Reliability Estimation with Time-Variant Loads and Resistances
Publication: Journal of Structural Engineering
Volume 126, Issue 5
Abstract
This paper presents an efficient simulation-based technique to estimate the system reliability of structures that experience variation in loads and resistance over time. To arrive at a realistic reliability estimate of such structures, random process description of load variation and consideration of resistance degradation and periodic repair must be included. An adaptive importance sampling methodology for estimating the time-dependent system reliability of brittle structures is presented in this paper. In the proposed method, a simple enumeration scheme is used to identify one complete failure sequence of the structural system. This defines the initial failure domain to start the simulation. As the simulation progresses, the initial failure domain is refined adaptively to include other significant failure sequences and to accurately estimate the failure probability of the system. The proposed method removes the idealized simplifying assumptions of earlier analytical methods, facilitates easy addition of the reliability analysis module to structural analysis, and provides a fast and accurate estimate of the failure probability. Numerical examples presented to illustrate the application of the proposed method demonstrate its efficiency and promise.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bucher, C. G. (1988). “Adaptive sampling—An iterative fast Monte Carlo procedure.” Struct. Safety, Amsterdam, 5, 119–126.
2.
Clark, L. A. (1988). “Modeling the structural effects of alkali-aggregate reactions on reinforced concrete.” ACI Mat. J., 88(3), 271–277.
3.
Clark, L. A. ( 1990). “Structural aspects of alkali-silica reaction.” Structural engineering review 2, Chapman & Hall, London, 81–87.
4.
Clifton, J. R., and Knab, L. I. ( 1989). “Service life of concrete.” NUREG/CR-5466, U.S. Nuclear Regulatory Commission, Washington, D.C.
5.
Dey, A. ( 1996). “Efficient simulation for system reliability analysis,” PhD dissertation, Vanderbilt University, Nashville, Tenn.
6.
Ditlevsen, O. (1979). “Narrow reliability bounds for structural systems.” J. Struct. Mech., 7(4), 453–472.
7.
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.
8.
Estes, A. C., Frangopol, D. M., and Hern, G. (1996). “Reliability based optimum bridge repair strategy.” Proc., 7th Spec. Conf., Probabilistic Mech. & Struct. Reliability, D. M. Frangopol, and M. D. Grigoriu, eds., ASCE, New York, 372–375.
9.
Geildl, V., and Saunders, S. (1987). “Calculation of reliability for time-varying loads and resistances.” Struct. Safety, Amsterdam, 4, 285–287.
10.
Gollwitzer, S., and Rackwitz, R. (1988). “An efficient numerical solution to the multinormal integral.” Probabilistic Engrg. Mech., 3(2), 98–101.
11.
Haldar, A., and Zhao, Z. (1966). “Reliability based maintenance strategy using NDI.” Proc., 7th Spec. Conf., Probabilistic Mech. & Struct. Reliability, D. M. Frangopol and M. D. Grigoriu, eds., ASCE, New York, 364–367.
12.
Hohenbichler, M., and Rackwitz, R. (1985). “A bound and an approximation to the multivariate normal distribution function.” Math. Jpn., 30(5), 821–828.
13.
Ibrahim, Y. (1991). “Observations on applications of importance sampling in structural reliability analysis.” Struct. Safety, Amsterdam, 9, 269–281.
14.
Jiang, M., Corotis, R. B., and Ellis, J. H. (1996). “Including inspection in optimizing structural management policies.” Proc., 7th Spec. Conf., Probabilistic Mech. & Struct. Reliability, D. M. Frangopol and M. D. Grigoriu, eds., ASCE, New York, 368–371.
15.
Kameda, H., and Koike, T. (1975). “Reliability theory of deteriorating structures.”J. Struct. Div., ASCE, 101(1), 295–310.
16.
Karamchandani, A. (1987). “Structural system reliability analysis methods.” Rep. No. 83, John A. Blume Earthquake Engrg. Ctr., Stanford University, Stanford, Calif.
17.
