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17 results on '"Mestapha Oumouni"'

1. Unified System Analysis for Time-Variant Reliability of a Floating Offshore Substation

Author

Franck Schoefs, Mestapha Oumouni, Morteza Ahmadivala, Neil Luxcey, Florian Dupriez-Robin, and Patrick Guerin

Subjects
offshore floating substation, offshore wind, system reliability, failure rate, Naval architecture. Shipbuilding. Marine engineering, VM1-989, Oceanography, GC1-1581
Abstract

Offshore wind is planned to become the first source of energy by 2050. That requires installing turbines in deeper seas. It is shown that only floating wind turbines will allow dealing with this challenge while keeping a reasonable cost of energy production and transport according to the levelized cost of electricity. A Floating Offshore Substation will be needed in many sites. This technology is still at a low technology readiness level. This paper aims to analyze the system reliability of such a structure for which the failure rates of structural components such as mooring lines and dynamic power cables are close to the ones of electro-technical systems. Consequently, only a system reliability assessment of the floating offshore substation will allow accurately quantifying its availability and the most sensitive components. Usually, structural reliability aims at quantifying the probability of failures, while electro-technical reliability relies on feedback and observed failure rates. The paper first unifies these two concepts in a single formulation and then evaluates the system’s reliability and availability. This methodology is illustrated in a study case localized in the French coasts of the Mediterranean Sea, where the effect of several mooring and substation designs on the system reliability is compared.

Published
2023
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2. Fractal Dimension as an Effective Feature for Characterizing Hard Marine Growth Roughness from Underwater Image Processing in Controlled and Uncontrolled Image Environments

Author

Franck Schoefs, Michael O’Byrne, Vikram Pakrashi, Bidisha Ghosh, Mestapha Oumouni, Thomas Soulard, and Marine Reynaud

Subjects
underwater inspections, infrastructure damage assessment, image-processing, biofouling, roughness, drag, Naval architecture. Shipbuilding. Marine engineering, VM1-989, Oceanography, GC1-1581
Abstract

Hard marine growth is an important process that affects the design and maintenance of floating offshore wind turbines. A key parameter of hard biofouling is roughness since it considerably changes the level of drag forces. Assessment of roughness from on-site inspection is required to improve updating of hydrodynamic forces. Image processing is rapidly developing as a cost effective and easy to implement tool for observing the evolution of biofouling and related hydrodynamic effects over time. Despite such popularity; there is a paucity in literature to address robust features and methods of image processing. There also remains a significant difference between synthetic images of hard biofouling and their idealized laboratory approximations in scaled wave basin testing against those observed in real sites. Consequently; there is a need for such a feature and imaging protocol to be linked to both applications to cater to the lifetime demands of performance of these structures against the hydrodynamic effects of marine growth. This paper proposes the fractal dimension as a robust feature and demonstrates it in the context of a stereoscopic imaging protocol; in terms of lighting and distance to the subject. This is tested for synthetic images; laboratory tests; and real site conditions. Performance robustness is characterized through receiver operating characteristics; while the comparison provides a basis with which a common measure and protocol can be used consistently for a wide range of conditions. The work can be used for design stage as well as for lifetime monitoring and decisions for marine structures, especially in the context of offshore wind turbines.

Published
2021
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5. Added value of monitoring for the maintenance of a reinforced concrete wharf with spatial variability of chloride content: a practical implementation

Author

Franck Schoefs, Mestapha Oumouni, Dominique Follut, Yann Lecieux, Virginie Gaillard, Cyril Lupi, and Dominique Leduc

Subjects
Mechanical Engineering, Ocean Engineering, Building and Construction, Geotechnical Engineering and Engineering Geology, Safety, Risk, Reliability and Quality, Civil and Structural Engineering
Published
2022
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6. Spatial variability assessment of structures from adaptive NDT measurements

Author

Franck Schoefs, Mestapha Oumouni, Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
021110 strategic, defence & security studies, Random field, Computer science, business.industry, Gaussian, 0211 other engineering and technologies, 020101 civil engineering, 02 engineering and technology, Building and Construction, 0201 civil engineering, Gaussian random field, symbols.namesake, [SPI]Engineering Sciences [physics], Nondestructive testing, symbols, Spatial variability, Minification, Medical diagnosis, Safety, Risk, Reliability and Quality, business, Material properties, Algorithm, Civil and Structural Engineering
Abstract

