E. Castillo, Extreme Value Theory in Engineering, 1988.

J. Aza¨?saza¨?s and M. Wschebor, Level Sets and Extrema of Random Processes and Fields, 2008.

F. Poirion, Karhunen Lo??ve expansion and distribution of non-Gaussian process maximum, Probabilistic Engineering Mechanics, vol.43, pp.85-90, 2016.
DOI : 10.1016/j.probengmech.2015.12.005

S. O. Rice, Mathematical Analysis of Random Noise, Bell System Technical Journal, vol.23, issue.3, pp.282-332, 1944.
DOI : 10.1002/j.1538-7305.1944.tb00874.x

R. G. Ghanem and P. D. Spanos, Stochastic finite elements: a spectral approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

D. Xiu and G. E. Karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.
DOI : 10.1137/S1064827501387826

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

G. Poëtte and D. Lucor, Non intrusive iterative stochastic spectral representation with application to compressible gas dynamics, Journal of Computational Physics, vol.231, issue.9, pp.3587-3609, 2012.
DOI : 10.1016/j.jcp.2011.12.038

X. Wan and G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Journal of Computational Physics, vol.209, issue.2, pp.617-642, 2005.
DOI : 10.1016/j.jcp.2005.03.023

M. Berveiller, B. Sudret, and M. Lemaire, Stochastic finite element: a non intrusive approach by regression, Revue europ??enne de m??canique num??rique, vol.15, issue.1-2-3, pp.81-92, 2006.
DOI : 10.3166/remn.15.81-92
URL : https://hal.archives-ouvertes.fr/hal-01665506

G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, issue.6, pp.2345-2367, 2011.
DOI : 10.1016/j.jcp.2010.12.021

D. Xiu and J. S. Hesthaven, High-Order Collocation Methods for Differential Equations with Random Inputs, SIAM Journal on Scientific Computing, vol.27, issue.3, pp.1118-1139, 2005.
DOI : 10.1137/040615201

S. Abraham, M. Raisee, G. Ghorbaniasl, F. Contino, and C. Lacor, A robust and efficient stepwise regression method for building sparse polynomial chaos expansions, Journal of Computational Physics, vol.332, pp.461-474, 2017.
DOI : 10.1016/j.jcp.2016.12.015

J. Hampton and A. Doostan, Coherence motivated sampling and convergence analysis of least squares polynomial Chaos regression, Computer Methods in Applied Mechanics and Engineering, vol.290, pp.73-97, 2015.
DOI : 10.1016/j.cma.2015.02.006

N. V. Queipo, R. T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan et al., Surrogate-based analysis and optimization, Progress in aerospace sciences, pp.1-28, 2005.
DOI : 10.1016/j.paerosci.2005.02.001
URL : http://hdl.handle.net/2060/20050186653

A. I. Forrester and A. J. Keane, Recent advances in surrogate-based optimization, Progress in Aerospace Sciences, vol.45, issue.1-3, pp.50-79, 2009.
DOI : 10.1016/j.paerosci.2008.11.001

T. W. Simpson, T. M. Mauery, J. J. Korte, and F. Mistree, Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization, AIAA Journal, vol.2, issue.1, pp.2233-2241, 2001.
DOI : 10.2514/6.2000-4895

J. P. Kleijnen, Design and analysis of simulation experiments, 2015.
DOI : 10.1007/978-3-319-18087-8

F. A. Viana, C. Gogu, and R. T. Haftka, Making the Most Out of Surrogate Models: Tricks of the Trade, Volume 1: 36th Design Automation Conference, Parts A and B, pp.2010-28813
DOI : 10.1115/DETC2010-28813

D. R. Jones, M. Schonlau, and W. J. Welch, Efficient global optimization of expensive black-box functions, Journal of Global Optimization, vol.13, issue.4, pp.455-4921008306431147, 1998.
DOI : 10.1023/A:1008306431147

A. Sóbester, S. J. Leary, and A. J. Keane, On the Design of Optimization Strategies Based on Global Response Surface Approximation Models, Journal of Global Optimization, vol.27, issue.5, pp.31-59, 2005.
DOI : 10.1007/978-1-4613-1997-9

S. Shan and G. G. Wang, Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions, Structural and Multidisciplinary Optimization, pp.219-241, 2010.

S. M. Ghler, T. Eifler, and T. J. Howard, Robustness Metrics: Consolidating the Multiple Approaches to Quantify Robustness, Journal of Mechanical Design, vol.138, issue.11, pp.111407-111407, 2016.
DOI : 10.1115/1.4034112

B. J. Williams, Sequential design of computer experiments to minimize integrated response functions, p.9983009, 2000.

J. Janusevskis and R. Le-riche, Simultaneous kriging-based estimation and optimization of mean response, Journal of Global Optimization, vol.10, issue.4, pp.313-336, 2013.
DOI : 10.1007/s10898-008-9354-2
URL : https://hal.archives-ouvertes.fr/emse-00674460

J. Zhang, A. Taflanidis, and J. Medina, Sequential approximate optimization for design under uncertainty problems utilizing Kriging metamodeling in augmented input space, Computer Methods in Applied Mechanics and Engineering, vol.315, pp.369-395, 2017.
DOI : 10.1016/j.cma.2016.10.042

N. M. Alexandrov, J. E. Dennis, R. M. Lewis, and V. Torczon, A trust-region framework for managing the use of approximation models in optimization, Structural Optimization, vol.12, issue.1, pp.16-23, 1998.
DOI : 10.1007/BF01197433

