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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 90
Robust Optimization of a Slat Track taking into account the Uncertainty of the Design Parameters G. Steenackers and P. Guillaume
Acoustics & Vibration Research Group, Department of Mechanical Engineering, Vrije Universiteit Brussel, Belgium G. Steenackers, P. Guillaume, "Robust Optimization of a Slat Track taking into account the Uncertainty of the Design Parameters", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 90, 2007. doi:10.4203/ccp.86.90
Keywords: optimization, robust design, regression techniques.
Summary
This paper concentrates on different optimal and robust design
techniques [1] in combination with response surface
models [2], taking into account the uncertainty of the
design parameters. Analytical expressions for the process mean and
variance are derived, both consisting of one and two design
parameter inputs and taking into account the uncertainty in the
parameters. Application and comparison of different optimal,
robust and generalized optimization approaches is suggested and
applied on a slat track finite element model, making use of mean
and variance response functions to model the uncertainty of the
finite element displacement values [3].
The optimal design solution gives the smallest process bias value where the mean value reaches the target value but also the highest sigmavalue is found. The smallest sigmavalue is found for the robust design solution optimizing only sigma. In addition, the optimized process mean is not situated in the allowable userdefined target region and the inequality constraint is not automatically satisfied. By making use of Lagrange multipliers, the process bias is reduced to the specified boundary value on the expense of the minimized sigmavalue, that has increased. When considering the mean squared error for the different objective function expressions, one finds the smallest value for the objective function consisting of both (mutau) and sigma as elements. The best compromise solution is typically gained by optimizing an objective function, which incorporates the prioritized demands of multiple responses. One can also conclude that for this slat track model, using Monte Carlo simulations in combination with finite element calculations is in practice not appropriate to generate accurate response surfaces to model parameter and output uncertainty. Even with the same number of finite element calculations, the calculated regression surfaces based on a coarse FE calculation grid will still yield a more accurate representation of the variance or uncertainty of the finite element output in contradiction to the Monte Carlo calculations [4]. References
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