Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method

Mechanical Systems and Signal Processing

Volumn 37, Issue 1-2, 2013, Pages 137-151

  Zhang, Hao ^a   Dai, Hongzhe ^b   Beer, Michael ^c   Wang, Wei ^b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

^c UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Epistemic uncertainty; Imprecise probability; Low discrepancy sequence; Probability box; Quasi Monte Carlo; Structural reliability

Indexed keywords

EPISTEMIC UNCERTAINTIES; IMPRECISE PROBABILITIES; LOW-DISCREPANCY SEQUENCES; PROBABILITY BOX; QUASI-MONTE CARLO; STRUCTURAL RELIABILITY;

GLOBAL OPTIMIZATION; PROBABILITY DISTRIBUTIONS; RANDOM VARIABLES; RELIABILITY ANALYSIS; UNCERTAINTY ANALYSIS;

MONTE CARLO METHODS;

EID: 84876918406     PISSN: 08883270     EISSN: 10961216     Source Type: Journal    
DOI: 10.1016/j.ymssp.2012.03.001     Document Type: Article

References (45)

1. D.A. Alvarez On the calculation of the bounds of probability of events using infinite random sets Int. J. Approximate Reasoning 43 2006 241 267
2. S.K. Au, and J.L. Beck Estimation of small failure probabilities in high dimensions by subset simulation Probab. Eng. Mech. 16 2001 263 277
3. P. Baraldi, I.C. Popescu, E. Zio, Predicting the time to failure of a randomly degrading component by a hybrid monte carlo and possibilistic method, in: IEEE Proceedings of International Conference on Prognostics and Health Management, 2008.
4. O.G. Batarseh, Y. Wang, Reliable simulation with input uncertainties using an interval-based approach, in: IEEE Proceedings of Winter Simulation Conference, 2008.
5. C. Baudrit, D. Dubois, and N. Perrot Representing parametric probabilistic models tainted with imprecision Fuzzy Sets Syst. 159 2008 1913 1928
6. M. Beer Engineering quantification of inconsistent information Int. J. Reliab. Saf. 3 1-3 2009 174 200
7. J. Burkardt, Quasirandom Sequence Generator: Source Codes 〈 http://people.sc.fsu.edu/∼jburkardt/cpp-src/cpp-src.html 〉.
8. R. Cranley, and T.N.L. Patterson Randomization of number theoretic methods for multiple integration SIAM J. Numer. Anal. 13 6 1976 904 914
9. H. Dai, and W. Wang Application of low-discrepancy sampling method in structural reliability analysis Struct. Saf. 31 2009 55 64
10. A. Der Kiureghian, and O. Ditlevsen Aleatory or epistemic? Does it matter? Struct. Saf. 31 2009 105 112
11. B.R. Ellingwood Acceptable risk bases for design of structures Prog. Struct. Eng. Mater. 3 2001 170 179
12. B.R. Ellingwood, and K. Kinali Quantifying and communicating uncertainty in seismic risk assessment Struct. Saf. 31 2009 179 187
13. B.R. Ellingwood, J.G. MacGregor, T.V. Galambos, and C.A. Cornell Probability based load criteria: load factors and load combinations ASCE J. Struct. Div. 108 5 1982 978 997
14. K.T. Fang, and Y. Wang Number-Theoretic Methods in Statistics 1994 Chapman & Hall London
15. S. Ferson, V. Kreinovich, L. Ginzburg, D.S. Myers, Constructing Probability Boxes and Dempster-Shafer Structures, Unabridged Version, Technical Report SAND2002-4015, Sandia National Laboratories, 2003.
16. S. Ferson, V. Kreinovich, L. Ginzburg, D.S. Myers, K. Sentz, Constructing Probability Boxes and Dempster-Shafer Structures, Technical Report SAND2002-4015, Sandia National Laboratories, 2003.
17. S. Ferson, R. Nelsen, J. Hajagos, D. Berleant, J. Zhang, W. Tucker, L. Ginzburg, W. Oberkampf, Dependence in Probabilistic Modeling, Dempster-Shafer Theory, and Probability Bounds Analysis, Technical Report SAND2004-3072, Sandia National Laboratories, 2004.
18. T. Fetz, and M. Oberguggenberger Multivariate models of uncertainty: a local random set approach Struct. Saf. 32 6 2010 417 424
