Time-Dependent Reliability Model of Deteriorating Structures Based on Stochastic Processes and Bayesian Inference Methods
Publication: Journal of Engineering Mechanics
Volume 141, Issue 3
Abstract
Performance and reliability of structures will deteriorate with time as a result of the effects of various loads and the environment. This paper aims to develop a time-dependent reliability model of deteriorating structures that considers both aging effects and random shocks. First, a deteriorating model is proposed in which the aging effect is modeled as a gamma process while random shock is described by a Poisson process. The time-dependent reliability of the structural components is then evaluated based on the model. To incorporate the effects of model uncertainties, Bayesian inference methods are further integrated with the reliability model to update the uncertain parameters in the model using sampling data. Numerical examples demonstrate that the proposed model provides a reasonable method for evaluating the reliability of deteriorating structures containing model uncertainties.
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Acknowledgments
This work is supported by the National Basic Research Program of China (2011CB013800).
References
Cheng, T., and Pandey, M. D. (2012). “An accurate analysis of maintenance cost of structures experiencing stochastic degradation.” Struct. Infrastruct. Eng., 8(4), 329–339.
Cheng, T., Pandey, M. D., and van der Weide, J. A. M. (2012). “The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution.” Reliab. Eng. Syst. Saf., 108(Dec), 65–76.
Ching, J., and Leu, S.-S. (2009). “Bayesian updating of reliability of civil infrastructure facilities based on condition-state data and fault-tree model.” Reliab. Eng. Syst. Saf., 94(12), 1962–1974.
Ciampoli, M. (1998). “Time dependent reliability of structural systems subject to deterioration.” Comp. Struct., 67(1–3), 29–35.
Cinlar, E. (1997). “Shock and wear models and Markov additive processes.” The theory and applications of reliability with emphasis on Bayesian and nonparametric methods, C. P. Tsokos and I. N. Shimi, eds., Academic, New York, 193–214.
Cinlar, E., Osman, E., and Bažant, Z. P. (1977). “Stochastic process for extrapolating concrete creep.” J. Eng. Mech. Div., 103(6), 1069–1088.
de Haan, L. (1990). “Fighting the arch–enemy with mathematics.” Statistica Neerlandica, 44(2), 45–68.
Ebrahimi, N. (1999). “Stochastic properties of a cumulative damage threshold crossing model.” J. Appl. Probab., 36(3), 720–732.
Finkelstein, M. (2005). “Shocks in homogeneous and heterogeneous populations.” MPIDR Working Paper WP 2005-024, Max Planck Institute for Demographic Research, Rostock, Germany.
Finkelstein, M. (2007). “Shocks in homogeneous and heterogeneous populations.” Reliab. Eng. Syst. Saf., 92(5), 569–574.
Frangopol, D. M., Kallen, M.-J., and van Noortwijk, J. M. (2004). “Probabilistic models for life-cycle performance of deteriorating structures: Review and future directions.” Prog. Struct. Eng. Mater., 6(4), 197–212.
Grall, A., Dieulle, L., Bérenguer, C., and Roussignol, M. (2002). “Continuous-time predictive-maintenance scheduling for a deteriorating system.” IEEE Trans. Reliab., 51(2), 141–150.
Graves, T. L., Hamada, M. S., Klamann, R. M., Koehler, A. C., and Martz, H. F. (2008). “Using simultaneous higher-level and partial lower-level data in reliability assessments.” Reliab. Eng. Syst. Saf., 93(8), 1273–1279.
Guan, X., He, J., Jha, R., and Liu, Y. (2012). “An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations.” Reliab. Eng. Syst. Saf., 97(1), 1–13.
Gunawan, S., and Papalambros, P. Y. (2006). “A Bayesian approach to reliability-based optimization with incomplete information.” J. Mech. Des., 128(4), 909–918.
Higuchi, S., and Macke, M. (2008). “Cost-benefit analysis for the optimal rehabilitation of deteriorating structures.” Struct. Saf., 30(4), 291–306.
