Summary
The need for robust optimisation in aircraft conceptual design, for which the design parameters are assumed stochastic, is introduced. We highlight two approaches, first-order method of moments and Sigma-Point reduced quadrature, to estimate the mean and variance of the design’s outputs. The method of moments requires the design model’s differentiation and here, since the model is implemented in Matlab, is performed using the automatic differentiation (AD) tool MAD. Gradient-based constrained optimisation of the stochastic model is shown to be more efficient using AD-obtained gradients than finite-differencing. A post-optimality analysis, performed using AD-enabled third-order method of moments and Monte-Carlo analysis, confirms the attractiveness of the Sigma-Point technique for uncertainty propagation.
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References
Barthelemy, J.F., Hall, L.E.: Automatic Differentiation as a Tool in Engineering Desing. TM 107661, NASA (1992)
Bischof, C.H., Griewank, A.: Computational Differentiation and Multidisciplinary Design. In: H. Engl, J. McLaughlin (eds.) Inverse Problems and Optimal Design in Industry, pp. 187–211. Teubner Verlag, Stuttgart (1994)
Chen, W., Allen, J.: A procedure for robust design: Minimizing variations caused by noise factors and control factors. Journal of Mechanical Design 118(4), 478–493 (1996)
Du, X., Chen, W.: Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design. AIAA Journal 40(3), 545–552 (2002)
Forth, S.A.: An efficient overloaded implementation of forward mode automatic differentiation in MATLAB. ACM Trans. Math. Softw. 32(2), 195–222 (2006). DOI: http://doi.acm.org/10.1145/1141885.1141888
Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. No. 19 in Frontiers in Applied Mathematics. SIAM, Philadelphia, PA (2000)
Helton, J.C., Davis, F.J.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Eng. System Safety 81(1), 23–69 (2003)
Huang, B., Du, X.: Uncertainty analysis by dimension reduction integration and saddlepoint approximations. Transactions of the ASME 18, 26–33 (2006)
Lewis, L., Parkinson, A.: Robust optimal design using a second order tolerance model. Research in Engineering Design 6(1), 25–37 (1994)
The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098: MATLAB Optimization Toolbox 3 - User’s guide (2007)
Padulo, M., Campobasso, M.S., Guenov, M.D.: Comparative Analysis of Uncertainty Propagation methods for Robust Engineering Design. In: International Conference on Engineering Design ICED07. Paris (2007)
Park, G.J., Lee, T.H., Lee, K.H., Hwang, K.H.: Robust Design: An Overview. AIAA Journal 44(1), 181–191 (2006)
Parkinson, A., Sorensen, C., Pourhassan: A General Approach for Robust Optimal Design. J. mech. Des 115(1), 74–80 (1993)
Putko, M., Newman, P., Taylor, A., Green, L.: Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives. In: Proceedings of the 15th AIAA Computational Fluid Dynamics Conference. Anaheim CA (2001). AIAA 2001–2528
Su, J., Renaud, J.E.: Automatic Differentiation in Robust Optimization. AIAA Journal 5(6), 1072–1079 (1996)
Tari, M., Dahmani, A.: Refined descriptive sampling: A better approach to Monte Carlo simulation. Simulation Modelling Practice and Theory 14(2), 143–160 (2006)
Torenbeek, E.: Synthesis of Subsonic Airplane Design. Delft University Press, Delft, Holland (1982)
Xiu, D., Karniadakis, E.M.: Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics 187, 137–167 (2003)
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Padulo, M., Forth, S.A., Guenov, M.D. (2008). Robust Aircraft Conceptual Design Using Automatic Differentiation in Matlab. In: Bischof, C.H., Bücker, H.M., Hovland, P., Naumann, U., Utke, J. (eds) Advances in Automatic Differentiation. Lecture Notes in Computational Science and Engineering, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68942-3_24
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DOI: https://doi.org/10.1007/978-3-540-68942-3_24
Publisher Name: Springer, Berlin, Heidelberg
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