Abstract
A new method for estimating the structural failure probability based on the directional importance sampling simulation combined with a numerical radial integration procedure to determine the conditional failure probability in the sampled direction is proposed. The standardized orthogonal space is divided with several concentric hyperspheres and the conditional failure probability in the sampled direction is evaluated by a radial piecewise integration of the failure probability volume contained in the respective concentric hyperspheres. Samples are generated from the importance sampling p.d.f.s centered at the design points on the respective limit state surfaces and directions from the origin to the respective sampled points are proposed to utilize as directional vector samples equivalently. Numerical examples show that the proposed method gives accurate estimations of the structural failure probability efficiently.
