Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Conservative Quadratic RSM combined with Incomplete Small Composite Design and Conservative Least Squares Fitting

  • Kim, Min-Soo (Graduate School of Automotive Engineering, Kookmin University) ;
  • Heo, Seung-Jin (School of Automotive Engineering, Kookmin University)
  • Published : 2003.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

A new quadratic response surface modeling method is presented. In this method, the incomplete small composite design (ISCD) is newly proposed to .educe 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 ever- 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.

Keywords

References

  1. 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 https://doi.org/10.1080/08905459908915692
  2. Barthelemy, J. F. M. and Haftka, R. T., 1993, 'Approximation Concepts for Optimum Structural Design-a Review,' Structural Optimization, Vol. 5, pp. 129-144 https://doi.org/10.1007/BF01743349
  3. 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
  4. 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 https://doi.org/10.1214/aoms/1177707047
  5. Draper, N. R., 1985, 'Small Composite Designs,' Technometrics, Vol. 27, No.2, pp. 173-180 https://doi.org/10.2307/1268765
  6. Draper, N. R. and Lin, D. K., 1990, 'Small Response-Surface Designs,' Technometrics, Vol. 32, No.2, pp. 187-194 https://doi.org/10.2307/1268862
  7. Fletcher, R., 1987, Practical Method of Optimization, John Wiley & Sons, Chichester, pp. 219-224
  8. 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 https://doi.org/10.1080/08905459908915700
  9. Hartley, H. O., 1959, 'Smallest Composite Designs for Quadratic Response Surfaces,' Biometrics, Vol. 15, pp.611-624 https://doi.org/10.2307/2527658
  10. Kim, M. S., 2002, Integrated Numerical Optimization Library: INOPL Series-C, www.inopl.com
  11. Myers, R. M. and Montgomery D. C., 1995, Response Surface methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, New York, pp.279-393
  12. Plackett, R. L. and Burman, J. P., 1946, 'The Design of Optimum Multi-factorial Experiments,' Biometrika, Vol. 33., pp. 3-5- 325 https://doi.org/10.1093/biomet/33.4.305
  13. 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
  14. Vanderplaats, G. N., 1984, Numerical Optimization Techniques for Engineering Design with Applications, McGraw-Hill, New York
  15. Westlake, W. J., 1965, 'Composite Designs based on Irregular Fractions of Factorials,' Biometrics, Vol. 21, pp. 324-336 https://doi.org/10.2307/2528093