An Efficient Algorithm for Structural Reliability Based on Dichotomy Method

Abstract

Monte Carlo Simulation (MCS) method is obviously a feasible and easy method for structural reliability evaluation, by which the multiple integral is replaced by sampling statistics. However, MCS is time-consuming because of its large number of simulations. To reduce the number of simulations, a structural reliability method based on dimensionality reduction and dichotomy has been presented, in the proposed method the dimensionality reduction technique is employed in grouping samples and the dichotomy method is applied to determining the partitioned limit state function (LSF). First, samples of direct MCS generated in original space are mapped to the independent standard Gaussian space and bi-dimensional space successively. Then the samples are divided into many groups according to the value of horizontal axis in the bi-dimensional space. Finally, the critical samples of each group are located by dichotomy method, and the partitioned LSF are approximated by the critical samples. With this method, the failure samples can be distinguished from whole samples by a relative little number of simulations. By several examples, the efficiency and robustness of the proposed algorithm were demonstrated, and the optimal number of the samples and the groups were respectively studied.