Abstract
A new quadratic response surface modeling method is presented. In this method, the incomplete small composite design (ISCD) is newly proposed to reduce the number of experimental runs than that of the SCD. Unlike the SCD, the proposed ISCD always gives a unique design assessed on the number of factors, although it may induce the rank-deficiency in the normal equation. Thus, the singular value decomposition (SVD) is employed to solve the normal equation. Then, the duality theory is used to newly develop the conservative least squares fitting (CONFIT) method. This can directly control the over- or the under-estimation behavior of the approximate functions. Finally, the performance of CONFIT is numerically shown by comparing its’ conservativeness with that of conventional fitting method. Also, optimizing one practical design problem numerically shows the effectiveness of the sequential approximate optimization (SAO) combined with the proposed ISCD and CONFIT.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bae, D. S., Kim, H. W., Yoo, H. H. and Suh, M. S., 1999, “A Decoupling Method for Implicit Numerical Integration of Constrained mechanical Systems,”Mechanics of Structures and Machines, Vol. 27, No. 2, pp. 129–141.
Barthelemy, J. F. M and Haftka, R. T., 1993, “Approximation Concepts for Optimum Structural Design-a Review,”Structural Optimization, Vol. 5, pp. 129–144.
Box, G. E. P. and Wilson, K. B., 1951, “On the Experimental Attainment of Optimum Conditions,”Journal of the Royal Statistical Society, Ser. B, Vol. 13, pp. 1–45.
Box, G. E. P. and Hunter, W. G., 1957, “Multifactor Experimental Designs for Exploring Response Surfaces,”Annals of Mathematical Statistics, Vol. 28, pp. 195–241.
Draper, N. R., 1985, “Small Composite Designs,”Technometrics, Vol. 27, No. 2, pp. 173–180.
Draper, N. R. and Lin, D. K., 1990, “Small Response-Surface Designs,”Technometrics, Vol. 32, No.2, pp. 187–194.
Fletcher, R., 1987,Practical Method of Optimization, John Wiley & Sons, Chichester, pp. 219–224.
Han, J. M., Bae, D.S. and Yoo, H.H., 1999, “A Generalized Recursive Formulation for Constrained Mechanical Systems,”Mechanics of Structures and Machines, Vol. 27, No. 3, pp. 293–315.
Hartley, H. O., 1959, “Smallest Composite Designs for Quadratic Response Surfaces,”Biometrics, Vol. 15, pp. 611–624.
Kim, M. S., 2002,Integrated Numerical Optimization Library : INOPL Series- C, www.inopl. com.
Myers, R. M and Montgomery DC, 1995.Response Surface methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, New York. pp. 279–393.
Plackett, R. L. and Burman, J. P., 1946, “The Design of Optimum Multi-factorial Experiments.”Biometrika, Vol. 33., pp. 3–5-325.
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling W. T., 1986,Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, New York, pp. 498–546.
Vanderplaats, G. N., 1984,Numerical Optimization Techniques for Engineering Design with Applications, McGraw-Hill, New York.
Westlake, W. J., 1965, “Composite Designs based on Irregular Fractions of Factorials,”Biometrics, Vol. 21, pp. 324–336.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, MS., Heo, SJ. Conservative quadratic RSM combined with incomplete small composite design and conservative least squares fitting. KSME International Journal 17, 698–707 (2003). https://doi.org/10.1007/BF02983865
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02983865