Fast Multi-Objective Aerodynamic Optimization Using Sequential Domain Patching and Multifidelity Models
Abstrakt
Exploration of design tradeoffs for aerodynamic surfaces requires solving of multi-objective optimization (MOO) problems. The major bottleneck here is the time-consuming evaluations of the computational fluid dynamics (CFD) model used to capture the nonlinear physics involved in designing aerodynamic surfaces. This, in conjunction with a large number of simulations necessary to yield a set of designs representing the best possible tradeoffs between conflicting objectives (referred to as a Pareto front), makes CFD-driven MOO very challenging. This paper presents a computationally efficient methodology aimed at expediting the MOO process for aerodynamic design problems. The extreme points of the Pareto front are obtained quickly using single-objective optimizations. Starting from these extreme points, identification of an initial set of Pareto-optimal designs is carried out using a sequential domain patching algorithm. Refinement of the Pareto front, originally obtained at the level of the low-fidelity CFD model, is carried out using local response surface approximations and adaptive corrections. The proposed algorithm is validated using a few multi-objective analytical problems and an aerodynamic problem involving MOO of two-dimensional transonic airfoil shapes where the figures of interest are the drag and pitching moment coefficients. A multifidelity model is constructed using CFD model and control points parameterizing the shape of the airfoil. The results demonstrate that an entire or a part of the Pareto front can be obtained at a low cost when considering up to eight design variables.
Cytowania
-
1 9
CrossRef
-
0
Web of Science
-
2 2
Scopus
Autorzy (3)
Cytuj jako
Pełna treść
- Wersja publikacji
- Accepted albo Published Version
- Licencja
- Copyright (2020 the American Institute of Aeronautics and Astronautics, Inc)
Słowa kluczowe
Informacje szczegółowe
- Kategoria:
- Publikacja w czasopiśmie
- Typ:
- artykuły w czasopismach
- Opublikowano w:
-
JOURNAL OF AIRCRAFT
nr 57,
strony 1 - 11,
ISSN: 0021-8669 - Język:
- angielski
- Rok wydania:
- 2020
- Opis bibliograficzny:
- Amrit A., Leifsson L., Kozieł S.: Fast Multi-Objective Aerodynamic Optimization Using Sequential Domain Patching and Multifidelity Models// JOURNAL OF AIRCRAFT -Vol. 57,iss. 3 (2020), s.1-11
- DOI:
- Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.2514/1.c035500
- Bibliografia: test
-
- Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E., and Mavriplis, D., "CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences," NASA CR-2014-218178, 2014. otwiera się w nowej karcie
- Koziel, S., and Leifsson, L., "Surrogate-Based Aerodynamic Shape Optimization by Variable-Resolution Models," AIAA Journal, Vol. 51, No. 1, 2013, pp. 94-106. https://doi.org/10.2514/1.J051583 otwiera się w nowej karcie
- Bandler, J. W., Cheng, Q. S., Dakroury, S., Mohamed, A. S., Bakr, M. H., Madsen, K., and Sondergaard, J., "Space Mapping: The State of the Art," IEEE Transactions of Microwave Theory and Techniques, Vol. 52, No. 1, 2004, pp. 337-361. https://doi.org/10.1109/TMTT.2003.820904 otwiera się w nowej karcie
- Koziel, S., and Bekasiewicz, A., "Multi-Objective Design Optimization of Antenna Structures Using Sequential Domain Patching with Auto- mated Patch Size Determination," Engineering Optimization, Vol. 50, No. 2, 2018, pp. 218-234. https://doi.org/10.1080/0305215X.2017.1311879 otwiera się w nowej karcie
- Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., and Tucker, P. K., "Surrogate-Based Analysis and Optimization," Progress in Aerospace Sciences, Vol. 41, No. 1, 2005, pp. 1-28. https://doi.org/10.1016/j.paerosci.2005.02.001 otwiera się w nowej karcie
- Haftka, R. T., "Combining Global and Local Approximations," AIAA Journal, Vol. 29, No. 9, 1991, pp. 1523-1525. https://doi.org/10.2514/3.10768 otwiera się w nowej karcie
- Rao, S. S., Engineering Optimization: Theory and Practice, 3rd ed., Wiley, New York, 1996.
