A sparse grid stochastic collocation method for structural reliability analysis

摘要

This paper develops a sparse grid stochastic collocation method for the reliability analysis of structures with uncertain parameters and loads. The method consists of two standard techniques in uncertainty quantification: the moment-based Gauss transformation and Smolyak-type sparse grid quadrature rule. Unlike the first-order reliability method (FORM) or second-order reliability method (SORM), the developed method does not need the evaluation of the first- or second-order partial derivatives of the limit state function considered and, moreover, does not suffer from the problem of multiple design points. In addition, the developed method is suitable for all problems whose deterministic solutions can be found and usually needs much fewer function evaluations than the Monte Carlo simulation method. Numerical examples demonstrate that the developed method is exact enough for evaluating the mean values, standard deviations, skewness and kurtosis of the limit state functions and small probabilities of failure as low as 10~(-4). Even for probabilities of failure as low as 10~(-5), the quality of approximation obtained by the method is also acceptable.