Metamodel-based importance sampling for structural reliability analysis

Probabilistic Engineering Mechanics

Volumn 33, Issue , 2013, Pages 47-57

  Dubourg, V ^a,b   Sudret, B ^c   Deheeger, F ^a  

^a now at Phimeca Engineering   (France)

^b UNIVERSITÉ CLERMONT AUVERGNE   (France)

^c ETH ZURICH   (Switzerland)

Author keywords

Active learning; Importance sampling; Kriging; Metamodeling error; Random fields

Indexed keywords

ACTIVE LEARNING; FINITE ELEMENT RELIABILITY; KRIGING; METAMODELING; POLYNOMIAL CHAOS EXPANSION; PRESCRIBED PERFORMANCE; RANDOM FIELDS; STRUCTURAL RELIABILITY ANALYSIS;

FINITE ELEMENT METHOD; INTERPOLATION; PROBABILITY; RELIABILITY ANALYSIS; ROBUSTNESS (CONTROL SYSTEMS);

IMPORTANCE SAMPLING;

EID: 84875473938     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2013.02.002     Document Type: Article

References (47)

1. Allen D. The prediction sum of squares as a criterion for selecting prediction variables. Technical Report 23, Department of Statistics, University of Kentucky; 1971.
2. S. Au, and J. Beck A new adaptive importance sampling scheme for reliability calculations Structural Safety 21 2 1999 135 158
3. S. Au, and J. Beck Estimation of small failure probabilities in high dimensions by subset simulation Probabilistic Engineering Mechanics 16 4 2001 263 277 (Pubitemid 33018562)
4. J. Bect, D. Ginsbourger, L. Li, V. Picheny, and E. Vazquez Sequential design of computer experiments for the estimation of a probability of failure Statistics and Computing 22 3 2012 773 793
5. B. Bichon, M. Eldred, L. Swiler, S. Mahadevan, and J. McFarland Efficient global reliability analysis for nonlinear implicit performance functions AIAA Journal 46 10 2008 2459 2468
6. J.-M. Bourinet, F. Deheeger, and M. Lemaire Assessing small failure probabilities by combined subset simulation and support vector machines Structural Safety 33 6 2011 343 353
7. Bourinet J-M, Mattrand C, Dubourg V. A review of recent features and improvements added to FERUM software. In: Proceedings of the ICOSSAR'09, international conference on structural safety and reliability, Osaka, Japan; 2009.
8. K. Breitung Asymptotic approximation for multinormal integrals Journal of Engineering Mechanics 110 3 1984 357 366
9. C. Bucher, and U. Bourgund A fast and efficient response surface approach for structural reliability problems Structural Safety 7 1990 57 66 (Pubitemid 20647315)
10. N. Büchter, E. Ramm, and D. Roehl Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept International Journal for Numerical Methods in Engineering 37 15 1994 2551 2568
11. J. Ching, S. Au, and J. Beck Reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting Computer Methods in Applied Mechanics and Engineering 194 12-16 2005 1557 1579 (Pubitemid 40262942)
12. J. Ching, J. Beck, and S. Au Hybrid subset simulation method for reliability estimation of dynamical systems subject to stochastic excitation Probabilistic Engineering Mechanics 20 3 2005 199 214 (Pubitemid 41145453)
13. B. Cochelin A path-following technique via an asymptotic-numerical method Computers and Structures 53 1994 1181 1192
14. P.-K. Das, and Y. Zheng Cumulative formation of response surface and its use in reliability analysis Probabilistic Engineering Mechanics 15 4 2000 309 315
15. 2SMART method. In: Proceedings of the 10th international conference on applications of statistics and probability in civil engineering (ICASP10), Tokyo, Japan.
16. A. Der Kiureghian, and T. Dakessian Multiple design points in first and second-order reliability Structural Safety 20 1 1998 37 49 (Pubitemid 128403470)
17. A. Der Kiureghian, and M. de Stefano Efficient algorithms for second order reliability analysis Journal of Engineering Mechanics 117 12 1991 2906 2923
18. O. Ditlevsen, and H. Madsen Structural reliability methods 1996 J. Wiley and Sons Chichester
19. Dubourg V. Adaptive surrogate models for reliability analysis and reliability-based design optimization. PhD thesis, Université Blaise Pascal, Clermont-Ferrand, France; 2011.
20. Dubourg V, Bourinet J-M, Sudret B, FE-based reliability analysis of the buckling of shells with random shape, material and thickness imperfections. In: Furuta H, Frangopol D, Shinozuka M. (Eds.), Proceedings of the 10th international conference structural safety and reliability (ICOSSAR'2009), Osaka, Japan; 2009.
