Abstract
In this paper, we develop an easy-to-implement approximate method to take uncertainties into account during a multidisciplinary optimization. Multidisciplinary robust design usually involves setting up a full uncertainty propagation within the system, requiring major modifications in every discipline and on the shared variables. Uncertainty propagation is an expensive process, but robust solutions can be obtained more easily when the disciplines affected by uncertainties have a significant effect on the objectives of the problem. A heuristic method based on local uncertainty processing (LOUP) is presented here, allowing approximate solving of specific robust optimization problems with minor changes in the initial multidisciplinary system. Uncertainty is processed within the disciplines that it impacts directly, without propagation to the other disciplines. A criterion to verify a posteriori the applicability of the method to a given multidisciplinary system is provided. The LOUP method is applied to an aircraft preliminary design industrial test case, in which it allowed to obtain robust designs whose performance is more stable than the one of deterministic solutions, relatively to uncertain parameter variations.
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References
Agarwal H, Renaud J (2004) Reliability based design optimization using response surfaces in application to multidisciplinary systems. Eng Optim 36(3):291–311. doi:10.1080/03052150410001666578
Alexandrov NM (1995) Multilevel methods for MDO. In: Alexandrov NM, Hussaini MY (eds) Multidisciplinary design optimization—state of the art. In: Proceedings of the ICASE/NASA Langley workshop
Allen JK, Seepersad C, Choi H, Mistree F (2006) Robust design for multiscale and multidisciplinary applications. J Mech Des 128(4):832–843. doi:10.1115/1.2202880
Apley DW, Liu J, Chen W (2006) Understanding the effects of model uncertainty in robust design with computer experiments. J Mech Des 128(4):945–958. doi:10.1115/1.2204974
Beyer HG, Sendhoff B (2007) Robust optimization—a comprehensive survey. Comput Methods Appl Mech Eng 196(33-34):3190–3218. doi:10.1016/j.cma.2007.03.003
Choi HJ, Allen JK, Rosen D, McDowell DL, Mistree F (2005) An inductive design exploration method for the integrated design of multi-scale materials and products. ASME Conference Proceedings 2005(4739X):859–870. doi:10.1115/DETC2005-85335
Cramer EJ, Dennis JE, Frank PD, Lewis RM, Shubin GR (1994) Problem formulation for multidisciplinary optimization. SIAM J Optim 4(4):754–776. doi:10.1137/0804044
Dodson M, Parks GT (2009) Robust aerodynamic design optimization using polynomial chaos. J Aircraft 46(2):635–646. doi:10.2514/1.39419
Du X, Chen W (2002) Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA J 40(3):545–552. doi:10.2514/2.1681
Du X, Wang Y, Chen W (2000) Methods for robust multidisciplinary design. In: AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 41st
Girard A (2004) Approximate methods for propagation of uncertainty with gaussian process models. PhD thesis, University of Glasgow
Gu X, Renaud JE, Batill SM, Brach RM, Budhiraja AS (2000) Worst case propagated uncertainty of multidisciplinary systems in robust design optimization. Struct Multidisc Optim 20(3):190–213. doi:10.1007/s001580050148
Gu XS, Renaud JE, Penninger CL (2006) Implicit uncertainty propagation for robust collaborative optimization. J Mech Des 128(4):1001–1013. doi:10.1115/1.2205869
Jin R (2004) Enhancements of metamodeling techniques in engineering design. PhD thesis, University of Illinois at Chicago
Kleijnen J (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716. doi:10.1016/j.ejor.2007.10.013
Li M, Azarm S (2008) Multiobjective Collaborative robust optimization with interval uncertainty and interdisciplinary uncertainty propagation. J Mech Des 130(8):081402-1–081402-11. doi:10.1115/1.2936898
Liu H, Chen W, Kokkolaras M, Papalambros PY, Kim HM (2006) Probabilistic analytical target cascading: a moment matching formulation for multilevel optimization under uncertainty. J Mech Des 128(4):991–1000. doi:10.1115/1.2205870
Oakley JE, O’Hagan A (2004) Probabilistic sensitivity analysis of complex models: a Bayesian approach. J R Stat Soc Ser B Stat Methodol 66(3):751–769. doi:10.2307/3647504
Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. Adaptive computation and machine learning, MIT Press
Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Statist Sci 4(4):409–423. doi:10.2307/2245858
Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer, Wiley. doi:10.1002/9780470725184
Sobieszczanski-Sobieski J, Haftka RT (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Struct Multidisc Optim 14(1):1–23. doi:10.1007/BF01197554
Wang WS, Orshansky M (2006) Robust estimation of parametric yield under limited descriptions of uncertainty. In: Proceedings of the 2006 IEEE/ACM international conference on computer-aided design, ACM, New York, NY, USA, ICCAD ’06, pp 884–890. doi:10.1145/1233501.1233686
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Baudoui, V., Klotz, P., Hiriart-Urruty, JB. et al. LOcal Uncertainty Processing (LOUP) method for multidisciplinary robust design optimization. Struct Multidisc Optim 46, 711–726 (2012). https://doi.org/10.1007/s00158-012-0798-0
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DOI: https://doi.org/10.1007/s00158-012-0798-0