Inspection by non-destructive testing (NDT) techniques is an effective way for assessing structures’ condition state, their pathologies and locating potential critical areas. However, establishing accurate diagnoses requires numerous measurements while available budget is limited. Nevertheless, determining the spatial variability of the material properties leads fewer of the required measurements, as it characterizes zones with almost identical properties and helps identify weak areas. But assessing this spatial variability still requires numerous measurements. It should be limited by a rational criterion that could be expressed in terms of accuracy and cost minimization. In the present work, we develop an adaptive approach to characterize spatial variability of structures’ material properties modelled by transformed Gaussian random fields. The methodology is performed in two steps. Firstly, the correlation length of the Gaussian random field is computed for a given accuracy. Secondly, the number of measurements is refined to estimate the first two moments of the random field with a given accuracy too. These two steps result in a minimization of the number of measurements (i.e the cost) for a target accuracy. The proposed methodology and theoretical results are illustrated using synthetic and real data.

Published
2021
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7. SCAP-1D : A Spatial Correlation Assessment Procedure from unidimensional discrete data

Author

Franck Schoefs, Romain Clerc, Mestapha Oumouni, Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Spatial correlation, Iterative method, media_common.quotation_subject, Ergodicity, Bilinear interpolation, 020101 civil engineering, 02 engineering and technology, 01 natural sciences, Industrial and Manufacturing Engineering, 0201 civil engineering, Correlation, 010104 statistics & probability, [SPI]Engineering Sciences [physics], Spatial variability, 0101 mathematics, Safety, Risk, Reliability and Quality, Constant (mathematics), Algorithm, Normality, media_common, Mathematics
Abstract

Optimal placement of Non-destructive Testing sensors is essential for structure diagnosis as it allows to get maximum information about degradation at minimum cost. Latest optimization methods consider spatial variability of quantities of interest and thus strongly rely on correlation lengths assessment. However, this assessment is usually done with straightforward techniques on raw data, which may not satisfy the required hypotheses of stationarity and ergodicity and induce important mis-estimations. In this paper, we propose a Spatial Correlation Assessment Procedure (SCAP-1D) which allows to rigorously assess correlation length of a quantity of interest modeled as a piecewise-trend-stationary Gaussian-Random-Field (GRF). The procedure is applicable to unidimensional limited data and comprises two steps. First, the correlation length is assessed through an iterative algorithm including mean changepoints detection. Then, stationarity, ergodicity, and normality are tested to validate both the model and estimations. In numerical studies, we demonstrate the ability of our procedure to accurately estimate correlation length of a GRF in the cases of constant, stepped and bilinear mean, with performance ranges assessment. Applications to experimental Half-Cell Potential measurements with effective mean and slope steps validate the capacity of our method to precisely determine mean changepoints and correlation length on real data.

Published
2019
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8. Modeling time and spatial variability of degradation through gamma processes for structural reliability assessment

Author

Franck Schoefs, Mestapha Oumouni, Bruno Castanier, Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), and Université d'Angers (UA)

Subjects
Failure time, Scale (ratio), Computer science, Gamma process, 0211 other engineering and technologies, Inference, 020101 civil engineering, Degradation model, 02 engineering and technology, Method of moments (statistics), Residual, 0201 civil engineering, Parameters estimation, Safety, Risk, Reliability and Quality, Uncertainty quantification, Civil and Structural Engineering, 021110 strategic, defence & security studies, [STAT.AP]Statistics [stat]/Applications [stat.AP], Random field, Mathematical model, Remaining lifetime, Building and Construction, Reliability, Spatial variability, [SPI.GCIV.STRUCT]Engineering Sciences [physics]/Civil Engineering/Structures, Algorithm
Abstract

International audience; The objective of this work is to propose a spatio-temporal random field for assessing the effect of spatial variability on the degradation process in structural reliability assessment. Our model extends the classical Gamma process which is usually developed for degradation temporal variability concerns to integrate spatial variability and heterogeneity issues. A log-normal distributed spatial random scale is then introduced in the Gamma process. Mathematical models for a structure degradation in space and time and estimation procedures are developed in this paper. Approximations and simulations are given to evaluate the failure time distribution and to characterize the residual lifetime after inspection. Simulation results are performed using pseudo-random data based on Monte-Carlo simulations to fit the model and the inference of their parameters. The two proposed estimation method – Method of Moments and Pseudo Maximum Likelihood – are numerically compared according to statistical measures. The accuracy of the methods are also discussed by numerical examples given the approximations of quantities of interests.

