Risk Analysis of Fatigue-Induced Sequential Failures by Branch-and-Bound Method Employing System Reliability Bounds
Publication: Journal of Engineering Mechanics
Volume 137, Issue 12
Abstract
Various types of structural systems are often subjected to the risk of fatigue-induced failures. If a structure does not have an adequate level of structural redundancy, local failures may initiate sequential failures and cause exceedingly large damage. For the risk-informed design and maintenance of such structural systems, it is thus essential to quantify the risk of fatigue-induced sequential failure. However, such risk analysis is often computationally intractable because one needs to explore innumerable failure sequences, each of which demands component and system reliability analyses in conjunction with structural analyses to account for various uncertainties and the effect of load redistributions. To overcome this computational challenge, many research efforts have been made to identify critical failure sequences with the highest likelihood and to quantify the overall risk by system reliability analysis based on the identified sequences. One of the most widely used approaches is the so-called “branch-and-bound” method. However, only the lower bound on the system risk is usually obtained because of challenges in system reliability analysis, while the changes of the lower bound by newly identified sequences are not diminishing monotonically. This paper aims to improve the efficiency and accuracy of risk analysis of fatigue-induced sequential failures by developing a new branch-and-bound method employing system reliability bounds (termed the method). On the basis of a recursive formulation of the limit-state functions of fatigue-induced failures, a system failure event is formulated as a disjoint cut-set system event. A new search scheme identifies critical fatigue-induced failure sequences in the decreasing order of their probabilities while it systematically updates both lower and upper bounds on the system failure probability without additional system reliability analyses. As a result, the method can provide reasonable criteria for terminating the branch-and-bound search without missing critical failure sequences and reduce the number of computational simulations required to obtain reliable estimates on the system risk. The method is tested and demonstrated by numerical examples of a multilayer Daniels system and a three-dimensional offshore structure.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the Midwest Structural Sciences Center (MSSC) under a cooperative agreement from the U.S. Air Force Research Laboratory Air Vehicles Directorate (contract number UNSPECIFIEDFA8650-06-2-3620). The opinions, findings, and conclusions stated are those of the writers and do not necessarily reflect those of the sponsor. This paper was cleared for public release on February 22, 2010 as case number 88ABW-2010-0762. The writers are grateful for the valuable comments from Mr. Nolan Kurtz at the University of Illinois at Urbana-Champaign.
References
Almar-Naess, A. (1985). Fatigue handbook: Offshore steel structures, Tapir Forlag, Trondheim, Norway.
Ambartzumian, R., Der Kiureghian, A., Ohanian, V., and Sukiasian, H. (1998). “Multinormal probability by sequential conditioned importance sampling: Theory and application.” Prob. Eng. Mech., 13(4), 299–308.
Ayala-Uraga, E., and Moan, T. (2007). “Fatigue-reliability-based assessment of welded joints applying consistent fracture mechanics formulations.” Int. J. Fatigue, 29(3), 444–456.
Daniels, H. E. (1945). “The statistical theory of the strength of bundles of threads.” Proc. R. Soc. London, Ser. A, 183(995), 405–435.
Der Kiureghian, A. (2005). “First- and second-order reliability methods.” Chapter 14, Engineering design reliability handbook, E. Nikolaidis, D. M. Ghiocel, and S. Singhal, eds., CRC Press, Boca Raton, FL.
Ditlevsen, O., and Bjerager, P. (1989). “Plastic reliability analysis by directional simulation.” J. Eng. Mech., 115(6), 1347–1362.
Genz, A. (1992). “Numerical computation of multivariate normal probabilities.” J. Comput. Graph. Stat., 1(2), 141–149.
Gharaibeh, E. S., Frangopol, D. M., and Onoufriou, T. (2002). “Reliability-based importance assessment of structural members with applications to complex structures.” Comput. Struct., 80(12), 1113–1131.
Guenard, Y. F. (1984). “Application of system reliability analysis to offshore structures.” Rep. 1, Reliability of Marine Structures Program, Stanford Univ., Stanford, CA.
Hohenbichler, H., and Rackwitz, R. (1983). “First-order concepts in system reliability.” Struct. Saf., 1(3), 177–188.
Hu, Y., Chen, B., and Ye, N. (1998). “Fatigue reliability analysis of redundant structural systems by using Monte Carlo simulation.” Proc., 17th Int. Conf. on Offshore Mechanics and Arctic Engineering, American Society of Mechanical Engineers, New York.
