Keywords: optimization, robust design, regression techniques.

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 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 [4].

1

Murphy, T.E., Tsui, K. and Allen, J.K., "A review of robust design methods for multiple responses", Research in Engineering Design, 15, 201-215, 2005. doi:10.1007/s00163-004-0054-8

2

Vining, G.G. and Myers, R.H., "Combining Taguchi and response surface philosophies: a dual response approach", J. Qual. Technol., 22, 38-45, 1990.

3

Steenackers, G., Guillaume, P. and Vanlanduit, S., "Structural Design Optimization using Regression Techniques", Proceedings of the 9th International Conference on Optimum Design in Engineering (OPTI9), Skiathos, Greece, 187-196, 2004.

4

Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, second edition, New York: Springer-Verlag, 2004.

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