J. L. Beck and L. S. Katafygiotis, Updating models and their uncertainties. I: Bayesian statistical framework, Journal of Engineering Mechanics, vol.124, issue.4, pp.455-461, 1998.

M. Berveiller, B. Sudret, and M. Lemaire, Stochastic finite element: a non-intrusive approach by regression, European Journal of Computational Mechanics, vol.15, pp.81-92, 2006.

E. Capiez-lernout and C. Soize, Nonparametric modeling of random uncertainties for dynamic response of mistuned bladed disks, Journal of Engineering for Gas Turbines and Power, vol.126, issue.3, pp.600-618, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00686199

E. Capiez-lernout, C. Soize, J. Lombard, C. Dupont, and E. Seinturier, Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk, Journal of Engineering for Gas Turbines and Power, vol.127, issue.3, pp.621-628, 2005.
DOI : 10.1115/1.1850497

URL : https://hal.archives-ouvertes.fr/hal-00688121

E. Capiez-lernout, M. Pellissetti, H. Pradlwarter, G. I. Schueller, and C. Soize, Data and model uncertainties in complex aerospace engineering systems, Journal of Sound and Vibration, vol.295, issue.3-5, pp.3-5, 2006.
DOI : 10.1016/j.jsv.2006.01.056

URL : https://hal.archives-ouvertes.fr/hal-00686152

E. Capiez-lernout and C. , Soize Design optimization with an uncertain vibroacoustic model, Journal of Vibration and Acoustics, vol.130, issue.2, pp.1-8, 2008.

E. Capiez-lernout and C. Soize, Robust Design Optimization in Computational Mechanics, Journal of Applied Mechanics, vol.75, issue.2, pp.210011-02100111, 2008.
DOI : 10.1115/1.2775493

URL : https://hal.archives-ouvertes.fr/hal-00686134

E. Capiez-lernout and C. Soize, Robust updating of uncertain damping models in structural dynamics for low-and medium-frequency ranges, Mechanical Systems and Signal Processing, pp.1774-1792, 2008.

H. Chebli and C. Soize, Experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems, The Journal of the Acoustical Society of America, vol.115, issue.2, pp.697-705, 2004.
DOI : 10.1121/1.1639335

URL : https://hal.archives-ouvertes.fr/hal-00686209

C. Chen, D. Duhamel, and C. Soize, Probabilistic approach for model and data uncertainties and its experimental identification in structural dynamics: Case of composite sandwich panels, Journal of Sound and Vibration, vol.294, issue.1-2, pp.64-81, 2006.
DOI : 10.1016/j.jsv.2005.10.013

URL : https://hal.archives-ouvertes.fr/hal-00686153

R. Cottereau, D. Clouteau, and C. Soize, Construction of a probabilistic model for impedance matrices, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.17-20, pp.17-20, 2007.
DOI : 10.1016/j.cma.2006.12.001

URL : https://hal.archives-ouvertes.fr/hal-00686151

S. Das, R. Ghanem, and J. C. Spall, Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach, SIAM Journal on Scientific Computing, vol.30, issue.5, pp.2207-2234, 2008.
DOI : 10.1137/060652105

C. Desceliers, C. Soize, and S. Cambier, Non-parametric -parametric model for random uncertainties in nonlinear structural dynamics -Application to earthquake engineering, Earthquake Engineering and Structural Dynamics, pp.315-327, 2004.

C. Desceliers, R. Ghanem, and C. Soize, Maximum likelihood estimation of stochastic chaos representations from experimental data, International Journal for Numerical Methods in Engineering, vol.11, issue.6, pp.978-1001, 2006.
DOI : 10.1002/nme.1576

URL : https://hal.archives-ouvertes.fr/hal-00686154

C. Desceliers, C. Soize, and R. Ghanem, Identification of chaos representations of elastic properties of random media using experimental vibration tests, Computational Mechanics, pp.831-838, 2007.

C. Desceliers, C. Soize, Q. Grimal, G. Haiat, and S. Naili, A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation, Wave Motion, vol.45, issue.4, pp.383-399, 2008.
DOI : 10.1016/j.wavemoti.2007.09.001

URL : https://hal.archives-ouvertes.fr/hal-00686136

J. Duchereau and C. Soize, Transient dynamics in structures with nonhomogeneous uncertainties induced by complex joints, Mechanical Systems and Signal Processing, pp.854-867, 2006.