- Amrit, A., Leifsson, L., and Koziel, S., "Design Strategies for Multi- Objective Optimization of Aerodynamic Surfaces," Engineering Com- putations, Vol. 34, No. 5, 2017, pp. 1724-1753. https://doi.org/10.1108/EC-07-2016-0239 otwiera się w nowej karcie
- Obayashi, S., and Sasaki, D., "Finding Tradeoffs by Using Multiobjective Optimization Algorithms," Transactions of JSASS, Vol. 47, No. 155, 2004, pp. 51-58. otwiera się w nowej karcie
- Buckley, H. P., Zhou, B. Y., and Zing, D. W., "Airfoil Optimization Using Practical Aerodynamic Design Requirements," Journal of Aircraft, Vol. 47, No. 5, 2010, pp. 1707-1719. https://doi.org/10.2514/1.C000256 otwiera się w nowej karcie
- Hwang, C. L., and Masud, A. S. M., Multiple Objective Decision Making, Methods and Applications: A State-of-the-Art Survey, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 1979. otwiera się w nowej karcie
- Mengistu, T., and Ghaly, W., "Aerodynamic Optimization of Turbomachi- nery Blades Using Evolutionary Methods and ANN-Based Surrogate Models," Optimization and Engineering, Vol. 9, No. 3, 2008, pp. 239-255. https://doi.org/10.1007/s11081-007-9031-1 otwiera się w nowej karcie
- Liem, R. P., Martins, J. R. R. A., and Kenway, G. K., "Expected Drag Minimization for Aerodynamic Design Optimization Based on Aircraft Operational Data," Aerospace Science and Technology, Vol. 63, April 2017, pp. 344-362. https://doi.org/10.1016/j.ast.2017.01.006 otwiera się w nowej karcie
- Zhao, K., Gao, Z., Huang, J., and Li, Q., "Aerodynamic Optimization of Rotor Airfoil Based on Multi-Layer Hierarchical Constraint Method," Chinese Journal of Aeronautics, Vol. 29, No. 6, 2016, pp. 1541-1552. https://doi.org/10.1016/j.cja.2016.09.005 otwiera się w nowej karcie
- Yang, Z., Cai, X., and Fan, Z., "Epsilon Constrained Method for Constrained Multiobjective Optimization Problems: Some Preliminary Results," Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation (GECCO Comp '14), Assoc. for Computing Machinery, New York, 2014, pp. 1181-1186. otwiera się w nowej karcie
- Eiben, A. E., and Smith, J., "From Evolutionary Computation to the Evolution of Things," Nature, Vol. 521, No. 7553, 2015, pp. 476-482. https://doi.org/10.1038/nature14544 otwiera się w nowej karcie
- Poli, R., Kennedy, J., and Blackwell, T., "Particle Swarm Optimization," Swarm Intelligence, Vol. 1, No. 1, 2007, pp. 33-57. https://doi.org/10.1007/s11721-007-0002-0 otwiera się w nowej karcie
- Storn, R., and Price, K., "Differential Evolution-A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces," Journal of Global Optimization, Vol. 11, No. 4, 1997, pp. 341-359. https://doi.org/10.1023/A:1008202821328 otwiera się w nowej karcie
- Yang, X. S., "Firefly Algorithms for Multimodal Optimization," Stochastic Algorithms: Foundations and Applications, SAGA 2009, Vol. 5792, Lecture Notes in Computer Sciences, Spring-Verlag, Berlin, Germany, 2009, pp. 169-178. otwiera się w nowej karcie
- Yang, X. S., and Deb, S., "Cuckoo Search: Recent Advances and Applications," Neural Computing and Applications, Vol. 24, No. 1, 2014, pp. 169-174. https://doi.org/10.1007/s00521-013-1367-1 otwiera się w nowej karcie
