Technical Papers
Mar 3, 2020

Multivariable Proportional Hazards-Based Probabilistic Model for Bridge Deterioration Forecasting

Publication: Journal of Infrastructure Systems
Volume 26, Issue 2

Abstract

Duration-based deterioration modeling approaches have been investigated over the past two decades with a view toward utilizing their prognostic capabilities in accurately identifying maintenance needs and improving asset management under constrained budgets. However, despite significant advances in asset management systems during this time, implementation of such approaches for probabilistic infrastructure deterioration modeling has been limited, resulting in underutilization of their predictive potential. In this paper, a comprehensive framework based on a combination of the Cox proportional hazards method and Markovian theory is presented to develop multivariable deterioration models that probabilistically incorporate the effects of explanatory factors on deterioration over the complete life cycle of a bridge component. Both stationary (time-independent) and nonstationary (time-dependent) transition probability approaches are introduced and compared. Sample results from implementation of this framework on North Carolina’s statewide bridge inspection database containing 35 years of data for more than 17,000 bridges are discussed. The predictive fidelity of the developed models is analyzed relative to the actually recorded condition ratings to demonstrate the effectiveness of these models in accurately forecasting deterioration.

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Acknowledgments

Most of the research presented in this paper was conducted as part of the research project RP 2014-07 sponsored by the North Carolina Department of Transportation. The financial support provided by this grant is greatly appreciated. The contents of this paper reflect the views of the authors and not necessarily the views of the NCDOT. The authors are responsible for the accuracy of the data presented herein. Additionally, this paper does not constitute a standard, specification, or regulation and does not necessarily reflect official policies of NCDOT. In particular, the authors appreciate the guidance and technical support provided by Cary Clemmons.

