Advanced Line Sampling for efficient robust reliability analysis

Structural Safety

Volumn 52, Issue PB, 2015, Pages 170-182

  de Angelis, Marco ^a   Patelli, Edoardo ^a   Beer, Michael ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Aleatory and epistemic uncertainty; Credal sets; Failure probability; Generalized uncertainty model; Line Sampling; Monte Carlo

Indexed keywords

DISTRIBUTION FUNCTIONS; MONTE CARLO METHODS; NUMERICAL METHODS; OPEN SOURCE SOFTWARE; OPEN SYSTEMS; PROBABILITY DISTRIBUTIONS; RISK ANALYSIS; RISK ASSESSMENT; SOFTWARE ENGINEERING; UNCERTAINTY ANALYSIS;

ALEATORY AND EPISTEMIC UNCERTAINTIES; CREDAL SETS; FAILURE PROBABILITY; LINE SAMPLINGS; UNCERTAINTY MODELING;

RELIABILITY ANALYSIS;

EID: 84918586942     PISSN: 01674730     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.strusafe.2014.10.002     Document Type: Article

References (35)

1. Barlow R.E., Proschan F. Mathematical theory of reliability 1996, vol. 17. Siam.
2. Sklar A. Random variables, distribution functions, and copulas - a personal look backward and forward. Distributions with fixed marginals and related topics 1996, 1-14. Institute of Mathematical Statistics, Hayward, CA. L. Rüschendorf, B. Schweizer, M. Taylor (Eds.).
3. Bjerager P. On computation methods for structural reliability analysis. Struct Saf 1990, 9(2):79-96.
4. Hammersley J., Handscomb D. Monte Carlo methods 1964, Methuen & Co Ltd, London, New York.
5. Metropolis N., Ulam S. The Monte Carlo method. J Am Stat Assoc 1949, 44(247):335-341.
6. Melchers R. Importance sampling in structural systems. Struct Saf 1989, 6(1):3-10.
7. Engelund S., Rackwitz R. A benchmark study on importance sampling techniques in structural reliability. Struct Saf 1993, 12(4):255-276.
8. Ditlevsen O., Bjerager P., Olesen R., Hasofer A. Directional simulation in gaussian processes. Probab Eng Mech 1988, 3(4):207-217.
9. Ditlevsen O., Melchers R.E., Gluver H. General multi-dimensional probability integration by directional simulation. Comput Struct 1990, 36(2):355-368.
10. Koutsourelakis P., Pradlwarter H., Schuëller G. Reliability of structures in high dimensions, part i: algorithms and applications. Probab Eng Mech 2004, 19(4):409-417.
11. Koutsourelakis P. Reliability of structures in high dimensions. part ii. theoretical validation. Probab Eng Mech 2004, 19(4):419-423.
12. Au S.-K., Beck J.L. Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 2001, 16(4):263-277.
13. Der Kiureghian A. Analysis of structural reliability under parameter uncertainties. Probab Eng Mech 2008, 23(4):351-358.
14. Ditlevsen O., Madsen H.O. Structural reliability methods 2007, vol. 178. CiteSeer.
15. Der Kiureghian A., Liu P.-L. Structural reliability under incomplete probability information. J Eng Mech 1986, 112(1):85-104.
16. Beer M., Ferson S., Kreinovich V. Imprecise probabilities in engineering analyses. Mech Syst Signal Process 2013, 37(1):4-29.
17. Beck J.L., Katafygiotis L.S. Updating models and their uncertainties. i: Bayesian statistical framework. J Eng Mech, ASCE 1998, 124(4):455-461.
18. Moens D., Vandepitte D. A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Methods Appl Mech Eng 2005, 194(12):1527-1555.
19. Moore R., Lodwick W. Interval analysis and fuzzy set theory. Fuzzy Sets Syst 2003, 135(1):5-9.
20. Ferson S., Kreinovich V., Hajagos J., Oberkampf W., Ginzburg L. Experimental Uncertainty Estimation and Statistics for Data having Interval Uncertainty 2007, Sandia National Laboratories.
21. Ben-Haim Y. A non-probabilistic concept of reliability. Struct Saf 1994, 14(4):227-245.
22. Tonon F. Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliab Eng Syst Saf 2004, 85(1):169-181.
23. Möller B., Graf W., Beer M. Fuzzy structural analysis using α-level optimization. Comput Mech 2000, 26(6):547-565.
24. Zadeh LA Fuzzy sets. Inf Control 1965, 8(3):338-353.
25. Zaffalon M. The naive credal classifier. J Stat Plan Inference 2002, 105(1):5-21.
26. Nelsen R.B. An introduction to copulas. Springer series in statistics 2010, Springer, New York. 2nd ed.
27. Jiang C., Han X., Lu G., Liu J., Zhang Z., Bai Y. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Comput Methods Appl Mech Eng 2011, 200(33):2528-2546.
28. Valdebenito M., Pradlwarter H., Schuëller G. The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities. Struct Saf 2010, 32(2):101-111.
29. Patelli E., Panayirci H.M., Broggi M., Goller B., Beaurepaire P., Pradlwarter H.J., et al. General purpose software for efficient uncertainty management of large finite element models. Finite Elem Anal Des 2012, 51:31-48.
30. Patelli E., Pradlwarter H. Monte Carlo gradient estimation in high dimensions. Int J Numer Methods Eng 2010, 81(2):172-188.
31. Breitung K. Asymptotic approximations for multinormal integrals. J Eng Mech 1984, 110(3):357-366.
32. Goldberg D.E., et al. Genetic algorithms in search, optimization, and machine learning 1989, vol. 412. Addison-wesley, Reading Menlo Park.
33. Powell M.J. The BOBYQA algorithm for bound constrained optimization without derivatives, Cambridge NA report NA2009/06 2009, University of Cambridge, Cambridge.
34. Patelli E., Broggi M., de Angelis M., Beer M. OpenCossan: an efficient open tool for dealing with epistemic and aleatory uncertainties. Vulnerability, Uncertainty, and Risk: Analysis, Modeling, and Management 2014, American Society of Civil Engineers. I.S.K. Au, J.W. Hall, M. Beer (Eds.).
35. Larman C. Applying UML and patterns: an introduction to object-oriented analysis and design and iterative development, 3/e 2012, Pearson Education India.