Optimal novel approach for estimating the pavement transition probabilities used in Markovian prediction models

Abstract

An optimal novel approach is proposed to estimate the transition probabilities associated with both homogeneous and non-homogeneous Markov chains. The approach applies an exhaustive optimisation technique to search for the optimal transition probabilities associated with minimal sum of squared errors (SSE), wherein the error defined as the difference between predicted and observed pavement condition ratings. Three state transitions are allowed in constructing the relevant transition probability matrix (TPM). In the homogenous chain, the approach yields one optimal TPM applicable to an analysis period of (n) years. Whereas, one distinct optimal TPM can be derived for each year if non-homogenous chain is deployed. A sequential iterative optimisation approach is proposed wherein the optimal TPM for a given year becomes the input for the subsequent year. Sample results are presented for two projects (A & B) with superior and inferior performances, respectively. The sample results indicate that the non-homogenous chain provided significant reduction in the SSE compared to the homogeneous one. However, the use of 10 condition states instead of 5 resulted in moderate reduction in the SSE considering both homogeneous and non-homogeneous Markov chains. Also, the results indicate that the use of three state transitions made significant impact when deploying 10 condition states instead of 5 especially in the case of inferior performance.