Kahle, W., and Wendt, H. (2004). “On a cumulative damage process and resulting first passages times.” Appl. Stochastic Models Data Anal., 20(1), 17–26.
Kallen, M. J., and van Noortwijk, J. M. (2005). “Optimum maintenance decisions under imperfect inspection.” Reliab. Eng. Syst. Saf., 90(2–3), 177–185.
Karlin, S., and Taylor, H. E. (1975). A first course in stochastic processes, 2nd Ed., Academic, San Diego.
Kuniewski, S. P., van der Weide, J. A. M., and van Noortwijk, J. M. (2009). “Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection.” Reliab. Eng. Syst. Saf., 94(9), 1480–1490.
Lawless, J., and Crowder, M. (2004). “Covariates and random effects in a gamma process model with application to degradation and failure.” Lifetime Data Anal., 10(3), 213–227.
Leadbetter, M. R. (1983). “Extremes and local dependence in stationary sequences.” Probab. Theory Relat. Fields, 65(2), 291–306.
Mercer, A. (1961). “Some simple wear-dependent renewal processes.” J. R. Stat. Soc., B, 23(2), 368–376.
Moran, P. A. P. (1954). “A probability theory of dams and storage systems.” Aust. J. Appl. Sci., 5(2), 116–124.
Moran, P. A. P. (1955). “A probability theory of dams and storage systems: Modifications of the release rules.” Aust. J. Appl. Sci., 6(2), 117–130.
Moran, P. A. P. (1956). “A probability theory of a dam with a continuous release.” Q. J. Math., 7(1), 130–137.
Morey, R. C. (1966). “Some stochastic properties of a compound-renewal damage model.” Oper. Res., 14(5), 902–908.
Mori, Y., and Ellingwood, B. R. (1993). “Time-dependent system reliability analysis by adaptive importance sampling.” Struct. Saf., 12(1), 59–73.
Pandey, M. D., Lu, D., and Komljenovic, D. (2011). “The impact of probabilistic modeling in life-cycle management of nuclear piping systems.” J. Eng. Gas Turbines Power, 133(1), 012901.
Pickands, J., III. (1971). “The two-dimensional Poisson process and extremal processes.” J. Appl. Probab., 8(4), 745–756.
Smith, W. L. (1958). “Renewal theory and its ramification.” J. R. Stat. Soc., B, 20(2), 243–302.
Tsai, C.-C., Tseng, S.-T., and Balakrishnan, N. (2011). “Mis-specification analyses of gamma and Wiener degradation processes.” J. Stat. Plan. Inference, 141(12), 3725–3735.
van der Weide, J. A. M., Pandey, M. D., and van Noortwijk, J. M. (2010). “Discounted cost model for condition-based maintenance optimization.” Reliab. Eng. Syst. Saf., 95(3), 236–246.
van Noortwijk, J. M. (2009). “A survey of the application of gamma processes in maintenance.” Reliab. Eng. Syst. Saf., 94(1), 2–21.
van Noortwijk, J. M., van der Weide, J. A. M., Kallen, M. J., and Pandey, M. D. (2007). “Gamma processes and peaks-over-threshold distributions for time-dependent reliability.” Reliab. Eng. Syst. Saf., 92(12), 1651–1658.
Wang, X., Rabiei, M., Hurtado, J., Modarres, M., and Hoffman, P. (2009). “A probabilistic-based airframe integrity management model.” Reliab. Eng. Syst. Saf., 94(5), 932–941.
Yuan, X.-X., Pandey, M. D., and Bickel, G. A. (2008). “A probabilistic model of wall thinning in CANDU feeders due to flow-accelerated corrosion.” Nucl. Eng. Des., 238(1), 16–24.
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Published In
Journal of Engineering Mechanics
Volume 141 • Issue 3 • March 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 27, 2013
Accepted: Jul 9, 2014
Published online: Jul 31, 2014
Published in print: Mar 1, 2015
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