Sensitivity-Based Parameterization for Aerodynamic Shape Global Optimization
Publication: Journal of Aerospace Engineering
Volume 35, Issue 2
Abstract
For aerodynamic shape design using gradient-free searching algorithms, which can be applied more flexibly than gradient-based ones, computing costs increase dramatically with dimensionality. Rational design variables are considered vital to elevate design performance in gradient-free optimization. In this paper, the Bèzier surface free-form deformation (FFD) parameterization based on adjoint surface sensitivity analysis is proposed for aerodynamic shape global optimization. Specifically, FFD point lattice is located where a wide variation is identified in adjoint surface sensitivity. In addition, input space has been adjusted accordingly to enhance space coverage due to the smoothness feature of Bernstein polynomial basis in Bèzier surface FFD. The proposed parameterization was applied to a transonic inviscid drag reduction problem for NACA 0012 with thickness constraints in dimensionality from 5 to 11, and 360.5 counts reduction in drag was achieved. In general, compared with the regularly spaced control lattice, the proposed parameterization effectively weakens the strong shock wave, and drag is decreased considerably using a small-scale sample database.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research was partially supported by the National Natural Science Foundation of China (Grant No. 11572284).
References
Berguin, S. H., and D. N. Mavris. 2015. “Dimensionality reduction using principal component analysis applied to the gradient.” AIAA J. 53 (4): 1078–1090. https://doi.org/10.2514/1.J053372.
Berguin, S. H., D. Rancourt, and D. N. Mavris. 2015. “Method to facilitate high-dimensional design space exploration using computationally expensive analyses.” AIAA J. 53 (12): 3752–3765. https://doi.org/10.2514/1.J054035.
Bisson, F., and S. Nadarajah. 2015. “Adjoint-based aerodynamic optimization of benchmark problems.” In Proc., 53rd AIAA Aerospace Sciences Meeting AIAA SciTech Forum. New York: AIAA.
Bu, Y., W. Song, Z. Han, Y. Zhang, and L. Zhang. 2020. “Aerodynamic/aeroacoustic variable-fidelity optimization of helicopter rotor based on hierarchical Kriging model.” Chin. J. Aeronaut. 33 (2): 476–492. https://doi.org/10.1016/j.cja.2019.09.019.
Campolongo, F., J. Cariboni, and A. Saltelli. 2007. “An effective screening design for sensitivity analysis of large models.” Environ. Modell. Software 22 (10): 1509–1518. https://doi.org/10.1016/j.envsoft.2006.10.004.
Carrese, R., H. Winarto, X. Li, A. Sóbester, and S. Ebenezer. 2012. “A comprehensive preference-based optimization framework with application to high-lift aerodynamic design.” Eng. Optim. 44 (10): 1209–1227. https://doi.org/10.1080/0305215X.2011.637558.
Cinquegrana, D., and E. Iuliano. 2018. “Investigation of adaptive design variables bounds in dimensionality reduction for aerodynamic shape optimization.” Comput. Fluids 174 (7): 89–109. https://doi.org/10.1016/j.compfluid.2018.07.012.
Constantine, P. G., and P. Diaz. 2017. “Global sensitivity metrics from active subspaces.” Reliab. Eng. Syst. Saf. 162 (Jun): 1–13. https://doi.org/10.1016/j.ress.2017.01.013.
Copeland, S. R., F. Palacios, and J. J. Alonso. 2014. “Adjoint-based aerothermodynamic shape design of hypersonic vehicles in non-equilibrium flows.” In Proc., 52nd Aerospace Sciences Meeting AIAA SciTech Forum. New York: AIAA.
Destarac, D., G. Carrier, G. R. Anderson, S. Nadarajah, D. J. Poole, J. C. Vassberg, and D. W. Zingg. 2018. “Example of a pitfall in aerodynamic shape optimization.” AIAA J. 56 (4): 1532–1540. https://doi.org/10.2514/1.J056128.
Eberhart, R., and J. Kennedy. 1995. “A new optimizer using particle swarm theory.” In Proc., 6th Int. Symp. on Micro Machine and Human Science, 39–43. New York: IEEE.
Eyi, S. 2013. “Aerothermodynamic design optimization in hypersonic flows.” In Proc., 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conf. New York: AIAA.
Fusi, F., G. Quaranta, A. Guardone, and P. M. Congedo. 2015. “Drag minimization of an isolated airfoil in transonic inviscid flow by means of genetic algorithms.” In Proc., 53rd AIAA Aerospace Sciences Meeting. New York: AIAA.
Grey, Z. J., and P. G. Constantine. 2018. “Active subspaces of airfoil shape parameterizations.” AIAA J. 56 (5): 2003–2017. https://doi.org/10.2514/1.J056054.
Han, Z., C. Xu, L. Zhang, Y. Zhang, K. Zhang, and W. Song. 2020. “Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids.” Chin. J. Aeronaut. 33 (1): 31–47. https://doi.org/10.1016/j.cja.2019.05.001.
