A new adaptive response surface method for reliability analysis

Nicolas Roussouly (1) , Frank Petitjean (2) , Michel Salaün (1)

1 DMSM - Département de Mécanique des Structures et Matériaux
2 ICAM - Institut Catholique d'Arts et Métiers

Response surface method is a convenient tool to assess reliability for a wide range of structural mechanical problems. More specifically, adaptive schemes which consist in iteratively refine the experimental design close to the limit state have received much attention. However, it is generally difficult to take into account a lot of variables and to well handle approximation error. The method, proposed in this paper, addresses these points using sparse response surface and a relevant criterion for results accuracy. For this purpose, a response surface is built from an initial Latin Hypercube Sampling (LHS) where the most significant terms are chosen from statistical criteria and cross-validation method. At each step, LHS is refined in a region of interest defined with respect to an importance level on probability density in the design point. Two convergence criteria are used in the procedure: The first one concerns localization of the region and the second one the response surface quality. Finally, a bootstrap method is used to determine the influence of the response error on the estimated probability of failure. This method is applied to several examples and results are discussed.

Mots clés: Structural reliability; Adaptive response surface; Regression; Prediction error; Bootstrap

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Nicolas Roussouly, Frank Petitjean, Michel Salaün. A new adaptive response surface method for reliability analysis. Probabilistic Engineering Mechanics, 2013, vol. 32, pp. 103-115. ⟨10.1016/j.probengmech.2012.10.001⟩. ⟨hal-00813479⟩