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Articles written by Sudret, B.

  1. Sudret, B.. "Global sensitivity analysis using polynomial chaos expansions" Reliability Engineering & System Safety. 93 (7). JUL 2008. pp. 964--979.

    Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol' indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression- based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2-3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol' indices. (C) 2007 Elsevier Ltd. All rights reserved.


  2. Blatman, G. and Sudret, B.. "Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach" Comptes RendusS Mecanique. 336 (6). JUN 2008. pp. 518--523.

    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.