References

Agrawal, A. K., A. Kawaguchi, and Z. Chen. 2009. Bridge element deterioration rates. New York: New York State Dept. of Transportation.
Agrawal, A. K., A. Kawaguchi, and Z. Chen. 2010. “Deterioration rates of typical bridge elements in New York.” J. Bridge Eng. 15 (4): 419–429. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000123.
Barbu, V., M. Boussemart, and N. Limnios. 2004. “Discrete-time semi-Markov model for reliability and survival analysis.” Commun. Stat. Theory Methods 33 (11): 2833–2868. https://doi.org/10.1081/STA-200037923.
Bulusu, S., and K. C. Sinha. 1997. “Comparison of methodologies to predict bridge deterioration.” Transp. Res. Rec. 1597 (1): 34–42. https://doi.org/10.3141/1597-05.
Butt, A., M. Y. Shahin, K. J. Feighan, and S. H. Carpenter. 1987. “Pavement performance prediction model using the Markov process.” Transp. Res. Rec. 1123 (1): 12–19.
Cinlar, E. 1975. Introduction to stochastic processes. Englewood Cliffs, NJ: Prentice Hall.
Cox, D. R. 1972. “Regression models and life-tables.” J. R. Stat. Soc. 34 (2): 187–202. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x.
Cox, D. R., and D. Oakes. 1984. Analysis of survival data. London: Chapman and Hall.
DeStefano, P. D., and D. A. Grivas. 1998. “Method for estimating transition probability in bridge deterioration models.” J. Infrastruct. Syst. 4 (2): 56–62. https://doi.org/10.1061/(ASCE)1076-0342(1998)4:2(56).
Duncan, S. A., and D. W. Johnston. 2002. Bridge management system update. Raleigh, NC: Dept. of Civil Engineering, North Carolina State Univ.
Fang, J., T. Ishida, and T. Yamazaki. 2018. “Quantitative evaluation of risk factors affecting the deterioration of RC deck slab components in East Japan and Tokyo regions using survival analysis.” Appl. Sci. 8 (9): 1470. https://doi.org/10.3390/app8091470.
Fleming, T. R., and D. P. Harrington. 1978. “Estimation for discrete time nonhomogeneous Markov chains.” Stochastic Processes Appl. 7 (2): 131–139. https://doi.org/10.1016/0304-4149(78)90012-1.
Frangopol, D. M., M.-J. Kallen, and J. M. Noortwijk. 2004. “Probabilistic models for life-cycle performance of deteriorating structures: Review and future directions.” Prog. Struct. Mater. Eng. 6 (4): 197–212. https://doi.org/10.1002/pse.180.
Golabi, K., and R. Shepard. 1997. “Pontis: A system for maintenance optimization and improvement of US bridge networks.” Interfaces 27 (1): 71–88. https://doi.org/10.1287/inte.27.1.71.
Goyal, R. 2015. “Development of a survival based framework for bridge deterioration modeling with large-scale application to the North Carolina bridge management system.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of North Carolina at Charlotte.
Goyal, R., M. Whelan, and T. Cavalline. 2016. “Characterizing the effect of external factors on deterioration rates of bridge components using multivariable proportional hazards regression.” Struct. Infrastruct. Eng. 13 (7): 894–905. https://doi.org/10.1080/15732479.2016.1217888.
Greene, W. H. 1997. Econometric analysis. 3rd ed. Upper Saddle River, NJ: Prentice Hall.
Hajnal, J. 1955. “The ergodic properties of non-homogeneous finite Markov chains.” Math. Proc. Cambridge Philos. Soc. 52 (1): 67–77. https://doi.org/10.1017/S0305004100030991.
Hatami, A., and G. Morcous. 2011. Developing deterioration models for Nebraska bridges. Lincoln, NE: Univ. of Nebraska–Lincoln.
Hawk, H., and E. P. Small. 1998. “The BRIDGIT bridge management system.” Struct. Eng. Int. 8 (4): 309–314. https://doi.org/10.2749/101686698780488712.
Hearn, G. 2012. Deterioration and cost information for bridge management. Denver: Colorado Dept. of Transportation.
Hosmer, D. W. J., and S. Lemeshow. 1999. Applied survival analysis: Regression modeling of time to event data. New York: Wiley.
Huang, C.-C. 1977. “Non-homogeneous Markov chains and their applications.” Ph.D. dissertation, Dept. of Mathematics, Iowa State Univ.
Hyman, W. A., and D. J. Hughes. 1983. “Computer model for life-cycle cost analysis of statewide bridge repair and replacement needs.” Transp. Res. Rec. 899 (1): 52–61.
Jiang, Y. 2010. “Application and comparison of regression and Markov chain methods in bridge condition prediction and system benefit optimization.” J. Transp. Res. Forum 49 (2): 91–110.
Jiang, Y., M. Saito, and K. C. Sinha. 1988. “Bridge performance prediction model using the Markov chain.” Transp. Res. Rec. 1180 (1): 25–32.
Kalbfleisch, J. D., and R. L. Prentice. 1980. The statistical analysis of failure time data. Waterloo, ON, Canada: Wiley.
Kallen, M. J., and J. M. van Noortwijk. 2005. “A study towards the application of Markovian deterioration processes for bridge maintenance modeling in the Netherlands.” In Proc., European Safety and Reliability Conf.: Advances in Safety and Reliability, edited by K. Kolowrocki, 1021–1028. Rotterdam, Netherlands: A.A. Balkema.
Kumar, D. 1995. “Proportional hazards modeling of repairable systems.” Qual. Reliab. Eng. Int. 11 (5): 361–369. https://doi.org/10.1002/qre.4680110507.
Kumar, D., and B. Klefsjõ. 1994. “Proportional hazards model: A review.” Reliab. Eng. Syst. Saf. 44 (2): 177–188. https://doi.org/10.1016/0951-8320(94)90010-8.
Lawless, J. F. 1982. Statistical models and methods for lifetime data. Waterloo, ON, Canada: Wiley.
Madanat, S., and W. H. W. Ibrahim. 1995. “Poisson regression models of infrastructure transition probabilities.” J. Transp. Eng. 121 (3): 267–272. https://doi.org/10.1061/(ASCE)0733-947X(1995)121:3(267).
