Probability Integration by Directional Simulation

Reliability evaluation methods based on directional simulation for structural reliability analysis is treated herein. The methods can be used to check results obtained by a first- or second-order reliability method. Directional importance sampling based on first- and second-order reliability results is used to reduce the variance on the probability estimator. Sampling densities and procedures for important types of failure surfaces considered in the space of independent and standardized Gaussian variables are set up. The types include hyper-spheres, hyperplanes, rotationally symmetrical hyperparaboloids, surfaces defining a convex polyhedral failure set, as well as series-systems failure surfaces.