Global sensitivity analysis using polynomial chaos expansions

Adaptive sparse polynomial chaos expansion based on least angle regression

http://www.ukm.my/kamal3/psm/pfpstochastics.pdf

The stochastic finite element method: Past, present and future

An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis

Time series analysis and its applications

The stochastic finite element method allows to solve stochastic boundary value problems where material properties and loads are random. The method is based on the expansion of the mechanical response onto the so-called polynomial chaos. In this paper, a non intrusive method based on a least-squares minimization procedure is presented. This method is illustrated by the study of the settlement of a foundation. Different analysis are proposed: the computation of the statistical moments of the response, a reliability analysis and a parametric sensitivity analysis.

/pdf/stochastic-finite-element-a-non-intrusive-approach-by-1hejxw06gf.pdf

Stochastic finite element: a non intrusive approach by regression

A new stochastic finite element procedure (SFEP) in the tradition of Ghanem’s work is presented. It allows to deal with any number of input random variables of any type that can model both material properties and loading. The method makes use of Hermite series expansion of the input random variables and polynomial chaos expansion of the response, for which an original implementation is proposed. The link with reliability analysis is also established. Three application examples in geotechnical engineering are given for the sake of illustration. The accuracy and efficiency of SFEP is thoroughly investigated by comparison with well-established approaches.

/pdf/a-stochastic-finite-element-procedure-for-moment-and-gatvjajvhm.pdf

A stochastic finite element procedure for moment and reliability analysis

La methode des elements finis stochastiques (MEFS) a ete developpee pour modeliser l'alea sous la forme de variables aleatoires de type quelconque dans le cadre de la mecanique lineaire elastique. Elle consiste a ecrire les composantes de la reponse aleatoire du systeme sous la forme d'une serie polynomiale de variables aleatoires (baptisee chaos polynomial), dont les coefficients sont obtenus par une methode de type Galerkin. Le champ d'application de cette methode etant limite, de nouvelles methodes, dites non intrusives, permettant le calcul du developpement de la reponse dans la base du chaos polynomial ont ete recherchees. Les methodes MEFS et non intrusive ont ete testees et comparees sur des exemples de mecanique elastique lineaire. Enfin les approches non intrusives ont ete utilisees dans un cas de mecanique de la rupture non lineaire.

https://tel.archives-ouvertes.fr/tel-00366225/document

Eléments finis stochastiques : approches intrusive et non intrusive pour des analyses de fiabilité

A non-intrusive stochastic finite-element method is proposed for uncertainty propagation through mechanical systems with uncertain input described by random variables. A polynomial chaos expansion (PCE) of the random response is used. Each PCE coefficient is cast as a multi-dimensional integral when using a projection scheme. Common simulation schemes, e.g. Monte Carlo Sampling (MCS) or Latin Hypercube Sampling (LHS), may be used to estimate these integrals, at a low convergence rate though. As an alternative, quasi-Monte Carlo (QMC) methods, which make use of quasi-random sequences, are proposed to provide rapidly converging estimates. The Sobol' sequence is more specifically used in this paper. The accuracy of the QMC approach is illustrated by the case study of a truss structure with random member properties (Young's modulus and cross section) and random loading. It is shown that QMC outperforms MCS and LHS techniques for moment, sensitivity and reliability analyses.

/pdf/quasi-random-numbers-in-stochastic-finite-element-analysis-21dsu3rkd7.pdf

Quasi-random numbers in stochastic finite element analysis

The time-dependent loss of prestress of cables in Nuclear Power Plant concrete inner containment buildings may affect the vessel leak-tightness and reduce its life extension. Thus, the assessment of the structural integrity of the containment vessel requires a correct estimation of the long-term creep strains. The article aims at computing and updating the evolution in time of a confidence interval on the creep strains by updating the prior density of input parameters that is specified in a Bayesian framework.

Marc Berveiller

Papers

Stochastic finite element: a non intrusive approach by regression

A stochastic finite element procedure for moment and reliability analysis

Eléments finis stochastiques : approches intrusive et non intrusive pour des analyses de fiabilité

Quasi-random numbers in stochastic finite element analysis

Updating the long-term creep strains in concrete containment vessels by using Markov chain Monte Carlo simulation and polynomial chaos expansions