Combination line sampling for structural reliability analysis

Line sampling is a method for efficient estimation of the failure (or rare event) probability. The method generates a set of samples on a hyperplane perpendicular to an important direction that points towards the failure domain, and estimates the probability of failure as a sample mean of one-dimensional probability integrals. The performance of the method strongly depends on the quality of the chosen important direction. Recently, an adaptive approach for adjusting the important direction during the simulation has been proposed, termed advanced line sampling (ALS). This contribution revisits the ALS method and shows that the ALS estimator can be viewed as a combination of estimators, each one corresponding to a direction in the adaptive sequence. We show that the combination implied by the original ALS is suboptimal and propose an alternative combination of estimators. The resulting method is termed combination line sampling (CLS). We demonstrate through three numerical examples that CLS outperforms the ALS estimator, in particular if the initially selected important direction is poor.