. Moreover, an optimisation analysis incorporating the MOR methods is proposed and discussed for a crashworthiness example. |
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| AbstractList | To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly reducing the computational cost. MOR methods for crashworthiness became only available in recent years; a detailed and comparative assessment of their potential is still lacking. Hence, this work evaluates the advantages and drawbacks of intrusive and non-intrusive projection based MOR methods in the framework of non-linear structural transient analysis. Both schemes rely on the collection of full-order training simulations and a subsequent subspace construction via Singular Value Decomposition. The intrusive MOR is based on a Galerkin projection and a consecutive hyper-reduction step. In this work, its inter-and extrapolation abilities are compared to the non-intrusive technique, which combines the subspace approach with machine learning methods. Moreover, an optimisation analysis incorporating the MOR methods is proposed and discussed for a crashworthiness example. |
| ArticleNumber | 190 |
| Author | Duddeck, Fabian Bach, Christopher Czech, Catharina Lesjak, Mathias |
| Author_xml | – sequence: 1 givenname: Catharina orcidid: 0000-0001-8628-7492 surname: Czech fullname: Czech, Catharina email: catharina.czech@tum.de organization: TUM School of Engineering and Design, Technical University of Munich – sequence: 2 givenname: Mathias surname: Lesjak fullname: Lesjak, Mathias organization: TUM School of Engineering and Design, Technical University of Munich, BMW Group, Research and Innovation Centre – sequence: 3 givenname: Christopher surname: Bach fullname: Bach, Christopher organization: BMW Group, Research and Innovation Centre – sequence: 4 givenname: Fabian surname: Duddeck fullname: Duddeck, Fabian organization: TUM School of Engineering and Design, Technical University of Munich |
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| Cites_doi | 10.1007/s00158-016-1592-1 10.1002/nme.5801 10.1177/0954410019890721 10.1137/090766498 10.1186/s40323-020-00151-8 10.1007/978-3-319-67988-4_137 10.1007/s00158-007-0130-6 10.1007/s00158-015-1315-z 10.1002/nme.167 10.1090/qam/910462 10.1007/s11831-018-9258-3 10.1016/j.cma.2020.113192 10.1002/nme.5535 10.1016/j.jcp.2016.10.033 10.1016/j.cma.2018.07.017 10.1002/nme.4668 10.1145/1457515.1409118 10.1016/j.compfluid.2018.07.021 10.1002/nme.6243 10.1177/0954407019893841 10.1007/s40324-019-00208-8 10.1016/j.cma.2016.10.022 10.1016/j.cma.2019.112650 10.1007/s12239-019-0026-7 10.1016/j.cma.2018.03.005 10.1002/nme.5283 10.1002/nme.6712 10.1080/13873954.2016.1198385 10.1016/j.compfluid.2004.11.006 10.1023/A:1008202821328 10.1016/j.cma.2020.112947 10.1002/nme.4820 10.1115/1.1760540 10.1007/BF02288367 10.1016/j.cma.2018.10.029 10.1002/nme.6009 10.1007/s00158-019-02485-3 10.1145/355744.355745 10.1016/j.tws.2013.08.021 10.1093/qmath/11.1.50 10.1007/s00158-016-1579-y 10.1002/nme.6303 10.2514/1.35374 10.2514/6.2004-889 |
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| Keywords | Intrusive reduced order modelling Reduced order model Optimisation Crashworthiness Nonlinear model order reduction Non-intrusive modelling |
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| SubjectTerms | Algorithms Computational Mathematics and Numerical Analysis Crashworthiness Decomposition Engineering Engineering Design Impact strength Machine learning Methods Model reduction Optimization Partial differential equations Research Paper Singular value decomposition Theoretical and Applied Mechanics Transient analysis |
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