Section: New Results

Reliability and Computer Experiments

Participants : Yves Auffray, Gilles Celeux, Rémy Fouchereau, Shuai Fu.

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.

Following the previous work of the past three years, Shuai Fu has concluded her Ph.D thesis under the direction of Gilles Celeux [1] . This year, the work was focused on controlling four main error quantities, in order to validate the methodology in the industrial framework. More precisely, the DAC criterion (Data Agreement Criterion), which has been proposed for assessing the relevance of the design of experiments (DOE) and the prior choice with the observed data was applied to a complex hydrological model, coding and testing the relevant algorithms [30] . For the purpose of controlling the emulator error in an adaptive kriging algorithm, two Bayesian criteria have been proposed for searching and adding new points into the current DOE. The computation time remains important, which makes the method meaningful only in the case where we have a really time-consuming code.

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 alloy lifetimes are reported as function of the stress. The aim is to propose a stochastic models for fatigue lifetime prediction based on a fracture mechanics-based approach. 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. Thus, we have provided engineers with a probabilistic tool for reliability design of mechanical parts, but also with a diagnostic tool for material elaboration.