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

Abstract

An empirical approach is proposed to estimate the transition probabilities associated with non-homogenous Markov chains typically used in developing stochastic-based pavement performance prediction models. A reliable pavement performance prediction model is a key component of any advanced pavement management system. The proposed empirical approach is designed to account for two major factors that cause the transition probabilities (i.e. deterioration rates) to increase over time. The first major factor is the progressive increase in traffic loading as represented by the equivalent single axle load applications. The second major factor is the gradual decline in the pavement structural capacity which can be represented by an appropriate pavement strength indicator such as the structural number. The proposed empirical model can recursively estimate the non-homogenous transition probabilities for an analysis period of (n) transitions by simply multiplying the first-year (i.e. present) transition probabilities by two adjustment factors, namely the load and strength factors. Once the empirical model is calibrated, these two factors can capture the impact of traffic load increases and gradual pavement structural losses on the transition probabilities over time. The calibration process requires the estimation of the model two exponents to be obtained from the minimisation of sum of squared errors wherein the error is defined as the difference between the observed and predicted pavement distress ratings (DRs). The predicted DRs are mainly estimated based on the state probabilities, which are recursively derived from the non-homogenous Markov model. A sample empirical model is presented with results indicating its effectiveness in estimating the pavement non-homogenous transition probabilities.

Keywords:

• transition probabilities
• Markovian processes
• pavement performance
• pavement management

Disclosure statement

No potential conflict of interest was reported by the author.