Technical Papers
Sep 29, 2016

Particle Swarm Optimization of Aerodynamic Shapes with Nonuniform Shape Parameter–Based Radial Basis Function

Publication: Journal of Aerospace Engineering
Volume 30, Issue 3

Abstract

Efficient global optimization of aerodynamic shapes with the high-fidelity method is of great importance in the design process of modern aircrafts. In this study, modifications are made to the particle swarm optimization (PSO) algorithm and the radial basis function (RBF) model for further improvements of efficiency and accuracy of optimization. Specifically, a PSO algorithm with randomly distributed cognitive and social parameters, exponential decrease of maximum velocity and inertia weight, and periodic mutation of particle position is proposed. Furthermore, a nonuniform shape parameters strategy is introduced for the RBF surrogate model. Validations on test functions show that the new PSO has remarkable speed of convergence, and the new RBF model has superior approximation accuracy. The PSO algorithm and RBF model are then combined to construct the computational fluid dynamics (CFD)–based optimization framework. Finally, optimizations of transonic airfoil and supersonic launch vehicle are performed and results show that the drag coefficients in the two cases are significantly reduced (14 and 15%, respectively). The successful applications also indicate that the proposed PSO and RBF as a whole have apparent advantages over their original versions, and the optimization framework is effective and practical for design of aerodynamic shapes.

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Acknowledgments

This work was supported by the State Key Development Program for Basic Research of China (Grant No. 2014CB340201) and the National Natural Science Foundation of China (Grant No. 11572284).

