Adaptive directional stratification for controlled estimation of the probability of a rare event

Within the structural reliability context, the aim of this paper is to present a new accelerated Monte-Carlo simulation method, named ADS, Adaptive Directional Stratification, and designed to overcome the following industrial constraints: robustness of the estimation of a low structural failure probability (less than 10(-3)), limited computational resources and complex (albeit often monotonic) physical model. This new stochastic technique is an original variant of adaptive accelerated simulation method, combining stratified sampling and directional simulation and including two steps in the adaptation stage (ADS-2). First, we theoretically study the properties of two possible failure probability estimators and get the asymptotic and non-asymptotic expressions of their variances. Then, we propose some improvements for our new method. To begin with, we focus on the root-finding algorithm required for the directional approach: we present a stop criterion for the dichotomic method and a strategy to reduce the required number of calls to the costly physical model under monotonic hypothesis. Lastly, to overcome the limit involved by the increase of the input dimension, we introduce the ADS-2(+) method which has the same ground as the ADS-2 method, but additionally uses a statistical test to detect the most significant inputs and carries out the stratification only along them. To conclude, we test the ADS-2 and ADS-2(+) methods on academic examples in order to compare them with the classical structural reliability methods and to make a numerical sensitivity analysis over some parameters. We also apply the methods to a flood model and a nuclear reactor pressurized vessel model, to practically demonstrate their interest on real industrial examples. (C) 2011 Elsevier Ltd. All rights reserved.