452
C. Sabater
Future work includes the use of more efficient Surrogate Based Optimization
methods for the optimization stage, and the combination of the uncertainty and
design spaces with the use of gradients in order to further reduce the computational
time.
Acknowledgments This work is funded by the European Commission’s H2020 programme,
through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant
Agreement number 722734.
The author also would like to thank Dr. Daigo Maruyama and Dr. Stefan Goertz for their insight
into optimization under uncertainty and surrogate modelling applied to aerodynamic design.
References
1. S.N. Skinner, H. Zare-Behtash, State-of-the-art in aerodynamic shape optimisation methods.
Appl. Soft Comput. 62, 933–962 (2018)
2. D. Maruyama, S. Goertz, D. Liu, Robust design measures for airfoil shape optimization, in
Uncertainty Management for Robust Industrial Design in Aeronautics (Springer, Berlin, 2018),
pp. 513–527
3. L. Huyse, Free-form airfoil shape optimization under uncertainty using maximum expected
value and second-order second-moment strategies. Techreport 2001-211020, NASA, 2001s
4. R. Duvigneau, Aerodynamic shape optimization with uncertain operating conditions using
metamodels. Resreport RR-6143, INRIA, 2007
5. J. Von Neumann, O. Morgenstern, H.W. Kuhn, J. Von Neumann, A. Rubinstein, Theory
of Games and Economic Behavior: 60th Anniversary Commemorative Edition (Princeton
University Press, Princeton, 2009)
6. D. Quagliarella, G. Petrone, G. Iaccarino, Optimization under uncertainty using the generalized inverse distribution function, In Computational Methods in Applied Sciences (Springer
Netherlands, 2014), pp. 171–190
7. D. Maruyama, D. Liu, S. Goertz, An efficient aerodynamic shape optimization framework for
robust design of airfoils using surrogate models, in Proceedings of the VII European Congress
on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress
2016) (Institute of Structural Analysis and Antiseismic Research School of Civil Engineering
National Technical University of Athens (NTUA) Greece, 2016)
8. R.M. Dudley, Uniform Central Limit Theorems (Cambridge University Press, Cambridge,
1999)
9. A.T. Beck, W.J.S. Gomes, Rafael .H. Lopez, L.F.F. Miguel, A comparison between robust and
risk-based optimization under uncertainty. Struct. Multidiscip. Optim. 52(3), 479–492 (2015)
10. R. Dwight, Z.-H. Han, Efficient uncertainty quantification using gradient-enhanced kriging, In
50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
(American Institute of Aeronautics and Astronautics, Reston, 2009)
11. A.I.J. Forrester, A. Sabester, A.J. Keane, Engineering Design via Surrogate Modelling (Wiley,
London, 2008)
12. M.D. McKay, R.J. Beckman, W.J. Conover, Comparison of three methods for selecting values
of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–
245 (1979)
13. R.E. Caflisch, Monte Carlo and quasi-Monte Carlo methods. Acta Numer. 7, 1 (1998)
14. S. Kucherenko, D. Albrecht, A. Saltelli, Exploring multi-dimensional spaces: a comparison of
Latin hypercube and quasi Monte Carlo sampling techniques (2015). ArXiv e-prints
15. I.M Sobol, On the distribution of points in a cube and the approximate evaluation of integrals.
USSR Comput. Math. Math. Phys. 7(4), 86–112 (1967)
C. Sabater
Future work includes the use of more efficient Surrogate Based Optimization
methods for the optimization stage, and the combination of the uncertainty and
design spaces with the use of gradients in order to further reduce the computational
time.
Acknowledgments This work is funded by the European Commission’s H2020 programme,
through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, Grant
Agreement number 722734.
The author also would like to thank Dr. Daigo Maruyama and Dr. Stefan Goertz for their insight
into optimization under uncertainty and surrogate modelling applied to aerodynamic design.
References
1. S.N. Skinner, H. Zare-Behtash, State-of-the-art in aerodynamic shape optimisation methods.
Appl. Soft Comput. 62, 933–962 (2018)
2. D. Maruyama, S. Goertz, D. Liu, Robust design measures for airfoil shape optimization, in
Uncertainty Management for Robust Industrial Design in Aeronautics (Springer, Berlin, 2018),
pp. 513–527
3. L. Huyse, Free-form airfoil shape optimization under uncertainty using maximum expected
value and second-order second-moment strategies. Techreport 2001-211020, NASA, 2001s
4. R. Duvigneau, Aerodynamic shape optimization with uncertain operating conditions using
metamodels. Resreport RR-6143, INRIA, 2007
5. J. Von Neumann, O. Morgenstern, H.W. Kuhn, J. Von Neumann, A. Rubinstein, Theory
of Games and Economic Behavior: 60th Anniversary Commemorative Edition (Princeton
University Press, Princeton, 2009)
6. D. Quagliarella, G. Petrone, G. Iaccarino, Optimization under uncertainty using the generalized inverse distribution function, In Computational Methods in Applied Sciences (Springer
Netherlands, 2014), pp. 171–190
7. D. Maruyama, D. Liu, S. Goertz, An efficient aerodynamic shape optimization framework for
robust design of airfoils using surrogate models, in Proceedings of the VII European Congress
on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress
2016) (Institute of Structural Analysis and Antiseismic Research School of Civil Engineering
National Technical University of Athens (NTUA) Greece, 2016)
8. R.M. Dudley, Uniform Central Limit Theorems (Cambridge University Press, Cambridge,
1999)
9. A.T. Beck, W.J.S. Gomes, Rafael .H. Lopez, L.F.F. Miguel, A comparison between robust and
risk-based optimization under uncertainty. Struct. Multidiscip. Optim. 52(3), 479–492 (2015)
10. R. Dwight, Z.-H. Han, Efficient uncertainty quantification using gradient-enhanced kriging, In
50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
(American Institute of Aeronautics and Astronautics, Reston, 2009)
11. A.I.J. Forrester, A. Sabester, A.J. Keane, Engineering Design via Surrogate Modelling (Wiley,
London, 2008)
12. M.D. McKay, R.J. Beckman, W.J. Conover, Comparison of three methods for selecting values
of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–
245 (1979)
13. R.E. Caflisch, Monte Carlo and quasi-Monte Carlo methods. Acta Numer. 7, 1 (1998)
14. S. Kucherenko, D. Albrecht, A. Saltelli, Exploring multi-dimensional spaces: a comparison of
Latin hypercube and quasi Monte Carlo sampling techniques (2015). ArXiv e-prints
15. I.M Sobol, On the distribution of points in a cube and the approximate evaluation of integrals.
USSR Comput. Math. Math. Phys. 7(4), 86–112 (1967)