First-order saddlepoint approximation for reliability analysis

AIAA Journal

Volumn 42, Issue 6, 2004, Pages 1199-1207

  Du, Xiaoping ^a,c   Sudjianto, Agus ^b,d  

^a MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

^b FORD MOTOR COMPANY   (United States)

^c Department of Mechanical Engineering ^*  (United States)

^d V Engine Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FUNCTIONS; MONTE CARLO METHODS; RANDOM PROCESSES; RELIABILITY; VECTORS;

GRADIENTS; SADDLE-POINTS; VARIABLES;

SYSTEMS ANALYSIS;

EID: 3042691241     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.3877     Document Type: Article

References (34)

1. Frangopol, D. M., and Klisinski, M., "Reliability-Based Structural Optimization," Advances in Design Optimization, edited by H. Adeli, Chapman and Hall, London, 1994, pp. 492-570.
2. Wang, L., Grandhi, R. V., and Hopkins, D. A., "Structural Reliability Optimization Using an Efficient Safety Index Calculation Procedure," International Journal for Numerical Methods in Engineering, Vol. 38, No. 10, 1995, pp. 1721-1738.
3. Tu, J., Choi, K. K., and Young, H. P., "A New Study on Reliability-Based Design Optimization," Journal of Mechanical Engineering, Vol. 121. No. 4, 1999, pp. 557-564.
4. Wu, Y.-T., and Wang, W., "A New Method for Efficient Reliability-Based Design Optimization," Probabilistic Mechanics & Structural Reliability: Proceedings of the 7th Special Conference, American Society of Civil Engineers, New York, 1996, pp. 274-277.
5. Du, X., and Chen, W., "Towards a Better Understanding of Modeling Feasibility Robustness in Engineering," Journal of Mechanical Design, Vol. 122, No. 4, 2000, pp. 357-583.
6. Du, X., and Chen, W., "Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design," AIAA Journal, Vol. 4, No. 3, 2002, pp. 545-552.
7. Du, X., and Chen, W., "Integrated Methodology for Uncertainty Propagation and Management in Simulation-Based Systems Design," AIM Journal, Vol. 38, No. 8, 2000, pp. 1471-1478.
8. Du, X., Sudjianto, A., and Chen, W., "An Integrated framework for Optimization Under Uncertainty Using Inverse Reliability Strategy," Proceedings of 2003 ASME International Design Engineering Technical Conferences and the Computers and Information in Engineering Conference [CD-ROM], American Society of Mechanical Engineers, Fairfield, NJ, 2003.
9. Harbitz, A., "An Efficient Sampling Method for Probability of Failure Calculation," Structural Safety, Vol. 3, No. 2, 1986, pp. 109-115.
10. Hasofer, A. M., and Lind, N. C., "Exact and Invariant Second-Moment Code Format," Journal of the Engineering Mechanics Division, ASCE, Vol. 100(EM1), 1974, pp. 111-121.
11. Breitung, K., "Asymptotic Approximations for Multinomial Integrals," Journal of Engineering Mechanics, Vol. 110, No. 3, 1984, pp. 357-367.
12. Ditlevsen, O., "Generalized Second Moment Reliability Index," Journal of Structural Mechanics, Vol. 7, No. 4, 1979, pp. 435-451.
13. Wu, Y.-T., Millwater, H. R., and Cruse, T. A., "Advance Probabilistic Analysis Method for Implicit Performance Function," AIAA Journal, Vol. 28, No. 9, 1990, pp. 1663-1669.
14. Wu, Y. T., and Wirsching, P. H., "New Algorithm for Structural Reliability Estimation," Journal of Engineering Mechanics, Vol. 113, No. 9, 1987, pp. 1319-1336.
15. Chen, X., and Lind, N. C., "Fast Probability Integration by Three-Parameter Normal Tail Approximation," Structural Safety, Vol. 1, No. 1, 1983, pp. 169-176.
16. Du, X., and Chen, W., "A Most Probable Point Based Method for Uncertainty Analysis," Journal of Design and Manufacturing Automation, Vol. 1, Nos. 1 and 2, 2001, pp. 47-66.
17. Haldar, A., and Mahadevan, S., Reliability Assessment Using Stochastic Finite Element Analysis, Wiley, New York, 2000, pp. 55-104
18. Melchers, R. E., Structural Reliability Analysis and Prediction, Wiley, Chichester, England, U.K. 1999, pp. 32-132.
19. Daniels, H. E., "Saddlepoint Approximations in Statistics," Annals of Mathematical Statistics, Vol. 25, 1954, pp. 631-650.
20. Rosenblatt, M., "Remarks on a Multivariate Transformation," Annals of Mathematical Statistics, Vol. 23, 1952, pp. 470-472.
21. Huzurbazar, S., "Practical Saddlepoint Approximations," American Statistician, Vol. 53, No. 3, 1999, pp. 225-232.
22. Marsh, P. W. N., "Saddlepoint Approximations or Noncentral Quadratic Forms," Econometric Theory, Vol. 14, No. 5, 1998, pp. 539-559.
23. Lugannani, R., and Rice, S. O., "Saddlepoint Approximation for the Distribution of the Sum of Independent Random Variables," Advances in Applied Probability, Vol. 12, 1980, pp. 475-490.
24. Barndorff-Nielsen, O. E., "Inference on Full or Partial Parameters Based on the Standardized Signed Log Likelihood Ratio," Biometrika, Vol. 73, 1986, pp. 307-322.
25. Barndorff-Nielsen, O. E., "Approximate Interval Probabilities," Journal of the Royal Statistical Society, Series B, Vol. 52, 1990, pp. 485-496.
26. Gatto, R., and Ronchetti, E., "General Saddlepoint Approximations of Marginal Densities and Tail Probabilities," Journal of the American Statistical Association, Vol. 91, No. 433, 1996, pp. 666-673.
27. Wood, A. T. A., Booth, J. G. B., and Butler, R. W., "Saddlepoint Approximations to the CDF of Some Statistics with Nonnormal Limit Distributions," Journal of the American Statistical Association, Vol. 422, No. 8, 1993, pp. 480-486.
28. Kuonen, D., "Computer-Intensive Statistical Methods: Saddlepoint Approximations with Applications in Bootstrap and Robust Inference," Ph.D. Dissertation, Dept. of Mathematics, Swiss Federal Inst. of Technology, 2001.
29. Goutis, C., and Casella, G., "Explaining the Saddlepoint Approximation," American Statistician, Vol. 53, No. 3, 1999, pp. 216-224.
30. Jensen, J. L., Saddlepoint Approximations, Clarendon, Oxford, 1995.
31. Mitteau, J. C., "Error Evaluations for the Computation of Failure Probability in Static Structural problems," Probabilistic Engineering Mechanics, Vol. 14, No. 1, 1999, pp. 119-135.
32. Johnson, N. L., and Kotz, S., Continuous Univariate Distributions-2, Wiley, New York, 1970.
33. Read, K. L. Q., "A Lognormal Approximation for the Collector's Problem," American Statistician, Vol. 52, No. 2, 1998, pp. 179-180.
34. Hoffman, R. M., Sudjianto, A., Du, X., and Stout, J., "Robust Piston Design and Optimization Using Piston Secondary Motion Analysis," Society of Automotive Engineers, SAE Paper 2003-01-0148, Warrendale, PA, 2003.