Madanat, S., R. Mishalani, and W. H. W. Ibrahim. 1995. “Estimation of infrastructure transition probabilities from condition rating data.” J. Infrastruct. Syst. 1 (2): 120–125. https://doi.org/10.1061/(ASCE)1076-0342(1995)1:2(120).
Madanat, S. M., M. G. Karlaftis, and P. S. McCarthy. 1997. “Probabilistic infrastructure deterioration models with panel data.” J. Infrastruct. Syst. 3 (1): 4–9. https://doi.org/10.1061/(ASCE)1076-0342(1997)3:1(4).
Markow, M. J., and W. A. Hyman. 2009. Bridge management systems for transportation agency decision making. Washington, DC: Transportation Research Board.
Mauch, M., and S. Madanat. 2001. “Semiparametric hazard rate models of reinforced concrete bridge deck deterioration.” J. Infrastruct. Syst. 7 (2): 49–57. https://doi.org/10.1061/(ASCE)1076-0342(2001)7:2(49).
Mishalani, R. G., and S. M. Madanat. 2002. “Computation of infrastructure transition probabilities using stochastic duration models.” J. Infrastruct. Syst. 8 (4): 139–148. https://doi.org/10.1061/(ASCE)1076-0342(2002)8:4(139).
Moomen, M., Y. Qiao, B. R. Agbelie, S. Labi, and K. C. Sinha. 2016. Bridge deterioration models to support Indiana’s bridge management system. West Lafayette, IN: Purdue Univ.
Morcous, G., Z. Lounis, and M. S. Mirza. 2003. “Identification of environmental categories for Markovian deterioration models of bridge decks.” J. Bridge Eng. 8 (6): 353–361. https://doi.org/10.1061/(ASCE)1084-0702(2003)8:6(353).
Morcous, G., H. Rivard, and A. M. Hanna. 2002. “Modeling bridge deterioration using case-based reasoning.” J. Infrastruct. Syst. 8 (3): 86–95. https://doi.org/10.1061/(ASCE)1076-0342(2002)8:3(86).
Nakat, Z. S., and S. M. Madanat. 2008. “Stochastic duration modeling of pavement overlay crack initiation.” J. Infrastruct. Syst. 14 (3): 185–192. https://doi.org/10.1061/(ASCE)1076-0342(2008)14:3(185).
Ng, S.-K., and F. Moses. 1998. “Bridge deterioration modeling using semi-Markov theory.” In Structural safety and reliability, edited by N. Shiraishi, M. Shinozuka, and Y. K. Wen, 113–120. Rotterdam, Netherlands: A.A. Balkema.
Osaki, S. 1985. Stochastic system reliability modeling. Philadelphia: World Scientific.
Ravirala, V., and D. A. Grivas. 1995. “State increment method of life-cycle cost analysis for highway management.” J. Infrastruct. Syst. 1 (3): 151–159. https://doi.org/10.1061/(ASCE)1076-0342(1995)1:3(151).
Ross, S. M. 1970. Applied probability models with optimization applications. San Francisco: Holden-Day.
Samrout, M., E. Chatelet, R. Kouta, and N. Chebbo. 2007. “Optimization of maintenance policy using the proportional hazard model.” Reliab. Eng. Syst. Saf. 94 (1): 44–52. https://doi.org/10.1016/j.ress.2007.12.006.
Scherer, W. T., and D. M. Glagola. 1994. “Markovian models for bridge maintenance management.” J. Transp. Eng. 120 (1): 37–51. https://doi.org/10.1061/(ASCE)0733-947X(1994)120:1(37).
Sobanjo, J. O. 2011. “State transition probabilities in bridge deterioration based on Weibull sojourn times.” Struct. Infrastruct. Eng. 7 (10): 747–764. https://doi.org/10.1080/15732470902917028.
Sobanjo, J. O., and P. D. Thompson. 2001. Development of agency maintenance, repair & rehabilitation (MR&R) cost data for Florida’s bridge management system. Tallahassee, FL: Florida Dept. of Transportation.
Sobanjo, J. O., and P. D. Thompson. 2011. Enhancement of FDOT’s project level and network level bridge management analysis tools. Tallahassee, FL: Florida Dept. of Transportation.
Vassiliou, P.-C. G. 1998. “The evolution of the theory of non-homogeneous Markov systems.” Appl. Stochastic Models Data Anal. 13 (3–4): 159–176. https://doi.org/10.1002/(SICI)1099-0747(199709/12)13:3/4%3C159::AID-ASM309%3E3.0.CO;2-Q.
Vassiliou, P.-C. G., and A. A. Papadopoulou. 1992. “Non-homogeneous semi-Markov systems and maintainability of state sizes.” J. Appl. Probab. 29 (3): 519–534. https://doi.org/10.2307/3214890.
Wang, K. C. P., J. Zaniewski, and G. Way. 1994. “Probabilistic behavior of pavements.” J. Transp. Eng. 120 (3): 358–375. https://doi.org/10.1061/(ASCE)0733-947X(1994)120:3(358).
Wellalage, N. K. W., T. Zhang, and R. Dwight. 2015. “Calibrating Markov chain–based deterioration models for predicting future conditions of railway bridge elements.” J. Bridge Eng. 20 (2): 04014060. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000640.
Yang, Y. N., M. M. Kumaraswamy, H. J. Pam, and H. M. Xie. 2013. “Integrating semiparametric and parametric models in survival analysis of bridge element deterioration.” J. Infrastruct. Syst. 19 (2): 176–185. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000115.

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Go to Journal of Infrastructure Systems
Journal of Infrastructure Systems
Volume 26Issue 2June 2020

History

Received: Oct 9, 2017
Accepted: Oct 7, 2019
Published online: Mar 3, 2020
Published in print: Jun 1, 2020
Discussion open until: Aug 3, 2020

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Authors

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Research Associate, Dept. of Civil and Environmental Engineering, Univ. of North Carolina at Charlotte, Charlotte, NC 28223 (corresponding author). ORCID: https://orcid.org/0000-0002-3645-4931. Email: [email protected]
Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of North Carolina at Charlotte, Charlotte, NC 28223. ORCID: https://orcid.org/0000-0001-6442-9496. Email: [email protected]
Tara L. Cavalline, M.ASCE [email protected]
Associate Professor, Dept. of Engineering Technology and Construction Management, Univ. of North Carolina at Charlotte, Charlotte, NC 28223-0001. Email: [email protected]

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