J. Durand, C. Soize, and L. Gagliardini, Structural-acoustic modeling of automotive vehicles in presence of uncertainties and experimental identification and validation, The Journal of the Acoustical Society of America, vol.124, issue.3, pp.1513-1525, 2008.
DOI : 10.1121/1.2953316

URL : https://hal.archives-ouvertes.fr/hal-00685108

B. Faverjon and R. Ghanem, Stochastic inversion in acoustic scattering, The Journal of the Acoustical Society of America, vol.119, issue.6, pp.3577-3588, 2006.
DOI : 10.1121/1.2200149

URL : https://hal.archives-ouvertes.fr/hal-00487842

S. Geman and D. Geman, Stochastic relaxation, Gibbs distribution and the Bayesian distribution of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, pp.721-741, 1984.

R. Ghanem and P. D. Spanos, Stochastic Finite Elements: A spectral Approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

R. Ghanem and R. M. Kruger, Numerical solution of spectral stochastic finite element systems, Computer Methods in Applied Mechanics and Engineering, vol.129, issue.3, pp.289-303, 1996.
DOI : 10.1016/0045-7825(95)00909-4

R. Ghanem, S. Masri, M. Pellissetti, and R. Wolfe, Identification and prediction of stochastic dynamical systems in a polynomial chaos basis, it Comput, Methods Appl. Mech. Engrg, vol.194, pp.12-16, 2005.

J. Guilleminot, C. Soize, D. Kondo, and C. Benetruy, Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites, International Journal of Solids and Structures, vol.45, issue.21, pp.45-5567, 2008.
DOI : 10.1016/j.ijsolstr.2008.06.002

URL : https://hal.archives-ouvertes.fr/hal-00333515

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.57-97, 1970.
DOI : 10.1093/biomet/57.1.97

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1957.
DOI : 10.1103/PhysRev.106.620

O. P. Le-maitre, H. N. Najm, and R. Ghanem, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics, vol.197, issue.2, pp.502-531, 2004.
DOI : 10.1016/j.jcp.2003.12.020

O. P. Le-maitre, H. N. Najm, and P. P. Pebay, Multi???Resolution???Analysis Scheme for Uncertainty Quantification in Chemical Systems, SIAM Journal on Scientific Computing, vol.29, issue.2, pp.864-889, 2007.
DOI : 10.1137/050643118

M. L. Mehta, Random Matrices, Revised and Enlarged Second Edition, 1991.

M. P. Mignolet and C. Soize, Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies, Probabilistic Engineering Mechanics, vol.23, issue.2-3, pp.267-278, 2008.
DOI : 10.1016/j.probengmech.2007.12.027

URL : https://hal.archives-ouvertes.fr/hal-00685147

M. P. Mignolet and C. Soize, Nonparametric stochastic modeling of structural dynamic systems with uncertain boundary conditions, AIAA Conference, pp.7-10, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00691355

M. P. Mignolet and C. Soize, Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.45-48, pp.45-48, 2008.
DOI : 10.1016/j.cma.2008.03.032

URL : https://hal.archives-ouvertes.fr/hal-00686140

A. A. Muravyov and S. A. Rizzi, Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures, Computers and Structures, pp.1513-1523, 2003.

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.45-484521, 2007.
DOI : 10.1016/j.cma.2007.05.016

URL : https://hal.archives-ouvertes.fr/hal-00366619

A. Nouy and O. P. Le-maitre, Generalized spectral decomposition for stochastic nonlinear problems, Journal of Computational Physics, vol.228, issue.1, pp.202-235, 2009.
DOI : 10.1016/j.jcp.2008.09.010

R. Ohayon and C. Soize, Structural Acoustics and Vibration, The Journal of the Acoustical Society of America, vol.109, issue.6, 1998.
DOI : 10.1121/1.1352086

URL : https://hal.archives-ouvertes.fr/hal-00689039

M. Pellissetti, E. Capiez-lernout, H. Pradlwarter, C. Soize, and G. I. Schueller, Reliability analysis of a satellite structure with a parametric and a non-parametric probabilistic model, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.2, pp.344-357, 2008.
DOI : 10.1016/j.cma.2008.08.004

R. Sampaio and C. Soize, On measures of non-linearity effects for uncertain dynamical systems -Application to a vibro-impact system, Journal of Sound and Vibration, vol.303, pp.3-5, 2007.

G. I. Schueller, Computational Methods in Stochastic Mechanics and Reliability Analysis, Special issue of Comput, Methods Appl. Mech. Engrg, vol.194, pp.12-16, 2005.

