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Optimization of aircraft structural components by using nature-inspired algorithms and multi-fidelity approximations

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Abstract

In this work, a flat pressure bulkhead reinforced by an array of beams is designed using a suite of heuristic optimization methods (Ant Colony Optimization, Genetic Algorithms, Particle Swarm Optimization and LifeCycle Optimization), and the Nelder-Mead simplex direct search method. The compromise between numerical performance and computational cost is addressed, calling for inexpensive, yet accurate analysis procedures. At this point, variable fidelity is proposed as a tradeoff solution. The difference between the low-fidelity and high-fidelity models at several points is used to fit a surrogate that corrects the low-fidelity model at other points. This allows faster linear analyses during the optimization; whilst a reduced set of expensive non-linear analyses are run “off-line,” enhancing the linear results according to the physics of the structure. Numerical results report the success of the proposed methodology when applied to aircraft structural components. The main conclusions of the work are (i) the variable fidelity approach enabled the use of intensive computing heuristic optimization techniques; and (ii) this framework succeeded in exploring the design space, providing good initial designs for classical optimization techniques. The final design is obtained when validating the candidate solutions issued from both heuristic and classical optimization. Then, the best design can be chosen by direct comparison of the high-fidelity responses.

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References

  1. Bruhn, E.F.: Analysis and Design of Flight Vehicle Structures. Jacobs Pub (1973)

  2. Niu, M.C., Niu, M.: Airframe Structural Design—Practical Design Information and Data on Aircraft Structures, 2nd edn, pp. 398. Adaso Adastra Engineering Center, USA (1999)

  3. Venter, G., Sobieszczanski-Sobieski, J.: Particle Swarm Optimization. In: Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, USA, AIAA-2002-1235, 22–25 Apr (2002)

  4. Venter, G., Sobieszczanski-Sobieski, J.: Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. In: Proceedings of the 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA (2002)

  5. Viana, F.A.C., Kotinda, G.I., Rade, D.A., Steffen, V., Jr.: Tuning Dynamic Vibration Absorbers by Using Ant Colony Optimization. Comput. Struc (2007). doi:10.1016/j.compstruc.2007.05.009

  6. Giunta, A.A., Balabanov, V., Haim, D., Grossman, B., Mason, W.H., Watson, L. T., Haftka, R. T.: Wing design for a high-speed civil transport using a design of experiments methodology. In: Proceedings of the 6th AIAA/NASA/USAF Multidisciplinary Analysis and Optimization Symposium, Bellevue, pp. 96–4001. WA, USA, AIAA, 4–6 Sept (1996)

  7. Alexandrov, N.M., Lewis, R.M., Gumbert, C.R., Green, L.L., Newman, P.A.: Optimization with Variable-fidelity Models applied to Wing Design. Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, USA, ICASE Technical Report N. 99–49 (1999)

  8. Marduel X., Tribes C., Trépanier J.Y.: Variable-Fidelity Optimization—Efficiency and Robustness. Optim. Eng. 7, 479–500 (2006). doi:10.1007/s11081-006-0351-3

    Article  Google Scholar 

  9. Vitali R., Haftka R.T., Sankar B.V.: Multi-fidelity design of stiffened composite panel with a crack. Struct. Optim. 23(5), 347–356 (2002)

    Article  Google Scholar 

  10. Przemieniecki J.S.: Theory of Matrix Structural, Analysis, pp. 468.. Dover Publications Inc., New York (1985)

    Google Scholar 

  11. Den Hartog J.P.: Advanced Strength of Materials, pp. 70–99. Dover Publications Inc., New York (1952)

    Google Scholar 

  12. Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design, 4th edn. Vanderplaats Research and Development, Inc., Colorado Springs (2005)

  13. Jin R., Chen W., Simpson T.W.: Comparative Studies of Metamodelling Techniques under Multiple Modeling Criteria. Struct. Multidisciplinary Optim. 23, 1–13 (2001). doi:10.1007/s00158-001-0160-4

    Article  Google Scholar 

  14. Simpson T.W., Poplinski J.D., Koch P.N., Allen J.K.: Metamodels for Computer-based Engineering Design: Survey and Recommendations. Eng. Comput. 17(2), 129–150 (2001). doi:10.1007/PL00007198

    Article  Google Scholar 

  15. Queipo N.V., Haftka R.T., Shyy W., Goel T., Vaidyanathan R., Tucker P.K.: Surrogate-Based Analysis and Optimization. Prog. Aerosp. Sci. 41(1), 1–28 (2005). doi:10.1016/j.paerosci.2005.02.001

