Adaptive numerical designs for the calibration of computer codes

Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters, are specific to the computer code and most often uncertain. The goal of statistical calibration consists in estimating these parameters with the help of a statistical model which links the code outputs with the field measurements. In a Bayesian setting, the posterior distribution of these parameters is normally sampled using MCMC methods. However, they are impractical when the code runs are high time-consuming. A way to circumvent this issue consists of replacing the computer code with a Gaussian process emulator, then sampling a cheap-to-evaluate posterior distribution based on it. Doing so, calibration is subject to an error which strongly depends on the numerical design of experiments used to fit the emulator. We aim at reducing this error by building a proper sequential design by means of the Expected Improvement criterion. Numerical illustrations in several dimensions assess the efficiency of such sequential strategies

Caractérisation des coefficients de Strickler d'un fleuve par inversion probabiliste

International audienceLa caractérisation statistique des coefficients de rugosité du lit et des berges d'un fleuve (coefficients de Strickler) permet à la fois d'évaluer les risques d'inondation et de prévoir le renforcement des ouvrages à proximité. Il s'agit dans cette étude de caractériser ces coefficients à partir de mesures de débit associées à des mesures de hauteurs d'eau. Un logiciel de calcul hydraulique donne les hauteurs d'eau à partir des coefficients de Strickler. Des algorithmes d'inversion probabiliste sont mis en oeuvre afin de modéliser la densité de probabilité des coefficients de Strickler. Deux approches sont testées : l'une est une variante de l'algorithme EM, l'autre est de type MCMC

Bayesian update of the parameters of probability distributions for risk assessment in a two-level hybrid probabilistic-possibilistic uncertainty framework

International audienceRisk analysis models describing aleatory (i.e., random) events contain parameters (e.g., probabilities, failure rates, ...) that are epistemically uncertain, i.e., known with poor precision. Whereas probability distributions are always used to describe aleatory uncertainty, alternative frameworks of representation may be considered for describing epistemic uncertainty, depending on the information and data available. In this paper, we use possibility distributions to describe the epistemic uncertainty in the parameters of the (aleatory) probability distributions. We address the issue of updating, in a Bayesian framework, the possibilistic representation of the epistemical-ly-uncertain parameters of (aleatory) probability distributions as new information (e.g., data) becomes availa-ble. A purely possibilistic counterpart of the classical, well-grounded probabilistic Bayes theorem is adopted. The feasibility of the method is shown on a literature case study involving the risk-based design of a flood protection dike

Propagation of aleatory and epistemic uncertainties in the model for the design of a flood protection dike

International audienceTraditionally, probability distributions are used in risk analysis to represent the uncertainty associated to random (aleatory) phenomena. The parameters (e.g., their mean, variance, ...) of these distributions are usually affected by epistemic (state-of-knowledge) uncertainty, due to limited experience and incomplete knowledge about the phenomena that the distributions represent: the uncertainty framework is then characterized by two hierarchical levels of uncertainty. Probability distributions may be used to characterize also the epistemic uncertainty affecting the parameters of the probability distributions. However, when sufficiently informative data are not available, an alternative and proper way to do this might be by means of possibilistic distributions. In this paper, we use probability distributions to represent aleatory uncertainty and possibility distributions to describe the epistemic uncertainty associated to the poorly known parameters of such probability distributions. A hybrid method is used to hierarchically propagate the two types of uncertainty. The results obtained on a risk model for the design of a flood protection dike are compared with those of a traditional, purely probabilistic, two-dimensional (or double) Monte Carlo approach. To the best of the authors' knowledge, this is the first time that a hybrid Monte Carlo and possibilistic method is tailored to propagate the uncertainties in a risk model when the uncertainty framework is characterized by two hierarchical levels. The results of the case study show that the hybrid approach produces risk estimates that are more conservative than (or at least comparable to) those obtained by the two-dimensional Monte Carlo method

Monte Carlo and fuzzy interval propagation of hybrid uncertainties on a risk model for the design of a flood protection dike

International audienceA risk model may contain uncertainties that may be best represented by probability distributions and others by possibility distributions. In this paper, a computational framework that jointly propagates probabilistic and possibilistic uncertainties is compared with a pure probabilistic uncertainty propagation. The comparison is carried out with reference to a risk model concerning the design of a flood protection dike

Quelques considérations sur l'utilisation pratique des modèles discrets de survie en fiabilité industrielle

International audienceLes modèles discrets de survie sont a priori à utiliser dans le cas de données discrètes de durée de vie. Des données de ce type peuvent provenir, par exemple, d'un matériel sollicité seulement par moments. La variable à modéliser est donc celle correspondant au numéro de la sollicitation à laquelle il y a défaillance. Nous nous sommes intéressés dans le cadre de cette étude aux deux modèles "Polya inverse", basé sur le schéma d'urne de Polya, et "Weibull 1", un des possibles analogues discrets du modèle continu de Weibull. Après en avoir présenté les principales propriétés mathématiques, nous mettons en évidence une faiblesse importante du modèle "Polya inverse" : il ne peut modéliser correctement que des matériels dont le vieillissement est décéléré. Cette contrainte limite considérablement son intérêt pratique. Le modèle "Weibull 1", plus flexible, ne souffre pas de ce problème. Néanmoins, il présente une grande ressemblance avec le modèle continu de Weibull, ressemblance qui est de plus en plus forte en présence de données de survie de valeur élevée (c'est-à-dire relatives à des matériaux qui défaillent au bout d'un grand nombre de sollicitations) ou censurées. Dans ces situations, qui sont celles qui se rencontrent le plus fréquemment dans un contexte industriel comme celui d'EDF, le modèle "Weibull 1" est bien approximé, et donc remplacé, par son analogue continu, mieux appréhendé par les ingénieurs et dont le maniement est beaucoup plus aisé