He, X., J. Li, C. A. Mader, A. Yildirim, and J. R. R. A. Martins. 2019. “Robust aerodynamic shape optimization—From a circle to an airfoil.” Aerosp. Sci. Technol. 87 (Apr): 48–61. https://doi.org/10.1016/j.ast.2019.01.051.
Holland, J. H. 1992. Adaptation in natural and artificial systems. Cambridge, UK: MIT Press.
Jameson, A. 1988. “Aerodynamic design via control theory.” J. Sci. Comput. 3 (3): 233–260. https://doi.org/10.1007/BF01061285.
Jeong, S., M. Murayama, and K. Yamamoto. 2005. “Efficient optimization design method using Kriging model.” J. Aircr. 42 (2): 413–420. https://doi.org/10.2514/1.6386.
Jeong, S., S. Obayashi, and K. Yamamoto. 2006. “A Kriging-based probabilistic optimization method with an adaptive search region.” Eng. Optim. 38 (5): 541–555. https://doi.org/10.1080/03052150600627073.
Jolliffe, I. T., and J. Cadima. 2016. “Principal component analysis: A review and recent developments.” Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci. 374 (2065): 20150202. https://doi.org/10.1098/rsta.2015.0202.
Keane, A. J., and P. B. Nair. 2005. Computational approaches for aerospace design. Chichester, UK: Wiley.
Kedward, L. J., C. B. Allen, and T. C. S. Rendall. 2019. “Regularisation of high fidelity aerodynamic shape optimisation problems using gradient limits.” In Proc., AIAA Aviation 2019 Forum. New York: AIAA.
Kedward, L. J., C. B. Allen, T. C. S. Rendall, and D. J. Poole. 2020. “Towards generic modal design variables for aerodynamic shape optimisation.” In Proc., AIAA Scitech 2020 Forum. New York: AIAA.
Kenway, G. K. W., C. A. Mader, P. He, and J. R. R. A. Martins. 2019. “Effective adjoint approaches for computational fluid dynamics.” Prog. Aerosp. Sci. 110 (Sep): 100542. https://doi.org/10.1016/j.paerosci.2019.05.002.
Khurana, M., and H. Winarto. 2010. “Development and validation of an efficient direct numerical optimisation approach for aerofoil shape design.” Aeronaut. J. 114 (1160): 611–628. https://doi.org/10.1017/S0001924000004097.
Kim, J., J. Kim, and K. Kim. 2011. “Axial-flow ventilation fan design through multi-objective optimization to enhance aerodynamic performance.” J. Fluids Eng. 133 (10): 101101. https://doi.org/10.1115/1.4004906.
Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi. 1983. “Optimization by simulated annealing.” Science 220 (4598): 671–680. https://doi.org/10.1126/science.220.4598.671.
Lee, C., D. Koo, K. Telidetzki, H. Buckley, H. Gagnon, and D. W. Zingg. 2015. “Aerodynamic shape optimization of benchmark problems using jet stream.” In Proc., 53rd AIAA Aerospace Sciences Meeting. New York: AIAA.
Leung, T. M., and D. W. Zingg. 2012. “Aerodynamic shape optimization of wings using a parallel Newton-Krylov approach.” AIAA J. 50 (3): 540–550. https://doi.org/10.2514/1.J051192.
Lukaczyk, T. W., F. Palacios, J. J. Alonso, and P. G. Constantine. 2014. “Active subspaces for shape optimization.” In Proc., AIAA SciTech Forum, 10th AIAA Multidisciplinary Design Optimization Conf. New York: AIAA.
Luo, J., and Y. Zheng. 2019. “Aerodynamic shape optimization of a turbine blade considering geometric uncertainty using an adjoint method.” In Proc., ASME Turbo Expo 2019: Turbomachinery Technical Conf. and Exposition. Volume 2C: Turbomachinery. New York: ASME.
Lyu, Z., G. Kenway, and J. R. R. A. Martins. 2015. “Aerodynamic shape optimization investigations of the common research model wing benchmark.” AIAA J. 53 (4): 968–985. https://doi.org/10.2514/1.J053318.
Marta, A. C., C. A. Mader, J. R. R. A. Martins, E. Van der Weide, and J. J. Alonso. 2007. “A methodology for the development of discrete adjoint solvers using automatic differentiation tools.” Int. J. Comput. Fluid Dyn. 21 (9–10): 307–327. https://doi.org/10.1080/10618560701678647.
Masters, D. A., D. J. Poole, N. J. Taylor, T. C. S. Rendall, and C. B. Allen. 2016a. “Impact of shape parameterisation on aerodynamic optimisation of benchmark problem.” In Proc., 54th AIAA Aerospace Sciences Meeting. New York: AIAA.
