Kurtaran,
H.
,
Eskandarian,
A.
,
Marzougui,
D.
, and
Bedewi,
N. E.
, 2002, “
Crashworthiness Design Optimization Using Successive Response Surface Approximations,” Comput. Mech.,
29(4–5), pp. 409–421.

[CrossRef]
Avalle,
M.
,
Chiandussi,
G.
, and
Belingardi,
G.
, 2002, “
Design Optimization by Response Surface Methodology: Application to Crashworthiness Design of Vehicle Structures,” Struct. Multidiscip. Optim.,
24(4), pp. 325–332.

[CrossRef]
Duddeck,
F.
, 2007, “
Multidisciplinary Optimization of Car Bodies,” Struct. Multidiscip. Optim.,
35(4), pp. 375–389.

[CrossRef]
Fang,
H.
,
Rais-Rohani,
M.
,
Liu,
Z.
, and
Horstemeyer,
M.
, 2005, “
A Comparative Study of Metamodeling Methods for Multiobjective Crashworthiness Optimization,” Comput. Struct.,
83(25–26), pp. 2121–2136.

[CrossRef]
Forsberg,
J.
, and
Nilsson,
L.
, 2006, “
Evaluation of Response Surface Methodologies Used in Crashworthiness Optimization,” Int. J. Impact Eng.,
32(5), pp. 759–777.

[CrossRef]
Gu,
L.
,
Yang,
R.
,
Tho,
C.
,
Makowskit,
M.
,
Faruquet,
O.
, and
Li,
Y.
, 2004, “
Optimisation and Robustness for Crashworthiness of Side Impact,” Int. J. Veh. Des.,
26(4), pp. 348–360.

Hou,
S.
,
Li,
Q.
,
Long,
S.
,
Yang,
X.
, and
Li,
W.
, 2008, “
Multiobjective Optimization of Multi-Cell Sections for the Crashworthiness Design,” Int. J. Impact Eng.,
35(11), pp. 1355–1367.

[CrossRef]
Lee,
S. H.
,
Chen,
W.
, and
Kwak,
B. M.
, 2008, “
Robust Design With Arbitrary Distributions Using Gauss-Type Quadrature Formula,” Struct. Multidiscip. Optim.,
39(3), pp. 227–243.

[CrossRef]
Youn,
B.
,
Choi,
K.
,
Yang,
R.-J.
, and
Gu,
L.
, 2004, “
Reliability-Based Design Optimization for Crashworthiness of Vehicle Side Impact,” Struct. Multidiscip. Optim.,
26(3–4), pp. 272–283.

[CrossRef]
Chen,
X.
,
Park,
E. J.
, and
Xiu,
D.
, 2013, “
A Flexible Numerical Approach for Quantification of Epistemic Uncertainty,” J. Comput. Phys.,
240, pp. 211–224.

[CrossRef]
Jakeman,
J.
,
Eldred,
M.
, and
Xiu,
D.
, 2010, “
Numerical Approach for Quantification of Epistemic Uncertainty,” J. Comput. Phys.,
229(12), pp. 4648–4663.

[CrossRef]
Der Kiureghian,
A.
, and
Ditlevsen,
O.
, 2009, “
Aleatory or Epistemic? Does It Matter?” Struct. Saf.,
31(2), pp. 105–112.

[CrossRef]
Ross,
J. L.
,
Ozbek,
M. M.
, and
Pinder,
G. F.
, 2009, “
Aleatoric and Epistemic Uncertainty in Groundwater Flow and Transport Simulation,” Water Resour. Res.,
45(12), p. W00b15.

Huang,
B.
, and
Du,
X.
, 2007, “
Analytical Robustness Assessment for Robust Design,” Struct. Multidiscip. Optim.,
34(2), pp. 123–137.

[CrossRef]
Zang,
C.
,
Friswell,
M. I.
, and
Mottershead,
J. E.
, 2005, “
A Review of Robust Optimal Design and Its Application in Dynamics,” Comput. Struct.,
83(4–5), pp. 315–326.

[CrossRef]
Youn,
B. D.
, and
Xi,
Z.
, 2008, “
Reliability-Based Robust Design Optimization Using the Eigenvector Dimension Reduction (EDR) Method,” Struct. Multidiscip. Optim.,
37(5), pp. 475–492.

