Calibrating Markov Chain–Based Deterioration Models for Predicting Future Conditions of Railway Bridge Elements
Publication: Journal of Bridge Engineering
Volume 20, Issue 2
Abstract
Existing nonlinear optimization-based algorithms for estimating Markov transition probability matrix (TPM) in bridge deterioration modeling sometimes fail to find optimum TPM values, and hence lead to invalid future condition prediction. In this study, a Metropolis-Hasting algorithm (MHA)-based Markov chain Monte Carlo (MCMC) simulation technique is proposed to overcome this limitation and calibrate the state-based Markov deterioration models (SBMDM) of railway bridge components. Factors contributing to rail bridge deterioration were identified; inspection data for 1,000 Australian railway bridges over 15 years were reviewed and filtered. The TPMs corresponding to a typical bridge element were estimated using the proposed MCMC simulation method and two other existing methods, namely, regression-based nonlinear optimization (RNO) and Bayesian maximum likelihood (BML). Network-level condition state prediction results obtained from these three approaches were validated using statistical hypothesis tests with a test data set, and performance was compared. Results show that the MCMC-based deterioration model performs better than the other two methods in terms of network-level condition prediction accuracy and capture of model uncertainties.
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Acknowledgments
This research was supported by the Cooperative Research Centre (CRC) for Rail Innovation Australia under Project R3.118: Life Cycle Management of Railway Bridges.
References
AASHTO. (2005). Pontis technical manual. Release 4.4, Washington, DC.
Agrawal, A. K., Kawaguchi, A., and Chen, Z. (2009). “Bridge element deterioration rates,” Rep. No. C-01-51, New York State DOT, Albany, NY.
Agrawal, A. K., Kawaguchi, A., and Chen, Z. (2010). “Deterioration rates of typical bridge elements in New York.” J. Bridge Eng., 419–429.
Baik, H.-S., Jeong, H. S., and Abraham, D. M. (2006). “Estimating transition probabilities in Markov chain-based deterioration models for management of wastewater systems.” J. Water Resour. Plann. Manage., 15–24.
Bolukbasi, M., Mohammadi, J., and Arditi, D. (2004). “Estimating the future condition of highway bridge components using National Bridge Inventory data.” Pract. Period. Struct. Des. Constr., 16–25.
Brooks, S. (1998). “Markov chain Monte Carlo method and its application.” J. R. Stat. Soc.: Ser. D, 47(1), 69–100.
Brooks, S., Gelman, A., Jones, G. L., and Meng, X.-L., eds. (2011). Handbook of Markov chain Monte Carlo, CRC Press, Boca Raton, FL.
Bu, G., Lee, J., Guan, H., Blumenstein, M., and Loo, Y.-C. (2012). “Development of an integrated method for probabilistic bridge-deterioration modeling.” J. Perform. Constr. Facil., 330–340.
Bulusu, S., and Sinha, K. C. (1997). “Comparison of methodologies to predict bridge deterioration.” Transportation Research Record 1597, Transportation Research Board, Washington, DC, 34–42.
Butt, A. A., Shahin, M. Y., Feighan, K. J., and Carpenter, S. H. (1987). “Pavement performance prediction model using the Markov process.” Transportation Research Record 1123, Transportation Research Board, Washington, DC, 12–19.
Camahan, J. V., Davis, W. J., Shahin, M. Y., Keane, P. L., and Wu, M. I. (1987). “Optimal maintenance decisions for pavement management.” J. Transp. Eng., 554–572.
Capper, O., Moulines, E., and Ryden, T. (2005). Inference in hidden Markov models, Springer, New York.
Chib, S., and Greenberg, E. (1995). “Understanding the Metropolis-Hastings algorithm.” J. Am. Stat. Assoc., 49(4), 327–335.
Cipra, B. A. (2000). “The best of the 20th century: Editors name top 10 algorithms.” SIAM News, 33(4), 〈http://www.siam.org/pdf/news/637.pdf〉 (Apr. 25, 2014).