Published
2019
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9. An adaptive sparse grid method for elliptic PDEs with stochastic coefficients

Author

Jocelyne Erhel, Zoubida Mghazli, Mestapha Oumouni, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Equipe d'Ingénierie MAthématique [Kenitra] (EIMA), Département de Mathématiques [Kénitra], Faculté des Sciences [Kenitra], Université Ibn Tofaïl (UIT)-Université Ibn Tofaïl (UIT)-Faculté des Sciences [Kenitra], Université Ibn Tofaïl (UIT)-Université Ibn Tofaïl (UIT), Inria EuroMed HYDRINV, ANR-07-CIS7-0004,MICAS,Modelling and Intensive Computation for Aquifer Simulations(2007), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
Work (thermodynamics), Mathematical optimization, Partial differential equation, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Mechanical Engineering, Computational Mechanics, Sparse grid, General Physics and Astronomy, Inverse, Upper and lower bounds, Computer Science Applications, Dimension (vector space), Mechanics of Materials, Collocation method, Applied mathematics, A priori and a posteriori, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

The stochastic collocation method based on the anisotropic sparse grid has become a significant tool to solve partial differential equations with stochastic inputs. The aim is to seek a vector weight and a convenient level for the method. The classical approach uses a posteriori approach on the solution, yielding to an additional prohibitive cost with a large stochastic dimension. In this work, we discuss an adaptive approach of this method to calculate the statistics of the solution. It is based on an adaptive approximation of the inverse diffusion parameter. We construct an efficient error indicator which is an upper bound of the error on the solution. In the case of unbounded variables, we use an appropriate error estimation to compute suitable weights of the method. Numerical examples are presented to confirm the efficiency of the approach and showing that the cost is considerably reduced without loss of accuracy.

Published
2015
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10. Added Value of Chloride Measurement on Wharves from SHM: a Case Study of iMareco2 Project

Author

Cyril Lupi, Mestapha Oumouni, Dominique Leduc, Virginie Gaillard, Franck Schoefs, Yann Lecieux, Marc Labégorre, Michel Roche, Pascal Lijour, and Dominique Follut

Subjects
Chloride Measurement, Added value, Environmental science, Pulp and paper industry
Abstract

With 80% of European trade exchange and a key role for European defense, harbours play a key socio- economic role. Inspection of wharves is very expensive due to the relative inaccessibility of components (need of a boat, team …) and the economical impact (service breakdown). Harbor concrete structures are designed to fulfill their function during a long time period (50 to 70 years). For RC structures exposed to marine environments, chloride-induced corrosion leads to deteriorations that can be associated to different exposure conditions: tidal, splash and atmospheric. The on-site assessment of the corrosion condition of the reinforcement in concrete relies on a corrosion diagnosis, which consists in different techniques and among them non destructive techniques (NDT )such as half-cell potential, resistivity and corrosion measurements. Thus the added value of SHM and accelerated tests in laboratory can be analyzed by comparing the maintenance with SHM with an optimized maintenance planning based on NDT.

Published
2018
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11. New Spatial Correlation Assessment Procedure: Application to Île-de- Ré Bridge Data

Author

Franck Schoefs, Mestapha Oumouni, and Romain Clerc

Subjects
Spatial correlation, business.industry, Structural engineering, business, Bridge (interpersonal), Geology
Abstract

Tomorrow’s Megastructures exploitation will require robust management policies, including Non- Destructive Techniques measurements and Structure Health Monitoring. These inspections strategies already allow acquisition of large amounts of data at reasonable cost. However, the bigger the structure, the costlier the data collecting. This raises the question of spatial optimization, closely related to the determination of spatial variability. Related studies have so far characterized it using covariograms on raw data without paying attention to their conditions of validity. As this lack of rigor may lead to severe misestimating, we propose a mathematically rigorous spatial variability assessment procedure and apply it to measurements coming from the Île de Ré bridge diagnosis, performed during the DéCoF-Ré (Décision par diagnostic de Corrosion en toute Fiabilité sur le pont de l’île de Ré) project. This unique data set of resistivity and corrosion potential measurements allow us to begin a spatial variability database for marine concrete structures.

Published
2018
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13. An Adaptive NDT Inspection Strategy to Assess the Spatial Variability of Concrete Structures

Author

Franck Schoefs and Mestapha Oumouni

Subjects
Computer science, business.industry, Nondestructive testing, Spatial variability, business, Remote sensing
Abstract

Spatial variability is an essential key in modeling material properties, loading or the deterioration process in structural engineering degradation. Non-destructive Testing (NDT) technique is a crucial tool to characterize this spatial variability. In this paper, we propose an original approach that enables to characterize the spatial variability of structure through discrete and limited measurements in efficient and accurate way. An adaptive approach based on two indicators errors is performed to model the quantities of interest. Firstly, an error indicator is run to estimate an accurate parameter of fluctuations using Maximum Likelihood Estimate (MLE) from a set of measurements. Secondly, the accuracy of the estimated moments of the field from the current number of measures is revised by analyzing the behavior of the second indicator. The advantage of this approach is that the spatial correlation is not neglected between measurements and the range of the correlation is given in good way within a desirable threshold. The potential of the presented approach is demonstrated through numerical examples with synthetic and experimental data.

