Estimating Markovian Transition Probabilities for Bridge Deterioration Forecasting

Abstract

In this paper, a methodology to estimate the Markovian transition probability model is presented to forecast the deterioration process of bridge components. The deterioration states of the bridge components are categorized into several ranks, and their deterioration processes are characterized by hazard models. The Markovian transition probabilities between the deterioration states which are deåned for the åxed intervals between the inspection points in time, are described by the exponential hazard models. The applicability of the estimation methodology presented in this paper is investigated by the empirical data set of steel bridges in New York city.

Improving the Estimation of Markov Transition Probabilities Using Mechanistic-Empirical Models

“…However, others have explicitly developed models where that is not the case (Tsuda et al, 2006). Being able to estimate transition probabilities with data that have been collected at both uniform and non-uniform time intervals and allowing elements to move more than one condition state per time interval, it has been shown to increase the accuracy of the estimation of the transition probabilities in Markov models (Tsuda et al, 2006;Kobayashi et al, 2012b;Mizutani et al, 2013;Lethanh et al, 2015).…”

“…Many of the models were developed with the assumption that elements could jump no more than one state per time period, such as those used in Klein (1962), Carnahan et al (1987), Jiang et al (1988), Madanat and BenAkiva (1994), and Thompson et al (1998). However, others were developed without this assumption, such as those developed by Tsuda et al (2006) and Kobayashi et al (2012a,b). The former have the advantage that they are relatively easy to compute.…”

Estimation of Markovian transition probabilities for pavement deterioration forecasting

“…The authors proposed a methodology to describe the transition process between two adjacent deterioration state ranks, related to each other with a perpendicular transition, by using exponential hazard models (Tsuda et al, 2005). The objective for this paper is to develop a statistical deterioration model to take into account the irregular inspection intervals.…”

“…By using the exponential hazard function it is possible to represent a deterioration process of a road section that satisfies the Markov condition (Tsuda et al, 2005;Chung et al, 2006).…”

“…The assumption θ i ≠θ i+1 implies π ii+1 <1. For more detailed description it is suggested to readers to look at the references (Tsuda et al, 2005). The distribution function and the probability density function of a period length in which a condition state j remains constant is denoted by F i (y i ) and f j (y j ) respectively.…”