Subset simulation and line sampling for advanced Monte Carlo reliability analysis

Abstract

In this paper, the recently developed Subset Simulation (SS) and Line Sampling (LS) techniques are considered for improving the efficiency of Monte Carlo Simulation (MCS) in the estimation of system failure probability. The SS method is founded on the idea that a small failure probability can be expressed as a product of larger conditional probabilities of some intermediate events: with a proper choice of the intermediate events, the conditional probabilities can be made sufficiently large to allow accurate estimation with a small number of samples. The LS method employs lines instead of random points in order to probe the failure domain of interest. An important direction is determined, which points towards the failure domain of interest; the high-dimensional reliability problem is then reduced to a number of conditional one-dimensional problems which are solved along the important direction. The two methods are applied on a structural reliability model of literature. The efficiency of the proposed techniques is evaluated in comparison to the commonly adopted standard MCS.