Hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability

Abstract

• Failure probability integral reformulated based on control variates technique. • Augmented probability density function used as control variate of the original probability density function. • Subset simulation computes roughed probability and a weighting term refines the roughness. • Markov Chain quickly transfers the conditional samples with high acceptance probability toward the failure set. The safety analysis of systems with nonlinear performance function and small probability of failure is a challenge in the field of reliability analysis. In this study, an efficient approach is presented for approximating small failure probabilities. To meet this aim, by introducing Probability Density Function (PDF) control variates, the original failure probability integral was reformulated based on the Control Variates Technique (CVT). Accordingly, using the adaptive cooperation of the subset simulation (SubSim) and the CVT, a new formulation was offered for the approximation of small failure probabilities. The proposed formulation involves a probability term (resulting from a fast-moving SubSim) and an adaptive weighting term that refines the obtained probability. Several numerical and engineering problems, involving nonlinear performance functions and system-level reliability problems, are solved by the proposed approach and common reliability methods. Results showed that the proposed simulation approach is not only more efficient, but is also robust than common reliability methods. It also presents a good potential for application in engineering reliability problems.