Bridge deck deterioration: A parametric hazard-based duration modeling approach

Christofas, PM; Karlaftis, MG

dc.contributor.author	Christofas, PM	en
dc.contributor.author	Karlaftis, MG	en
dc.date.accessioned	2014-03-01T02:50:19Z
dc.date.available	2014-03-01T02:50:19Z
dc.date.issued	2006	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35055
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-56749101657&partnerID=40&md5=2b6bdc3c9e204c3334845587fe71661e	en
dc.subject.other	Accurate predictions	en
dc.subject.other	Aft models	en
dc.subject.other	Bridge inventory datums	en
dc.subject.other	Censored datums	en
dc.subject.other	Censored observations	en
dc.subject.other	Concrete bridge decks	en
dc.subject.other	Condition evaluations	en
dc.subject.other	Covariates	en
dc.subject.other	Data base	en
dc.subject.other	Data sets	en
dc.subject.other	Dependent variables	en
dc.subject.other	Deterioration mechanisms	en
dc.subject.other	Deterioration phenomenons	en
dc.subject.other	Discrete models	en
dc.subject.other	Discrete representations	en
dc.subject.other	Duration models	en
dc.subject.other	Error terms	en
dc.subject.other	Estimation results	en
dc.subject.other	Explanatory variables	en
dc.subject.other	Extreme values	en
dc.subject.other	Failure times	en
dc.subject.other	Future researches	en
dc.subject.other	Indiana	en
dc.subject.other	Infra structures	en
dc.subject.other	Infrastructure facilities	en
dc.subject.other	Infrastructure maintenances	en
dc.subject.other	Inspection records	en
dc.subject.other	Linear regression models	en
dc.subject.other	Model specifications	en
dc.subject.other	Modeling approaches	en
dc.subject.other	Multicollinearity	en
dc.subject.other	Negative coefficients	en
dc.subject.other	Network levels	en
dc.subject.other	Normal models	en
dc.subject.other	ON currents	en
dc.subject.other	Ordinary Least squares	en
dc.subject.other	Parametric approaches	en
dc.subject.other	Parametric failures	en
dc.subject.other	Parametric forms	en
dc.subject.other	Parametric methods	en
dc.subject.other	Probabilistic models	en
dc.subject.other	Project levels	en
dc.subject.other	Protective systems	en
dc.subject.other	Quantitative variables	en
dc.subject.other	Rating systems	en
dc.subject.other	Reinforced concrete bridge decks	en
dc.subject.other	Road bridges	en
dc.subject.other	Statistical analysis	en
dc.subject.other	Stochastic processes	en
dc.subject.other	Sub structures	en
dc.subject.other	Survival datums	en
dc.subject.other	Survival models	en
dc.subject.other	Survival times	en
dc.subject.other	Time periods	en
dc.subject.other	Transition probabilities	en
dc.subject.other	Weibull	en
dc.subject.other	Bridge components	en
dc.subject.other	Bridge decks	en
dc.subject.other	Building materials	en
dc.subject.other	Concrete bridges	en
dc.subject.other	Concrete construction	en
dc.subject.other	Curve fitting	en
dc.subject.other	Deterioration	en
dc.subject.other	Drops	en
dc.subject.other	Forecasting	en
dc.subject.other	Hazards	en
dc.subject.other	Inspection	en
dc.subject.other	Life cycle	en
dc.subject.other	Linear regression	en
dc.subject.other	Maintenance	en
dc.subject.other	Management	en
dc.subject.other	Maximum likelihood estimation	en
dc.subject.other	Normal distribution	en
dc.subject.other	Probability	en
dc.subject.other	Probability distributions	en
dc.subject.other	Problem solving	en
dc.subject.other	Regression analysis	en
dc.subject.other	Reinforced concrete	en
dc.subject.other	Specifications	en
dc.subject.other	Statistical methods	en
dc.subject.other	Theorem proving	en
dc.subject.other	Bridges	en
dc.title	Bridge deck deterioration: A parametric hazard-based duration modeling approach	en
heal.type	conferenceItem	en
heal.publicationDate	2006	en
heal.abstract	Infrastructure Maintenance and Rehabilitation (M&R) decision making, either at the network level or at the project level, is based on current (measured) and future (predicted) infrastructure facility conditions. Therefore, accurate predictions of future infrastructure conditions are essential for effective M&R decision-making. Infrastructure condition is often represented by discrete ratings. For example, for bridge decks, the FHWA bridge-rating system is used most commonly. Bridge inspectors employ ratings of 0 to 9, with 9 representing near-perfect condition (FHWA 1979). The use of discrete representation of facility condition makes it necessary to develop discrete models of deterioration (Mauch and Madanat 2001). The deterioration of a concrete bridge deck is a stochastic process that varies widely with several factors, many of which are generally not captured by the available data. Therefore, probabilistic models are used to predict the deterioration of infrastructure facilities such as bridge decks. In this paper, we present duration models that predict the time between changes in condition-state for reinforced concrete bridge decks. To accomplish this, we used hazard based duration models that