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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
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", Civil-Comp Press, Stirlingshire, UK, Paper 90, 2007. doi:10.4203/ccp.86.90
Keywords: optimization, robust design, regression techniques.
This paper concentrates on different optimal and robust design techniques  in combination with response surface models , 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 .
The optimal design solution gives the smallest process bias value where the mean value reaches the target value but also the highest sigma-value is found. The smallest sigma-value is found for the robust design solution optimizing only sigma. In addition, the optimized process mean is not situated in the allowable user-defined 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 sigma-value, 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 (mu-tau) 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 .
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