Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach

Géraud Blatman; Bruno Sudret

doi:10.1016/j.crme.2008.02.013

Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach

Presented by: Jean-Baptiste Leblond

Géraud Blatman ^1,² ; Bruno Sudret ²

¹ IFMA-LaMI, Campus des Cézeaux, BP 265, 63175 Aubière cedex, France
² EDF R&D, Département matériaux et mécanique des composants, site des Renardières, 77250 Moret-sur-Loing cedex, France

Comptes Rendus. Mécanique, Volume 336 (2008) no. 6, pp. 518-523.

Abstract
Résumé

A method is proposed to build a sparse polynomial chaos (PC) expansion of a mechanical model whose input parameters are random. In this respect, an adaptive algorithm is described for automatically detecting the significant coefficients of the PC expansion. The latter can thus be computed by means of a relatively small number of possibly costly model evaluations, using a non-intrusive regression scheme (also known as stochastic collocation). The method is illustrated by a simple polynomial model, as well as the example of the deflection of a truss structure.

Dans cette communication, on propose un algorithme permettant de construire une représentation par chaos polynomial creux de la réponse d'un modèle mécanique dont les paramètres d'entrée sont aléatoires. L'algorithme construit de façon adaptative une représentation creuse en détectant automatiquement les termes importants et en supprimant ceux qui sont négligeables. A chaque étape, le calcul des coefficients s'effectue par minimisation au sens des moindres carrés (méthode non-intrusive dite de régression). L'algorithme est déroulé pas à pas sur un modèle polynomial, puis appliqué à l'étude de la fiabilité d'un treillis élastique.

Received: 2008-01-18
Accepted: 2008-02-25
Published online: 2008-04-28

DOI: 10.1016/j.crme.2008.02.013

Keywords: Solids and structures, Adaptive stochastic finite elements, Sparse polynomial chaos, Stochastic collocation, Regression, Structural reliability
Mots-clés : Solides et structures, Eléments finis stochastiques adaptatifs, Chaos polynomial creux, Collocation stochastique, Régression, Fiabilité

Author's affiliations:

Géraud Blatman ^{1, 2}; Bruno Sudret ²

¹ IFMA-LaMI, Campus des Cézeaux, BP 265, 63175 Aubière cedex, France
² EDF R&D, Département matériaux et mécanique des composants, site des Renardières, 77250 Moret-sur-Loing cedex, France

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     title = {Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach},
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     pages = {518--523},
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     number = {6},
     year = {2008},
     doi = {10.1016/j.crme.2008.02.013},
     language = {en},
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Géraud Blatman; Bruno Sudret. Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach. Comptes Rendus. Mécanique, Volume 336 (2008) no. 6, pp. 518-523. doi : 10.1016/j.crme.2008.02.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.02.013/

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