Kang, W.-H., and Song, J. (2010). “Evaluation of multivariate normal integrals for general systems by sequential compounding.” Struct. Saf., 32(1), 35–41.
Kang, W.-H., Lee, Y.-J., Song, J., and Gencturk, B. (2011). “Further development of matrix-based system reliability method and applications to structural systems.” Struct. Infrastruct. Eng., (Jan. 22, 2011).
Karamchandani, A., Dalane, J. I., and Bjerager, P. (1991). “Systems reliability or offshore structures including fatigue and extreme wave loading.” Mar. Struct., 4(4), 353–379.
Karamchandani, A., Dalane, J. I., and Bjerager, P. (1992). “Systems reliability approach to fatigue of structures.” J. Struct. Eng., 118(3), 684–700.
Karsan, D. I., and Kumar, A. (1990). “Fatigue failure paths for offshore platform inspection.” J. Struct. Eng., 116(6), 1679–1695.
Kirkemo, F. (1988). “Applications of probabilistic fracture mechanics to offshore structures.” Appl. Mech. Rev., 41(2), 61–84.
Melchers, R. E. (1994). “Structural system reliability assessment using directional simulation.” Struct. Saf., 16(1–2), 23–37.
Melchers, R. E., and Tang, L. K. (1984). “Dominant failure modes in stochastic structural systems.” Struct. Saf., 2(2), 127–143.
Millwater, H. R., Wu, Y.-T., and Cardinal, J. W. (1994). “Probabilistic structural analysis of fatigue and fracture.” Proc., 35th AIAA Structures, Structural Dynamics, and Materials Conf., American Institute of Aeronautics and Astronautics, Reston, VA.
Moan, T. (2005). “Safety of offshore structures.” Rep. 2005-04, Center for Offshore Research and Engineering (CORE), Singapore.
Moan, T., and Ayala-Uraga, E. (2008). “Reliability-based assessment of deteriorating ship structures operating in multiple sea loading climates.” Reliab. Eng. Syst. Saf., 93(3), 433–446.
Moan, T., Hovde, G. O., and Blanker, A. M. (1993). “Reliability-based fatigue design criteria for offshore structures considering the effect of inspection and repair.” Proc., Offshore Technology Conf., Richardson, TX.
Moan, T., and Song, R. (2000). “Implications of inspection updating on system fatigue reliability of offshore structures.” J. Offshore Mech. Arctic Eng., 122(3), 173–180.
Moses, F. (1982). “System reliability development in structural engineering.” Struct. Saf., 1(1), 3–13.
Murotsu, Y. (1984). “Automatic generation of stochastically dominant modes of structural failure in frame.” Struct. Saf., 2(1), 17–25.
Newman, J. C., and Raju, I. S. (1981). “An empirical stress intensity factor equation for the surface crack.” Eng. Fract. Mech., 15(1–2), 185–192.
Pandey, M. D. (1998). “An effective approximation to evaluate multinormal integrals.” Struct. Saf., 20(1), 51–67.
Paris, P., and Erdogan, F. (1963). “A critical analysis of crack propagation laws.” J. Basic Eng., 85(4), 528–534.
Shabakhty, N., Boonstra, H., and Van Gelder, P. (2003). “System reliability of jack-up structures based on fatigue degradation.” Safety and reliability, T. Bedford and P. H. A. J. M. van Gelder, eds., Taylor & Francis, London, 1437–1445.
Song, J., and Der Kiureghian, A. (2003). “Bounds on system reliability by linear programming.” J. Eng. Mech., 129(6), 627–636.
Song, J., and Kang, W.-H. (2009). “System reliability and sensitivity under statistical dependence by matrix-based system reliability method.” Struct. Saf., 31(2), 148–156.
Straub, D., and Der Kiureghian, A. (2007). “Risk acceptance in deteriorating structural systems.” Proc., Joint Committee on Structural Safety Workshop on Risk Acceptance and Risk Communication, Dept. of Civil Engineering, Technical Univ. of Denmark, Lyngby, Denmark.
Thoft-Christensen, P., and Murotsu, Y. (1986). Application of structural system reliability theory, Springer-Verlag, Berlin.
Wang, Y., Shi, Y., Wang, C., and Li, S. (2006). “A new method for system fatigue reliability analysis of offshore steel jacket.” Adv. Struct. Eng., 9(2), 185–193.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 137 • Issue 12 • December 2011
Pages: 807 - 821
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Feb 23, 2010
Accepted: Jun 14, 2011
Published online: Jun 16, 2011
Published in print: Dec 1, 2011
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.