Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty

Vincent Chabridon (1, 2) , Mathieu Balesdent (1) , Jean-Marc Bourinet (2) , Jérôme Morio (3) , Nicolas Gayton (2)

1 DTIS, ONERA, Université Paris Saclay (COmUE) [Palaiseau]
2 SIGMA Clermont - SIGMA Clermont
3 DTIS, ONERA, Université de Toulouse [Toulouse]

This paper aims at presenting sensitivity estimators of a rare event probability in the context of uncertain distribution parameters (which are often not known precisely or poorly estimated due to limited data). Since the distribution parameters are also affected by uncertainties, a possible solution consists in considering a second probabilistic uncertainty level. Then, by propagating this bi-level uncertainty, the failure probability becomes a random variable and one can use the mean estimator of the distribution of the failure probabilities (i.e. the " predictive failure probability " , PFP) as a new measure of safety. In this paper, the use of an augmented framework (composed of both basic variables and their probability distribution parameters) coupled with an Adaptive Importance Sampling strategy is proposed to get an efficient estimation strategy of the PFP. Consequently, double-loop procedure is avoided and the computational cost is decreased. Thus, sensitivity estimators of the PFP are derived with respect to some deterministic hyper-parameters parametrizing a priori modeling choice. Two cases are treated: either the uncertain distribution parameters follow an unbounded probability law, or a bounded one. The method efficiency is assessed on two different academic test-cases and a real space system computer code (launch vehicle stage fallback zone estimation).

Mots clés: DISTRIBUTION PARAMETER UNCERTAINTY; RARE EVENT SIMULATION; ADAPTIVE IMPORTANCE SAMPLING; RELIABILITY SENSITIVITY ANALYSIS; SCORE FUNCTIONS

Mots clés: SENSIBILITÉ; INCERTITUDES; FIABILITE

Domaines: Logique en informatique [cs.LO]; Base de données [cs.DB]

Vincent Chabridon, Mathieu Balesdent, Jean-Marc Bourinet, Jérôme Morio, Nicolas Gayton. Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty. Reliability Engineering and System Safety, 2018, 178, pp.164-178. ⟨10.1016/j.ress.2018.06.008⟩. ⟨hal-01850651⟩