Type of Document Dissertation Author Thomas, Omar St. A. A. URN etd-07052011-181038 Title Stochastic Preservation Model for Transportation Infrastructure Degree Doctor of Philosophy Department Civil and Environmental Engineering, Department of Advisory Committee
Advisor Name Title John Sobanjo Committee Chair Lisa Spainhour Committee Member Primus Mtenga Committee Member Eric Chicken University Representative Keywords
- Asset Management
- Markov Chain
- Sojourn Time
- Bridge Management
- Pavement Management
Date of Defense 2011-06-16 Availability unrestricted AbstractIn 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.
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