Open AccessMéthode du gradient projeté avec contrôle d’erreur
Author(s) -
X. Nguyen,
Fredéric Duprat,
Alain Sellier,
Gérard Pons
Publication year - 2008
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/emn.17.1039-1056
Subject(s) - algorithm , mathematics , probabilistic logic , gradient method , perturbation (astronomy) , function (biology) , limit (mathematics) , constraint (computer aided design) , mathematical optimization , computer science , mathematical analysis , statistics , physics , geometry , quantum mechanics , evolutionary biology , biology
Probabilistic approaches are today frequently used in the design of new civil engineering structures and durability analysis of existing constructions. The so-called Hasofer-Lind’s reliability index is the most popular reliability measure in design codes. This index can be determined by several minimizations under constraint algorithms, such as Rackwitz-Fiessler’s algorithm which is based on the projected gradient method. The drawback of this method lies in the estimation of the gradient vector of the limit state function which is often carried out by finite differences. If the perturbation chosen for this estimation gives a variation of the result lower than the accuracy of the limit state function, the algorithm could give erroneous results, not even to converge. In order to circumvent this drawback, we propose a method called projected gradient method with error control. The principle is to add to Rackwitz-Fiessler’s algorithm a procedure for choosing judiciously the perturbation for calculating the gradient vector accounting for the numerical accuracy of the limit state function. The efficiency of the proposed method can be judged from examples taken from the literature.