Mechanics & Industry
Volume 24, 2023
History of matter: from its raw state to its end of life
|Number of page(s)
|06 December 2023
Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties
INSA Centre Val de Loire, Univ. Orléans, Univ. Tours, Laboratoire Gabriel Lamé, France
* e-mail: firstname.lastname@example.org
Accepted: 20 October 2023
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.
Key words: Structural vibrations / uncertainty quantification / stochastic metamodeling / a posteriori error estimation / polynomial chaos
© Q. Serra and E. Florentin, Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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