Stochastic Preservation Model for Transportation Infrastructure

In this dissertation new methodologies were developed to address some of the existing needs as it relates to Transportation Asset Management Systems (TAMS). The goal of TAMS is to model the performance and preservation of transportation infrastructure. Currently, traditional Bridge Management Systems (BMS) such as Pontis® and BRIDGIT® utilize Markov chain processes in their performance and preservation models. Markov models have also been suggested and used at some State transportation agencies for modeling the performance of highway pavement structures. The Markov property may be considered restrictive when modeling the deterioration of transportation assets, primarily because of the "memoryless" property. In other words, the Markov property assumes that the sojourn times in the condition states follows an exponential distribution for the continuous-time Markov chain, and a geometric distribution for the discrete-time Markov chain. This research addresses some of the limitations that arise from the use of purely Markov chain deterioration and performance models for transportation infrastructure, by introducing alternative approaches that are based on the semi-Markov process and reliability functions. The research outlines in detail an approach to develop semi-Markov deterioration models for flexible highway pavements and American Association of State Highway Transportation Officials (AASHTO) Commonly Recognized (CoRe) Bridge Elements. This takes into consideration the probability of transitions between condition states and the sojourn time in a particular condition state before transitioning to another condition state. The proposed semi-Markov models are compared against the traditional Markov chain models. With Weibull distribution as the assumed distribution of the sojourn time in each condition state, for both the pavement and bridge deterioration models, Maximum Likelihood Estimation (MLE) was used to determine the estimates of the distribution parameters. For the pavement deterioration, the comparison of the semi-Markov and Markov chain models is presented, based on a Monte Carlo simulation of the condition. For the bridge element deterioration, the proposed semi-Markov model is compared against another semi-Markov approach outlined by Black et al. (2005a,b). A Bayesian-updated model was also compared to the proposed semi-Markov model. The research findings on the semi-Markov modeling validates the hypothesis that the rate of deterioration of pavements and bridge elements tends to increase over time. The results obtained from this study outlined a feasible alternative method in which historical condition data can be used to model the deterioration of pavement and bridge elements based on semi-Markov processes. For pavement deterioration, the semi-Markov model appeared to be superior to that of the Markov chain model in predicting the pavement conditions for the first five years subsequent to a major rehabilitation. The approach by Black et al. (2005a,b), which was applied to bridge element deterioration, assumes that the proportion of asset in state i at interval t is equal to the total probability of that asset being in state i after the t-th interval. It was discovered that this may not be true when the sample size of the asset being analyzed gets relatively small. Black et al. (2005a,b) used a least squares optimization technique to estimate the parameters of the (Weibull) sojourn time distribution, obtaining local optimal values, which may not best estimate the condition of the asset. An adaptive control approach for modeling the preservation of CoRe Bridge Elements based on Semi-Markov Decision Processes (SMDP) is also outlined in this dissertation. The methodology outlined in this study indicated that the use of SMDP can be used to determine the minimum long-term costs for the preservation of bridge elements from the CoRe Bridge Element data. The use of semi-Markov process to model deterioration relaxes the assumption of the distribution of the sojourn time between condition states for deterioration and improvement works, and therefore the SMDP model is less restrictive than Markov Decision Process (MDP) model. Also, Reliability (survival) functions were developed for both pavement segments and bridge elements to estimate their service lives. The Weibull regression and Cox Proportional Hazards models developed showed the association between factors, such as Average Daily Traffic (ADT) and the environment, and the condition of the asset over time. The proposed methodology outlined above is being researched at a time when there is a need for increased efficiency in the spending of government resources, while ensuring the preservation of the nation's transportation assets and network. The proposed stochastic models are based on the principles of semi-Markov processes, and address some of the limitations of the traditional Markov chain model. The survival analyses using the historical condition data allows for quick estimations as it relates to the service lives for bridge segments and bridge elements.