21. V. Dubourg, B. Sudret, and J.-M. Bourinet Reliability-based design optimization using Kriging and subset simulation Structural and Multidisciplinary Optimization 44 5 2011 673 690
22. B. Echard, N. Gayton, and M. Lemaire AK-MCS an active learning reliability method combining Kriging and Monte Carlo simulation Structural Safety 33 2 2011 145 154
23. Hurtado J. Structural reliability - Statistical learning perspectives. Volume 17 of lecture notes in applied and computational mechanics. Springer; 2004.
24. I. Kaymaz Application of Kriging method to structural reliability problems Structural Safety 27 2 2005 133 151 (Pubitemid 40019888)
25. S.-H. Kim, and S.-W. Na Response surface method using vector projected sampling points Structural Safety 19 1 1997 3 19 (Pubitemid 127411403)
26. T. Lee, and J. Jung A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO constraint boundary sampling Computers and Structures 86 13-14 2008 1463 1476 (Pubitemid 351609084)
27. S. Lophaven, H. Nielsen, and J. Søndergaard DACE a matlab Kriging toolbox 2002 Technical University of Denmark
28. J. MacQueen Some methods for classification and analysis of multivariate observations L.M. Le Cam, J. Neyman, Proceedings of the Berkeley symposium on mathematical statistics and probability vol. 1 1967 University of California Press Berkeley, CA 281 297
29. M.D. McKay, R.J. Beckman, and W.J. Conover A comparison of three methods for selecting values of input variables in the analysis of output from a computer code Technometrics 2 1979 239 245 (Pubitemid 9452235)
30. R. Melchers Importance sampling in structural systems Structural Safety 6 1989 3 10
31. R. Neal Slice sampling Annals of Statistics 31 2003 705 767
32. Noirfalise C, Bourinet J-M, Fogli M, Cochelin B. Reliability analysis of the buckling of imperfect shells based on the Karhunen-Loève expansion. In: Proceedings of the 8th world congress of computational mechanics (WCCM8) and 5th European congress on computer methods in applied mechanics and engineering (ECCOMAS 2008), Venice, Italy; 2008.
33. J. Oakley Estimating percentiles of uncertain computer code outputs Journal of the Royal Statistical Society: Series C 53 1 2004 83 93 (Pubitemid 38254792)
34. M. Papadrakakis, and N. Lagaros Reliability-based structural optimization using neural networks and Monte Carlo simulation Computer Methods in Applied Mechanics and Engineering 191 32 2002 3491 3507 (Pubitemid 34811229)
35. K. Phoon, S. Huang, and S. Quek Simulation of second-order processes using Karhunen-Loève expansion Computers & Structures 80 12 2002 1049 1060 (Pubitemid 34772001)
36. Picheny V. Improving accuracy and compensating for uncertainty in surrogate modeling. PhD thesis, University of Florida; 2009.
37. V. Picheny, D. Ginsbourger, O. Roustant, and R. Haftka Adaptive designs of experiments for accurate approximation of a target region Journal of Mechanical Design 132 7 2010 071008
38. R. Rackwitz Reliability analysis - review and some perspectives Structural Safety 23 2001 365 395 (Pubitemid 34696460)
39. C. Robert, and G. Casella Monte Carlo statistical methods 2nd ed. 2004 Springer Series in Statistics. Springer Verlag
40. R. Rubinstein, and D. Kroese Simulation and the Monte Carlo method 2008 Wiley Series in Probability and Statistics. Wiley
41. J. Sacks, W. Welch, T. Mitchell, and H. Wynn Design and analysis of computer experiments Statistical Science 4 1989 409 435
42. T. Santner, B. Williams, and W. Notz The design and analysis of computer experiments 2003 Springer New York
43. A.C. Scordelis, and K.S. Lo Computer analysis of cylindrical shells ACI Journal 61 1961 539 561
44. M. Stone Cross-validatory choice and assessment of statistical predictions Journal of the Royal Statistical Society: Series C 36 1974 111 147
45. Vazquez E, Bect J. A sequential Bayesian algorithm to estimate a probability of failure. In: 15th IFAC symposium on system identification. IFAC, Saint-Malo; 2009.
46. W. Welch, R. Buck, J. Sacks, H. Wynn, T. Mitchell, and M. Morris Screening, predicting, and computer experiments Technometrics 34 1992 15 25
47. Y. Zhang, and A. Der Kiureghian Two improved algorithms for reliability analysis R. Rackwitz, G. Augusti, A. Bori, Proceedings of the 6th IFIP WG7.5 on reliability and optimization of structural systems, Assisi, Italy 1995 Chapman & Hall London