A. R. Conn, N. I. Gould, and P. L. Toint, Trust region methods, 2000.
DOI : 10.1137/1.9780898719857

D. P. Kouri, M. Heinkenschloss, D. Ridzal, and B. G. Van-bloemen-waanders, A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty, SIAM Journal on Scientific Computing, vol.35, issue.4, pp.1847-1879, 2013.
DOI : 10.1137/120892362

D. P. Kouri, M. Heinkenschloss, D. Ridzal, and B. G. Van-bloemen-waanders, Inexact Objective Function Evaluations in a Trust-Region Algorithm for PDE-Constrained Optimization under Uncertainty, SIAM Journal on Scientific Computing, vol.36, issue.6, pp.3011-3029, 2014.
DOI : 10.1137/140955665

A. A. Taflanidis and J. C. Medina, Simulation-based optimization in design-underuncertainty problems through iterative development of metamodels in augmented design/random variable space, Simulation and Modeling Methodologies, pp.251-273, 2015.

B. Sudret, Uncertainty propagation and sensitivity analysis in mechanical models contributions to structural reliability and stochastic spectral methods, 2007.

W. Betz, I. Papaioannou, and D. Straub, Numerical methods for the discretization of random fields by means of the Karhunen???Lo??ve expansion, Computer Methods in Applied Mechanics and Engineering, vol.271, pp.109-129, 2014.
DOI : 10.1016/j.cma.2013.12.010

B. Pascual and S. Adhikari, Hybrid perturbation-Polynomial Chaos approaches to the random algebraic eigenvalue problem, Computer Methods in Applied Mechanics and Engineering, vol.217, issue.220, pp.220-153, 2012.
DOI : 10.1016/j.cma.2012.01.009

P. Kersaudy, B. Sudret, N. Varsier, O. Picon, and J. Wiart, A new surrogate modeling technique combining Kriging and polynomial chaos expansions ??? Application to uncertainty analysis in computational dosimetry, Journal of Computational Physics, vol.286, pp.103-117, 2015.
DOI : 10.1016/j.jcp.2015.01.034
URL : https://hal.archives-ouvertes.fr/hal-01143146

R. H. Cameron and W. T. Martin, The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals, The Annals of Mathematics, vol.48, issue.2, pp.385-392, 1947.
DOI : 10.2307/1969178

R. Lebrun and A. Dutfoy, A generalization of the Nataf transformation to distributions with elliptical copula, Probabilistic Engineering Mechanics, vol.24, issue.2, pp.172-178, 2009.
DOI : 10.1016/j.probengmech.2008.05.001

V. Yadav and S. Rahman, Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing, Computer Methods in Applied Mechanics and Engineering, vol.274, pp.56-83, 2014.
DOI : 10.1016/j.cma.2014.01.027

Z. Perko, L. Gilli, D. Lathouwers, and J. Kloosterman, Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis, Journal of Computational Physics, vol.260, pp.54-84, 2014.
DOI : 10.1016/j.jcp.2013.12.025

J. G. Winokur, Adaptive Sparse Grid Approaches to Polynomial Chaos Expansions for Uncertainty Quantification, 2015.

D. G. Krige, A statistical approach to some mine evaluations and allied problems at the witwatersrand, Master's thesis, 1951.

C. E. Rasmussen and C. K. Williams, Gaussian processes for machine learning, Adaptive computation and machine learning, 2006.

A. Forrester, A. Sobester, and A. Keane, Engineering design via surrogate modelling: a practical guide, 2008.
DOI : 10.1002/9780470770801

M. Arnst, R. Ghanem, E. Phipps, and J. , Red-Horse, Dimension reduction in stochastic modeling of coupled problems, International Journal for Numerical Methods in Engineering, vol.92, issue.11

M. J. Sasena, Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations, 2002.

M. Buhmann, Radial Basis Functions: Theory and Implementations, Cambridge Monographs on Applied and Computational Mathematics, 2003.
DOI : 10.1017/CBO9780511543241

M. J. Powell, Direct search algorithms for optimization calculations, Acta Numerica, vol.8, pp.287-336, 1998.
DOI : 10.1007/BF00933295
URL : http://www.damtp.cam.ac.uk/user/na/NA_papers/NA1998_04.ps.gz

D. Kraft, A software package for sequential quadratic programming, Tech. Rep. DFVLR-FB?88-28, DLR German Aerospace Center Institute for Flight Mechanics, 1988.

T. Derbyshire and K. Sidwell, Pan air summary document, Tech. Rep. NASA Contractor Report, vol.3250, 1982.

M. A. Bouhlel, N. Bartoli, A. Otsmane, and J. Morlier, Improving kriging surrogates of high-dimensional design models by partial least squares dimension reduction , Structural and Multidisciplinary Optimization, pp.935-952, 2016.

K. Konakli and B. Sudret, Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions, Journal of Computational Physics, vol.321, pp.1144-1169, 2016.
DOI : 10.1016/j.jcp.2016.06.005
URL : https://hal.archives-ouvertes.fr/hal-01432141

M. Chevreuil and A. Nouy, Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics, International Journal for Numerical Methods in Engineering, vol.5, issue.2-4
DOI : 10.1016/j.jcp.2005.03.023
URL : https://hal.archives-ouvertes.fr/hal-00603342