Evaluation of failure probability via surrogate models

Journal of Computational Physics

Volumn 229, Issue 23, 2010, Pages 8966-8980

  Li, Jing ^a   Xiu, Dongbin ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Failure probability; Polynomial chaos; Sampling; Stochastic computation

Indexed keywords

IMPORTANCE SAMPLING; STOCHASTIC MODELS;

FAILURE PROBABILITY; HYBRID APPROACH; ORIGINAL SYSTEMS; POLYNOMIAL CHAOS; PROBABILITY SPACES; PROPERTY; SAMPLING METHOD; STOCHASTIC COMPUTATIONS; SURROGATE MODELING; SYSTEM RESPONSE;

STOCHASTIC SYSTEMS;

EID: 77956916374     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.08.022     Document Type: Article

References (36)

1. Au S.K., Beck J. A new adaptive importance sampling scheme for reliability calculations. Struct. Safety 1999, 21(2):135-158.
2. Au S.K., Beck J. Estimation of small failure probabilities in high dimensions by subset simulation. Prob. Eng. Mech. 2001, 16:263-277.
3. Bjerager P. Probability integration by directional simulation. J. Eng. Mech. 1988, 114:1285-1302.
4. Bucher C.G., Bourgund U. A fast and efficient response surface approach for structural reliability problems. Struct. Safety 1990, 7:57-66.
5. Cai G.Q., Elishakoff I. Refined second-order reliability analysis. Struct. Safety 1994, 14:235-246.
6. Der Kiureghian A., De Stefano M. Efficient algorithm for second-order reliability analysis. J. Eng. Mech. 1991, 117(12):2904-2923.
7. Der Kiureghian A., Lin H.Z., Hwang S.J. Second-order reliability approximations. J. Eng. Mech. 1987, 113(8):1208-1225.
8. Ditlevsen O., Bjerager P. Methods of structural systems reliability. Struct. Safety 1986, 3:195-229.
9. Engelund S., Rackwitz R. A benchmark study on importance sampling techniques in structural reliability. Struct. Safety 1993, 12:255-276.
10. Faravelli L. Response surface approach for reliability analysis. J. Eng. Mech. 1989, 115(12):2763-2781.
11. Fiessler B., Neumann H.-J., Rackwitz R. Quadratic limit states in structural reliability. J. Eng. Mech. 1979, 105(4):661-676.
12. Gayton N., Bourinet J.M., Lemaire M. CQ2RS: a new statistical approach to the response surface method for reliability analysis. Struct. Safety 2003, 25:99-121.
13. Ghanem R.G., Spanos P. Stochastic Finite Elements: A Spectral Approach 1991, Springer-Verlag.
14. Gupta S., Manohar C.S. An improved response surface method for the determination of failure probability and importance measures. Struct. Safety 2004, 26:123-139.
15. Hohenbichler M., Gollwitzer S., Kruse W., Rackwitz R. New light on first- and second-order reliability methods. Struct. Safety 1987, 4:267-284.
16. Hohenbichler M., Rackwitz R. First-order concepts in system reliability. Struct. Safety 1983, 1:177-188.
17. Hohenbichler M., Rackwitz R. Improvement of second-order reliability estimates by importance sampling. J. Eng. Mech 1988, 114(12):2195-2199.
18. Koutsourelakis P.S., Pradlwarter H.J., Schueller G.I. Reliability of structures in high dimensions part I: algorithms and applications. Prob. Eng. Mech. 2004, 19:409-417.
19. Koyluoglu H.U., Nielsen S.R.K. New approximations for SORM integrals. Struct. Safety 1994, 13:235-246.
20. Melchers R.E. Structural system reliability assessment using directional simulation. Struct. Safety 1994, 16:23-37.
21. Nie J., Ellingwood B.R. Directional methods for structural reliability. Struct. Safety 2000, 22:233-249.
22. Paffrath M., Wever U. Adapted polynomial chaos expansion for failure detection. J. Comput. Phys. 2007, 226(1):263-281.
23. R. Pulch. Polynomial chaos for the computation of failure probabilities in periodic problems. In J. Roos and L. Costa, editors, Scientific Computing in Electrical Engineering SCEE 2008, 2010.
24. Rackwitz R. Reliability analysis - a review and some perspectives. Struct. Safety 2001, 23:365-395.
25. Rajashekhar M.R., Ellingwood B.R. A new look at the response surface approach for reliability analysis. Struct. Safety 1993, 12:205-220.
26. Schueller G.I., Pradlwarter H.J., Koutsourelakis P.S. A critical appraisal of reliability estimation procedures for high dimensions. Prob. Eng. Mech 2004, 19:463-474.
27. Schueller G.I., Stix R. A critical appraisal of methods to determine failure probabilities. Struct. Safety 1987, 4:293-309.
28. Shvartsman S.Y., Hagan M.P., Yacoub A., Dent P., Wiley H.S., Lauffenburger D.A. Autocrine loops with positive feedback enable context-dependent cell signaling. Am. J. Physiol. Cell Physiol. 2002, 282(3):C545-559.
29. Wong F.S. Slope reliability and response surface method. J. Geo. Eng. 1985, 111:32-53.
30. Xiu D. Efficient collocational approach for parametric uncertainty analysis. Comm. Comput. Phys. 2007, 2(2):293-309.
31. Xiu D. Fast numerical methods for stochastic computations: a review. Comm. Comput. Phys. 2009, 5:242-272.
32. Xiu D. Numerical Methods For Stochastic Computations: A Spectral Method Approach 2010, Princeton University Press, Princeton, New Jersey.
33. Xiu D., Hesthaven J.S. High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 2005, 27(3):1118-1139.
34. Xiu D., Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 2002, 24(2):619-644.
35. Xiu D., Karniadakis G.E. Supersensitivity due to uncertain boundary conditions. Int. J. Numer. Meth. Engng. 2004, 61(12):2114-2138.
36. Zhao Y.-G., Ono T. A general procedure for first/second-order reliability method (FORM/SORM). Struct. Safety 1999, 21:95-112.