# Régis LebrunAirbus Central Research & Technology · Virtual Product Engineering

Régis Lebrun

PhD

Airbus probability&statistics expert
Scientific coordinator of the OpenTURNS software (www.openturns.org)

## About

27

Publications

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937

Citations

Introduction

I am working in the Airbus Applied Mathematics team as an expert in probability and statistics, with a focus on dependence modelling and uncertainty quantification.

## Publications

Publications (27)

Modeling high-dimensional multivariate distributions is a computationally challenging task. In the discrete case, Bayesian networks have been successfully used to reduce the complexity and to simplify the problem. However, they lack of a general model for continuous variables. In order to overcome this problem, Elidan (2010) proposed the model of c...

We propose a new framework to learn non-parametric graphical models from continuous observational data. Our method is based on concepts from information theory in order to discover independences and causality between variables: the conditional and multivariate mutual information (such as \cite{verny2017learning} for discrete models). To estimate th...

The recent transformation in the aeronautical industry gives new prospects in the field of product geometry assurance. These include, in particular the creation of sophisticated virtual models, or digital twins, which can reflect the as-built geometry of physical products and optimize the assembly operations consequently. One of the current obstacl...

We consider the problem of the estimation of a high-dimensional probability distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density with respect to a product measure, possibly discrete for handling the...

For this section, we aim to demonstrate the use of open source software for aircraft preliminary design at the example of a wing configuration robust design optimization. On airfoil level, we demonstrate the meta-modelling of the relation between the lift and drag coefficients and the parameters used to describe the airfoil shape. The meta-model is...

OpenTURNS is an open source library for uncertainty propagation by probabilistic
methods. Developed in a partnership of five industrial companies (EDF, Airbus, Phimeca,
IMACS and ONERA), it benefits from a strong practical feedback. Classical algorithms of UQ
are available : central dispersion, probability of exceedance, sensitivity analysis, metam...

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic...

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic...

The joint distribution of order statistics is characterized without reference to a parent distribution. To this end, the possible univariate margins of such a distribution are first determined. The class of possible copulas KK is then characterized under the assumption of continuous margins through a description of their minimal support. A truncati...

The computation of rectangular probabilities of multivariate discrete integer distributions such as the multinomial, multivariate hypergeometric or multivariate Pólya distributions is of great interest both for statistical applications and for probabilistic modeling purpose. All these distributions are members of a broader family of multivariate di...

In this thesis, we study the modeling of stochastic dependence for random vectors from the copula viewpoint. The first part is a numerical exploration of the notions of copulas and dependence measures in the context of uncertainty modeling for numerical simulation. The second part focus on the Nataf and Rosenblatt transformations. We show that the...

In this paper, we propose a low-rank approximation method based on discrete
least-squares for the approximation of a multivariate function from random,
noisy-free observations. Sparsity inducing regularization techniques are used
within classical algorithms for low-rank approximation in order to exploit the
possible sparsity of low-rank approximati...

Modelling the stochastic dependence between random inputs of a system is of uttermost importance for a sensible evaluation of its reliability. Most of the time, this modelling is made using some linear correlation coefficients. The current paper underlines the potential pitfalls of such an approach and gives a short introduction to the concept of c...

This article is the third in a series dedicated to the mathematical study of isoprobabilistic transformations and their relationship with stochastic dependence modelling, see [R. Lebrun, A. Dutfoy, An innovating analysis of the Nataf transformation from the viewpoint of copula, Probabilistic Engineering Mechanics (2008). doi: 10.1016/j.probengmech....

This article gives new insight on the Nataf transformation, a widely used tool in reliability analysis. After recalling some basics concerning the copula theory, we explain this transformation in the light of the copula theory and we uncover all the hidden hypothesis made on the dependence structure of the probabilistic model when using this transf...

In the first article [Lebrun R, Dutfoy A. An innovating viewpoint of the isoprobabilistic Nataf transformation with the copula theory within exceedance threshold uncertainty analysis. Probabilistic Structure Engineering Structural Reliability. 2008 [in press]], we showed that the Nataf transformation is a way to model the dependence structure of a...

The need to assess robust performance for complex systems have led to a considerable rise of industrial interest in the simulation challenges to treat and propagate uncertainty through complex physical and numerical simulation frameworks. The industrial stakes require that both the methodology and the numerical methods for uncertainty treatment hav...

The need to assess robust performance for complex systems have led to a considerable rise of industrial interest in the simulation challenges: to treat and propagate uncertainty through complex physical and numerical simulation frameworks. The industrial stakes require that both the methodology and the numerical methods for uncertainty treatment ha...

Dans l'étude de la fiabilité d'un système, il est fréquent que les paramètres aléatoires du modèle de fiabilité soient dépendantes. L'évaluation de la probabilité de défaillance du système nécessite alors de connaitre la loi jointe de ces paramètres, qui est souvent supposée inaccessible. La dépendance est alors décrite par une matrice de corrélati...

The length scale is not accounted for in classical modelling of strain localisation, either in shear band development or in fracture problems. The length scale can be introduced directly in the constitutive equations (nonlocal models) ; it can also be set by taking into account additional physical phenomena : heat conduction, inertia terms. A gener...

Structure reliability guaranty requires prior evaluation of non destructive testing methods. The concept of Probability Of Detection (POD) is generally used to quantitatively assess performances and reliability of testing operations. High costs of POD campaigns combined with continuous increase in configurations needing POD determination make cost...

Dans une analyse de fiabilite, nous nous intressons a l'evaluation de probabilites de defaillances faibles. Une methode de choix pour ce calcul est la methode FORM (First Order Reliability Method). Une etape primordiale de cette methode est la determination du point de conception du systeme, et l'approximation FORM consiste a lineariser la frontier...

## Projects

Projects (3)

We implement an efficient eigensolver in OpenTURNS (www.openturns.org) based on a compression of the covariance matrix and a sparse representation of the P1 Gram matrix. We then need an iterative solver to compute the n largest eigenvalues and the associated eigenvactors.