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

R. Mace, W. Worden, and G. Manson, Uncertainty in structural dynamics. Special issue of the, Journal of Sound and Vibration, vol.288, issue.3, pp.431-790, 2005.

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

P. Spanos and R. Ghanem, Stochastic Finite Element Expansion for Random Media, Journal of Engineering Mechanics, vol.115, issue.5, pp.1035-1053, 1989.
DOI : 10.1061/(ASCE)0733-9399(1989)115:5(1035)

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

R. Ghanem, Ingredients for a general purpose stochastic finite elements implementation, Computer Methods in Applied Mechanics and Engineering, vol.168, issue.1-4, pp.19-34, 1999.
DOI : 10.1016/S0045-7825(98)00106-6

R. Ghanem, Stochastic Finite Elements with Multiple Random Non-Gaussian Properties, Journal of Engineering Mechanics, vol.125, issue.1, pp.26-40, 1999.
DOI : 10.1061/(ASCE)0733-9399(1999)125:1(26)

R. Ghanem and J. Red-horse, Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach, Physica D: Nonlinear Phenomena, vol.133, issue.1-4, pp.1-4, 1999.
DOI : 10.1016/S0167-2789(99)00102-5

R. Ghanem and F. Romeo, A wavelet-based approach for model and parameter identification of non-linear systems, International Journal of Non-Linear Mechanics, vol.36, issue.5, pp.835-859, 2001.
DOI : 10.1016/S0020-7462(00)00050-0

R. Ghanem and M. Pellissetti, Adaptive data refinement in the spectral stochastic finite element method, Communications in Numerical Methods in Engineering, vol.60, issue.4, pp.141-151, 2002.
DOI : 10.1002/cnm.476

R. Ghanem and A. Sarkar, Reduced models for the medium-frequency dynamics of stochastic systems, The Journal of the Acoustical Society of America, vol.113, issue.2, pp.834-846, 2003.
DOI : 10.1121/1.1538246

L. Maitre, O. Knio, and O. , A stochastic particle-mesh scheme for uncertainty propagation in vortical flows, Journal of Computational Physics, vol.226, issue.1, pp.645-671, 2007.
DOI : 10.1016/j.jcp.2007.04.030

L. Maitre, O. Najm, H. Pebay, and P. , 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

L. Maitre, O. Knio, O. Najm, and H. , Uncertainty propagation using Wiener???Haar expansions, Journal of Computational Physics, vol.197, issue.1, pp.28-57, 2004.
DOI : 10.1016/j.jcp.2003.11.033

L. Maitre, O. Najm, H. Ghanem, and R. , 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

R. Ghanem, S. Masri, and M. Pellissetti, Identification and prediction of stochastic dynamical systems in a polynomial chaos basis, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-16, 2005.
DOI : 10.1016/j.cma.2004.05.031

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. 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, vol.60, issue.5, pp.831-838, 2007.
DOI : 10.1007/s00466-006-0072-7
URL : https://hal.archives-ouvertes.fr/hal-00686150

I. Babuska, R. Tempone, and G. Zouraris, Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-16, 2005.
DOI : 10.1016/j.cma.2004.02.026

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, 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, Probabilistic models for computational stochastic mechanics and applications, in Structural Safety and Reliability ICOSSAR'05, pp.23-42, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00687868

C. 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

E. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630171, 1957.
DOI : 10.1103/PhysRev.106.620

R. Serfling, Approximation Theorems of Mathematical Statistics, 1980.

J. Kapur and H. Kesavan, Entropy Optimization Principles and Their Applications, 1992.
DOI : 10.1007/978-94-011-2430-0_1

G. M. Jumarie and . Entropy, Information Without Probability and Complex Fractal.K l u w e rA c a d e m i c Publishers, 2000.

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

T. Anderson, Introduction to Multivariate Statistical Analysis, 1958.

C. Soize, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, The Journal of the Acoustical Society of America, vol.109, issue.5, pp.1979-1996, 2001.
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

M. 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

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 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

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

J. Duchereau and C. Soize, Transient dynamics in structures with non-homogeneous uncertainties induced by complex joints, Mechanical Systems and Signal Processing, vol.20, issue.4, pp.854-867, 2006.
DOI : 10.1016/j.ymssp.2004.11.003
URL : https://hal.archives-ouvertes.fr/hal-00686155

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.
DOI : 10.1115/1.1760527
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

R. Cottereau, D. Clouteau, and C. Soize, Probabilistic nonparametric model of impedance matrices. Application to the seismic design of a structure, Revue europ??enne de m??canique num??rique, vol.15, issue.1-2-3, pp.1-2, 2006.
DOI : 10.3166/remn.15.131-142
URL : https://hal.archives-ouvertes.fr/hal-00686296

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

M. 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

E. Capiez-lernout, M. Pellissetti, H. Pradlwarter, G. 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

C. Soize, Random matrix theory for modeling uncertainties in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-161333, 2005.
DOI : 10.1016/j.cma.2004.06.038
URL : https://hal.archives-ouvertes.fr/hal-00686187

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

M. Arnst, D. Clouteau, H. Chebli, R. Othman, and G. Degrande, A non-parametric probabilistic model for ground-borne vibrations in buildings, Probabilistic Engineering Mechanics, vol.21, issue.1, pp.18-34, 2006.
DOI : 10.1016/j.probengmech.2005.06.004
URL : https://hal.archives-ouvertes.fr/hal-00018949

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. Durand, Modélisation de véhicules automobiles en vibroacoustique numérique avec incertitudes de modélisation et validation expérimentale.U n i v e r s i t ´ e Paris-Est Marne-la-Vallée, 2007.

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.
DOI : 10.1115/1.2827988
URL : https://hal.archives-ouvertes.fr/hal-00686133

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

C. Desceliers, C. Soize, and S. Cambier, Non-parametric???parametric model for random uncertainties in non-linear structural dynamics: application to earthquake engineering, Earthquake Engineering & Structural Dynamics, vol.33, issue.3, pp.315-327, 2004.
DOI : 10.1002/eqe.352
URL : https://hal.archives-ouvertes.fr/hal-00686208

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.

M. 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