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Robustness Measures for Multi-objective Robust Design

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Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS,volume 55)

Abstract

A significant step to engineering design is to take into account uncertainties and to develop optimal designs that are robust with respect to perturbations. Furthermore, when multiple optimization objectives are involved it is important to define suitable descriptions for robustness. We introduce robustness measures for robust design with multiple objectives that are suitable for considering the effect of uncertainties in objective space. A direct formulation and a two-phase formulation based on expected losses in objective space are presented for finding robust optimal solutions. We apply both formulations to the robust design of an airfoil. Fluid mechanical quantities are optimized under the consideration of aleatory uncertainties. The uncertainties are propagated with the help of the non-intrusive polynomial chaos approach. The resulting multi-objective optimization problem is solved with a constraint-based approach, that combines adjoint-based optimization methods and evolutionary methods evaluated on surrogate models.

Keywords

  • Multi-objective optimization
  • Robust design
  • Aerodynamic shape optimization

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  • DOI: 10.1007/978-3-030-57422-2_12
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References

  1. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evolu Comput 6(2):182–197. https://doi.org/10.1109/4235.996017

  2. Deb K, Gupta H (2005) Searching for robust pareto-optimal solutions in multi-objective optimization. In: Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Proceedings of 3rd international conference on evolutionary multi-objective optimization, lecture notes in computer science, vol 3410. Springer, Berlin, pp 150–164. https://doi.org/10.1007/978-3-540-31880-4_11

  3. Kusch L, Gauger NR (2019) Robust airfoil design in the context of multi-objective optimization. In: Minisci E, Vasile M, Periaux J, Gauger N, Giannakoglou K, Quagliarella D (eds) Advances in evolutionary and deterministic methods for design, optimization and control in engineering and sciences, computational methods in applied sciences, vol 48. Springer, Berlin, pp 391–403. https://doi.org/10.1007/978-3-319-89988-6_23

  4. Teich J (1993) Pareto-front exploration with uncertain objectives. In: Zitzler E, Thiele L, Deb K, Coello Coello CA, Corne DW (eds) First international conference on evolutionary multi-criterion optimization, lecture notes in computer science. Springer, Berlin, pp 314–328. https://doi.org/10.1007/3-540-44719-9_22

  5. Li M, Silva R, Guimaraes F, Lowther D (2015) A new robust dominance criterion for multiobjective optimization. IEEE Trans Mag 51(3):1–4. https://doi.org/10.1109/TMAG.2014.2372692

  6. Gunawan S, Azarm S (2005) A feasibility robust optimization method using sensitivity region concept. J Mech Des 127(5):858–865. https://doi.org/10.1115/1.1903000

  7. Xiu D, Karniadakis GM (2002) The wiener-askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644

    Google Scholar 

  8. Marglin SA (1967) Public investment criteria. MIT Press, Cambridge, MA

    Google Scholar 

  9. Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic Publishers, Boston

    Google Scholar 

  10. Kusch L, Gauger NR, Spiller M (2014) Efficient calculation of Pareto-optimal points for shape optimization. In: Full paper compilation: evolutionary and deterministic methods for design, optimization and control with applications to industrial and societal problems—EUROGEN 2013, ISBN 978-84-617-2141-2, Universidad de Las Palmas de Gran Canaria, Spain

    Google Scholar 

  11. Özkaya E, Gauger NR (2019) Global aerodynamic design optimization via primal-dual aggregation method. arXiv:1811.00433v1 (submitted to STAB Proceedings)

  12. Economon TD, Palacios F, Copeland SR, Lukaczyk TW, Alonso JJ (2016) SU2: an open-source suite for multiphysics simulation and design. AIAA J 54(3):828–846. https://doi.org/10.2514/1.J053813

  13. Albring T, Zhou BY, Gauger NR, Sagebaum M (2015) An aerodynamic design framework based on algorithmic differentiation. ERCOFTAC Bull 102:10–16

    Google Scholar 

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Acknowledgements

We would like to thank Lionel Mathelin from LIMSI-CNRS for the joint development of the two-phase approach for multi-objective robust design.

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Correspondence to Lisa Kusch .

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Kusch, L., Gauger, N.R. (2021). Robustness Measures for Multi-objective Robust Design. In: Gaspar-Cunha, A., Periaux, J., Giannakoglou, K.C., Gauger, N.R., Quagliarella, D., Greiner, D. (eds) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-030-57422-2_12

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  • DOI: https://doi.org/10.1007/978-3-030-57422-2_12

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