Semi-Markov Models for the Deterioration of Bridge Elements
Publication: Journal of Infrastructure Systems
Volume 22, Issue 3
Abstract
Many bridge management systems (BMSs) use a Markov chain model to forecast the deterioration process. The Markov property may be considered to be restrictive when modeling the deterioration of transportation assets, primarily because of the memoryless property and assumption of exponential distribution for sojourn times in the condition states. This study addresses some of the limitations that arise from the use of purely Markov chain deterioration models for transportation infrastructure by introducing alternative approaches that are based on the semi-Markov process. Two semi-Markov approaches for modeling the deterioration of certain bridge elements are developed. These are compared against a previously developed semi-Markov approach, the traditional Markov chain deterioration approach, and the change in the average actual condition indices of bridge elements that deteriorated for 8 years after being constructed. The results obtained from this study indicated that semi-Markov models are feasible and more flexible than the traditional Markov chain models when forecasting the future deterioration of transportation infrastructure. The semi-Markov models that were developed produced condition indices that were closer to the values of the average actual condition indices of bridge elements when compared against the values based on the traditional Markov chain model.
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Acknowledgments
We would like to acknowledge the Florida Department of Transportation for the use of the Florida bridge element condition data for this study.
References
Birolini, A. (2007). Reliability engineering: Theory and practice, 5th Ed., Springer, Silver Spring, MD.
Black, M., Brint, A. T., and Brailsford, J. R. (2005a). “A semi-Markov approach for modeling asset deterioration.” J. Oper. Res. Soc., 56(11), 1241–1249.
Black, M., Brint, A. T., and Brailsford, J. R. (2005b). “Comparing probabilistic methods for the asset management of distributed items.” J. Infrastruct. Syst., 102–109.
Borot, F., Zonta, D., and Zandonini, R. (2006). “A bridge management strategy based on future reliability and semi-Markov deterioration models.” Proc., 3rd Int. ASRANet Colloquium, ASRANet, Glasgow, U.K.
Bulusu, S. and Sinha, K. C. (1992). “Simulation approach to prediction of highway structure conditions.” Transp. Res. Rec., 1347, 11–17.
Casella, G., and Berger, R. L. (2001). Statistical inference, Pacific Grove, CA.
Durango, P. L., and Madanat, S. M. (2002). “Optimal maintenance and repair policies in infrastructure management under uncertain facility deterioration rates: An adaptive control approach.” Transp. Res., Part A: Policy Pract., 36, 763–778.
Durango-Cohen, P. L. (2004). “Maintenance and repair decision making for infrastructure facilities without a deterioration model.” J. Infrastruct. Syst., 1–8.
Fox, B. (1967). Semi-Markov processes: A primer, RAND, Santa Monica, CA.
Golabi, K., and Shepard, R. (1997). “Pontis: A system for maintenance optimization and improvement of us bridge networks.” Acad. J., 27(1), 71–88.
Howard, R. A. (1971). Dynamic probabilistic systems. Volume II: Semi-Markov and decision processes, Wiley, Toronto.
Howard, R. A. (2007). Dynamic probabilistic systems. Volume II: Semi-Markov and decision processes, Wiley, Toronto.
Hu, Y.-T., Kiesel, R., and Perraudin, W. (2002). “The estimation of transition matrices for sovereign credit ratings.” J. Bank. Financ., 26(7), 1383–1406.
Ibe, O. C. (2009). Markov processes for stochastic modeling, Elsevier, Burlington, MA.
Kuhn, K. (2006). “Uncertainty in infrastructure deterioration modeling and robust maintenance policies for Markovian management.” Ph.D. dissertation, Univ. of California, Berkeley, CA.
Lin, L. I. (1989). “A concordance correlation coefficient to evaluate reproducibility.” Biometrics, 45(1), 255–268.
Ng, S.-K., and Moses, F. (1998). “Bridge deterioration modeling using semi-Markov theory.” Structural safety and reliability, N. Shiraishi, M. Shinozuka, and Y. K. Wen, eds., Vol. 1, A.A. Balkema, Rotterdam, Netherlands, 113–120.
Pontis [Computer software]. AASHTO, Washington, DC.
Robelin, C-A., and Madanat, S. (2007). “History-dependent bridge deck maintenance and replacement optimization with Markov decision processes.” J. Infrastruct. Syst., 195–201.
Roberts, J. E., and Shepard, R. (2000). “Bridge management for the 21st century.” Transp. Res. Rec., 1696, 197–203.
Ross, S. M. (1996). Stochastic processes, 2nd Ed., Wiley, Rotterdam, Netherlands.
Shepard, R. W., and Johnson, M. B. (2001). “California bridge health index—A diagnostic tool to maximize bridge longevity, investment.” Transp. Res. Rec., 215, 6–11.
Sobanjo, J. O. (2011). “State transition probabilities in bridge deterioration based on Weibull sojourn times.” Struct. Infrastruct. Eng.: Maintenance, Manage., Life-Cycle Des. Perform., 7(10), 747–764.
Sobanjo, J. O., and Thompson, P. D. (2001). “Enhancement of the FDOT’s project level and network level bridge management analysis tools. Final report.”, Florida Dept. of Transportation, Tallahassee, FL.
Thomas, O., and Sobanjo, J. (2013). “Comparison of Markov chain and semi-Markov models for crack deterioration on flexible pavements.” J. Infrastruct. Syst., 186–195.
Thompson, P. D., and Shepard, R. W. (2000). “AASHTO commonly-recognized bridge elements: Successful applications and lessons learned.” Materials for National Workshop on Commonly Recognized Measures for Maintenance, AASHTO, Scottsdale, AZ.
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Information
Published In
Journal of Infrastructure Systems
Volume 22 • Issue 3 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 20, 2015
Accepted: Dec 7, 2015
Published online: Feb 23, 2016
Discussion open until: Jul 23, 2016
Published in print: Sep 1, 2016
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