426
E. M. Tirado and D. Quagliarella
Table 13.2 Risk measurement based on the obtained cumulative distribution functions
0.9 − V aR · 10 4
0.9 − CV aR · 10 4
Baseline NACA 2412 airfoil
74.5
75.0
Deterministic optimized airfoil
63.4
64.8
Robust optimized airfoil
62.2
62.5
by the observation of the value Value-at-Risk and Conditional Value-at-Risk with
α = 0.9 provided in Table 13.2.
References
1. S. Amaral, D. Allaire, K. Willcox, Optimal L 2 -norm empirical importance weights for the
change of probability measure. Stat. Comput., 1–19 (2016)
2. P. Artzner, F. Delbaen, J.-M. Eber, D. Heath, Coherent measures of risk. Mathematical Finance
9(3), 203–228 (1999)
3. P. Billingsley, Probability and Measure, 3rd edn. (Wiley, New York, NY, 1995)
4. J.K. Blitzstein, J. Hwang, Introduction to Probability (Chapman and Hall/CRC, London, 2014)
5. M. Drela, H. Youngren, XFOIL 6.94 User Guide (MIT Aero & Astro, 2001)
6. B. Efron, Bootstrap methods: another look at the jackknife, in Breakthroughs in statistics
(Springer, New York, 1992), pp. 569–593
7. G. Gori, M. Zocca, G. Cammi, A. Spinelli, P.M. Congedo, A. Guardone, Accuracy assessment
of the Non-Ideal Computational Fluid Dynamics model for siloxane MDM from the opensource SU2 suite. Eur. J. Mech. B Fluids 79, 109–120 (2020)
8. N. Hansen, The CMA evolution strategy: A comparing review, in Towards a New Evolutionary
Computation: Advances in the Estimation of Distribution Algorithms, ed. by J.A. Lozano, P.
Larrañaga, I. Inza, E. Bengoetxea (Springer, Berlin, Heidelberg, 2006), pp. 75–102
9. D.S. Lee, L.F. Gonzalez, J. Périaux, K. Srinivas, Efficient hybrid-game strategies coupled
to evolutionary algorithms for robust multidisciplinary design optimization in aerospace
engineering. IEEE Trans. Evol. Comput. 15(2), 133–150 (2011)
10. M. Padulo, M.S. Campobasso, M.D. Guenov, Novel uncertainty propagation method for robust
aerodynamic design. AIAA J. 49(3), 530–543 (2011)
11. G.-J. Park, T.-H. Lee, K.H. Lee, K.-H. Hwang, Robust design: An overview. AIAA J. 44(1),
181–191 (2006)
12. D. Quagliarella, E. Iuliano, Robust design of a supersonic natural laminar flow wing-body.
IEEE Comput. Intell. Mag. 12(4), 14–27 (2017)
13. D. Quagliarella, Value-at-risk and conditional value-at-risk in optimization under uncertainty,
in Uncertainty Management for Robust Industrial Design in Aeronautics: Findings and Best
Practice Collected During UMRIDA, a Collaborative Research Project (2013–2016) Funded
by the European Union, ed. by C. Hirsch, D. Wunsch, J. Szumbarski, Ł. Łaniewski-Wołłk, J.
Pons-Prats (Springer International Publishing, Cham, 2019), pp. 541–565
14. D. Quagliarella, E.M. Tirado, A. Bornaccioni, Risk measures applied to robust aerodynamic
shape design optimization, in Flexible Engineering Toward Green Aircraft (Springer, New
York, 2020), pp. 153–168
15. A.A. Trindade, S. Uryasev, A. Shapiro, G. Zrazhevsky, Financial prediction with constrained
tail risk. J. Bank. Finance 31(11), 3524–3538 (2007)
16. A.W. van der Vaart, Asymptotic Statistics (Cambridge University Press, Cambridge, 1998)
17. J. Van Ingen, The eN method for transition prediction. Historical review of work at TU Delft,
in 38th Fluid Dynamics Conference and Exhibit, p. 3830 (2008)
E. M. Tirado and D. Quagliarella
Table 13.2 Risk measurement based on the obtained cumulative distribution functions
0.9 − V aR · 10 4
0.9 − CV aR · 10 4
Baseline NACA 2412 airfoil
74.5
75.0
Deterministic optimized airfoil
63.4
64.8
Robust optimized airfoil
62.2
62.5
by the observation of the value Value-at-Risk and Conditional Value-at-Risk with
α = 0.9 provided in Table 13.2.