- Forrester, A. I. J., and Keane, A. J., "Recent Advances in Surrogate- Based Optimization," Progress in Aerospace Sciences, Vol. 45, Nos. 1-3, 2009, pp. 50-79. https://doi.org/10.1016/j.paerosci.2008.11.001 otwiera się w nowej karcie
- Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., "Design and Analysis of Computer Experiments," Statistical Science, Vol. 4, No. 4, 1989, pp. 409-423. https://doi.org/10.1214/ss/1177012413 otwiera się w nowej karcie
- Yondo, R., Andres, E., and Valero, E., "A Review on Design of Experi- ments and Surrogate Models in Aircraft Real-Time and Many-Query Aerodynamic Analyses," Progress in Aerospace Sciences, Vol. 96, Jan. 2018, pp. 23-61. https://doi.org/10.1016/j.paerosci.2017.11.003 otwiera się w nowej karcie
- Knowles, J., "ParEGO: A Hybrid Algorithm with On-Line Landscape Approximation for Expensive Multiobjective Optimization Problems," IEEE Transactions on Evolutionary Computation, Vol. 10, No. 1, 2006, pp. 50-66. https://doi.org/10.1109/TEVC.2005.851274 otwiera się w nowej karcie
- Shan, S., and Wang, G., "An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions," Journal of Mechanical Design, Vol. 127, No. 5, 2005, pp. 866-874. https://doi.org/10.1115/1.1904639 otwiera się w nowej karcie
- Forrester, A., Sobester, A., and Keane, A., Engineering Design via Surrogate Modelling: A Practical Guide, Wiley, New York, 2008.
- Praveen, C., and Duvigneau, R., "Low Cost PSO Using Metamodels and Inexact Pre-Evaluation: Application to Aerodynamic Shape Design," Computer Methods in Applied Mechanics and Engineering, Vol. 198, Nos. 9-12, 2009, pp. 1087-1096. https://doi.org/10.1016/j.cma.2008.11.019 otwiera się w nowej karcie
- Karakasis, M. K., and Giannakoglou, K. C., "On the Use of Metamodel- Assisted, Multi-Objective Evolutionary Algorithms," Engineering Optimization, Vol. 38, No. 8, 2006, pp. 941-957. https://doi.org/10.1080/03052150600848000 otwiera się w nowej karcie
- Li, M., Li, G., and Azarm, S., "A Kriging Metamodel Assisted Multi- Objective Genetic Algorithm for Design Optimization," Journal of Mechanical Design, Vol. 130, No. 3, 2008, Paper 031401. https://doi.org/10.1115/1.2829879 otwiera się w nowej karcie
- Hu, W., Li, M., Azarm, S., and Almansoori, A., "Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts," Journal of Mechanical Design, Vol. 133, No. 6, 2011, Paper 061002. https://doi.org/10.1115/1.4003918 otwiera się w nowej karcie
- Hu, W. W., Saleh, K. H., and Azarm, S. S., "Approximation Assisted Multiobjective Optimization with Combined Global and Local Meta- modeling," International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Vol. 3: 38th Design Automation Conference, Parts A and B, ASME, New York, 2012, pp. 753-764. otwiera się w nowej karcie
- Zhang, L., Zhang, J., Li, T., and Zhang, Y., "Multiobjective Aerody- namic Optimization Design of High-Speed Train Head Shape," Journal of Zhejiang University-Science A, Vol. 18, No. 11, 2017, pp. 841-854. https://doi.org/10.1631/jzus.A1600764 otwiera się w nowej karcie
- Wang, W., Mo, R., and Zhang, Y., "Multi-Objective Aerodynamic Optimization Design Method of Compressor Rotor Based on Isight," Procedia Engineering, Vol. 15, Dec. 2011, pp. 3699-3703. https://doi.org/10.1016/j.proeng.2011.08.693 otwiera się w nowej karcie
