Shubin, G. R.
, 1994, “Optimization Problem Formulation for Multidisciplinary Design,” Proceedings of the Conference Inverse Problems and Optimal Design in Industry, Philadelphia, July 8–10, Vieweg+Teubner Verlag, Springer, Wiesbaden, pp. 213–216.

Alexandrov, N. M.
, and
Lewis, R. M.
, 2000, “Algorithmic Perspectives on Problem Formulations in MDO,” AIAA Paper No. 2000-4719.

Belytschko, T.
, 1980, “Fluid-Structure Interaction,” Comput. Struct., 12(4), pp. 459–469.

[CrossRef]
McNamara, J. J.
, and
Friedmann, P. P.
, 2011, “Aeroelastic and Aerothermoelastic Analysis in Hypersonic Flow: Past, Present, and Future,” AIAA J., 49(6), pp. 1089–1122.

[CrossRef]
Yao, W.
,
Chen, X. Q.
,
Luo, W. C.
,
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]
Matthies, H. G.
, 2007, “Quantifying Uncertainty: Modern Computational Representation of Probability and Applications,” Extreme Man-Made and Natural Hazards in Dynamics of Structures, Springer, Dordrecht, the Netherlands, pp. 105–135.

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

[CrossRef]
Kennedy, M. C.
, and
O'Hagan, A.
, 2001, “Bayesian Calibration of Computer Models,” J. R. Stat. Soc., Ser. B, 63(3), pp. 425–464.

[CrossRef]
Zaman, K.
, and
Mahadevan, S.
, 2013, “Robustness-Based Design Optimization of Multidisciplinary System Under Epistemic Uncertainty,” AIAA J., 51(5), pp. 1021–1031.

[CrossRef]
Helton, J. C.
,
Johnson, J. D.
,
Sallaberry, C. J.
, and
Storlie, C. B.
, 2006, “Survey of Sampling-Based Methods for Uncertainty and Sensitivity Analysis,” Reliab. Eng. Syst. Saf., 91(10–11), pp. 1175–1209.

[CrossRef]
Landau, D. P.
, and
Binder, K.
, 2005, A Guide to Monte Carlo Simulations in Statistical Physics, 2nd ed., Cambridge University Press, New York.

Robert, C.
, and
Casella, G.
, 1999, Monte Carlo Statistical Methods, Springer, New York.

Thoft-Cristensen, P.
, and
Baker, M. J.
, 1982, Structural Reliability Theory and Its Applications, Springer, New York.

Green, L. L.
,
Lin, H.-Z.
, and
Khalessi, M. R.
, 2002, “Probabilistic Methods for Uncertainty Propagation Applied to Aircraft Design,” AIAA Paper No. 2002.3140.

Cao, H.
, and
Duan, B.
, 2004, “Uncertainty Analysis for Multidisciplinary Systems Based on Convex Models,” AIAA Paper No. 2004-4504.

Du, X.
,
Guo, J.
, and
Beeram, H.
, 2008, “Sequential Optimization and Reliability Assessment for Multidisciplinary Systems Design,” Struct. Multidiscip. Optim., 35(2), pp. 117–130.

[CrossRef]
Guo, J.
, and
Du, X. P.
, 2010, “Reliability Analysis for Multidisciplinary Systems With Random and Interval Variables,” AIAA J., 48(1), pp. 82–91.

[CrossRef]
Gu, X.
, and
Renaud, J. E.
, 2002, “Implementation Study of Implicit Uncertainty Propagation (IUP) in Decomposition-Based Optimization,” AIAA Paper No. 2002-5416.

Gu, X. S.
,
Renaud, J. E.
, and
Penninger, C. L.
, 2006, “Implicit Uncertainty Propagation for Robust Collaborative Optimization,” ASME J. Mech. Des., 128(4), pp. 1001–1013.

[CrossRef]
Du, X.
, and
Chen, W.
, 2002, “Collaborative Reliability Analysis for Multidisciplinary Systems Design,” AIAA Paper No. 2002-5474.

Du, X.
, and
Chen, W.
, 2005, “Collaborative Reliability Analysis Under the Framework of Multidisciplinary Systems Design,” Optim. Eng., 6(1), pp. 63–84.