    Article  Google Scholar 

  16. Montgomery D.C.: Design and Analysis of Experiments, 6th edn. Wiley, New York (2004)

    Google Scholar 

  17. Box G.E.P., Hunter W.G., Hunter J.S.: Statistics for experimenters. Wiley, New York (1978)

    Google Scholar 

  18. Myers R.H., Montgomery D.C.: Response Surface Methodology—Process and Product Optimization using Designed Experiments, 2nd edn. Wiley-Interscience, USA (2002)

    Google Scholar 

  19. Smith M.: Neural Networks for Statistical Modeling. Von Nostrand Reinhold, New York (1993)

    Google Scholar 

  20. Cheng B., Titterington D.M.: Neural Networks—a Review from a Statistical Perspective. Stat. Sci. 9, 2–54 (1994). doi:10.1214/ss/1177010638

    Article  Google Scholar 

  21. Sacks J., Welch W.J., Mitchell T.J., Wynn H.P.: Design and Analysis of Computer Experiments. Stat. Sci. 4(4), 409–435 (1989). doi:10.1214/ss/1177012413

    Article  Google Scholar 

  22. Lophaven, S.N., Nielsen, H.B., Søndergaard, J.: DACE—A MATLAB Kriging Toolbox. Technical Report IMM-TR-2002-12, Informatics and Mathematical Modelling, Technical University of Denmark (2002)

  23. Smola A.J., Scholkopf B.: A tutorial on support vector regression. Stat. Comput. 14, 199–222 (2004). doi:10.1023/B:STCO.0000035301.49549.88

    Article  Google Scholar 

  24. Clarke S.M., Griebsch J.H., Simpson T.W.: Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses. J. Mech. Des. 127, 1077–1087 (2005). doi:10.1115/1.1897403

    Article  Google Scholar 

  25. Meckesheimer M., Booker A.J., Barton R.R., Simpson T.W.: Computationally Inexpensive Metamodel Assessment Strategies. AIAA J. 40(10), 2053–2060 (2002). doi:10.2514/2.1538

    Article  Google Scholar 

  26. Balabanov, V., Venter, G.: Multi-fidelity optimization with high-fidelity analysis and low-fidelity gradients. In Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, USA (2004)

  27. Lagarias J.C., Reeds J.A., Wright M.H., Wright P.E.: Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM J. Optim. 9(1), 112–147 (1998). doi:10.1137/S1052623496303470

    Article  Google Scholar 

  28. Dorigo, M.: Optimization, Learning and Natural Algorithms. PhD thesis, Politecnico di Milano, Italy (1992)

  29. Socha, K.: ACO for continuous and mixed-variable optimization. In: Proceedings in ANTS 2004 - Fourth International Workshop on Ant Colony Optimization and Swarm Intelligence, Brussels, Belgium (2004)

  30. Di Caro G., Dorigo M.: AntNet—Distributed Strigmergic Control for Communication Networks. J. Artif. Intell. Res 9, 317–365 (1998)

    Google Scholar 

  31. Gen M., Cheng R.: Genetic Algorithms and Engineering Optimization. Wiley-Interscience, New York, USA (1999)

    Book  Google Scholar 

  32. Michalewicz Z., Fogel D.B.: How to Solve it—Modern Heuristics, 1st edn. Springer-Verlag, New York, USA (2000)

    Google Scholar 

  33. Haupt R.L., Haupt S.E.: Pratical Genetic Algorithms, 2nd edn. Wiley-Interscience Publication, New York USA (2004)

    Google Scholar 

  34. Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks, pp. 1942–1948. Perth, Australia (1995)

  35. Krink, T., Løvberg, M.: The lifecycle model—combining particle swarm optimisation, genetic algorithms and hill-climbers. In Proceedings of the 7th International Conference on Parallel Problem Solving from Nature, 621–630 (2002)

  36. Rojas J.E., Viana F.A.C., Rade D.A., Steffen V. Jr: Identification of External Forces in Mechanical Systems by using Lifecycle Model and Stress-Stiffening Effect. Mech Syst Signal Process 21(7), 2900–2917 (1998)

    Google Scholar 

  37. Viana, F.A.C., Steffen, V., Jr.: SIMPLE Optimization ToolBox—Users Guide, 2th edn. http://fchegury.110mb.com/, [Cited 5 Nov 2006] (2006)

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Correspondence to Valder Steffen Jr..

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Viana, F.A.C., Steffen, V., Butkewitsch, S. et al. Optimization of aircraft structural components by using nature-inspired algorithms and multi-fidelity approximations. J Glob Optim 45, 427–449 (2009). https://doi.org/10.1007/s10898-008-9383-x

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  • DOI: https://doi.org/10.1007/s10898-008-9383-x

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