Structural Reliability Estimation Based on a Efficient Numerical Integration Method (A Determination Method of Pseudo Directional Importance Sampling Probability Densities Weighted in the Direction of the Design Points)

publisher[Abstract] This paper is concerned with the evaluation of structural failure probability based on numerical integration combined with a pseudo directional importance sampling method. Samples are generated in Cartesian coordinates from the importance sampling p.d.f.s centered at the design points on the limit state surfaces of the respective failure modes and directional vector samples are determined by the directions from the origin to the respective sampled points. The probability contents along hyperconical shaped volumes in the respective sampled directions are evaluated numerically and regarded as pseudo directional importance sampling probability densities. The Importance sampling method using those pseudo directional importance sampling probability densities are used to calculate the accurate value of the failure areas on the surfaces of each respective hypersphere in the restrictedregion. Numerical example to estimate the failure probability of structures shows that the proposed method gives accurate estimations of structural failure probabilities efficiently