Identification of multi-modal random variables through mixtures of polynomial chaos expansions

Anthony Nouy

doi:10.1016/j.crme.2010.09.003

Identification of multi-modal random variables through mixtures of polynomial chaos expansions
[Identification de variables aléatoires multi-modales par mélange de décompositions sur la chaos polynômial]

Anthony Nouy ¹

¹ GeM - UMR CNRS 6183, École centrale Nantes, Université de Nantes, 1, rue de la Noë, 44321 Nantes, France

Comptes Rendus. Mécanique, Volume 338 (2010) no. 12, pp. 698-703.

Résumé
Abstract

Une méthodologie est proposée pour l'identification d'une variable aléatoire multi-modale à partir d'échantillons. La variable aléatoire est vue comme un mélange fini de variables aléatoires uni-modales. Une représentation fonctionnelle de la variable aléatoire est utilisée. Elle peut être interprétée comme un mélange de décompositions sur le chaos polynômial. Après une séparation adaptée des échantillons en sous-ensembles d'échantillons uni-modaux, les coefficients de la décomposition sont identifiés en utilisant une technique de projection empirique. Cette procédure d'identification permet une représentation générique d'une large classe de variables aléatoires multi-modales avec une décomposition sur chaos polynômial généralisé de faible degré.

A methodology is introduced for the identification of a multi-modal real-valued random variable from a collection of samples. The random variable is seen as a finite mixture of uni-modal random variables. A functional representation of the random variable is used, which can be interpreted as a mixture of polynomial chaos expansions. After a suitable separation of samples into sets of uni-modal samples, the coefficients of the expansion are identified by using an empirical projection technique. This identification procedure allows for a generic representation of a large class of multi-modal random variables with low-order generalized polynomial chaos representations.

Reçu le : 2010-03-18
Accepté le : 2010-09-21
Publié le : 2010-10-02

DOI : 10.1016/j.crme.2010.09.003

Keywords: Statistics, Uncertainty quantification, Identification, Multi-modal density, Polynomial chaos, Finite mixture model, Spectral stochastic methods
Mots-clés : Statistique, Quantification d'incertitudes, Identification, Densité multi-modale, Chaos Polynômial, Modèle de mélange fini, Méthodes spectrales stochastiques

Affiliations des auteurs :

Anthony Nouy ¹

¹ GeM - UMR CNRS 6183, École centrale Nantes, Université de Nantes, 1, rue de la Noë, 44321 Nantes, France

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Anthony Nouy. Identification of multi-modal random variables through mixtures of polynomial chaos expansions. Comptes Rendus. Mécanique, Volume 338 (2010) no. 12, pp. 698-703. doi : 10.1016/j.crme.2010.09.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.09.003/

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