An improved sieve point method for the reliability analysis of structures

Abstract

The efficiency of existing stochastic analysis method depends on the discretization of the random variables domain. The number theoretical method has been proposed to discretize the random variable space and solve the generalized density evolution equation via sampling strategy. This method traditionally involves hyper-ball sieving (HS) algorithm to sample the representative point set. However, the sieving radius of the hyper-ball is determined subjectively, and the efficiency and accuracy of the analysis depend on the selected radius. To avoid this subjective selection, an equal volume hyper-ball sieving method is presented in this paper. By transforming the hypercube spatial volume of random variables into that of an equivalent hyper-ball, the radius of the equal volume hyper-ball is obtained analytically. This radius is further optimized with a minimum star discrepancy in the representative point set. The performance and accuracy of the proposed method are checked in four numerical examples, and the representative point set such obtained is more uniform with smaller NRP leading to more accurate and efficient subsequent stochastic analysis than the HS method.