A critical appraisal of reliability estimation procedures for high dimensions

Probabilistic Engineering Mechanics

Volumn 19, Issue 4, 2004, Pages 463-474

  Schueller G I ^a   Pradlwarter, H J ^a   Koutsourelakis, P S ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Approximate methods; Monte Carlo simulation; Reliability; Stochastic structural mechanics; Variance reduction techniques

Indexed keywords

FINITE ELEMENT METHOD; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; RELIABILITY; VECTORS;

APPROXIMATE METHODS; SECOND ORDER RELIABILITY METHODS (SORM); STOCHASTIC STRUCTURAL MECHANICS; VARIANCE REDUCTION TECHNIQUES;

STRUCTURAL ANALYSIS;

EID: 4644289660     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2004.05.004     Document Type: Article

References (33)

1. Markov Chain Monte Carlo Preprint Service. http://www.statslab.cam.ac.uk/mcmc/ .
2. Ang G.L., Ang A.H.-S., Tang W.H. Optimal importance sampling density estimator. J Engng Mech. 118:(6):1992;1146-1163.
3. Au S.K., Beck J. A new adaptive importance sampling scheme for reliability calculations. Struct Safety. 21:(2):1999;135-158.
4. Au S.K., Beck J. Estimation of small failure probabilities in high dimensions by subset simulation. Probab Engng Mech. 16:2001;263-277.
5. Au S.K., Beck J. Important sampling in high dimensions. Struct Safety. 25:(2):2003;139-163.
6. Au S.K., Beck J.L. Subset simulation and its applications to seismic risk based on dynamic analysis. J Engng Mech, ASCE. 129:(8):2003;901.
7. Besag J. Markov Chain Monte Carlo for statistical inference. Technical Report, University of Washington, Seattle, USA; April 2001.
8. Breitung K.W. Asymptotic approximations for probability integrals. Lecture Notes in Mathematics, 1592. 1994;Springer, Berlin.
9. Der Kiureghian A. The geometry of random vibrations and solutions by FORM and SORM. Probab Engng Mech. 15:(1):2000;81-90.
10. Ditlevsen O., Bjerager P. Methods of structural systems reliability. Struct Safety. 3:(3/4):1986;195.
11. Freudenthal A.M. Safety and the probability of structural failure. ASCE Trans. 121:1956;1337-1397.
12. Gilks W.R., Richardson S., Spiegelhalter D.J. Markov chain Monte Carlo in practice. 1996;Chapman & Hall, London.
13. Hohenbichler M. An approximation to the multivariate normal distribution. Mohr G. In reliability theory of structural engineering systems DIALOG 6-82. Proceedings of Euromech 155, Lyngby. June 1982;79-110.
14. Hurtado J.E. An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory. Struct Safety. 26:(3):2004;271-293.
15. Katafygiotis L., Cheung S.H. A novel Markov chain Monte Carlo based simulation method for solving structural reliability problems. Grundmann H., Schuëller G.I. Proceedings of EURODYN 2002, Munich, Germany. 2002;789-794 Swets and Zeitlinger, Lisse.
16. Kijawatworawet W., Pradlwarter H.J., Schuëller G.I. Structural reliability estimation by adaptive importance directional sampling. Shiraishi N., Shinozuka M., Wen Y.K. Proceedings of the Seventh International Conference on Structural Safety and Reliability (ICOSSAR'97), Kyoto, Japan. November 1998;891-897 Balkema, Rotterdam, The Netherlands.
17. Koutsourelakis P.S., Pradlwarter H.J., Schuëller G.I. Reliability of structures in high dimensions. Proc Appl Math Mech (PAMM). 3:(1):2003;495-496.
18. Koutsourelakis P.S., Pradlwarter H.J., Schuëller G.I. Reliability of structures in high dimensions. Part I. Algorithms and applications. Probab Engng Mech. 2004;. this issue. doi:10.1016/j.probengmech.2004.05.001.
19. Liu J.S. Monte Carlo strategies in scientific computing. Springer Series in Statistics. 2001;Springer, Berlin.
20. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equations of state calculations by fast computing. J Chem Phys. 1953.
21. Metropolis N., Ulam S. The Monte Carlo method. J Am Stat Assoc. 44:1949;335-341.
22. Moøller J. Notes on Markov chain Monte Carlo methods. Lecture Notes. Technical Report. 1999;Department of Mathematical Sciences, Aalborg University.
23. Nie J., Ellingwood R. Directional methods for structural reliability. Struct Safety. 22:2000;233.
24. Olsson G., Sandberg A., Dahlblom O. On latin hypercube sampling for structural reliability analysis. Struct Safety. 25:(1):2003;47-68.
25. Pradlwarter H.J., Schenk C.A., Pellissetti M.F., Schuëller G.I., Kreis A., Fransen B., Calvi A., Klein M. Realistic and efficient reliability estimation in space engineering. Computer Meth Appl Mech Engng. 2004;. in press.
26. Rackwitz R. Reliability analysis: a review and some perspectives. Struct Safety. 23:(4):2001;365-395.
27. Schraudolph NN. Optimization of entropy under uncertainty. PhD Thesis, University of California, San Diego; 1995.
28. Schuëller G. Structural reliability: recent advances: Freudenthal lecture. Shiraishi N., Shinozuka M., Wen. Proceedings of the Seventh International Conference on Structural Safety and Reliability (ICOSSAR'97). 1998;3-35 Balkema, Rotterdam, The Netherlands.
29. Schuëller G.I., Stix R. A critical appraisal of methods to determine failure probabilities. Struct Safety. 4:(4):1987;293-309.
30. Tierney L. Markov chains for exploring posterior distributions (with discussion). Ann Stat. 22:1994;1701-1762.
31. Tierney L. Introduction to general state-space Markov chain theory. Gilks W.R., Richardson S., Spiegelhalter D.J. Markov Chain Monte Carlo in practice. 1996;59-88 Chapman & Hall, London. [chapter 4].
32. Torrie G.M., Valleau J.P. Non-physical sampling distributions in Monte Carlo free energy estimation: umbrella sampling. J Comput Phys. 23:(2):1977;187-199.
33. Tvedt L. Distribution of quadratic forms in normal space-application to structural reliability. J Engng Mech. 116:(6):1990;1183-1197.