Estimation of rare event probabilities and extreme quantiles. Applications in the aerospace domain

Rudy Pastel 1, 2
1 ASPI - Applications of interacting particle systems to statistics
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : Rare event dedicated techniques are of great interest for the aerospace industry because of the large amount money that can be lost because of risks associated with minute probabilities. This thesis is focused on the search of probability techniques able to estimate rare event probabilities and extreme quantiles associated with a black box system with static random inputs through two case studies from the industry. The first one is the estimation of the probability of collision between satellites Iridium and Cosmos. The cross-entropy (CE), the non-parametric adaptive importance sampling (NAIS) and an adaptive splitting technique (AST) are compared. Through the comparison, an improved version of NAIS is designed. Whereas NAIS needs to be initiated with a auxiliary random variable which straight away generates rare events, the adaptive NAIS (ANAIS) allows one to use the original input random as initial auxiliary density and therefore does not require a priori knowledge. The second case is the estimation of the safety zone with respect to the fall of a spacecraft booster. Though they can be estimated via ANAIS or AST, extreme quantiles are shown to be not adapted to spatial distribution. For that purpose, the minimum volume set (MVS) concept is chosen from the literature. The crude Monte Carlo (CMC) plug-in MVS estimator being not adapted to extreme level MVS estimation, both ANAIS and AST are adapted into plug-in extreme MVS estimators.These two algorithms outperform the CMC plug-in MVS estimator.
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Rudy Pastel. Estimation of rare event probabilities and extreme quantiles. Applications in the aerospace domain. Probability [math.PR]. Université Européenne de Bretagne; Université Rennes 1, 2012. English. ⟨tel-00728108⟩

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