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Error Estimation of Polynomial Chaos Approximations in Transient Structural Dynamics

T. Dao 1 Quentin Serra 1 Sébastien Berger 1 Éric Florentin 1
1 DivS - Dynamique interactions vibrations Structures
LaMé - Laboratoire de Mécanique Gabriel Lamé
Abstract : Usually, within stochastic framework, a testing dataset is used to evaluate the approximation error between a surrogate model (e.g. a Polynomial Chaos expansion) and the exact model. We propose here another method to estimate the quality of an approximated solution of a stochastic process, within the context of structural dynamics. We demonstrate that the approximation error is governed by an equation based on the residue of the approximate solution. This problem can be solved numerically using an approximated solution, here a coarse Monte Carlo simulation. The developed estimate is compared to a reference solution on a simple case. The study of this comparison makes it possible to validate the efficiency of the proposed method. This validation has been observed using different sets of simulations. To illustrate the applicability of the proposed approach to a more challenging problem, we also present a problem with a large number of random parameters. This illustration shows the interest of the method compared to classical estimates.
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https://hal.archives-ouvertes.fr/hal-02375432
Contributor : Quentin Serra <>
Submitted on : Wednesday, December 9, 2020 - 3:06:29 PM
Last modification on : Thursday, April 22, 2021 - 10:40:01 AM
Long-term archiving on: : Wednesday, March 10, 2021 - 7:25:39 PM

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T. Dao, Quentin Serra, Sébastien Berger, Éric Florentin. Error Estimation of Polynomial Chaos Approximations in Transient Structural Dynamics. International Journal of Computational Methods, World Scientific Publishing, 2020, 17 (10), ⟨10.1142/S0219876220500036⟩. ⟨hal-02375432⟩

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