- Leusink, D., Alfano, D., and Cinnella, P., "Multi-Fidelity Optimization Strategy for the Industrial Aerodynamic Design of Helicopter Rotor Blades," Aerospace Science and Technology, Vol. 42, April 2015, pp. 136-147. https://doi.org/10.1016/j.ast.2015.01.005 otwiera się w nowej karcie
- Leifsson, L., Koziel, S., and Tesfahunegn, A. Y., "Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates," AIAA Journal, Vol. 54, No. 2, 2016, pp. 531-541. https://doi.org/10.2514/1.J054128 otwiera się w nowej karcie
- Koziel, S., Tesfahunegn, A. Y., and Leifsson, L., "Expedited Constrained Multi-Objective Aerodynamic Shape Optimization by means of Physics- Based Surrogates," Applied Mathematical Modelling, Vol. 40, Nos. 15- 16, 2016, pp. 7204-7215. https://doi.org/10.1016/j.apm.2016.03.020 otwiera się w nowej karcie
- Fincham, J. H. S., and Friswell, M. I., "Aerodynamic Optimization of a Camber Morphing Aerofoil," Aerospace Science and Technology, Vol. 43, June 2015, pp. 245-255. https://doi.org/10.1016/j.ast.2015.02.023 otwiera się w nowej karcie
- Peherstorfer, B., Willcox, K., and Gunzburger, M., "Survey of Multi- fidelity Methods in Uncertainty Propagation, Inference, and Optimiza- tion," SIAM Review, Vol. 60, No. 3, 2018, pp. 550-591. otwiera się w nowej karcie
- Han, Z. H., Gortz, S., and Zimmermann, R., "Improving Variable- Fidelity Surrogate Modeling via Gradient-Enhanced Kriging and a Generalized Hybrid Bridge Function," Aerospace Science and Technol- ogy, Vol. 25, No. 1, 2013, pp. 177-189. https://doi.org/10.1016/j.ast.2012.01.006 otwiera się w nowej karcie
- Rathinam, M., and Petzold, L., "A New Look at Proper Orthogonal Decomposition," SIAM Journal on Numerical Analysis, Vol. 41, No. 5, 2003, pp. 1893-1925. https://doi.org/10.1137/S0036142901389049 otwiera się w nowej karcie
- Rozza, G., Huynh, D. B. P., and Patera, A. T., "Reduced Basis Approxi- mation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations," Archives of Computa- tional Methods in Engineering, Vol. 15, No. 3, 2008, pp. 229-275. https://doi.org/10.1007/s11831-008-9019-9 otwiera się w nowej karcie
- Scholkopf, B., and Smola, A. J., Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, Cam- bridge, MA, 2001. otwiera się w nowej karcie
- March, A., and Willcox, K., "Constrained Multifidelity Optimization Using Model Calibration," Structural and Multidisciplinary Optimiza- tion, Vol. 46, No. 1, 2012, pp. 93-109. https://doi.org/10.1007/s00158-011-0749-1 otwiera się w nowej karcie
- Keane, A. J., "Cokriging for Robust Design Optimization," AIAA Jour- nal, Vol. 50, No. 11, 2012, pp. 2351-2364. https://doi.org/10.2514/1.J051391 otwiera się w nowej karcie
- Laurenceau, J., and Sagaut, P., "Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging," AIAA Journal, Vol. 46, No. 2, 2008, pp. 498-507. https://doi.org/10.2514/1.32308 otwiera się w nowej karcie
- Qian, P. Z., and Wu, C. J., "Bayesian Hierarchical Modeling for Inte- grating Low-Accuracy and High-Accuracy Experiments," Technomet- rics, Vol. 50, No. 2, 2008, pp. 192-204. https://doi.org/10.1198/004017008000000082 otwiera się w nowej karcie