[CrossRef]
Dubourg,
V.
,
Sudret,
B.
, and
Bourinet,
M.
, 2011, “
Reliability-Based Design Optimization Using Kriging Surrogates and Subset Simulation,” Struct. Multidiscip. Optim.,
44(5), pp. 673–690.

[CrossRef]
Dubourg,
V.
, 2011, “
Adaptive Surrogate Models for Reliability Analysis and Reliability-Based-Design-Optimization,” Ph.D. thesis, Blaise Pascal University Clermont II, Clermont-Ferrand, France.

Dubourg,
V.
,
Sudret,
B.
, and
Deheeger,
F.
, 2013, “
Metamodel-Based Importance Sampling for Structural Reliability Analysis,” Probab. Eng. Mech.,
33, pp. 47–57.

[CrossRef]
Debbarma,
R.
,
Chakraborty,
S.
, and
Ghosh,
S.
, 2010, “
Unconditional Reliability-Based Design of Tuned Liquid Column Dampers Under Stochastic Earthquake Load Considering System Parameters Uncertainties,” J. Earthquake Eng.,
14(7), pp. 970–988.

[CrossRef]
Marczyk,
J.
, 2000, “
Stochastic Multidisciplinary Improvement: Beyond Optimization,” AIAA Paper No. 2000-4929.

Yao,
W.
,
Chen,
X.
,
Luo,
W.
,
van Tooren,
M.
, and
Guo,
J.
, 2011, “
Review of Uncertainty-Based Multidisciplinary Design Optimization Methods for Aerospace Vehicles,” Prog. Aerosp. Sci.,
47(6), pp. 450–479.

[CrossRef]
Fang,
J.
,
Gao,
Y.
,
Sun,
G.
,
Xu,
C.
, and
Li,
Q.
, 2015, “
Multiobjective Robust Design Optimization of Fatigue Life for a Truck Cab,” Reliab. Eng. Syst. Saf.,
135, pp. 1–8.

[CrossRef]
Diez,
M.
, and
Peri,
D.
, 2010, “
Robust Optimization for Ship Concept Design,” Ocean Eng.,
37(11–12), pp. 966–977.

[CrossRef]
Roy,
B. K.
, and
Chakraborty,
S.
, 2015, “
Robust Optimum Design of Base Isolation System in Seismic Vibration Control of Structures Under Random System Parameters,” Struct. Saf.,
55, pp. 49–59.

[CrossRef]
Roy,
B. K.
,
Chakraborty,
S.
, and
Mihsra,
S. K.
, 2012, “
Robust Optimum Design of Base Isolation System in Seismic Vibration Control of Structures Under Uncertain Bounded System Parameters,” J. Vib. Control,
20(5), pp. 786–800.

[CrossRef]
Gerstl,
S.
, 1973, “
Second-Order Perturbation-Theory and Its Application to Sensitivity Studies in Shield Design Calculations,” Trans. Am. Nucl. Soc.,
16, pp. 342–343.

Kamiski,
M.
, 2004, “
Stochastic Perturbation Approach to the Wavelet-Based Analysis,” Numer. Linear Algebra Appl.,
11(4), pp. 355–370.

[CrossRef]
Echard,
B.
,
Gayton,
N.
, and
Lemaire,
M.
, 2011, “
AK-MCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation,” Struct. Saf.,
33(2), pp. 145–154.

[CrossRef]
Echard,
B.
,
Gayton,
N.
,
Lemaire,
M.
, and
Relun,
N.
, 2013, “
A Combined Importance Sampling and Kriging Reliability Method for Small Failure Probabilities With Time-Demanding Numerical Models,” Reliab. Eng. Syst. Saf.,
111, pp. 232–240.

[CrossRef]
Kaymaz,
I.
, 2005, “
Application of Kriging Method to Structural Reliability Problems,” Struct. Saf.,
27(2), pp. 133–151.

[CrossRef]
Ng,
S. H.
, and
Yin,
J.
, 2013, “
Bayesian Kriging Analysis and Design for Stochastic Simulations,” ACM Trans. Model. Comput. Simul.,
22(3), p. 17.