Published
2018
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15. A combined collocation and Monte Carlo method for advection-diffusion equation of a solute in random porous media

Author

Jocelyne Erhel, Mestapha Oumouni, Zoubida Mghazli, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Equipe d'Ingénierie MAthématique [Kenitra] (EIMA), Département de Mathématiques [Kénitra], Faculté des Sciences [Kenitra], Université Ibn Tofaïl (UIT)-Université Ibn Tofaïl (UIT)-Faculté des Sciences [Kenitra], Université Ibn Tofaïl (UIT)-Université Ibn Tofaïl (UIT), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematical optimization, T57-57.97, Applied mathematics. Quantitative methods, Stochastic process, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Numerical analysis, 010102 general mathematics, Monte Carlo method, Sparse grid, 010103 numerical & computational mathematics, Mixed finite element method, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols.namesake, Collocation method, symbols, QA1-939, Applied mathematics, Gaussian quadrature, 0101 mathematics, Convection–diffusion equation, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

In this work, we present a numerical analysis of a method which combines a deterministic and a probabilistic approaches to quantify the migration of a contaminant, under the presence of uncertainty on the permeability of the porous medium. More precisely, we consider the flow equation in a random porous medium coupled with the advection-diffusion equation. Quantities of interest are the mean spread and the mean dispersion of the solute. The means are approximated by a quadrature rule, based on a sparse grid defined by a truncated Karhunen-Loève expansion and a stochastic collocation method. For each grid point, the flow model is solved with a mixed finite element method in the physical space and the advection-diffusion equation is solved with a probabilistic Lagrangian method. The spread and the dispersion are expressed as functions of a stochastic process. A priori error estimates are established on the mean of the spread and the dispersion. Keywords: Uncertainty quantification, elliptic PDE with random coefficients, advection-diffusion equation, collocation techniques, anisotropic sparse grids, Monte Carlo method, Euler scheme for SDE.

Published
2014

17. Calcul de l'espérance de la solution d'une EDP stochastique unidimensionnelle à l'aide d'une base réduite

Author

Zoubida Mghazli, Jocelyne Erhel, Mestapha Oumouni, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Equipe d'Ingénierie MAthématique [Kenitra] (EIMA), Département de Mathématiques [Kénitra], Faculté des Sciences [Kenitra], Université Ibn Tofaïl (UIT)-Université Ibn Tofaïl (UIT)-Faculté des Sciences [Kenitra], Université Ibn Tofaïl (UIT)-Université Ibn Tofaïl (UIT), contrat SARIMA, Inria-Maroc, CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)

Subjects
010101 applied mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 010103 numerical & computational mathematics, General Medicine, 0101 mathematics, 01 natural sciences, Humanities, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; In this Note, we present an efficient method to approximate the expectation of the response of a one-dimensional elliptic problem with stochastic inputs. In conventional methods, the computational effort and cost of the approximation of the response can be dramatic. Our method presented here is based on the Karhunen-Loève (K-L) expansion of the inverse of the diffusion parameter, allowing us to build a base of random variables in reduced numbers, from which we construct a projected solution. We show that the expectation of this projected solution is a good approximation, and give an a priori error estimate. A numerical example is presented to show the efficiency of this approach.; On présente dans cette Note une méthode efficace pour calculer une approximation de lʼespérance de la réponse dʼun problème elliptique unidimensionnel avec des entrées stochastiques. Dans les méthodes classiques, lʼeffort de calcul et le coût de lʼapproximation de la réponse, peuvent être exorbitants. La méthode présentée ici est basée sur la décomposition de Karhunen-Loève (K-L) de lʼinverse du paramètre de diffusion nous permettant de construire une base de variables aléatoires en nombre réduit et de calculer un projeté de la solution. Nous montrons que lʼespérance de ce projeté est une bonne approximation de celle de la réponse de notre problème, et on donne une estimation a priori de lʼerreur. Un exemple numérique est présenté pour montrer lʼefficacité de cette approche.

Published
2011
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