19. G. Fu, D. Butler, S.-T. Khu, and S. Sun Imprecise probabilistic evaluation of sewer flooding in urban drainage systems using random set theory Water Resour. Res. 47 2011 W02534
20. J. Halton On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals Numer. Math. 2 1960 84 90
21. C. Joslyn, S. Ferson, Approximate representations of random intervals for hybrid uncertainty quantification in engineering modeling, in: K. Hanson, F. Hemez (Eds.), Proceedings of 4th International Conference on Sensitivity Analysis of Model Output (SAMO), Santa Fe, New Mexico, USA, 2004, pp. 453-469.
22. M.H. Kalos, and P.A. Whitlock Monte Carlo Methods: Basics vol. 1 1986 John Wiley New York
23. G.J. Klir Uncertainty and Information: Foundations of Generalized Information Theory 2006 Wiley-Interscience
24. L. Kocis, and W.J. Whiten Computational investigations of low-discrepancy sequences ACM Trans. Math. Software 23 2 1997 266 294
25. N.M. Korobov The approximate computation of multiple integrals Dokl. Akad. Nauk SSSR 124 1959 1207 1210 (in Russian)
26. P.S. Koutsourelakis, H.J. Pradlwarter, and G.I. Schuëller Reliability of structures in high dimensions, Part I: algorithms and applications Probab. Eng. Mech. 19 2004 409 417
27. C. Lemieux Monte Carlo and Quasi-Monte Carlo Sampling 2009 Springer New York
28. R.E. Melchers Structural Reliability Analysis and Prediction second ed. 1999 John Wiley & Sons West Sussex, England
29. D. Moens, and D. Vandepitte A survey of non-probabilistic uncertainty treatment in finite element analysis Comput. Methods Appl. Mech. Eng. 194 2005 1527 1555
30. B. Möller, and M. Beer Fuzzy-Randomness-Uncertainty in Civil Engineering and Computational Mechanics 2004 Springer-Verlag
31. B. Möller, and M. Beer Engineering computation under uncertainty-capabilities of non-traditional models Comput. Struct. 86 10 2008 1024 1041
32. B. Möller, M. Beer, W. Graf, and J.-U. Sickert Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness Comput. Struct. 84 2006 585 603
33. B. Möller, W. Graf, and S.H. Nguyen Modeling the life cycle of a structure using fuzzy processes Comput. Aided Civ. Infrastruct. Eng. 19 2004 157 169
34. R.E. Moore Interval Analysis 1966 Prentice-Hall, Inc. Englewood Cliffs, NJ
35. W.J. Morokoff, and R.E. Caflisch Quasi-random sequences and their discrepancies SIAM J. Sci. Comput. 15 1994 1251 1279
36. J. Nie, and B.R. Ellingwood A new directional simulation method for system reliability, Part I: application of deterministic point sets Probab. Eng. Mech. 19 4 2004 425 436
37. J. Nie, and B.R. Ellingwood Finite element-based structural reliability assessment using efficient directional simulation ASCE J. Eng. Mech. 131 3 2005 259 267
38. H. Niederreiter Random Number Generation and Quasi-Monte Carlo Methods 1992 SIAM Philadelphia
39. M. Oberguggenberger, and W. Fellin Reliability bounds through random sets: non-parametric methods and geotechnical applications Comput. Struct. 86 10 2008 1093 1101
40. M. Shinoda Quasi-Monte Carlo simulation with low-discrepancy sequence for reinforced soil slopes ASCE J. Struct. Eng. 133 4 2007 393 404
41. P. Walley Statistical Reasoning with Imprecise Probabilities 1991 Chapman and Hall London
42. P. Walley Towards a unified theory of imprecise probability Int. J. Approximate Reasoning 24 2000 125 148
43. H. Zhang, Nondeterministic Linear Static Finite Element Analysis: An Interval Approach, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA, USA, 2005.
44. H. Zhang, R.L. Mullen, and R.L. Muhanna Interval Monte Carlo methods for structural reliability Struct. Saf. 32 2010 183 190
45. M. Zhang, M. Beer, S.T. Quek, and Y.S. Choo Comparison of uncertainty models in reliability analysis of offshore structures under marine corrosion Struct. Saf. 32 2010 425 432