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Proper orthogonal decomposition, surrogate modelling and evolutionary optimization in aerodynamic design. (English) Zbl 1290.76051

Summary: A computational methodology is proposed for CFD-based aerodynamic design to exploit a reduced order model as surrogate evaluator. The model is based on the Proper Orthogonal Decomposition of an ensemble of CFD solutions. A zonal approach is presented to better solve the shock wave region and improve the surrogate prediction in transonic flow. Model validation and in-fill criteria are shown as valid tools to examine the accuracy of the surrogate and, therefore, to feed the model back with “intelligent” information. The reduced order model is integrated in an evolutionary optimization framework and used as fitness evaluator to improve the aerodynamic performances of a two-dimensional airfoil. Finally, the performances of the surrogate-based shape optimization are compared to the efficiency of a meta-model assisted optimization and to the accuracy of a plain optimization, where, instead, each aerodynamic evaluation is performed with the high-fidelity model.

MSC:

76G25 General aerodynamics and subsonic flows

Software:

EGO
Full Text: DOI

References:

[1] Jones, D. R.; Schonlau, M.; Welch, W. J., Efficient global optimization of expensive black-box functions, J Global Optim, 13, 455-492 (1998) · Zbl 0917.90270
[2] Schonlau, M.; Welch, W. J.; Jones, D. R., Global versus local search in constrained optimization of computer models, Lect Notes-Monogr Ser, 34 (1998)
[3] Jones, D. R., A taxonomy of global optimization methods based on response surfaces, J Global Optim, 21, 345-383 (2001) · Zbl 1172.90492
[5] Booker, A. J.; Dennis, J. E.; Frank, P. D.; Serafini, D. B.; Torczon, V.; Trosset, M. W., A rigorous framework for optimization of expensive functions by surrogates, Struct Multidiscip Optim, 17, 1-13 (1999)
[6] Queipo, N.; Haftka, R.; Shyy, W.; Goel, T.; Vaidyanathan, R.; Kevintucker, P., Surrogate-based analysis and optimization, Prog Aerosp Sci, 41, 1, 1-28 (2005)
[8] Forrester, A. I.J.; Keane, A. J., Recent advances in surrogate-based optimization, Prog Aerosp Sci, 45, 1-3, 50-79 (2009)
[9] Sóbester, A.; Leary, S.; Keane, A., A parallel updating scheme for approximating and optimizing high fidelity computer simulations, Struct Multidiscip Optim, 27, 371-383 (2004)
[10] Gutmann, H. M., A radial basis function method for global optimization, J Global Optim, 19, 201-227 (2001) · Zbl 0972.90055
[11] Goel, T.; Haftka, R. T.; Shyy, W.; Queipo, N. V., Ensemble of surrogates, Struct Multidiscip Optim, 33, 3, 199-216 (2007)
[13] Loeve, M., Probability theory (1977), Springer-Verlag: Springer-Verlag New York, ISBN:0387902104 0387902104. · Zbl 0359.60001
[14] Lumley, J. L., The structure of inhomogeneous turbulent flows, (Yaglom, A. M.; Tatarski, V. I., Atmospheric turbulence and radio propagation (1967), Nauka: Nauka Moscow), 166-178
[16] Epureanu, B., A parametric analysis of reduced order models of viscous flows in turbomachinery, J Fluids Struct, 17, 7, 971-982 (2003)
[18] Bui-Thanh, T.; Damodaran, M.; Willcox, K., Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition, AIAA J, 42, 8, 1505-1516 (2004)
[19] Sirovich, L., Turbulence and the dynamics of coherent structures. I - Coherent structures. II - Symmetries and transformations. III - Dynamics and scaling, Quart Appl Math, 45, 561-571 (1987) · Zbl 0676.76047
[20] Holmes, P.; Lumley, J.; Berkooz, G., Turbulence, coherent structures, dynamical systems and symmetry (1996), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0890.76001
[22] Hall, K. C.; Thomas, J. P.; Dowell, E. H., Reduced-order modeling of unsteady small-disturbance flows using a frequency-domain proper orthogonal decomposition technique, AIAA J, 38, 10, 1853-1862 (2000)
[23] Everson, R.; Sirovich, L., Karhunen-Loève procedure for gappy data, J Opt Soc Am A, 12, 8, 1657-1664 (1995)
[26] Lucia, D. J.; King, P. I.; Beran, P. S., Reduced order modeling of a two-dimensional flow with moving shocks, Comput Fluids, 32, 7, 917-938 (2003) · Zbl 1040.76042
[28] Buffoni, M.; Telib, H.; Iollo, A., Iterative methods for model reduction by domain decomposition, Comput Fluids, 38, 6, 1160-1167 (2009) · Zbl 1242.76231
[29] Toal, D. J.J.; Bressloff, N. W.; Keane, A. J.; Holden, C. M.E., Geometric filtration using pod for aerodynamic design optimization, AIAA J, 48, 5, 916-928 (2010)
[30] Braconnier, T.; Ferrier, M.; Jouhaud, J. C.; Montagnac, M.; Sagaut, P., Towards an adaptive POD/SVD surrogate model for aeronautic design, Comput Fluids, 40, 1, 195-209 (2011) · Zbl 1245.76063
[33] Reed, M.; Simon, B., Methods of modern mathematical physics I: functional analysis (1980), Academic Press · Zbl 0459.46001
[34] Sirovich, L., Turbulence and the dynamics of coherent structures. Part 1: coherent structures, Quart Appl Math, 45, 3, 561-571 (1987) · Zbl 0676.76047
[39] Rippa, S., An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation, Adv Comput Math, 11, 193-210 (1999) · Zbl 0943.65017
[41] Kulfan, B. M., Universal parametric geometry representation method, J Aircraft, 45, 1, 142-158 (2008)
[42] Montgomery, D. C., Design and analysis of experiments (2006), John Wiley & Sons, ISBN: 0470088109
[43] McKay, M.; Conover, W.; Beckman, R., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239-245 (1979) · Zbl 0415.62011
[45] Amato, M.; Catalano, P., Non linear κε turbulence modeling for industrial applications, (ICAS 2000 congress (2000), IOS Press: IOS Press Harrogate, UK)
[46] Eldred, M.; Bichon, B.; Adams, B.; Mahadevan, S., Structural design optimization considering uncertainties, (Structures and infrastructures series. Structures and infrastructures series, Overview of reliability analysis and design capabilities in DAKOTA with application to shape optimization of MEMS, vol. 1 (2008), Taylor & Francis Group), 401-432, [chap.]
[49] Quagliarella, D.; Vicini, A., GAs for aerodynamic shape design I: general issues, shape parametrization problems and hybridization techniques, (Lecture series 2000-07. Lecture series 2000-07, Genetic algorithms for optimisation in aeronautics and turbomachinery (2000), Von Karman Institute: Von Karman Institute Belgium)
[50] Quagliarella, D.; Vicini, A., GAs for aerodynamic shape design II: multiobjective optimization and multi-criteria design, (Lecture series 2000-07. Lecture series 2000-07, Genetic algorithms for optimisation in aeronautics and turbomachinery (2000), Von Karman Institute: Von Karman Institute Belgium)
[52] Catalano, P.; Amato, M., An evaluation of rans turbulence modelling for aerodynamic applications, Aerosp Sci Technol, 7, 493-509 (2003) · Zbl 1045.76531
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