A statistical deterioration forecasting method using hidden Markov model for infrastructure management

The application of Markov models as deterioration-forecasting tools has been widely documented in the practice of infrastructure management. The Markov chain models employ monitoring data from visual inspection activities over a period of time in order to predict the deterioration progress of infrastructure systems. Monitoring data play a vital part in the managerial framework of infrastructure management. As a matter of course, the accuracy of deterioration prediction and life cycle cost analysis largely depends on the soundness of monitoring data. However, in reality, monitoring data often contain measurement errors and selection biases, which tend to weaken the correctness of estimation results. In this paper, the authors present a hidden Markov model to tackle selection biases in monitoring data. Selection biases are assumed as random variables. Bayesian estimation and Markov Chain Monte Carlo simulation are employed as techniques in tackling the posterior probability distribution, the random generation of condition states, and the model’s parameters. An empirical application to the Japanese national road system is presented to demonstrate the applicability of the model. Estimation results highlight the fact that the properties of the Markov transition matrix have greatly improved in comparison with the properties obtained from applying the conventional multi-stage exponential Markov model.

[1]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[2]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[3]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[4]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Samer Madanat,et al.  Estimation of infrastructure transition probabilities from condition rating data , 1995 .

[6]  C. Robert,et al.  Estimation of Finite Mixture Distributions Through Bayesian Sampling , 1994 .

[7]  Tony Lancaster,et al.  The Econometric Analysis of Transition Data. , 1992 .

[8]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[9]  C. Robert,et al.  Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method , 2000 .

[10]  Eric Moulines,et al.  Inference in hidden Markov models , 2010, Springer series in statistics.

[11]  Haikady N. Nagaraja,et al.  Inference in Hidden Markov Models , 2006, Technometrics.

[12]  Le Thanh Nam,et al.  Stochastic optimization methods for infrastructure management with incomplete monitoring data , 2009 .

[13]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[14]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[15]  Kiyoyuki Kaito,et al.  BAYESIAN ESTIMATION OF WEIBULL HAZARD MODELS FOR DETERIORATION FORECASTING , 2006 .

[16]  Samer Madanat,et al.  Optimal infrastructure management decisions under uncertainty , 1993 .

[17]  Pablo Luis Durango-Cohen,et al.  A time series analysis framework for transportation infrastructure management , 2007 .

[18]  Frannie Humplick,et al.  HIGHWAY PAVEMENT DISTRESS EVALUATION: MODELING MEASUREMENT ERROR , 1992 .

[19]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[20]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[21]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[22]  Pablo Luis Durango-Cohen,et al.  Estimation of infrastructure performance models using state-space specifications of time series models , 2007 .

[23]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[24]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[25]  Moshe E. Ben-Akiva,et al.  Optimal Inspection and Repair Policies for Infrastructure Facilities , 1994, Transp. Sci..

[26]  Eun Sug Park,et al.  A Bayesian approach for improved pavement performance prediction , 2008 .

[27]  M. Y. Shahin,et al.  Pavement Management for Airports, Roads, and Parking Lots , 2006 .

[28]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[29]  Walter Zucchini,et al.  Series of Seminars: Hidden Markov Models for Time Series , 2013 .

[30]  Kiyoyuki Kaito,et al.  ESTIMATING MARKOVIAN TRANSITION PROBABILITIES FOR BRIDGE DETERIORATION FORECASTING , 2005 .

[31]  Kamal Golabi,et al.  Pontis: A System for Maintenance Optimization and Improvement of US Bridge Networks , 1997 .

[32]  Frank E. Grubbs,et al.  Errors of Measurement, Precision, Accuracy and the Statistical Comparison of Measuring Instruments , 1973 .

[33]  D. Hegsted,et al.  Errors of measurement. , 1989, Nutrition and cancer.

[34]  C. Robert.  Mixtures of Distributions: Inference and Estimation , 1996 .

[35]  Pablo Luis Durango-Cohen,et al.  Estimation of dynamic performance models for transportation infrastructure using panel data , 2008 .

[36]  S. Richardson,et al.  Mixtures of distributions: inference and estimation , 1995 .

[37]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[38]  Jorge A Prozzi,et al.  Estimation of Pavement Performance Deterioration Using Bayesian Approach , 2006 .

[39]  Liying Gong,et al.  Optimal infrastructure condition sampling over space and time for maintenance decision-making under uncertainty , 2009 .

[40]  S. P. Pederson,et al.  Hidden Markov and Other Models for Discrete-Valued Time Series , 1998 .

[41]  Samer Madanat,et al.  DEVELOPMENT OF A STOCHASTIC MODEL OF PAVEMENT DISTRESS INITIATION , 2003 .

[42]  Moshe Ben-Akiva,et al.  Infrastructure management under uncertainty: Latent performance approach , 1993 .

[43]  Subal C. Kumbhakar,et al.  Stochastic frontier analysis , 2000 .

[44]  W. G. Cochran.  Errors of Measurement in Statistics , 1968 .

[45]  Samer Madanat.  Incorporating inspection decisions in pavement management , 1993 .

[46]  Jeff Gill,et al.  Bayesian Methods: A Social and Behavioral Sciences Approach, Second Edition , 2007 .

[47]  Semyon G. Rabinovich,et al.  Measurement Errors and Uncertainties: Theory and Practice , 1999 .

[48]  By W. R. GILKSt,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 2010 .

[49]  Moshe E. Ben-Akiva,et al.  An Approach for Predicting Latent Infrastructure Facility Deterioration , 1993, Transp. Sci..

[50]  Chang‐Jin Kim,et al.  State-Space Models with Regime-Switching: Classical and Gibbs Sampling Approaches with Applications , 1999 .

[51]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[52]  S. L. Scott.  Bayesian Methods for Hidden Markov Models , 2002 .