Karamchandani A., Bjerager, P., and Cornell, C. A. (1989). “Adaptive importance sampling.” Proc., ICOSSAR 89, A. H.-S. Ang, M. Shinozuka, and G. I. Schuëller, eds., ASCE, New York, 855–862.
18.
Karamchandani, A., and Cornell, C. A. (1991). “Adaptive hybrid conditional expectation approaches for reliability estimation.” Struct. Safety, Amsterdam, 11, 59–74.
19.
Mahadevan, S., and Xiao, Q. (1995). “Time-variant reliability of brittle structural systems.”J. Engrg. Mech., ASCE, 121(3), 414–423.
20.
MacGregor, J. G., Mirza, S. A., and Ellingwood, B. (1983). “Statistical analysis of resistance of reinforced and prestressed concrete members.” J. Am. Concrete Inst., 80(3), 167–176.
21.
Melchers, R. E. (1991). “Search-based importance sampling.” Struct. Safety, Amsterdam, 9, 117–128.
22.
Mori, Y., and Ellingwood, B. R. (1993a). “Reliability-based service-life assessment of aging concrete structures.”J. Struct. Engrg., ASCE, 119(5), 1600–1621.
23.
Mori, Y., and Ellingwood, B. R. (1993b). “Time-dependent system reliability analysis by adaptive importance sampling.” Struct. Safety, Amsterdam, 12, 59–73.
24.
Oswald, G. F., and Schueller, G. I. (1984). “Reliability of deteriorating structures.” Engrg. Fracture Mech., 20(3), 479–488.
25.
Pommersheim, J., and Clifton, J. (1985). “Prediction of concrete service-life.” Mat. and Struct., Paris, 18(103), 21–30.
26.
Shao, L. C., Murphy, A. J., Chokshi, N., Kuo, P., and Chang, T. Y. (1998). “Seismic responses and resistance of age degraded structures and components.” Nuclear Engrg. and Des., 181, 3–15.
27.
Shuman, R., et al. ( 1988). “Performance assessment for low-level waste disposal facilities.” EPRI NP-5745SP, Rogers and Associates Engineering Corp., Salt Lake City.
28.
Stewart, M. G., and Rosowsky, D. V. (1998). “Time-dependent reliability of deteriorating reinforced concrete bridges.” Struct. Safety, Amsterdam, 20, 91–109.
29.
Taylor, H. M., and Karlin, S. (1984). An introduction to stochastic modeling. Academic, Orlando, Fla.
30.
Walton, J. C., Plansky, L. E., and Smith, R. W. ( 1990). “Models for estimation of service life of concrete barriers in low-level radioactive waste disposal.” NUREG/CR-5542, U.S. Nuclear Regulatory Commission, Washington, D.C.
31.
Wen, Y.-K. (1977). “Statistical combination of extreme loads.”J. Struct. Div., ASCE, 103(5), 1079–1093.
32.
Wen, Y.-K., and Chen, Y.-C. (1989). “System reliability under time varying loads: II.”J. Engrg. Mech., ASCE, 115(4), 824–839.
33.
Wirshing, P. H., Ferensic, J., and Thayamballi, A. (1997). “Reliability with respect to ultimate strength of a corroding ship hull.” Marine Struct., 10, 501–518.
34.
Xiao, Q., and Mahadevan, S. (1994). “Fast failure mode identification for structural system reliability.” Struct. Safety, Amsterdam, 13, 207–226.
35.
Zhao, Z., Haldar, A., and Breen, F. L., Jr. (1994). “Fatigue-reliability evaluation of steel bridges.”J. Struct. Engrg., ASCE, 120(5), 1608–1623.
36.
Zhao, A., and Haldar, A. ( 1997). “Reliability-based structural fatigue damage evaluation and maintenance using non-destructive inspections.” Uncertainty modeling in finite element, fatigue and stability of systems, A. Haldar, A. Guran, and B. M. Ayyub, eds., Series on Stability Vibration and Control of Systems Series B, Vol. 9, 159–214.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 126 • Issue 5 • May 2000
Pages: 612 - 620
History
Received: Mar 7, 1997
Published online: May 1, 2000
Published in print: May 2000
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.