Finite Element-Based Structural Reliability Assessment Using Efficient Directional Simulation
Publication: Journal of Engineering Mechanics
Volume 131, Issue 3
Abstract
Reliability analysis of structural systems often requires finite element (FE)-based simulation to estimate failure probabilities. Common simulation methods, even those incorporating variation reduction techniques, usually involve a very large number of FE analyses to achieve acceptable accuracy. A recently developed directional approach significantly improves the efficiency of directional simulation by utilizing deterministic point sets to preserve the underlying joint probability distribution of the random vector describing the structure and by employing neural networks to focus the simulation effort in the significant regions. This paper investigates the application of this method to structural system reliability analysis. The method is illustrated using deformation-based system limit states, proposed for performance-based engineering, for two plane steel frames.
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Acknowledgments
The research described in this paper was supported, in part, by the National Science Foundation under Grant No. CMS-0084590, Reliability-based simulation basis for performance-based design, and by Sandia National Laboratory under Award No. A0356-15896, Decision-theoretic methods for performance-based structural engineering. This support is gratefully acknowledged.
References
American Institute of Steel Construction (AISC). (1999). Load & resistance factor design, 3rd Ed., AISC, Chicago.
Bjerager, P. (1988). “Probability integration by directional simulation.” J. Eng. Mech., 114(8), 1288–1302.
Borri, A., and Speranzini, E. (1997). “Structural reliability analysis using a standard deterministic finite element code.” Struct. Safety, 19(4), 361–382.
Conway, J. H., and Sloane, N. J. A. (1998). Sphere packings, lattices and groups, 3rd Ed., Springer-Verlag, New York.
Ditlevsen, O., Melchers, R. E., and Gluver, H. (1990). “General multi-dimensional probability integration by directional simulation.” Comput. Struct., 36(2), 355–368.
Ellingwood, B. R. (1994). “Probability-based codified design: Past accomplishments and future challenges.” Struct. Safety, 13(3), 159–176.
Ellingwood, B. R. (1998). “Reliability-based performance concept for building construction.” Proc., Structural Engineers World Congress at San Francisco, Elsevier, Chicago.
Ellingwood, B. R. (2001). “Earthquake risk assessment of building structures.” Reliability Eng. Sys. Safety, 74, 251–262.
Ellingwood, B., MacGregor, J. G., Galambos, T. V., and Cornell, C. A. (1982). “Probability based load criteria: Load factors and load combinations.” J. Struct. Div. ASCE, 108(5), 978–997.
Fang, K. T., and Wang, Y. (1994). Number-theoretic methods in statistics, Chapman & Hall, London.
Federal Emergency Management Agency (FEMA). (2000). “Prestandard and commentary for the seismic rehabilitation of buildings.” Rep.FEMA 356, Washington, D.C.
Galambos, T. V., Ellingwood, B., MacGregor, J. G., and Cornell, C. A. (1982). “Probability based load criteria: Assessment of current design practice.” J. Struct. Div. ASCE, 108(5), 959–977.
International Code Council (ICC). (2003). Performance code for buildings and facilities, Country Club Hills, Ill.
Katsuki, S., and Frangopol, D. M. (1994). “Hyperspace division method for structural reliability.” J. Eng. Mech., 120(11), 2405–2427.
Katsuki, S., and Frangopol, D. M. (1998). “Advanced hyperspace division method for structural reliability.” Structural Safety and Reliability, M. Shinozuka and Y. K. Wen, eds., 631–638.
Kijawatworawet, W., Pradlwarter, H. J., and Schuëller, G. I. (1998). “Structural reliability estimation by adaptive importance directional sampling.” The 7th Int. Conf. on Structural Safety and Reliability, N. Shiraishi, M. Shinozuka, and Y. K. Wen, eds., Vol. 2, 891–897.
Kim, S., and Na, S. (1997). “Response surface method using vector projected sampling points.” Struct. Safety, 19(1), 3–19.
Liu, P. L., and Kiureghian, A. D. (1986). “Multivariate distribution models with prescribed marginals and covariances.” Probab. Eng. Mech., 1(2), 105–112.
Maymon, G. (1994). “Direct computation of the design point of a stochastic structure using a finite element code.” Struct. Safety, 14(3), 185–202.
Melchers, R. E. (1990). “Radial importance sampling for structural reliability.” J. Eng. Mech., 116(1), 189–203.
Melchers, R. E. (1992). “Load space formulation for time-dependent structural reliability.” J. Eng. Mech., 118(5), 853–870.
Melchers, R. E. (1994). “Structural system reliability assessment using directional simulation.” Struct. Safety, 16, 23–37.
Melchers, R. E. (1999). Structural reliability analysis and prediction, 2nd Ed., Wiley, New York.
Moarefzadeh, M. R., and Melchers, R. E. (1999). “Directional importance sampling for ill-proportioned spaces.” Struct. Safety, 21, 1–22.
Mohamed, A., and Lemaire, M. (1998). “Discussion on: Structural reliability analysis using a standard deterministic finite element code.” Struct. Safety, 20(4), 391–397.
Nie, J. (2003). “A new directional method to assess structural system reliability in the context of performance-based design,” PhD thesis, The Johns Hopkins University.
Nie, J., and Ellingwood, B. R. (2000). “Directional methods for structural reliability analysis.” Struct. Safety, 22, 233–249.
Nie, J., and Ellingwood, B. R. (2003). “New developments in directional methods for system reliability assessment.” Proc., 9th Int. Conf. on Applications of Statistics and Probability in Civil Engineering, Millpress, Rotterdam, 85–90.
Nie, J., and Ellingwood, B. R. (2004a). “A new directional simulation method for system reliability. Part I: Application of deterministic point sets.” Probab. Eng. Mech., in press.
Nie, J., and Ellingwood, B. R. (2004b). “A new directional simulation method for system reliability. Part II: Application of neural networks.” Probab. Eng. Mech., in press.
Prakash, V., Powell, G. H., and Campbell, S. (1993). “DRAIN-2DX base program description and user guide.” Rep. No. UCB/SEMM-93/17, Dept. of Civil Engineering, UC Berkeley, Berkeley, Calif.
Rajashekhar, M. R., and Ellingwood, B. R. (1993). “A new look at the response surface approach for reliability analysis.” Struct. Safety, 12, 205–220.
Saff, E. B., and Kuijlaars, A. B. J. (1997). “Distributing many points on a sphere.” Math. Intell., 19(1), 5–11.
Song, J., and Ellingwood, B. R. (1999). “Seismic reliability of special moment steel frames with welded connections: II.” J. Struct. Eng., 125(4), 372–384.
Yao, T. H., and Wen, Y. K. (1996). “Response surface method for time-variant reliability analysis.” J. Struct. Eng., 122(2), 193–201.
Ziemian, R. D., McGuire, W., and Deierlein, G. G. (1992). “Inelastic limit states design. Part I: Planar frame studies.” J. Struct. Eng., 118(9), 2532–2549.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 3 • March 2005
Pages: 259 - 267
Copyright
© 2005 ASCE.
History
Received: Aug 18, 2003
Accepted: Jul 2, 2004
Published online: Mar 1, 2005
Published in print: Mar 2005
Notes
Note. Associate Editor: Gerhart I. Schueller
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