Abstract
In these lecture notes attention is focused on the use of Response Surface Models as approximation models in engineering optimization. Common strategies are discussed for efficient model construction, based on principles from statistical experimental design theory. Furthermore, modifications of the experimental design theory will be treated, which are necessary and useful on behalf of numerical experimental designs. Finally, guidelines are presented for building and application of response surface models, based on numerical computations.
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References
Atkinson, A.C., and Donev, A.N. (1992). Optimum Experimental Designs. Oxford University Press, Oxford.
Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Clarendon Press, Oxford.
Box, G.E.P., and Draper, N.R. (1987). Emperical Model Building and Response Surfaces. John Wiley, New York.
Box, G.E.P., Hunter, W.G., and Hunter, J.S. (1978). Statistics for Experimenters. John Wiley, New York.
Draper, N.R., and Smith, H. (1998). Applied Regression Analysis. 3td ed., John Wiley, New York.
Fedorov, V.V. (1972). Theory of Optimal Experiments. Academic Press, New York.
Friedman, J.H. (1991). Multivariate Adaptive Regression Splines. The Annals of Statistics, 19: 1–141
Giunta, A., Watson, L.T., Koehler, J. (1998). A Comparison of Approximation Modeling Techniques: Polynomial versus Interpolating Models. 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, paper AIAA-98–4758.
Haftka, R.T., and Gürdal, Z. (1992). Elements of Structural Optimization. Kluwer Academic Publishers, Dordrecht.
Jin, R., Chen, W., Simpson, T.W. (2000). Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, paper AIAA-2000–4801.
Kiefer, J., and Wolfowitz, J. (1959). Optimum Designs in Regression Problems. Canadian Journal of Mathematics, 12: 363–366.
Koehler, J.R., Owen, A.B. (1996). Computer Experiments. In: Handbook of Statistics, vol.13 (eds. Ghosh, S., Rao, C.R. ), Elsevier Science, Amsterdam.
Lancaster, P., Salkauskas, K. (1986). Curve and Surface Fitting: an Introduction. Academic Press, London.
Marquardt, D.W. (1970). Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation. Technometrics, 12: 591–612.
Mitchell, T.J. (1974). An Algorithm for the Construction of D-optimal Experimental Designs. Technometrics, 16: 203–210.
Montgomery, D.C., and Peck, E.A. (1992). Introduction to Linear Regression Analysis. 2 °d ed., John Wiley, New York.
Montgomery, D.C. (1996). Design and Analysis of Experiments, 4t° ed. John Wiley, New York.
Myers, R.H., Montgomery, D.C. (1995). Response Surface Methodology: Process and Product Optimization using Designed Experiments. J. Wiley, New York.
Nagtegaal, R. (1987). Computer Aided Design of Experiments. A program for experimental design and model building. (in Dutch). Report WFW 87.005, Eindhoven University Press.
Powell, M.J.D. (1987). Radial Basis Functions for Multivariable Interpolation: a Review. in: Algorithms for Approximation (eds. Mason, J.C., Cox, M.G.) Oxford University Press, London.
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P. (1989). Design and Analysis of Computer Experiments. Statistical Science, 4: 409–435.
Schoofs, A.J.G., Klink, M.B.M., van Campen, D.H. (1992). Approximation of structural optimization problems by means of designed numerical experiments. Structural Optimization, 4: 206–212.
Schoofs, A.J.G., Houten, M.H. van, Etman, L.F.P., Campen, D.H. van (1997). Global and Mid-Range Function Approximation for Engineering Optimization. Mathematical Methods of Operations Research, 46:.335–359.
Smith, K. (1918). On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function and its Constants and the Guidance They Give Towards a Proper Choice of the Distribution of Observations. Biometrica, 12: 1–85.
Welch, W.J. (1982). Branch and Bound Search for Experimental Designs Based on D-Optimality and Other Criteria. Technometrics, 24: 41–48
Welch, W.J. (1983). A Mean Squared Error Criterion for the Design of Experiments. Biometrica, 70: 205–223.
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Schoofs, A.J.G., Rijpkema, J.J.M. (2001). Response Surface Approximations for Engineering Optimization. In: Blachut, J., Eschenauer, H.A. (eds) Emerging Methods for Multidisciplinary Optimization. International Centre for Mechanical Sciences, vol 425. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2756-8_4
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DOI: https://doi.org/10.1007/978-3-7091-2756-8_4
Publisher Name: Springer, Vienna
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