G. I. Schueller, Uncertainties in Structural Mechanics and Analysis-Computational Methods, Special issue of Computer and Structures, pp.1031-1150, 2005.

R. J. Serfling, Approximation Theorems of Mathematical Statistics., Biometrics, vol.37, issue.4, 1980.
DOI : 10.2307/2530199

C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

C. Soize, The Fokker-Planck Equation for Stochastic Dynamical Systems and its Explicit Steady State Solutions, 1994.
DOI : 10.1142/2347

URL : https://hal.archives-ouvertes.fr/hal-00770411

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, vol.15, issue.3, pp.277-294, 2000.
DOI : 10.1016/S0266-8920(99)00028-4

URL : https://hal.archives-ouvertes.fr/hal-00686293

C. Soize, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, The Journal of the Acoustical Society of America, vol.109, issue.5, 1979.
DOI : 10.1121/1.1360716

URL : https://hal.archives-ouvertes.fr/hal-00686287

C. Soize, Random matrix theory and non-parametric model of random uncertainties in vibration analysis, Journal of Sound and Vibration, vol.263, issue.4, pp.893-916, 2003.
DOI : 10.1016/S0022-460X(02)01170-7

URL : https://hal.archives-ouvertes.fr/hal-00686213

C. Soize, Uncertain Dynamical Systems in the Medium-Frequency Range, Journal of Engineering Mechanics, vol.129, issue.9, pp.1017-1027, 2003.
DOI : 10.1061/(ASCE)0733-9399(2003)129:9(1017)

URL : https://hal.archives-ouvertes.fr/hal-00686212

C. Soize, Random matrix theory for modeling uncertainties in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-16, 2005.
DOI : 10.1016/j.cma.2004.06.038

URL : https://hal.archives-ouvertes.fr/hal-00686187

C. Soize, A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics, Journal of Sound and Vibration, vol.288, issue.3, pp.623-652, 2005.
DOI : 10.1016/j.jsv.2005.07.009

URL : https://hal.archives-ouvertes.fr/hal-00686182

C. Soize, Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.1-3, pp.26-64, 2006.
DOI : 10.1016/j.cma.2004.12.014

URL : https://hal.archives-ouvertes.fr/hal-00686157

C. Soize, Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size, Probabilistic Engineering Mechanics, vol.23, issue.2-3, pp.307-323, 2008.
DOI : 10.1016/j.probengmech.2007.12.019

URL : https://hal.archives-ouvertes.fr/hal-00685154

C. Soize, Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices, International Journal for Numerical Methods in Engineering, vol.195, issue.4, pp.76-1583, 2008.
DOI : 10.1002/nme.2385

URL : https://hal.archives-ouvertes.fr/hal-00684517

C. Soize, Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem, International Journal for Numerical Methods in Engineering, vol.197, issue.45??????48, 2009.
DOI : 10.1002/nme.2563

URL : https://hal.archives-ouvertes.fr/hal-00684335

C. Soize and H. Chebli, Random Uncertainties Model in Dynamic Substructuring Using a Nonparametric Probabilistic Model, Journal of Engineering Mechanics, vol.129, issue.4, pp.449-457, 2003.
DOI : 10.1061/(ASCE)0733-9399(2003)129:4(449)

URL : https://hal.archives-ouvertes.fr/hal-00686215

C. Soize and R. Ghanem, Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.395-410, 2004.
DOI : 10.1137/S1064827503424505

URL : https://hal.archives-ouvertes.fr/hal-00686211

C. Soize and R. Ghanem, Reduced chaos decomposition with random coefficients of vectorvalued random variables and random fields, Comput. Methods Appl. Mech. Engrg, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00684487

C. Soize, E. Capiez-lernout, and R. Ohayon, Robust Updating of Uncertain Computational Models Using Experimental Modal Analysis, AIAA Journal, vol.46, issue.11, pp.2955-2965, 2008.
DOI : 10.2514/1.38115

URL : https://hal.archives-ouvertes.fr/hal-00787847

C. Soize, E. Capiez-lernout, J. Durand, C. Fernandez, and L. Gagliardini, Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.1, pp.150-163, 2008.
DOI : 10.1016/j.cma.2008.04.007

URL : https://hal.archives-ouvertes.fr/hal-00686138

J. C. Spall, Introduction to Stochastic Search and Optimization, 2003.
DOI : 10.1002/0471722138

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268