Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties
Surface response models, such as polynomial chaos Expansion, are commonly used to deal with the case of uncertain input parameters. Such models are only surrogates, so it is necessary to develop tools to assess the level of error between the reference solution (unknown in general), and the value pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2023-01-01
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| Series: | Mechanics & Industry |
| Subjects: | |
| Online Access: | https://www.mechanics-industry.org/articles/meca/full_html/2023/01/mi220127/mi220127.html |
| _version_ | 1797343914658627584 |
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| author | Serra Quentin Florentin Eric |
| author_facet | Serra Quentin Florentin Eric |
| author_sort | Serra Quentin |
| collection | DOAJ |
| description | Surface response models, such as polynomial chaos Expansion, are commonly used to deal with the case of uncertain input parameters. Such models are only surrogates, so it is necessary to develop tools to assess the level of error between the reference solution (unknown in general), and the value provided by the surrogate. This is called a posteriori model verification. In most works, people usually search for the mean quadratic error between the reference problem and the surrogate. They use statistical approaches such as resampling or cross-fold validation, residual based approaches, or properties of the surrogate such as variance decay. Here, we propose a new approach for the specific framework of structural vibrations. Our proposition consists of a residual-based approach combined with a polynomial chaos expansion to evaluate the error as a full random variable, not only its mean square. We propose different variants for evaluating the error. Simple polynomial interpolation gives good results, but introducing a modal basis makes it possible to obtain the error with good accuracy and very low cost. |
| first_indexed | 2024-03-08T10:54:44Z |
| format | Article |
| id | doaj.art-d78ca33c474847b7ac0dc87d298199c6 |
| institution | Directory Open Access Journal |
| issn | 2257-7777 2257-7750 |
| language | English |
| last_indexed | 2024-03-08T10:54:44Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Mechanics & Industry |
| spelling | doaj.art-d78ca33c474847b7ac0dc87d298199c62024-01-26T16:40:26ZengEDP SciencesMechanics & Industry2257-77772257-77502023-01-01244210.1051/meca/2023037mi220127Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertaintiesSerra Quentin0https://orcid.org/0000-0002-9479-5590Florentin Eric1INSA Centre Val de Loire, Univ. Orléans, Univ. Tours, Laboratoire Gabriel LaméINSA Centre Val de Loire, Univ. Orléans, Univ. Tours, Laboratoire Gabriel LaméSurface response models, such as polynomial chaos Expansion, are commonly used to deal with the case of uncertain input parameters. Such models are only surrogates, so it is necessary to develop tools to assess the level of error between the reference solution (unknown in general), and the value provided by the surrogate. This is called a posteriori model verification. In most works, people usually search for the mean quadratic error between the reference problem and the surrogate. They use statistical approaches such as resampling or cross-fold validation, residual based approaches, or properties of the surrogate such as variance decay. Here, we propose a new approach for the specific framework of structural vibrations. Our proposition consists of a residual-based approach combined with a polynomial chaos expansion to evaluate the error as a full random variable, not only its mean square. We propose different variants for evaluating the error. Simple polynomial interpolation gives good results, but introducing a modal basis makes it possible to obtain the error with good accuracy and very low cost.https://www.mechanics-industry.org/articles/meca/full_html/2023/01/mi220127/mi220127.htmlstructural vibrationsuncertainty quantificationstochastic metamodelinga posteriori error estimationpolynomial chaos |
| spellingShingle | Serra Quentin Florentin Eric Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties Mechanics & Industry structural vibrations uncertainty quantification stochastic metamodeling a posteriori error estimation polynomial chaos |
| title | Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties |
| title_full | Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties |
| title_fullStr | Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties |
| title_full_unstemmed | Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties |
| title_short | Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties |
| title_sort | verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties |
| topic | structural vibrations uncertainty quantification stochastic metamodeling a posteriori error estimation polynomial chaos |
| url | https://www.mechanics-industry.org/articles/meca/full_html/2023/01/mi220127/mi220127.html |
| work_keys_str_mv | AT serraquentin verificationofpolynomialchaossurrogatesintheframeworkofstructuralvibrationswithuncertainties AT florentineric verificationofpolynomialchaossurrogatesintheframeworkofstructuralvibrationswithuncertainties |