Metamodel-based importance sampling for the simulation of rare events

Applications of Statistics and Probability in Civil Engineering -Proceedings of the 11th International Conference on Applications of Statistics and Probability in Civil Engineering

Volumn , Issue , 2011, Pages 661-668

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

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b now at Phimeca Engineering   (France)

Author keywords

[No Author keywords available]

Indexed keywords

PROBABILITY; RELIABILITY ANALYSIS;

COMPUTER EXPERIMENT; KRIGING META MODELS; MONTE CARLO ESTIMATORS; REAL ENGINEERING; REFERENCE PROBABILITY; RELIABILITY METHODS; STRUCTURAL RELIABILITY; STRUCTURAL RELIABILITY ANALYSIS;

IMPORTANCE SAMPLING;

EID: 84856738165     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1201/b11332-100     Document Type: Conference Paper

References (28)

1. Au, S. & J. Beck (2001). Estimation of small failure probabilities in high dimensions by subset simulation. Prob. Eng. Mech. 16(4), 263-277.
2. Bichon, B., M. Eldred, L. Swiler, S. Mahadevan, & J. McFarland (2008). Efficient global reliability analysis for nonlinear implicit performance functions. AIAA Journal 46(10), 2459-2468.
3. Bourinet, J.-M., F. Deheeger, & M. Lemaire (2010). Assessing small failure probabilities by combined subset simulation and support vector machines. Submitted to Structural Safety.
4. Bourinet, J.-M., C. Mattrand, & V. Dubourg (2009). A review of recent features and improvements added to FERUM software. In Proc. ICOSSAR'09, Int Conf. on Structural Safety And Reliability, Osaka, Japan.
5. Bucher, C. & U. Bourgund (1990). A fast and efficient response surface approach for structural reliability problems. Structural Safety 7(1), 57-66.
6. Cannamela, C., J. Garnier, & B. Iooss (2008). Controlled stratification for quantile estimation. Annals of Applied Statistics 2(4), 1554-1580.
7. Deheeger, F. (2008). Couplage mécano-fiabiliste, 2SMARTméthodologie d'apprentissage stochastique en fiabilité. Ph.D. thesis, Université Blaise Pascal-Clermont II.
8. Deheeger, F. & M. Lemaire (2007). Support vector machine for efficient subset simulations: 2SMART method. In Proc. 10th Int. Conf. on Applications of Stat. and Prob. in Civil Engineering (ICASP10), Tokyo, Japan.
9. der Kiureghian, A. & T. Dakessian (1998). Multiple design points in first and second-order reliability. Structural Safety 20(1), 37-49.
10. Ditlevsen, O. & H. Madsen (1996). Structural reliability methods (Internet (v2.3.7, June-Sept 2007) ed.). John Wiley & Sons Ltd, Chichester.
11. Dubourg, V., B. Sudret, & J.-M. Bourinet (2011). Reliability-based design optimization using kriging and subset simulation. Struct. Multidisc. Optim. Accepted.
12. eDF, R&D Division (2006). Code-Aster: Analyse des structures et thermo-mécanique pour des études et des recherches, V.7. http://www.code-aster.org.
13. Hurtado, J. (2004). Structural reliability-Statistical learning perspectives, Volume 17 of Lecture notes in applied and computational mechanics. Springer.
14. Kaymaz, I. (2005). Application of kriging method to structural reliability problems. Structural Safety 27(2), 133-151.
15. Lebrun, R. & A. Dutfoy (2009). An innovating analysis of the Nataf transformation from the copula viewpoint. Prob. Eng. Mech. 24(3), 312-320.
16. Lee, T. & J. Jung (2008). A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: Constraint boundary sampling. Computers & Structures 86(13-14), 1463-1476.
17. Lemaire, M. (2009). Structural Reliability. John Wiley & Sons Inc.
18. MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In J. Le Cam, L.M. & Neyman (Ed.), Proc. 5th Berkeley Symp. on Math. Stat. & Prob., Volume 1, Berkeley, CA, pp. 281-297. University of California Press.
19. Melchers, R. (1989). Importance sampling in structural systems. Structural Safety 6(1), 3-10.
20. Neal, R. (2003). Slice sampling. Annals Stat., 31, 705-767.
21. Papadrakakis, M. & N. Lagaros (2002). Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput. Methods Appl. Mech. Engrg. 191(32), 3491-3507.
22. Phoon, K., S. Huang, & S. Quek (2002). Simulation of second-order processes using Karhunen-Loève expansion. Computers & Structures 80(12), 1049-1060.
23. Picheny, V. (2009). Improving accuracy and compensating for uncertainty in surrogate modeling. Ph.D. thesis, University of Florida.
24. Platt, J. (1999). Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In Advances in large margin classifiers, pp. 61-74. MIT Press.
25. Rubinstein, R. & D. Kroese (2008). Simulation and the Monte Carlo method. Wiley Series in Probability and Statistics. Wiley.
26. Santner, T., B. Williams, & W. Notz (2003). The design and analysis of computer experiments. Springer series in Statistics. Springer.
27. Severini, T. (2005). Elements of distribution theory. Cambridge series in Statistical and Probabilistic mathematics. Cambridge University Press.
28. Vapnik, V. (1995). The nature of statistical learning theory. Springer.