[CrossRef]
Xiong, F.
,
Yin, X.
,
Chen, W.
, and
Yang, S.
, 2010, “Enhanced Probabilistic Analytical Target Cascading With Application to Multi-Scale Design,” Eng. Optim., 42(6), pp. 581–592.

[CrossRef]
Sankararaman, S.
, and
Mahadevan, S.
, 2012, “Likelihood-Based Approach to Multidisciplinary Analysis Under Uncertainty,” ASME J. Mech. Des., 134(3), p. 031008.

[CrossRef]
Liang, C.
, and
Mahadevan, S.
, 2013, “Stochastic Multidisciplinary Analysis With High Dimensional Coupling,” Tenth World Congress on Structural and Multidisciplinary Optimization, Orlando, FL, May 19–24.

Sankararaman, S.
, and
Mahadevan, S.
, 2011, “Likelihood-Based Representation of Epistemic Uncertainty Due to Sparse Point Data and/or Interval Data,” Reliab. Eng. Syst. Saf., 96(7), pp. 814–824.

[CrossRef]
Zhang, S. L.
,
Zhu, P.
,
Chen, W.
, and
Arendt, P.
, 2013, “Concurrent Treatment of Parametric Uncertainty and Metamodeling Uncertainty in Robust Design,” Struct. Multidiscip. Optim., 47(1), pp. 63–76.

[CrossRef]
Gu, X.
,
Renaud, J. E.
,
Batill, S. M.
,
Brach, R. M.
, and
Budhiraja, A. S.
, 2000, “Worst Case Propagated Uncertainty of Multidisciplinary Systems in Robust Design Optimization,” Struct. Multidiscip. Optim., 20(3), pp. 190–213.

[CrossRef]
Du, X.
, and
Chen, W.
, 2000, “An Efficient Approach to Probabilistic Uncertainty Analysis in Simulation-Based Multidisciplinary Design,” AIAA Paper No. 2000-0423.

Du, X.
, and
Chen, W.
, 2000, “Methodology for Managing the Effect of Uncertainty in Simulation-Based Design,” AIAA J., 38(8), pp. 1471–1478.

[CrossRef]
Du, X.
, and
Chen, W.
, 2002, “Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design,” AIAA J., 40(3), pp. 545–552.

[CrossRef]
Jiang, X. M.
, and
Mahadevan, S.
, 2009, “Bayesian Hierarchical Uncertainty Quantification by Structural Equation Modeling,” Int. J. Numer. Methods Eng., 80(6–7), pp. 717–737.

[CrossRef]
Jiang, X. M.
, and
Mahadevan, S.
, 2009, “Bayesian Structural Equation Modeling Method for Hierarchical Model Validation,” Reliab. Eng. Syst. Saf., 94(4), pp. 796–809.

[CrossRef]
Sankararaman, S.
,
McLemore, K.
,
Mahadevan, S.
,
Bradford, S. C.
, and
Peterson, L. D.
, 2013, “Test Resource Allocation in Hierarchical Systems Using Bayesian Networks,” AIAA J., 51(3), pp. 537–550.

[CrossRef]
Allaire, D.
,
He, Q.
,
Deyst, J.
, and
Willcox, K.
, 2012, “An Information-Theoretic Metric of System Complexity With Application to Engineering System Design,” ASME J. Mech. Des., 134(10), p. 100906.

[CrossRef]
Sacks, J.
,
Welch, W. J.
,
Mitchell, T. J.
, and
Wynn, H. P.
, 1989, “Design and Analysis of Computer Experiments,” Stat. Sci., 4(4), pp. 409–423.

[CrossRef]
Conti, S.
,
Gosling, J. P.
,
Oakley, J. E.
, and
O'Hagan, A.
, 2009, “Gaussian Process Emulation of Dynamic Computer Codes,” Biometrika, 96(3), pp. 663–676.

[CrossRef]
Conti, S.
, and
O'Hagan, A.
, 2010, “Bayesian Emulation of Complex Multi-Output and Dynamic Computer Models,” J. Stat. Plann. Inference, 140(3), pp. 640–651.