References

Acar, E. (2010). “Optimizing the shape parameters of radial basis functions: An application to automobile crashworthiness.” Proc. Inst. Mech. Eng. Part D: J. Automobile Eng., 224(12), 1541–1553.
Ahmed, M. Y. M., and Qin, N. (2012). “Surrogate-based multi-objective aerothermodynamic design optimization of hypersonic spiked bodies.” AIAA J., 50(4), 797–810.
Benini, E., and Ponza, R. (2010). “Nonparametric fitting of aerodynamic data using smoothing thin-plate splines.” AIAA J., 48(7), 1403–1419.
Buhmann, M. D. (2003). Radial basis functions: Theory and implementations, Cambridge University Press, Cambridge, U.K.
Carlson, R. E., and Foley, T. A. (1991). “The parameter R2 in multiquadric interpolation.” Comput. Math. Appl., 21(9), 29–42.
Diaz-Manriquez, A., Toscano-Pulido, G., and Gomez-Flores, W. (2011). “On the selection of surrogate models in evolutionary optimization algorithms.” IEEE Congress of Evolutionary Computation (CEC), Institute of Electrical and Electronics Engineers Congress, IEEE Computational Intelligence Society, New York.
Duvigneau, R. (2006). “Adaptive parameterization using free-form deformation for aerodynamic shape optimization.”, Institut national de recherche en informatique et en automatique (INRIA), Sophia Antipolis, France.
Forrester, A., Sobester, A., and Keane, A. (2008). Engineering design via surrogate modelling: A practical guide, Wiley, Chichester, U.K.
Franke, R. (1982). “Scattered data interpolation: Tests of some methods.” Math. Comput., 38(157), 181–200.
Golbabai, A., and Rabiei, H. (2012). “Hybrid shape parameter strategy for the RBF approximation of vibrating systems.” Int. J. Comput. Math., 89(17), 2410–2427.
Hardy, R. L. (1971). “Multiquadric equations of topography and other irregular surfaces.” J. Geophys. Res., 76(8), 1905–1915.
Huang, W., Li, S., Yan, L., and Tan, J. (2014). “Multiobjective design optimization of a cantilevered ramp injector using the surrogate-assisted evolutionary algorithm.” J. Aerosp. Eng., .
Jakubcová, M., Máca, P., and Pech, P. (2014). “A comparison of selected modifications of the particle swarm optimization algorithm.” J. Appl. Math., 2014, 293087.
Jones, D. R., Schonlau, M., and Welch, W. J. (1998). “Efficient global optimization of expensive black-box functions.” J. Global Optim., 13(4), 455–492.
Kennedy, J., and Eberhart, R. C. (1995). “Particle swarm optimization.” Proc., IEEE Int. Conf. on Neural Networks, IEEE, New York.
Kim, K. H., Kim, C., and Rho, O. (2001). “Methods for the accurate computations of hypersonic flows. I: AUSMPW+ scheme.” J. Comput. Phys., 174(1), 38–80.
Li, J., Gao, Z. H., Huang, J. T., and Zhao, K. (2013). “Aerodynamic design optimization of nacelle/pylon position on an aircraft.” Chin. J. Aeronaut., 26(4), 850–857.
Liu, D. (2012). “Research on PID parameters tuning based on improved PSO algorithm.” Master’s thesis, Univ. of South China, Changsha, China.
Ma, Y., Wang, D. D., Yang, T., Feng, Z. W., and Zhang, Q. B. (2014). “Optimization design of shroud configuration of transporter based on surrogate model.” J. Aerosp. Power, 29(1), 192–198.
Martinelli, L., and Jameson, A. (2013). “Computational aerodynamics: Solvers and shape optimization.” J. Heat Transfer, 135(1), 11002.
Menter, F. R., Kuntz, M., and Langtry, R. B. (2003). “Ten years of industrial experience with the SST turbulence model.” 4th Int. Symp. on Turbulence, Heat and Mass Transfer, International Centre for Heat and Mass Transfer (ICHMT), Ankara, Turkey.
Mullur, A. A., and Messac, A. (2005). “Extended radial basis functions: More flexible and effective metamodeling.” AIAA J., 43(6), 1306–1315.
Pehlivanoglu, Y. V. (2013). “A new particle swarm optimization method enhanced with a periodic mutation strategy and neural networks.” Evol. Comput. IEEE Trans. on, 17(3), 436–452.
Peter, J., and Marcelet, M. (2008). “Comparison of surrogate models for turbomachinery design.” WSEAS Trans. Fluid Mech., 3(1), 10–17.
Praveen, C., and Duvigneau, R. (2009). “Low cost PSO using metamodels and inexact pre-evaluation: Application to aerodynamic shape design.” Comput. Methods Appl. Mech. Eng., 198(9), 1087–1096.
Rippa, S. (1999). “An algorithm for selecting a good value for the parameter c in radial basis function interpolation.” Adv. Comput. Math., 11(2–3), 193–210.
Roque, C., and Ferreira, A. J. (2010). “Numerical experiments on optimal shape parameters for radial basis functions.” Numer. Methods Partial Differ. Equ., 26(3), 675–689.
Sederberg, T. W., and Parry, S. R. (1986). “Free-form deformation of solid geometric models.” Proc., 13th Annual Conf. on Computer Graphics and Interactive Techniques, Association for Computing Machinery (ACM), New York.
Shao, C., Cao, Y. F., Zou, L., and Chen, W. F. (2015). “Active flow control applications with zero new mass flux actuator in flow field of supersonic inlet.” Eng. Mech., 32(4), 206–211.
Shi, Y., and Eberhart, R. (1998). “A modified particle swarm optimizer.” Proc., IEEE Int. Conf. on Evolutionary Computation, IEEE, New York.
Thompson, J. F., Soni, B. K., and Weatherill, N. P. (1998). Handbook of grid generation, CRC Press, Boca Raton.
Venter, G., and Sobieszczanski-Sobieski, J. (2004). “Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization.” Struct. Multidiscip. Optim., 26(1–2), 121–131.
Wang, B. P. (2004). “Parameter optimization in multiquadric response surface approximations.” Struct. Multidiscip. Optim., 26(3–4), 219–223.
Yoon, S., and Jameson, A. (1988). “Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations.” AIAA J., 26(9), 1025–1026.
Zhan, Z. H., Zhang, J., Li, Y., and Chung, H. S.-H. (2009). “Adaptive particle swarm optimization.” IEEE Trans. Syst. Man Cybern. Part B: Cybern., 39(6), 1362–1381.
Zhang, W., and Sun, M. (2013). “Design optimization of aerodynamic shapes of a wing and its winglet using modified quantum-behaved particle swarm optimization algorithm.” Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng., 228(9), 1638–1647.

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Go to Journal of Aerospace Engineering
Journal of Aerospace Engineering
Volume 30Issue 3May 2017

History

Received: May 31, 2015
Accepted: Jul 6, 2016
Published online: Sep 29, 2016
Discussion open until: Feb 28, 2017
Published in print: May 1, 2017

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Authors

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Chen-chao Xia [email protected]
Ph.D. Candidate, School of Aeronautics and Astronautics, Zhejiang Univ., Zhejiang 310027, China. E-mail: [email protected]
Ting-ting Jiang [email protected]
Ph.D. Candidate, School of Aeronautics and Astronautics, Zhejiang Univ., Zhejiang 310027, China. E-mail: [email protected]
Wei-fang Chen [email protected]
Professor, School of Aeronautics and Astronautics, Zhejiang Univ., Zhejiang 310027, China (corresponding author). E-mail: [email protected]

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