Cowles, M. K., and Carlin, B. P. (1996). “Markov chain Monte Carlo convergence diagnostics: A comparative review.” J. Am. Stat. Assoc., 91(434), 883–904.
Devraj, D. (2009). “Application of non-homogeneous Markov chains in bridge management systems.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Wayne State Univ., Detroit.
Frangopol, D., Kallen, M., and Noortwijk, J. (2004). “Probabilistic models for life-cycle performance of deteriorating structures: Review and future directions.” Prog. Struct. Eng. Mater., 6(4), 197–212.
Gelman, A. (1996). “Inference and monitoring convergence.” Markov chain Monte Carlo in practice, W. R. Gilks, S. Richardson, and D. T. Spiegelhalter, eds., Chapman & Hall, London, 131–143.
Gelman, A., Carlin, J., Stern, H., and Rubin, D. (2004). Bayesian data analysis, 2nd Ed., Chapman & Hall, London.
Gelman, A., and Rubin, D. B. (1992). “Inference from iterative simulation using multiple sequences.” Stat. Sci., 7(4), 403–532.
Hong, F., and Prozzi, J. A. (2006). “Estimation of pavement performance deterioration using Bayesian approach.” J. Infrastruct. Syst., 77–86.
Jiang, Y. (1990). “The development of performance prediction and optimization models for bridge management systems.” Ph.D. thesis, Purdue Univ., West Lafayette, IN.
Jiang, Y., and Sinha, K. C. (1989a). “Bridge service life prediction model using the Markov chain.” Transportation Research Record 1223, Transportation Research Board, Washington, DC, 24–30.
Jiang, Y., and Sinha, K. C. (1989b). “The development of optimal strategies for maintenance, rehabilitation and replacement of highway bridges: Vol. 6—Performance analysis and optimization.” Rep. No. FHWA/IN/JHRP-89/13, Purdue Univ, West Lafayette, IN.
Kallen, M. J. (2010). “A comparison of statistical models for visual inspection data.” Safety, reliability and risk of structures, infrastructures and engineering systems, H. Furuta, D. M. Frangopol, and M. Shinozuka, eds., Taylor & Francis Group, London, 3235–3242.
Kobayashi, K., Kaito, K., and Lethanh, N. (2012). “A statistical deterioration forecasting method using hidden Markov model for infrastructure management.” Transp. Res. Part B: Method., 46(4), 544–561.
Le, B., and Andrews, J. (2013). “Modelling railway bridge asset management.” J. Rail Rapid Transit, 227(4), 644–656.
Madanat, S., Mishalani, R., and Ibrahim, W. H. W. (1995). “Estimation of infrastructure transition probabilities from condition rating data.” J. Infrastruct. Sys., 120–125.
Manamperi, P., and Lake, N. (2013). “Bridge management using performance models,” Project No. AT1537, Austroads, Sydney, Australia.
Martinez, W. L., and Martinez, A. R. (2002). Computational statistics handbook with MATLAB 2002, CRC Press, Boca Raton, FL.
MATLAB 8.0.0.783 (R2012b) [Computer software]. Natick, MA, MathWorks.
Micevski, T., Kuczera, G., and Coombes, P. (2002). “Markov model for storm water pipe deterioration.” J. Infrastruct. Syst., 49–56.
Mishalani, R. G., and Madanat, S. M. (2002). “Computation of infrastructure transition probabilities using stochastic duration models.” J. Infrastruct. Syst., 139–148.
Morcous, G. (2006). “Performance prediction of bridge deck systems using Markov chains.” J. Perform. Constr. Facil., 146–155.
Morcous, G., and Hatami, A. (2011). “Developing deterioration models for Nebraska bridges.” Project No. SPR-P1(11) M302, Final Rep., Nebraska Dept. of Roads, Lincoln, NE.