[CrossRef]
Higdon, D.
,
Kennedy, M.
,
Cavendish, J. C.
,
Cafeo, J. A.
, and
Ryne, R. D.
, 2004, “Combining Field Data and Computer Simulations for Calibration and Prediction,” SIAM J. Sci. Comput., 26(2), pp. 448–466.

[CrossRef]
Higdon, D.
,
Gattiker, J.
,
Williams, B.
, and
Rightley, M.
, 2008, “Computer Model Calibration Using High-Dimensional Output,” J. Am. Stat. Assoc., 103(482), pp. 570–583.

[CrossRef]
Arendt, P. D.
,
Apley, D. W.
, and
Chen, W.
, 2012, “Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability,” ASME J. Mech. Des., 134(10), p. 100908.

[CrossRef]
Arendt, P. D.
,
Apley, D. W.
,
Chen, W.
,
Lamb, D.
, and
Gorsich, D.
, 2012, “Improving Identifiability in Model Calibration Using Multiple Responses,” ASME J. Mech. Des., 134(10), p. 100909.

[CrossRef]
Jiang, Z.
,
Chen, W.
,
Fu, Y.
, and
Yang, R.-J.
, 2013, “Reliability-Based Design Optimization With Model Bias and Data Uncertainty,” SAE Int. J. Mater. Manuf., 6(3), pp. 502–516.

[CrossRef]
Rasmussen, C. E.
, and
Williams, C. K. I.
, 2006, Gaussian Processes for Machine Learning, The MIT Press, Cambridge, MA.

Kennedy, M. C.
, and
O'Hagan, A.
, 2000, “Predicting the Output From a Complex Computer Code When Fast Approximations Are Available,” Biometrika, 87(1), pp. 1–13.

[CrossRef]
Hasselman, T. K.
,
Yap, K.
,
Lin, C.-H.
, and
Cafeo, J. A.
, 2005, “A Case Study in Model Improvement for Vehicle Crashworthiness Simulation,” 23rd International Modal Analysis Conference (IMAC-XXIII), Orlando, FL, Jan. 31–Feb. 3.

Chen, W.
,
Xiong, Y.
,
Tsui, K. L.
, and
Wang, S.
, 2008, “A Design-Driven Validation Approach Using Bayesian Prediction Models,” ASME J. Mech. Des., 130(2), p. 021101.

[CrossRef]
Qian, P. Z. G.
, and
Wu, C. F. J.
, 2008, “Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments,” Technometrics, 50(2), pp. 192–204.

[CrossRef]
Wang, S. C.
,
Chen, W.
, and
Tsui, K. L.
, 2009, “Bayesian Validation of Computer Models,” Technometrics, 51(4), pp. 439–451.

[CrossRef]
Bayarri, M. J.
,
Berger, J. O.
,
Paulo, R.
,
Sacks, J.
,
Cafeo, J. A.
,
Cavendish, J.
,
Lin, C. H.
, and
Tu, J.
, 2007, “A Framework for Validation of Computer Models,” Technometrics, 49(2), pp. 138–154.

[CrossRef]
Liu, F.
,
Bayarri, M. J.
,
Berger, J. O.
,
Paulo, R.
, and
Sacks, J.
, 2008, “A Bayesian Analysis of the Thermal Challenge Problem,” Comput. Methods Appl. Mech. Eng., 197(29–32), pp. 2457–2466.

[CrossRef]
Renaud, J.
, and
Gabriele, G.
, 1994, “Approximation in Nonhierarchic System Optimization,” AIAA J., 32(1), pp. 198–205.

[CrossRef]
Padula, S. L.
,
Alexandrov, N.
, and
Green, L. L.
, 1996, “MDO Test Suite at NASA Langley Research Center,” AIAA Paper No. 96-4028.

Kodiyalam, S.
, and
Sobieszczanski-Sobieski, J.
, 2001, “Multidisciplinary Design Optimization: Some Formal Methods, Framework Requirements, and Application to Vehicle Design,” Int. J. Veh. Des., 25(1–2), pp. 3–22.

[CrossRef]