Gaussian Outcrossings from Safe Convex Polyhedrons

Abstract

A simple upper and lower bound technique developed for the evaluation of the failure probability of a “weakest link” structural system is applied to a structural system having a convex, polyhedral safe set in the space of basic variables. The structure is subjected to a Gaussian vector‐load‐effect process. Conditional second moment calculus, as applied to the set of linear safety margins that completely define the problem, turn out to be an easy and elegant tool for this type of calculations. The upper bound is constructed by bounding the mean outcrossing rate of the vector process while the lower bound is obtained by discretizing the time variable in an optimal way.