- Teckentrup, A. L., Jantsch, P., Webster, C. G., and Gunzburger, M., "A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data," SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, No. 1, 2015, pp. 1046-1074. https://doi.org/10.1137/140969002 otwiera się w nowej karcie
- Fonseca, C., "Multiobjective Genetic Algorithms with Applications to Control Engineering Problems," Ph.D. Thesis, Det. of Automatic Control and Systems Engineering, Univ. of Sheffield, Sheffield, England, U.K., 1995. otwiera się w nowej karcie
- Ren, Z., Thelen, A. S., Amrit, A., Du, X., Leifsson, L., Tesfahunegn, Y. A., and Koziel, S., "Application of Multifidelity Optimization Tech- niques to Benchmark Aerodynamic Design Problems," 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-1542, 2016. otwiera się w nowej karcie
- Booker, A. J., Dennis, J. E., Jr., Frank, P. D., Serafini, D. B., Torczon, V., and Trosset, M. W., "A Rigorous Framework for Optimization of Expensive Functions by Surrogates," Structural Optimization, Vol. 17, No. 1, 1999, pp. 1-13. https://doi.org/10.1007/BF01197708 otwiera się w nowej karcie
- Fonzeca, C. M., and Fleming, P. J., "An Overview of Evolutionary Algorithms in Multiobjective Optimization," Evolutionary Computa- tion, Vol. 3, No. 1, 1995, pp. 1-16. https://doi.org/10.1162/evco.1995.3.1.1 otwiera się w nowej karcie
- Economon, T. D., Palacios, F., Copeland, S. R., Lukaczyk, T. W., and Alonso, J. J., "SU2: An Open-Source Suite for Multiphysics Simulation and Design," AIAA Journal, Vol. 54, No. 3, 2016, pp. 828-846. https://doi.org/10.2514/1.J053813 otwiera się w nowej karcie
- Spalart, P. R., and Allmaras, S. R., "A One Equation Turbulence Model for Aerodynamic Flows," 38th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 1992-0439, Jan. 1992. otwiera się w nowej karcie
- Jameson, A., Schmidt, W., and Turkel, E., "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time- Stepping Schemes," AIAA 14th Fluid and Plasma Dynamic Conference, AIAA Paper 1981-1259, June 1981. otwiera się w nowej karcie
- Kinsey, D. W., and Barth, T. J., "Description of a Hyperbolic Grid Generation Procedure for Arbitrary Two-Dimensional Bodies," AFWAL TM 84-191-FIMM, Wright-Patterson Air Force Base Aero- nautical Lab., 1984. otwiera się w nowej karcie
- Koziel, S., Echeverría-Ciaurri, D., and Leifsson, L., "Surrogate-Based Methods," Computational Optimization, Methods and Algorithms, Series: Studies in Computational Intelligence, edited by S. Koziel, and X. S. Yang, Springer-Verlag, Berlin, Germany, 2011, pp. 33-60. otwiera się w nowej karcie
- Weryfikacja:
- Politechnika Gdańska
wyświetlono 66 razy
Publikacje, które mogą cię zainteresować
Multi-fidelity aerodynamic design trade-off exploration using point-by-point Pareto set identification
- A. Amrit,
- L. Leifsson,
- S. Kozieł
Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates
- L. Leifsson,
- S. Kozieł,
- Y. Tesfahunegn
Variable-fidelity CFD models and co-Kriging for expedited multi-objective aerodynamic design optimization
- S. Kozieł,
- Y. Tesfahunegn,
- L. Leifsson
Expedited constrained multi-objective aerodynamic shape optimization by means of physics-based surrogates
- S. Kozieł,
- Y. Tesfahunegn,
- L. Leifsson