Analyse de sensibilité d'un robinet à soupape à l'aide de développements sur chaos polynomial

International audienceL'objectif de cette communication est de présenter une méthode d'analyse de sensibilité basée sur un métamodèle de type chaos polynomial creux et adaptatif. Cette méthode consiste à ajouter progressivement les termes significatifs du chaos, jusqu'à ce que la précision du métamodèle dépasse une valeur cible. Au final, seul un faible nombre de termes sont retenus (représentation creuse) par rapport à un chaos polynomial classique de type plein. La méthode est utilisée pour analyser la sensibilité du comportement d'un robinet industriel (via trois quantités d'intérêt) à differents paramètres incertains (matériaux, chargement et géométrie)

Use of polynomial chaos expansions and maximum likelihood estimation for probabilistic inverse problems

The present paper deals with the identification of probabilistic models of input variables using response measurements. The input random variables, whose probability density function has to be identified, are represented by their polynomial chaos expansion (PCE). The proposed method allows to solve the probabilistic inverse problem using an efficient maximum likelihood approach. An advanced optimization algorithm is used to maximize this likelihood and get the optimal values of unknown PCE coefficients. The approach is illustrated by determining the variability of the loading applied to a series of similar simply supported beams when a database of measured maximum deflection is at hand

Open TURNS: An industrial software for uncertainty quantification in simulation

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, and 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 methodology has emerged from the joint effort of several industrial companies and academic institutions. EDF R&D, Airbus Group and Phimeca Engineering started a collaboration at the beginning of 2005, joined by IMACS in 2014, for the development of an Open Source software platform dedicated to uncertainty propagation by probabilistic methods, named OpenTURNS for Open source Treatment of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial challenges attached to uncertainties, which are transparency, genericity, modularity and multi-accessibility. This paper focuses on OpenTURNS and presents its main features: openTURNS is an open source software under the LGPL license, that presents itself as a C++ library and a Python TUI, and which works under Linux and Windows environment. All the methodological tools are described in the different sections of this paper: uncertainty quantification, uncertainty propagation, sensitivity analysis and metamodeling. A section also explains the generic wrappers way to link openTURNS to any external code. The paper illustrates as much as possible the methodological tools on an educational example that simulates the height of a river and compares it to the height of a dyke that protects industrial facilities. At last, it gives an overview of the main developments planned for the next few years

A non-adapted sparse approximation of PDEs with stochastic inputs

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems (with slow decay in the spectrum)

Predicting Railway Wheel Wear under Uncertainty of Wear Coefficient, using Universal Kriging

Railway wheel wear prediction is essential for reliability and optimal maintenance strategies of railway systems. Indeed, an accurate wear prediction can have both economic and safety implications. In this paper we propose a novel methodology, based on Archard's equation and a local contact model, to forecast the volume of material worn and the corresponding wheel remaining useful life (RUL). A universal kriging estimate of the wear coefficient is embedded in our method. Exploiting the dependence of wear coefficient measurements with similar contact pressure and sliding speed, we construct a continuous wear coefficient map that proves to be more informative than the ones currently available in the literature. Moreover, this approach leads to an uncertainty analysis on the wear coefficient. As a consequence, we are able to construct wear prediction intervals that provide reasonable guidelines in practice

Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC

[EN] Population dynamics models consisting of nonlinear difference equations allow us to get a better understanding of the processes involved in epidemiology. Usually, these mathematical models are studied under a deterministic approach. However, in order to take into account the uncertainties associated with the measurements of the model input parameters, a more realistic approach would be to consider these inputs as random variables. In this paper, we study the random time-discrete epidemiological models SIS, SIR, SIRS, and SEIR using a powerful unified approach based upon the so-called adaptive generalized polynomial chaos (gPC) technique. The solution to these random difference equations is a stochastic process in discrete time, which represents the number of susceptible, infected, recovered, etc individuals at each time step. We show, via numerical experiments, how adaptive gPC permits quantifying the uncertainty for the solution stochastic process of the aforementioned random time-discrete epidemiological model and obtaining accurate results at a cheap computational expense. We also highlight how adaptive gPC can be applied in practice, by means of an example using real data.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. The authors are grateful for the helpful and valuable reviewers' comments that have considerably improved the final form of this manuscript.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M.; Villanueva Micó, RJ. (2018). Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC. Mathematical Methods in the Applied Sciences. 41(18):9618-9627. https://doi.org/10.1002/mma.5315S96189627411