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Wing stiffness parameterisation for surrogate models

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Abstract

Surrogate models are key enablers for robust, multidisciplinary design in aerospace. However, a critical question for their efficient use remains in terms of how the aircraft should be parameterised into design variables. This study investigates the parameterisation of wing stiffness for a long-range, twin-engine transport aircraft by comparing the predictions of surrogates with different input parameterisations to the outputs of a physics-based aircraft load analysis. The stiffness parameters were defined to be percent changes in wing stiffness versus a baseline aircraft applied on discrete spanwise sections of the wing box. The number of stiffness parameters was varied between 6 and 64 to see if some of the wing box sections could be grouped together by averaging the stiffness changes across the wing section to reduce the dimensionality of the problem. In addition, a sensitivity analysis using Sobol indices was performed which demonstrated which stiffness parameters contributed most to the variability in wing loads during various manoeuver and static and dynamic gust cases. It was found that geometry-based stiffness parameters show poor consistency between parameterisations and thus the stiffness changes applied over discrete sections of the wing cannot be combined into an average stiffness change without a significant sacrifice in accuracy. However, good consistency was shown in the sensitivity of load responses between different parameterisations.

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Abbreviations

DOE:

Design of experiments

FEM:

Finite element model

MDO:

Multidisciplinary design optimisation

OLHS:

Optimised Latin hypercube sampling

PCA:

Principal component analysis

RSM:

Response surface methodology

SMT:

Shear–moment–torque

UQ&M:

Uncertainty quantification and management

References

  1. Prigent, S., Marechal, P., Rondepierre, A., Druot, T., Belleville, M.: A robust optimization methodology for preliminary aircraft design. Eng. Optim. 48, 883–899 (2016)

    Article  MathSciNet  Google Scholar 

  2. Sobieszczanski-Sobieski, J., Haftka, R.T.: Multidisciplinary aerospace design optimisation: survey of recent developments. Struct. Optim. 14, 1–23 (1997)

    Article  Google Scholar 

  3. Du, X., Chen, W.: Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA J. 40, 545–552 (2002)

    Article  Google Scholar 

  4. Xiu, D., Karniadakis, G.E.: The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24, 619–644 (2006)

    Article  MathSciNet  Google Scholar 

  5. Helton, J.C., Davis, F.J.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab. Eng. Syst. Saf. 81, 23–69 (2003)

    Article  Google Scholar 

  6. Forrester, A.I.J., Keane, A.J.: Recent advances in surrogate-based optimisation. Prog. Aerosp. Sci. 45, 50–79 (2009)

    Article  Google Scholar 

  7. Xu, Q., Wehrle,E., Baier, H.: Adaptive and engineering knowledge based metamodeling in multidisciplinary design optimization of aircraft wing structures. In: 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Indianapolis, 17–19 Sep 2012 (2012)

  8. Castellani, M., Lemmens, Y., Cooper, J.E.: Parametric reduced order model approach for rapid dynamic loads prediction. Aerosp. Sci. Technol. 52, 29–40 (2016)

    Article  Google Scholar 

  9. Werter, N.P.M., De Breuker, R.: Aeroelastic tailoring and structural optimisation using an advanced dynamic aeroelastic framework. In: International Forum on Aeroelasticity and Structural Dynamics, Saint Petersburg, 28 June 2015–2 July 2015 (2015)

  10. Tartaruga, I., Cooper, J., Sartor, P., Lowenberg, M., Lemmens, Y.: Geometrical based method for the uncertainty quantification of correlated aircraft loads. J. Aeroelast. Struct. Dyn. 4, 1–20 (2016)

    Google Scholar 

  11. Tartaruga, I., Cooper, J., Sartor, P., Lowenberg, M., Lemmens, Y., Coggon, S.: Efficient prediction and uncertainty propagation of correlated loads. In: 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, 5–9 Jan 2015 (2015)

  12. Lieberman, C., Willcox, K., Ghattas, O.: Parameter and state model reduction for large-scale statistical inverse problems. SIAM J. Sci. Comput. 32, 2523–2542 (2010)

    Article  MathSciNet  Google Scholar 

  13. Morris, M.D., Mitchell, T.J.: Exploratory designs for computational experiments. J. Stat. Plan. Inference 43, 381–402 (1995)

    Article  Google Scholar 

  14. Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55, 271–280 (2001)

    Article  MathSciNet  Google Scholar 

  15. Saltelli, A.: Global Sensitivity Analysis. The Primer, 4.6th edn. Wiley, New York (2008)

    MATH  Google Scholar 

  16. Iorga, L., Malmedy, V., Stodieck, O., Coggon, S., Loxham, J.: Preliminary sizing optimisation of aircraft structures: industrial challenges and practices. In: 6th Aircraft Structural Design Conference, Bristol, 15 Sep 2018 (2018)

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Acknowledgements

This work would not exist without the resources provided by Airbus Group, as well as Joseph Loxham and Lucia Garcia Matas whose constant support has been essential for this project. In addition, the authors wish to thank Clive Staines and Vijay Nelluri whose expertise was invaluable.

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Authors and Affiliations

  1. Airbus Operations Ltd., Pegasus House, Aerospace Ave, Filton, Bristol, BS34 7PA, UK

    Bennett Leong & Simon Coggon

  2. Department of Aerospace Engineering, University of Bristol, Queens Building, University Walk, Bristol, BS8 1TH, UK

    Jonathan Cooper

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  1. Bennett Leong
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  2. Simon Coggon
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  3. Jonathan Cooper
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Correspondence to Bennett Leong.

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Leong, B., Coggon, S. & Cooper, J. Wing stiffness parameterisation for surrogate models. CEAS Aeronaut J 11, 609–622 (2020). https://doi.org/10.1007/s13272-020-00439-w

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  • DOI: https://doi.org/10.1007/s13272-020-00439-w

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