Back-calculation of transition probabilities for Markovian-based pavement performance prediction models

Abstract

This paper presents a new technique to estimate the transition probabilities used in the Markovian-based pavement performance prediction models. The proposed technique is based on the 'back-calculation' of the discrete-time Markov model using only two consecutive cycles of pavement distress assessment. The transition probabilities, representing the pavement deterioration rates, are the main elements of the Markov model used in predicting future pavement conditions. The paper also presents a simplified procedure for evaluating the pavement state of distress using the two major pavement defect groups, namely cracking and deformation. These two defect groups are to be identified and evaluated for pavement sections using visual inspection and simple linear measurements. The extent of these two major defect groups is measured using the defected pavement areas (or lengths) and the defect severity is measured based on the average crack width and average deformation depth. A case study is presented to demonstrate the 'back-calculation' of transition probabilities. In particular, the impacts of the pavement section length on the distress rating and on the estimation of the transition probabilities have been investigated. The results have indicated that the estimated transition probabilities become highly unstable as the section length gets larger and the sample size becomes smaller.

Empirical approach for estimating the pavement transition probabilities used in non-homogenous Markov chains

“…The non-homogenous transition probabilities, P(k) i,iþ1 , representing pavement deterioration rates, can analytically be derived from the outlined non-homogenous Markov model as a function of the state probabilities associated with two consecutive transitions, (k) and (k 2 1) (Abaza 2014). The result of this matrix multiplication product is presented in Equation (4).…”

“…This means the transition probabilities associated with the transition matrix remain unchanged over time which is an unrealistic assumption when modelling pavement performance. The transition probabilities representing pavement deterioration rates are generally expected to increase over time due to the increase in traffic loading and weakening of the pavement structure (Abaza 2014 1xm ¼ (1xm) column vector representing state probabilities after k transitions, S ð0Þ mx1 ¼ (mx1) row vector representing initial state probabilities, P ðkÞ mxm ¼ (mxm) transition matrix raised to the kth power, m ¼ number of deployed pavement condition states and n ¼ number of deployed discrete-time intervals (transitions).…”

“…Estimation of a transition probability matrix requires conducting pavement distress assessment for two q 2015 Taylor & Francis *Email: kabaza@birzeit.edu International Journal of Pavement Engineering, 2015Engineering, http://dx.doi.org/10.1080Engineering, /10298436.2015 consecutive transitions; therefore, historical records of pavement distress must be available for the entire analysis period if the non-homogenous transition probabilities are to be estimated. A recent publication by Abaza (2014) has proposed a staged-homogenous Markov chain in which a new transition probability matrix can be introduced every five-year period, thus providing an economical alternative over the non-homogenous approach.…”

Developing Pavement Distress Deterioration Models for Pavement Management System Using Markovian Probabilistic Process

“…A TPM represents the probability that a segment will stay in a speci c condition for a speci c year. For example, Table 2 represents a TPM of a roadway network [6,7,18]. It was assumed that the pavement condition ranges from 1 to 5, where 5 represents the best condition and 1 is for the worst.…”

Remaining Useful Life Estimation Based on Asynchronous Multisource Monitoring Information Fusion

“…Si et al in [6] reviewed the statistical data driven approaches for RUL estimation. The existing methods were classified into two categories: direct condition monitoring data based approaches and indirect condition monitoring data based approaches, which can be further divided into stochastic filtering based methods [7][8][9][10], covariance based hazard model methods [11,12], Wiener-process-based methods [13,14], Gamma process based methods [15,16], and Markovian-based methods [17] and others.…”