Stochastic Modeling of Bridge Deterioration Using Classification Tree and Logistic Regression
Publication: Journal of Infrastructure Systems
Volume 25, Issue 1
Abstract
This paper presents a new method to develop stochastic deterioration models using a combination of methods including Markov chains, logistic regression, and classification trees. It is computationally more efficient to use logistic regression with the Markov chain process than it is to use optimization-based approaches, and the former is shown to marginally improve the prediction of condition ratings for small data sets. Annually inspected bridge data are split into groups using a classification tree, and logistic regression is used to determine transition probabilities for a Markov chain process. A case study was conducted to determine the effectiveness of using the proposed logistic regression and Markov chain approach for the small data sets created by the classification tree. Wyoming bridge inspection data were split into 15 subsets based on 5 explanatory variables, and deterioration models were developed for each subset. Error analysis showed that logistic regression performed marginally better than traditional methods when estimating the transition probability matrix when limited data are accessible.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors appreciate the cooperation from WyDOT employees Paul Cortez, Brenden Schaefer, and Hyungseop Shim.
References
Abed-Al-Rahim, I. J., and D. W. Johnston. 1995. “Bridge element deterioration rates.” Transp. Res. Rec. 1490: 9–18.
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.
Ariaratnam, S. T., A. El-Assaly, and Y. Yang. 2001. “Assessment of infrastructure inspection needs using logistic models.” J. Infrastruct. Syst. 7 (4): 160–165. https://doi.org/10.1061/(ASCE)1076-0342(2001)7:4(160).
Baik, H. S., H. S. Jeong, and D. M. Abraham. 2006. “Estimating transition probabilities in Markov chain-based deterioration models for management of wastewater systems.” J. Water Resour. Plann. Manage. 132 (1): 15–24. https://doi.org/10.1061/(ASCE)0733-9496(2006)132:1(15).
Ben-Akiva, M., and D. Gopinath. 1995. “Modeling infrastructure performance and user costs.” J. Infrastruct. Syst. 1 (1): 33–43. https://doi.org/10.1061/(ASCE)1076-0342(1995)1:1(33).
Bocchini, P., D. Saydam, and D. M. Frangopol. 2013. “Efficient, accurate, and simple Markov chain model for the life-cycle analysis of bridge groups.” Struct. Saf. 40: 51–64. https://doi.org/10.1016/j.strusafe.2012.09.004.
Bu, G. P., J. H. Lee, H. Guan, Y. C. Loo, and M. Blumenstein. 2014. “Prediction of long-term bridge performance: Integrated deterioration approach with case studies.” J. Perform. Constr. Facil 29 (3): 04014089. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000591.
Butt, A. A., M. Y. Shahin, K. J. Feighan, and S. H. Carpenter. 1987. “Pavement performance prediction model using the Markov process.” Transp. Res. Rec. 1123: 12–19.
Cesare, M. A., C. Santamarina, C. Turkstra, and E. H. Vanmarcke. 1992. “Modeling bridge deterioration with Markov chains.” J. Transp. Eng. 118 (6): 820–833. https://doi.org/10.1061/(ASCE)0733-947X(1992)118:6(820).
Chang, M., M. Maguire, and S. Yan. 2017. “Framework for mitigating human bias in selection of explanatory variables for bridge deterioration modeling.” J. Infrastruct. Syst. 23 (3): 04017002. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000352.
Chase, S. B., and L. Gáspár. 2000. “Modeling the reduction in load capacity of highway bridges with age.” J. Bridge Eng. 5 (4): 331–336. https://doi.org/10.1061/(ASCE)1084-0702(2000)5:4(331).
Cox, D. R. 1958. “The regression analysis of binary sequences.” J. R. Stat. Soc. Ser. B (Methodol.) 20 (2): 215–242.
Davis, S. L., D. Goldberg, K. DeGood, N. Donohue, and J. Corless. 2013. The fix we’re in for: The state of our nation’s bridges 2013. Washington, DC: Transportation for America.
Estes, A. C., and D. M. Frangopol. 2001. “Minimum expected cost-oriented optimal maintenance planning for deteriorating structures: Application to concrete bridge decks.” Reliab. Eng. Syst. Saf. 73 (3): 281–291. https://doi.org/10.1016/S0951-8320(01)00044-8.
FHWA (Federal Highway Administration). 2011. Bridge preservation guide: Maintaining a state of good repair using cost effective investment strategies. Washington, DC: FHWA.
FHWA (Federal Highway Administration). 2014. “National Bridge Inventory (NBI).” Accessed December 31, 2016. http://www.fhwa.dot.gov/bridge/nbi.cfm.