Zhao,
W.
,
Liu,
J. K.
,
Li,
X. Y.
,
Yang,
Q. W.
, and
Chen,
Y. Y.
, 2013, “
A Moving Kriging Interpolation Response Surface Method for Structural Reliability Analysis,” Comput. Model. Eng. Sci.,
93(6), pp. 469–488.

Mukhopadhyay,
T.
,
Chakraborty,
S.
,
Dey,
S.
,
Adhikari,
S.
, and
Chowdhury,
R.
, 2016, “
A Critical Assessment of Kriging Model Variants for High-Fidelity Uncertainty Quantification in Dynamics of Composite Shells,” Arch. Comput. Methods Eng., (in press).

Desai,
A.
,
Witteveen,
J. A. S.
, and
Sarkar,
S.
, 2013, “
Uncertainty Quantification of a Nonlinear Aeroelastic System Using Polynomial Chaos Expansion With Constant Phase Interpolation,” ASME J. Vib. Acoust.,
135(5), p. 051034.

Jacquelin,
E.
,
Adhikari,
S.
,
Sinou,
J.
, and
Friswell,
M. I.
, 2014, “
Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems,” J. Eng. Mech.,
141(4), pp. 1–11.

Pascual,
B.
, and
Adhikari,
S.
, 2012, “
A Reduced Polynomial Chaos Expansion Method for the Stochastic Finite Element Analysis,” Sadhana-Acad. Proc. Eng. Sci.,
37(3), pp. 319–340.

Pascual,
B.
, and
Adhikari,
S.
, 2012, “
Combined Parametric-Nonparametric Uncertainty Quantification Using Random Matrix Theory and Polynomial Chaos Expansion,” Comput. Struct.,
112–113, pp. 364–379.

[CrossRef]
Wiener,
N.
, 1938, “
The Homogeneous Chaos,” Am. J. Math.,
60(4), pp. 897–936.

[CrossRef]
Xiu,
D.
, and
Karniadakis,
G. E.
, 2002, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations,” SIAM J. Sci. Comput.,
24(2), pp. 619–644.

[CrossRef]
Hu,
C.
, and
Youn,
B. D.
, 2010, “
Adaptive-Sparse Polynomial Chaos Expansion for Reliability Analysis and Design of Complex Engineering Systems,” Struct. Multidiscip. Optim.,
43(3), pp. 419–442.

[CrossRef]
Wei,
D.
,
Cui,
Z.
, and
Chen,
J.
, 2008, “
Uncertainty Quantification Using Polynomial Chaos Expansion With Points of Monomial Cubature Rules,” Comput. Struct.,
86(23–24), pp. 2102–2108.

[CrossRef]
Goswami,
S.
, and
Chakraborty,
S.
, 2016, “
An Efficient Adaptive Response Surface Method for Reliability Analysis of Structures,” Struct. Saf.,
60, pp. 56–66.

Kang,
S.-C.
,
Koh,
H.-M.
, and
Choo,
J. F.
, 2010, “
An Efficient Response Surface Method Using Moving Least Squares Approximation for Structural Reliability Analysis,” Probab. Eng. Mech.,
25(4), pp. 365–371.

[CrossRef]
Li,
J.
,
Wang,
H.
, and
Kim,
N. H.
, 2012, “
Doubly Weighted Moving Least Squares and Its Application to Structural Reliability Analysis,” Struct. Multidiscip. Optim.,
46(1), pp. 69–82.

[CrossRef]
Taflanidis,
A. A.
, and
Cheung,
S.-H.
, 2012, “
Stochastic Sampling Using Moving Least Squares Response Surface Approximations,” Probab. Eng. Mech.,
28, pp. 216–224.

[CrossRef]
Xiong,
F.
,
Greene,
S.
,
Chen,
W.
,
Xiong,
Y.
, and
Yang,
S.
, 2009, “
A New Sparse Grid Based Method for Uncertainty Propagation,” Struct. Multidiscip. Optim.,
41(3), pp. 335–349.

[CrossRef]
Hu,
C.
, and
Youn,
B. D.
, 2011, “
An Asymmetric Dimension-Adaptive Tensor-Product Method for Reliability Analysis,” Struct. Saf.,
33(3), pp. 218–231.

