Estimation of Failure Probability by Limit State Sampling

Abstract

This paper presents a novel approach, referred to as Limit State Sampling, for estimating failure probabilities of engineering structures. The majority of methods used to evaluate failure probabilities involve a large number of simulations of the structural model. In situations with low failure probability and numerically complex structural models this can become a computationally unpractical task. The Limit State Sampling approach is developed here with the intention of reducing the number of simulations of the structural model in the process of evaluation of the failure probability. This is performed by introducing a pseudo probabilistic density function with the purpose of sampling around the failure limit state. Samples from the pseudo probability density function are then used to construct a surrogate model of the structural behavior at the failure limit state. Finally, the failure probability is estimated by utilizing the efficiency of the surrogate model, with reduced computational expense. The novelty of the approach comes from the formulation of the pseudo probability density function and the application to the probabilistic analysis of structures.