Frangopol, D. M., M. J. Kallen, and J. M. Van 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.
Ford, K. M., M. H. R. Arman, S. Labi, K. C. Sinha, P. D. Thompson, A. M. Shirole, and Z. Li. 2012. Estimating life expectancies of highway assets. Washington, DC: Transportation Research Board.
Grall, A., L. Dieulle, C. Bérenguer, and M. Roussignol. 2002. “Continuous-time predictive-maintenance scheduling for a deteriorating system.” IEEE Trans. Reliab. 51 (2): 141–150. https://doi.org/10.1109/TR.2002.1011518.
Hatami, A., and G. Morcous. 2011. “Developing deterioration models for Nebraska bridges.”. Lincoln, NE: Nebraska Department of Roads (NDOR).
Hatami, A., and G. Morcous. 2015. “Deterministic and probabilistic lifecycle cost assessment: Applications to Nebraska bridges.” J. Perform. Constr. Facil 30 (2): 04015025. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000772.
Hearn, G., D. Frangopol, M. Chakravorty, S. Myers, B. Pinkerton, and A. J. Siccardi. 1993. “Automated generation of NBI reporting fields from Pontis BMS database.” In Infrastructure: Planning and management, edited by J. L. Gifford, D. R. Uzarski, and S. McNeil, 226–230. Reston, VA: ASCE.
Hong, T., M. J. Chae, D. Kim, C. Koo, K. S. Lee, and K. H. Chin. 2013. “Infrastructure asset management system for bridge projects in South Korea.” KSCE J. Civ. Eng. 17 (7): 1551–1561. https://doi.org/10.1007/s12205-013-0408-8.
Jiang, Y., M. Saito, and K. C. Sinha. 1988. “Bridge performance prediction model using the Markov chain.” Transp. Res. Rec. 1180: 25–32.
Koo, D. H., and S. T. Ariaratnam. 2006. “Innovative method for assessment of underground sewer pipe condition.” Autom. Constr. 15 (4): 479–488. https://doi.org/10.1016/j.autcon.2005.06.007.
Lewis, R. J. 2000. “An introduction to classification and regression tree (CART) analysis.” In Proc., Annual Meeting of the Society for Academic Emergency Medicine, 1–14. Des Plaines, IL: Society for Academic Emergency Medicine.
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).
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).
Morcous, G. 2006. “Performance prediction of bridge deck systems using Markov chains.” J. Perform. Constr. Facil 20 (2): 146–155. https://doi.org/10.1061/(ASCE)0887-3828(2006)20:2(146).
Pittou, M., M. G. Karlaftis, and Z. Li. 2009. “Nonparametric binary recursive partitioning for deterioration prediction of infrastructure elements.” Adv. Civ. Eng. 2009: 809767. https://doi.org/10.1155/2009/809767.
Ranjith, S., S. Setunge, R. Gravina, and S. Venkatesan. 2011. “Deterioration prediction of timber bridge elements using the Markov chain.” J. Perform. Constr. Facil 27 (3): 319–325. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000311.
Saeed, T. U., M. Moomen, A. Ahmed, J. Murillo-Hoyos, M. Volovski, and S. Labi. 2017. “Performance evaluation and life prediction of highway concrete bridge superstructure across design types.” J. Perform. Constr. Facil 31 (5): 04017052. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001051.
Sinha, K. C., M. Saito, Y. Jiang, S. Murthy, A. B. Tee, and M. D. Bowman. 1988. The development of optimal strategies for maintenance, rehabilitation and replacement of highway bridges, Vol. 1: The elements of the Indiana bridge management system (IBMS). West Lafayette, IN: Joint Highway Research Project, Indiana Dept. of Transportation and Purdue Univ.
Sobanjo, J., P. Mtenga, and M. Rambo-Roddenberry. 2010. “Reliability-based modeling of bridge deterioration hazards.” J. Bridge Eng. 15 (6): 671–683. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000074.
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.
Tibshirani, R. 1996. “Regression shrinkage and selection via the LASSO.” J. R. Statist. Soc. Ser. B 58 (1): 267–288.
Veshosky, D., C. R. Beidleman, G. W. Buetow, and M. Demir. 1994. “Comparative analysis of bridge superstructure deterioration.” J. Struct. Eng. 120 (7): 2123–2136. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:7(2123).
Information & Authors
Information
Published In
Journal of Infrastructure Systems
Volume 25 • Issue 1 • March 2019
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jan 25, 2017
Accepted: Aug 10, 2018
Published online: Dec 11, 2018
Published in print: Mar 1, 2019
Discussion open until: May 11, 2019
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.