[CrossRef]
Bollig,
E. F.
,
Flyer,
N.
, and
Erlebacher,
G.
, 2012, “
Solution to PDEs Using Radial Basis Function Finite-Differences (RBF-FD) on Multiple GPUs,” J. Comput. Phys.,
231(21), pp. 7133–7151.

[CrossRef]
Deng,
J.
,
Gu,
D.
,
Li,
X.
, and
Yue,
Z. Q.
, 2005, “
Structural Reliability Analysis for Implicit Performance Functions Using Artificial Neural Network,” Struct. Saf.,
27(1), pp. 25–48.

[CrossRef]
Jamshidi,
A. A.
, and
Kirby,
M. J.
, 2010, “
Skew-Radial Basis Function Expansions for Empirical Modeling,” SIAM J. Sci. Comput.,
31(6), pp. 4715–4743.

[CrossRef]
Lazzaro,
D.
, and
Montefusco,
L. B.
, 2002, “
Radial Basis Functions for the Multivariate Interpolation of Large Scattered Data Sets,” J. Comput. Appl. Math.,
140(1–2), pp. 521–536.

[CrossRef]
Marchi,
S. D.
, and
Santin,
G.
, 2013, “
A New Stable Basis for Radial Basis Function Interpolation,” J. Comput. Appl. Math.,
253, pp. 1–13.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2016, “
Assessment of Polynomial Correlated Function Expansion for High-Fidelity Structural Reliability Analysis,” Struct. Saf.,
59, pp. 9–19.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2015, “
A Semi-Analytical Framework for Structural Reliability Analysis,” Comput. Methods Appl. Mech. Eng.,
289(1), pp. 475–497.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2016, “
Modelling Uncertainty in Incompressible Flow Simulation Using Galerkin Based Generalised ANOVA,” Comput. Phys. Commun.,
208, pp. 73–91.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2016, “
Sequential Experimental Design Based Generalised ANOVA,” J. Comput. Phys.,
317, pp. 15–32.

[CrossRef]
Chakraborty,
S.
,
Mandal,
B.
,
Chowdhury,
R.
, and
Chakrabarti,
A.
, 2016, “
Stochastic Free Vibration Analysis of Laminated Composite Plates Using Polynomial Correlated Function Expansion,” Compos. Struct.,
135, pp. 236–249.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2015, “
Polynomial Correlated Function Expansion for Nonlinear Stochastic Dynamic Analysis,” J. Eng. Mech.,
141(3), p. 04014132.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2017, “
Polynomial Correlated Function Expansion,” Modeling and Simulation Techniques in Structural Engineering,
IGI Global, Hershey, PA, pp. 348–373.

[CrossRef]
Hooker,
G.
, 2007, “
Generalized Functional ANOVA Diagnostics for High-Dimensional Functions of Dependent Variables,” J. Comput. Graphical Stat.,
16(3), pp. 709–732.

[CrossRef]
Li,
G.
, and
Rabitz,
H.
, 2012, “
General Formulation of HDMR Component Functions With Independent and Correlated Variables,” J. Math. Chem.,
50(1), pp. 99–130.

[CrossRef]
Biswas,
S.
,
Kundu,
S.
, and
Das,
S.
, 2015, “
Inducing Niching Behavior in Differential Evolution Through Local Information Sharing,” IEEE Trans. Evol. Comput.,
19(2), pp. 246–263.

[CrossRef]
Das,
S.
, and
Suganthan,
P. N.
, 2011, “
Differential Evolution: A Survey of the State-of-the-Art,” IEEE Trans. Evol. Comput.,
15(1), pp. 4–31.

[CrossRef]
Storn,
R.
, and
Price,
K.
, 1997, “
Differential Evolution–A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,” J. Global Optim.,
11, pp. 341–359.

[CrossRef]
Stutz,
L. T.
,
Tenenbaum,
R. A.
, and
Correa,
R. A. P.
, 2015, “
The Differential Evolution Method Applied to Continuum Damage Identification Via Flexibility Matrix,” J. Sound Vib.,
345, pp. 86–102.

[CrossRef]
Beyer,
H. G.
, and
Sendhoff,
B.
, 2007, “
Robust Optimization–A Comprehensive Survey,” Comput. Methods Appl. Mech. Eng.,
196(33–34), pp. 3190–3218.

