Section: New Results

Reliability and Computer Experiments

Participants : Yves Auffray, Gilles Celeux, Rémi Fouchereau, Shuai Fu, Pascal Massart.

In the computer experiments field, the goal is to approximate an expensive black box function from a limited number of evaluations. The choice of these evaluations i.e. the choice of a design of (computer) experiments is a major issue.

This year Yves Auffray and Pierre Barbillon, in collaboration with Jean-Michel Marin (Université de Montpellier) have considered estimating the probability of rare events in the context of computer experiments. These rare events depends on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, a crude Monte Carlo estimator does not perform well. Two strategies have been developed to cope with this difficulty: a Bayesian estimate and an importance sampling method. Both methods relies on Kriging metamodeling. They are able to achieve sharp upper confidence bounds on the rare event probability. These methods have been applied to a toy example and a real case study which consists of finding an upper bound of the probability that the trajectory of an airborne load collides the aircraft that has released it.

Following the previous work of the first year, Shuai Fu, under the direction of Gilles Celeux, focus on the design of experiments and its validation, which has become the main issues of the thesis. It leads both to theoretical and computational developments. An original DAC criterion has been proposed and leads to a Bayesian procedure of DAC-test to measure the quality of a design. For improving the design of experiments, an adaptive kriging procedure well adapted to the specific problem has been proposed. However, the algorithms require a too important computation time which should be reduced in future work.

In the framework of a CIFRE convention with Snecma-SAFRAN Rémy Fouchereau has started a thesis on the modeling of fatigue damage for Inco718 supervised by Gilles Celeux. Inco718 is a Zinc-based alloy. To determine its minimum lifetime, a lot of stress tests are made. The lloay lifetimes are reported as function of the stress. The aim of this work is to analyse the resulting curves. A mixture model with a lognormal component and a sum of two lognormals components is considered. Since the sum of two or more lognormal distribution is not closed form. Inference on this model needs Monte Carlo integration within the EM algorithm. Despite some unstability for small sample sizes, this model show encouraging and easily interpretable results.