Masters, D. A., N. J. Taylor, T. C. S. Rendall, and C. B. Allen. 2016b. “A locally adaptive subdivision parameterisation scheme for aerodynamic shape optimisation.” In Proc., 34th AIAA Applied Aerodynamics Conf. New York: AIAA.
Masters, D. A., N. J. Taylor, T. C. S. Rendall, C. B. Allen, and D. J. Poole. 2017. “Geometric comparison of aerofoil shape parameterization methods.” AIAA J. 55 (5): 1575–1589. https://doi.org/10.2514/1.J054943.
Meheut, M., D. Destarac, G. Carrier, G. Anderson, S. Nadarajah, D. Poole, J. Vassberg, and D. W. Zingg. 2015. “Gradient-based single and multi-points aerodynamic optimizations with the Elsa Software.” In Proc., 53rd AIAA Aerospace Sciences Meeting AIAA SciTech Forum. New York: AIAA.
Morris, M. D. 1991. “Factorial sampling plans for preliminary computational experiments.” Technometrics 33 (2): 161–174. https://doi.org/10.1080/00401706.1991.10484804.
Myers, R. H., and D. C. Montgomery. 2002. Response surface methodology. New York: Wiley.
Palacios, F., et al. 2014. “Stanford University Unstructured (SU2): Open-source analysis and design technology for turbulent flows.” In Proc., 52nd Aerospace Sciences Meeting. New York: AIAA.
Peter, J. E. V., and R. P. Dwight. 2010. “Numerical sensitivity analysis for aerodynamic optimization: A survey of approaches.” Comput. Fluids 39 (3): 373–391. https://doi.org/10.1016/j.compfluid.2009.09.013.
Poole, D. J., C. B. Allen, and T. Rendall. 2015. “Control point-based aerodynamic shape optimization applied to AIAA ADODG test cases.” In Proc., 53rd AIAA Aerospace Sciences Meeting. New York: AIAA.
Rashedi, E., H. Nezamabadi-Pour, and S. Saryazdi. 2009. “GSA: A gravitational search algorithm.” Inf. Sci. 179 (13): 2232–2248. https://doi.org/10.1016/j.ins.2009.03.004.
Samareh, J. A. 2001. “Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimization.” AIAA J. 39 (5): 877–884. https://doi.org/10.2514/2.1391.
Sederberg, T. W., and S. R. Parry. 1986. “Free-form deformation of solid geometric models.” In Proc., 13th Annual Conf. on Computer Graphics and Interactive Techniques (SIGGRAPH ’86), 151–160. New York: Association for Computing Machinery.
Smith, N., J. Camberos, and E. Alyanak. 2012. “Design of experiments for aeroelastic analysis.” In Proc., ASME 2012 Int. Mechanical Engineering Congress and Exposition. Volume 1: Advances in Aerospace Technology, 49–57. New York: ASME.
Smith, S., M. Nemec, and S. Krist. 2013. “Integrated nacelle-wing shape optimization for an ultra-high bypass fanjet installation on a single-aisle transport configuration.” In Proc., 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. New York: AIAA.
Sobol, I. M. 2001. “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.” Math. Comput. Simul. 55 (1): 271–280. https://doi.org/10.1016/S0378-4754(00)00270-6.
Song, L., Z. Guo, J. Li, and Z. Feng. 2016. “Research on metamodel-based global design optimization and data mining methods.” J. Eng. Gas Turbines Power 138 (9): 092604. https://doi.org/10.1115/1.4032653.
Song, W., and A. J. Keane. 2007. “Surrogate-based aerodynamic shape optimization of a civil aircraft engine nacelle.” AIAA J. 45 (10): 2565–2574. https://doi.org/10.2514/1.30015.
Srinath, D. N., and S. Mittal. 2009. “Optimal airfoil shapes for low Reynolds number flows.” Int. J. Numer. Methods Fluids 61 (4): 355–381. https://doi.org/10.1002/fld.1960.
Takenaka, K., K. Hatanaka, W. Yamazaki, and K. Nakahashi. 2008. “Multidisciplinary design exploration for a winglet.” J. Aircr. 45 (5): 1601–1611. https://doi.org/10.2514/1.33031.
Vassberg, J. C., N. A. Harrison, D. L. Roman, and A. Jameson. 2011. “A systematic study on the impact of dimensionality for a two-dimensional aerodynamic optimization model problem.” In Proc., 29th AIAA Applied Aerodynamics Conf. New York: AIAA.
Vassberg, J. C., and A. Jameson. 2009. “In pursuit of grid convergence, part I: Two-dimensional Euler solutions.” In Proc., 27th AIAA Applied Aerodynamics Conf. New York: AIAA.
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Published In
Journal of Aerospace Engineering
Volume 35 • Issue 2 • March 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 23, 2020
Accepted: Aug 6, 2021
Published online: Nov 19, 2021
Published in print: Mar 1, 2022
Discussion open until: Apr 19, 2022
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