Morcous, G., Rivard, H., and Hanna, A. M. (2002). “Case-based reasoning system for modeling infrastructure deterioration.” J. Comput. Civ. Eng., 104–114.
Nielsen, D., Chattopadhyay, G., and Dhamodharan, R. (2012). “Life cycle management of railway bridges: Defect management.” Proc., Conf. on Railway Engineering, Railway Technical Society of Australasia, Canberra, Australia, 425–434.
Onar, A., Thomas, F., Choubane, B., and Byron, T. (2007). “Bayesian degradation modeling in accelerated pavement testing with estimated transformation parameter for the response.” J. Transp. Eng., 677–687.
Prasad, P., Bridgwood, M., and Coe, D. (2007). “Implementation of a bridge management system with the Australian Rail Track Corporation.” Proc., 2nd Australian Small Bridges Conf., CommStrat, VIC, Australia, 1–11.
Radomski, W. (2002). Bridge rehabilitation, 1st Ed., Imperial College Press, London.
Ranjith, S., Setunge, S., Gravina, R., and Venkatesan, S. (2013). “Deterioration prediction of timber bridge elements using the Markov chain.” J. Perform. Constr. Facil., 319–325.
Robert, C., Ryden, T., and Titterington, D. M. (2000). “Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method.” J. R. Stat. Soc.: Ser. B, 62(1), 57–75.
Roberts, G. O., and Rosenthal, J. S. (2001). “Optimal scaling for various Metropolis-Hastings algorithms.” Stat. Sci., 16(4), 312–390.
Roelfstra, G., Hajdin, R., Adey, B., and Brühwiler, E. (2004). “Condition evolution in bridge management systems and corrosion-induced deterioration.” J. Bridge Eng., 268–277.
Scherer, W. T., and Glagola, D. M. (1994). “Markovian models for bridge maintenance management.” J. Transp. Eng., 37–51.
Schervish, M. J. (1995). Theory of statistics, Springer, New York.
Scott, S. L. (2002). “Bayesian methods for hidden Markov models: Recursive computing in the 21st century.” J. Am. Stat. Assoc., 97(457), 337–351.
Sorensen, D., and Gianola, D. (2002). Likelihood, Bayesian and MCMC methods in quantitative genetics, Springer, New York.
Tran, H. D. (2007). “Investigation of deterioration models for stormwater pipe systems.” Ph.D. thesis, School of Architectural, Civil and Mechanical Engineering, Victoria Univ., Melbourne, Australia.
Tran, H. D., Perera, B., and Ng, A. (2009). “Comparison of structural deterioration models for stormwater drainage pipes.” Comput. Aided Civ. Infrastruct. Eng., 24(2), 145–156.
Veshosky, D., and Beidleman, C. R. (1996). “Closure to ‘Comparative analysis of bridge superstructure deterioration’ by David Veshosky and Carl R. Beidleman.” J. Struct. Eng., 710–711.
Veshosky, D., Beidleman, C. R., Buetow, G. W., and Demir, M. (1994). “Comparative analysis of bridge superstructure deterioration.” J. Struct. Eng., 2123–2136.
Yin, F., Mou, J., and Qiu, J. (2011). “A Bayesian MCMC approach to study the safety of vessel traffic.” Proc., 1st Int. Conf. on Transportation Information and Safety (ICTIS), X. Yan, P. Yi, C. Wu, and M. Zhong, eds., ASCE, Reston, VA, 1838–1847.
Zhang, J., Wan, C., and Sato, T. (2013). “Advanced Markov chain Monte Carlo approach for finite element calibration under uncertainty.” Comput. Aided Civ. Infrastruct. Eng., 28(7), 522–530.
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Published In
Journal of Bridge Engineering
Volume 20 • Issue 2 • February 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 8, 2013
Accepted: Apr 11, 2014
Published online: May 14, 2014
Published in print: Feb 1, 2015
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