Reduction of ordering effect in reliability-based design optimization using dimension reduction method

AIAA Journal

Volumn 47, Issue 4, 2009, Pages 994-1004

  Noh, Yoojeong ^a,b   Choi, K K ^a,b   Lee, Ikjin ^a,b  

^a UNIVERSITY OF IOWA   (United States)

^b Mechanical and Industrial Engineering Department   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION PARAMETERS; CUMULATIVE DISTRIBUTION FUNCTION; DIMENSION REDUCTION METHOD; FIRST ORDER RELIABILITY METHODS; GAUSSIAN VARIABLES; INDUSTRY APPLICATIONS; INPUT VARIABLES; INVERSE RELIABILITY ANALYSIS; JOINT CUMULATIVE DISTRIBUTION FUNCTION; NUMBER OF DATUM; ORDERING EFFECTS; POINT-BASED; RELIABILITY-BASED DESIGN OPTIMIZATION; SECOND-ORDER RELIABILITY METHODS;

DISTRIBUTION FUNCTIONS; INVERSE PROBLEMS; MACHINE DESIGN; MOORING; QUALITY ASSURANCE; STEEL STRUCTURES; STRUCTURAL ANALYSIS;

RELIABILITY ANALYSIS;

EID: 67649221425     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.40224     Document Type: Article

References (27)

1. Socie, D. F., "Probabilistic Aspects of Fatigue," Fatigue Calculator [online database], 2003, http://www.fatiguecalculator.com/ [retrieved 8 May 2008].
2. Annis, C., "Probabilistic Life Prediction Isn't as Easy as It Looks," Journal of ASTM International, Vol. 1, No. 2, 2004, Paper JAI11557. 10.1520/JAI11557
3. Efstratios, N., Ghiocel, D. M., and Singhal, S., Engineering Design Reliability Handbook, CRC Press, Boca Raton, FL, 2004.
4. Rosenblatt, M., "Remarks on a Multivariate Transformation," Annals of Mathematical Statistics, Vol. 23, No. 3, 1952, pp. 470-472. doi:10.1214/aoms/1177729394
5. Pham, H. (ed.), Springer Handbook of Engineering Statistics, Springer, London, 2006.
6. Lee, I., Choi, K. K., Du, L., and Gorsich, D., "Inverse Analysis Method Using MPP-Based Dimension Reduction for Reliability-Based Design Optimization of Nonlinear and Multi-Dimensional Systems," Computer Methods in Applied Mechanics and Engineering, Vol. 198, No. 1, 2008, pp. 14-27. doi:10.1016/j.cma.2008.03.004
7. Nelsen, R. B., An Introduction to Copulas, Springer, New York, 1999.
8. Bravais, A., "Analyse Mathématique sur les Probabilités des Erreurs de Situation d'un Point," Mémoires présentés par divers Savants à l' Académie Royale des Sciences de l'Institut de France, Vol. 9, 1846, pp. 255-332.
9. Pearson, K., "Mathematical Contributions to the Theory of Evolution, 3: Regression, Heredity and Panmixia," Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 187, 1896, pp. 253-318. doi:10.1098/rsta.1896.0007
10. Embrechts, P., Lindskog, F., and McNeil, A., "Modeling Dependence with Copulas and Applications to Risk Management," Handbook of Heavy Tailed Distributions in Finance, Elsvier, Amsterdam, 2003, Chap. 8, pp. 329-384.
11. Stander, Y., "The Use of Copulas in Risk Management," M.S. Thesis, Univ. of Johannesburg, Johannesburg, South Africa, 2006.
12. Kendall, M., "A New Measure of Rank Correlation," Biometrika, Vol. 30, Nos. 1-2, 1938, pp. 81-89. doi:10.1093/biomet/30.1- 2.81
13. Huard, D., Évin, G., and Favre, A. C., "Bayesian Copula Selection," Computational Statistics and Data Analysis, Vol. 51, No. 2, 2006, pp. 809-822. doi:10.1016/j.csda.2005.08.010
14. Noh, Y., Choi, K. K., and Du, L., "Selection of Copula to Generate Input Joint CDF for RBDO," 34th Design Automation Conference, American Society of Mechanical Engineers, Paper DETC2008-49494, Aug. 2008.
15. Tu, J., and Choi, K. K., "A New Study on Reliability-Based Design Optimization," Journal of Mechanical Design, Vol. 121, No. 4, 1999, pp. 557-564. doi:10.1115/1.2829499
16. Madsen, H. O., Krenk, S., and Lind, N. C., Methods of Structural Safety, Prentice-Hall, Englewood Cliffs, NJ, 1986.
17. Youn, B. D., Choi, K. K., and Du, L., "Enriched Performance Measure Approach for Reliability-Based Design Optimization," AIAA Journal, Vol. 43, No. 4, 2005, pp. 874-884. doi:10.2514/1.6648
18. Hasofer, A. M., and Lind, N. C., "An Exact and Invariant First-Order Reliability Format," Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol. 100, No. EM1, 1974, pp. 111-121.
19. Tu, J., Choi, K. K., and Park, Y. H., "Design Potential Method for Reliability-Based System Parameter Design Using Adaptive Probabilistic Constraint Evaluation," AIAA Journal, Vol. 39, No. 4, 2001, pp. 667-677. doi:10.2514/2.1360
20. Hohenbichler, M., and Rackwitz, R., "Improvement of Second-Order Reliability Estimates by Importance Sampling," Journal of Engineering Mechanics, Vol. 114, No. 12, 1988, pp. 2195-2199. doi:10.1061/ (ASCE)0733-9399 (1988) 114:12 (2195)
21. Breitung, K., "Asymptotic Approximations for Multinormal Integrals," Journal of Engineering Mechanics, Vol. 110, No. 3, 1984, pp. 357-366.
22. Rahman, S., and Wei, D., "A Univariate Approximation at Most Probable Point for Higher-Order Reliability Analysis," International Journal of Solids and Structures, Vol. 43, No. 9, 2006, pp. 2820-2839. doi:10.1016/j.ijsolstr.2005.05.053
23. Wei, D., "A Univariate Decomposition Method for Higher-Order Reliability Analysis and Design Optimization," Ph. D. Dissertation, Mechanical and Industrial Department, Univ. of Iowa, Iowa City, IA, 2006.
24. Xu, H., and Rahman, S., "A Moment-Based Stochastic Method for Response Moment and Reliability Analysis," Proceedings of the 2nd MIT Conference on Computational Fluid and Solid Mechanics, Elsevier, New York, 17-20 June 2003, pp 2402-2404.
25. Atkinson, K. E., An Introduction to Numerical Analysis, Wiley, Hoboken, NJ, 1989, Chap. 5.
26. Ba-abbad, M. A., Nikolaidis, E., and Kapania, R. K., "New Approach For System Reliability-Based Design Optimization," AIAA Journal, Vol. 44, No. 5, 2006, pp. 1087-1096. doi:10.2514/1.17237
27. Schittkowski, K., More Test Examples for Nonlinear Programming Codes, Springer-Verlag, New York, 1987.