References
1. S. Amaral, D. Allaire, K. Willcox, Optimal L 2 -norm empirical importance weights for the
change of probability measure. Stat. Comput., 1–19 (2016)
2. P. Artzner, F. Delbaen, J.-M. Eber, D. Heath, Coherent measures of risk. Mathematical Finance
9(3), 203–228 (1999)
3. P. Billingsley, Probability and Measure, 3rd edn. (Wiley, New York, NY, 1995)
4. J.K. Blitzstein, J. Hwang, Introduction to Probability (Chapman and Hall/CRC, London, 2014)
5. M. Drela, H. Youngren, XFOIL 6.94 User Guide (MIT Aero & Astro, 2001)
6. B. Efron, Bootstrap methods: another look at the jackknife, in Breakthroughs in statistics
(Springer, New York, 1992), pp. 569–593
7. G. Gori, M. Zocca, G. Cammi, A. Spinelli, P.M. Congedo, A. Guardone, Accuracy assessment
of the Non-Ideal Computational Fluid Dynamics model for siloxane MDM from the opensource SU2 suite. Eur. J. Mech. B Fluids 79, 109–120 (2020)
8. N. Hansen, The CMA evolution strategy: A comparing review, in Towards a New Evolutionary
Computation: Advances in the Estimation of Distribution Algorithms, ed. by J.A. Lozano, P.
Larrañaga, I. Inza, E. Bengoetxea (Springer, Berlin, Heidelberg, 2006), pp. 75–102
9. D.S. Lee, L.F. Gonzalez, J. Périaux, K. Srinivas, Efficient hybrid-game strategies coupled
to evolutionary algorithms for robust multidisciplinary design optimization in aerospace
engineering. IEEE Trans. Evol. Comput. 15(2), 133–150 (2011)
10. M. Padulo, M.S. Campobasso, M.D. Guenov, Novel uncertainty propagation method for robust
aerodynamic design. AIAA J. 49(3), 530–543 (2011)
11. G.-J. Park, T.-H. Lee, K.H. Lee, K.-H. Hwang, Robust design: An overview. AIAA J. 44(1),
181–191 (2006)
12. D. Quagliarella, E. Iuliano, Robust design of a supersonic natural laminar flow wing-body.
IEEE Comput. Intell. Mag. 12(4), 14–27 (2017)
13. D. Quagliarella, Value-at-risk and conditional value-at-risk in optimization under uncertainty,
in Uncertainty Management for Robust Industrial Design in Aeronautics: Findings and Best
Practice Collected During UMRIDA, a Collaborative Research Project (2013–2016) Funded
by the European Union, ed. by C. Hirsch, D. Wunsch, J. Szumbarski, Ł. Łaniewski-Wołłk, J.
Pons-Prats (Springer International Publishing, Cham, 2019), pp. 541–565
14. D. Quagliarella, E.M. Tirado, A. Bornaccioni, Risk measures applied to robust aerodynamic
shape design optimization, in Flexible Engineering Toward Green Aircraft (Springer, New
York, 2020), pp. 153–168
15. A.A. Trindade, S. Uryasev, A. Shapiro, G. Zrazhevsky, Financial prediction with constrained
tail risk. J. Bank. Finance 31(11), 3524–3538 (2007)
16. A.W. van der Vaart, Asymptotic Statistics (Cambridge University Press, Cambridge, 1998)
17. J. Van Ingen, The eN method for transition prediction. Historical review of work at TU Delft,
in 38th Fluid Dynamics Conference and Exhibit, p. 3830 (2008)