incorporate parametric methods. Hazard based duration models predict changes in condition over time as a function of a set of explanatory variables and are used to compute infrastructure transition probabilities. The remainder of the paper is organized as follows. Section 2 reviews the available data set and the basic specification for the hazard based duration model. Section 3, examines model specification issues and the estimation results for both the Log-Logistic and the Weibull hazard based duration models. The final Section summarizes the findings of this research. The data set used in this paper is part of the Indiana Bridge Inventory data base. It consists of approximately 5,700 state owned bridges from Indiana, and is a subset of the National Bridge Inventory (NBI) data base. The data set contains inspection records from 1978 through 1988. The condition evaluation rates the condition of the major bridge components, e.g. deck, superstructure, substructure, and so on, on a scale from 0 to nine, where bridges with a 0 rating are in the poorest condition and those with a rating of 9 in the best condition. The dependent variable of interest in our models is the time spent by a bridge deck in a given condition-state (variable name is 'time-in-state' (TIS)), extracted from consecutive inspection reports (earliest inspection year in the database was 1974 and most recent 1996). The class of parametric failure time models estimated in this paper are also known as the accelerated failure time (AFT) models. What is actually estimated, in practice, is a model rather similar to an ordinary linear regression model. In a linear regression model it is typical to assume that the error term (εi) has a normal distribution with a mean and variance that are constant over i, and that the es are independent across observations. One member of the AFT class, the log-normal model, has exactly these assumptions. Other AFT models allow distributions for ε other than the Normal (such as the extreme value, log-gamma, and logistic), but retain the assumptions of constant mean and variance, as well as the independence across observations. If there were no censored data, the parametric survival models could be estimated using Ordinary Least Squares (OLS). But, survival data typically have at least some censored observations, and these are difficult to handle with OLS. As a result, Maximum Likelihood is used to estimate the parameters. The basic thinking behind duration modeling is to examine whether the longer a bridge deck remains in the same condition state the more likely it is that it will drop one or more condition states within a specified time period. As is well known, the sign of coefficient estimates indicates the 'direction' of the relationship between the independent and dependent variables. The negative coefficient for AGE indicates that aging bridges drop to a lower condition state at higher rates than do newer bridges, as was expected. Interestingly, the magnitudes for the coefficients are, per se, informative as reported; but, with a simple transformation, these estimates lead to some interesting and intaitive interpretations. For a 0-1 variable such as WEARSURF, taking eβ (in the Log-Normal model) yields the estimated ratio of the expected (mean) survival times for the two groups; in the model presented above, for example, e-0.544 = 0.52. Therefore, controlling for other covariates, the expected time in a state for bridges with no protective systems is 52% lower than bridges with protective systems. For a quantitative variable such as AGE, the transformation 100(eβ - 1) is used, giving the percent decrease in fhe expected survival time for each one-unit increase in the variable. Thus, using this transformation for age, each additional year of age for an interstate and primary road bridge is associated with a 51,74% decrease in expected time in a state, holding other covariates constant. It is interesting to note that, for a number of variables such as REGION and AVGADT, the statistical analysis performed in this paper did not indicate a statistically significant relationship between these variables and TIS for a bridge deck. This result, although surprising at first, clearly indicates that the deterioration phenomenon is complex, with a number of interrelations affecting statistical analyses; this suggests that further refinement of the models is required and that non-parametric approaches that generally do not suffer from multicollinearity or make restricting assumptions regarding the parametric form of the underlying deterioration mechanism may be a promising avenue for future research. © 2006 Taylor & Francis Group.	en
heal.journalName	Proceedings of the 3rd International Conference on Bridge Maintenance, Safety and Management - Bridge Maintenance, Safety, Management, Life-Cycle Performance and Cost	en
dc.identifier.spage	449	en
dc.identifier.epage	450	en