Robust design with arbitrary distribution using Gauss-type quadrature formula

12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO

Volumn , Issue , 2008, Pages

  Lee, Sang Hoon ^a   Chen, Wei ^a   Kwak, Byung Man ^b  

^a Northwestern University   (United States)

^b Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC DESIGN; ARBITRARY DISTRIBUTION; DESIGN SENSITIVITY ANALYSIS; DIMENSION REDUCTION; FUNCTION CALLS; INTEGRATION METHOD; NON-NORMAL DISTRIBUTION; POINT ESTIMATE METHOD; QUADRATURE FORMULA; ROBUST DESIGN OPTIMIZATION; ROBUST DESIGNS; ROBUST OPTIMIZATION; STATISTICAL MOMENTS; TENSOR PRODUCTS; UNIVARIATE;

DESIGN OF EXPERIMENTS; GAUSSIAN DISTRIBUTION; NORMAL DISTRIBUTION; OPTIMIZATION; TENSORS;

SENSITIVITY ANALYSIS;

EID: 78049500477     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (33)

1. Taguchi, G., and Wu, Y., Introduction to off-line quality control, Central Japan Quality Control Association, Nagoya, Japan, 1980.
2. Phadke, M. S., Quality engineering using robust design, Prentice Hall, Upper Saddle River, NJ, USA, 1995.
3. Parkinson, A., Sorensen, C., and Pourhassan, N., "A general approach for robust optimal design," ASME Journal of Mechanical Design," Vol. 115, 1993, pp. 74-80.
4. Sundaresan, S., Ishii, K., and Houser, D. R., "A robust optimization procedure with variations on design variables and constraints," Engineering Optimization, Vol. 24, 1995, pp. 101-117.
5. Chen, W., Allen, J. K., Tsui, K. L., and Mistree, F. "Procedure for robust design: Minimizing variations caused by noise factors and control factors," ASME Journal of Mechanical Design, Vol. 118, 1996, pp. 478-485.
6. Ramakrishnan, B., and Rao, S. S., "A general loss function based optimization procedure for robust design," Engineering Optimization, Vol. 25, 1996. pp. 255-276.
7. Du, X., and Chen, W., "Towards a better understanding of modeling feasibility robustness in engineering design," ASME Journal of Mechanical Design, Vol. 122, 2000, pp. 385-394.
8. Lee, K. H., and Park, G. J., "Robust optimization considering tolerances of design variables," Computers and Structures, Vol. 79, 2001, pp. 77-86.
9. Jung, D. H., and Lee, B. C., "Development of a simple and efficient method for robust optimization," International Journal for Numerical Methods in Engineering, Vol. 53, 2002, pp. 2201-2215.
10. Han, J. S., and Kwak, B. M., "Robust optimization using a gradient index: Mems applications," Structural and Multidisciplinary Optimization, Vol. 27, 2004, pp. 469-478.
11. Taguchi, G. "Performance analysis design," International Journal of Production Research, Vol. 16, 1978, pp. 521-530.
12. D'Errico, J. R., and Zaino, N. A., "Statistical tolerancing using a modification of Taguchi's method," Technometrics, Vol. 30, (1988), pp. 397-405.
13. Seo, H. S., and Kwak, B. M., "Efficient statistical tolerance analysis for general distributions using three-point information," International Journal of Production Research, Vol. 40, 2002, pp. 931-944.
14. Lee, S. H., and Kwak, B. M., "Response surface augmented moment method for efficient reliability analysis," Structural Safety, Vol. 28, 2006, pp. 261-272.
15. Lee, S. H., Choi, H. S., and Kwak, B. M., "Multi-level design of experiments for statistical moment and probability calculation," Structural and Multidisciplinary Optimization, DOI 10.1007/s00158-007-0215-2, 2008.
16. Rosenblueth, E. "Two point estimates in probabilities," Applied Mathematical Modeling, Vol. 5, 1981, pp. 329-335.
17. Hong, H. P., "An efficient point estimate method for probabilistic analysis," Reliability Engineering and System Safety, Vol. 59, 1998, pp. 261-267.
18. Harr, M. E., "Probability estimate for multivariate analysis," Applied Mathematical Modeling, Vol. 13, 1989, pp. 313-318.
19. Li, K. S., "Point-estimate method for calculating statistical moments," ASCE Journal of Engineering Mechanics, Vol. 118, 1992, pp. 1506-1511.
20. Zhao, Y. G., and Ono, T., "Moment methods for structural reliability," Structural Safety, Vol. 23, 2001, pp. 47-75.
21. Wang, L., Beeson, D., and Wiggs, G., "Efficient and accurate point estimate method for moments and probability distribution estimation," Proceedings of 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, USA, Aug. 30-Sep.1 2004.
22. Abramowitz, M., and Stegun, I. A., Handbook of mathematical functions, with formulas, graphs, and mathematical tables, Dover, New York, 1965.
23. Evans, D. H., "An application of numerical integration techniques to statistical tolerancing," Technometrics, Vol. 9, 1967, pp. 441-456.
24. Rahman, S., and Xu, H., "A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics," Probabilistic Engineering Mechanics, Vol. 19, 2004, pp. 393-408.
25. Krylov, V. I., Approximate calculation of integrals. Translated by AH Stroud. Macmillan, New York, 1962.
26. Hahn, G. J., and Shapiro, S. S., Statistical models in engineering, Wiley, New York, 1967.
27. Gautschi, W., "Algorithm 726; orthpol-a package of routines for generating orthogonal polynomials and gauss-type quadrature rules," ACM Transactions on Mathematical Software, Vol. 20, 1994, pp. 21-62.
28. Rosenblatt, M., "Remarks on a multivariate transformation," Annals of Mathematical Statistics, Vol. 23, 1952, pp. 470-472.
29. Engels, H., Numerical quadrature and cubature. Academic Press, London, 1980.
30. Youn, B. D., Xi, Z., Lee, J. W., and Wang, P., "Enhanced dimension-reduction (edr) method for sensitivity-free uncertainty quantification," Proceedings of 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 6-8 September 2006.
31. Xu, H., and Rahman, S., "A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics," International Journal for Numerical Methods in Engineering, Vol. 61, 2004, pp. 1992-2019.
32. Lee, S. H., and Chen, W., "A comparative study of uncertainty propagation methods for black-box type problems," Structural and Multidisciplinary Optimization, DOI:10.1007/s00158-008-0234-7, 2008.
33. Lee, I., Choi, K. K., Du, L., and Gorsich, D., "Dimension reduction method for reliability-based robust design optimization," Computers and Structures, doi:10.1016/j.compstruc. 2007.05.020, 2007.