[CrossRef]
Chen,
W.
,
Allen,
J.
,
Tsui,
K.
, and
Mistree,
F.
, 1996, “
Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors,” ASME J. Mech. Des.,
118(4), pp. 478–485.

[CrossRef]
Park,
G.
,
Lee,
T.
,
Kwon,
H.
, and
Hwang,
K.
, 2006, “
Robust Design: An Overview,” AIAA J.,
44(1), pp. 181–191.

[CrossRef]
Schuëller,
G.
, and
Jensen,
H.
, 2008, “
Computational Methods in Optimization Considering Uncertainties An Overview,” Comput. Methods Appl. Mech. Eng.,
198(1), pp. 2–13.

[CrossRef]
De Groot,
M.
, 1970, Optimal Statistical Decisions,
McGraw-Hill,
New York.

Taguchi,
G.
, 1986, Quality Engineering Through Design Optimization,
Krauss International Publications,
White Plains, NY.

Doltsinis,
I.
, and
Kang,
Z.
, 2004, “
Robust Design of Structures Using Optimization Methods,” Comput. Methods Appl. Mech. Eng.,
193(23–26), pp. 2221–2237.

[CrossRef]
Chakraborty,
S.
, and
Chowdhury,
R.
, 2015, “
Multivariate Function Approximations Using D-MORPH Algorithm,” Appl. Math. Model.,
39(23–24), pp. 7155–7180.

[CrossRef]
Alis,
O. F.
, and
Rabitz,
H.
, 2001, “
Efficient Implementation of High Dimensional Model Representations,” J. Math. Chem.,
29(2), pp. 127–142.

[CrossRef]
Rabitz,
H.
, and
Ali,
Ö. F.
, 1999, “
General Foundations of High Dimensional Model Representations,” J. Math. Chem.,
25(2–3), pp. 197–233.

[CrossRef]
Sobol,
I. M.
, 1993, “
Sensitivity Estimates for Nonlinear Mathematical Models,” Math. Model.,
2(1), pp. 112–118.

Li,
G.
,
Rey-de Castro,
R.
, and
Rabitz,
H.
, 2012, “
D-MORPH Regression for Modeling With Fewer Unknown Parameters Than Observation Data,” J. Math. Chem.,
50(7), pp. 1747–1764.

[CrossRef]
Li,
G.
, and
Rabitz,
H.
, 2010, “
D-MORPH Regression: Application to Modeling With Unknown Parameters More Than Observation Data,” J. Math. Chem.,
48(4), pp. 1010–1035.

[CrossRef]
Rao,
C.
, and
Mitra,
S. K.
, 1971, Generalized Inverse of Matrix and Its Applications,
Wiley,
New York.

Ma,
X.
, and
Zabaras,
N.
, 2010, “
An Adaptive High-Dimensional Stochastic Model Representation Technique for the Solution of Stochastic Partial Differential Equations,” J. Comput. Phys.,
229(10), pp. 3884–3915.

[CrossRef]
Ren,
X.
, and
Rahman,
S.
, 2013, “
Robust Design Optimization by Polynomial Dimensional Decomposition,” Struct. Multidiscip. Optim.,
48(1), pp. 127–148.

[CrossRef]
Heiss,
F.
, and
Winschel,
V.
, 2008, “
Likelihood Approximation by Numerical Integration on Sparse Grids,” J. Econometrics,
144(1), pp. 62–80.

[CrossRef]
Lee,
I.
,
Choi,
K.
,
Du,
L.
, and
Gorsich,
D.
, 2008, “
Dimension Reduction Method for Reliability-Based Robust Design Optimization,” Comput. Struct.,
86(13–14), pp. 1550–1562.

[CrossRef]
Bratley,
P.
, and
Fox,
B. L.
, 1988, “
Implementing Sobols Quasirandom Sequence Generator,” ACM Trans. Math. Software,
14(1), pp. 88–100.

[CrossRef]
Sobol, I
. M.
, 1976, “
Uniformly Distributed Sequences With an Additional Uniform Property,” USSR Comput. Math. Math. Phys.,
16(5), pp. 236–242.

[CrossRef]