Keywords: Markov theory, optimisation, pavement deterioration, pavement management, probabilistic models, transition matrices.

Intuitively, the deterioration pattern of pavements is not deterministic but is instead probabilistic in nature [1]. It is therefore suggested that those management systems utilising stochastic models are better able to match the likely patterns of pavement deterioration. Such models require distributions of current condition and associated transition matrices to model the deterioration of the road network. Distributions of condition can be satisfactorily determined from any sound road database. Clearly, the challenge is therefore to determine the transition matrix with which to model the process.

The derivation of transition matrices has traditionally been effected using one of two methods. The standard approach is to observe, from historical data, the way in which a road network deteriorates from one year to the next and use this to estimate the transition matrix probabilities. Alternatively, a panel of experienced engineers can be used to estimate the probabilities using expert opinion. A third method utilising previously calibrated deterministic deterioration models, coupled with an estimate of scatter or confidence in the model, has been developed by Ortiz-Garcia et al. [2]. This third method has now been taken forward and encapsulated in an analytical tool, called the transition matrix calculator, to assist the engineer in the formulation of transition matrices.

The approach is based on utilising previously calibrated deterministic deterioration models. As these have already been calibrated an estimate of scatter or confidence in the model will be known. The optimisation process consists of obtaining the transition probabilities, , of the transition matrix that minimise the difference between the condition distribution obtained from the deterministic model over the analysis period and that obtained from the transition matrix itself. The optimisation is performed using the Generalised Reduced Gradient (GRG2) non-linear optimisation code developed by Fylstra et al. [3] incorporated within the `Solver' program.

The transition matrix calculator is described and demonstrated through its use to produce a stochastic model for the prediction of ride comfort. The original deterministic model predicts the value of Riding Comfort Index, , as a function of the pavement age, , the previous Riding Comfort Index, , and the change in age, , between successive calculations [4]. The results of the optimisation are presented in the form of a deterioration trend line for both the original deterministic model and the resultant transition matrix, as represented by the average of the yearly distributions. While these can be visually compared for `goodness of fit' it should, however, be noted that the yearly distributions of condition using both methods should also be compared to assess the success or otherwise of the optimisation process.

The transition matrix calculator, developed as part of this research, provides a platform for engineers to develop transition matrices from the more familiar deterministic models. However, it is important to note that the deterministic models selected to generate the matrices should be chosen with care, as the predictive power of the transition matrix depends solely on the accuracy of the original deterministic model and its associated scatter.

1

Butt, A.A., Shahin, M.Y., Feighan, K.J., Carpenter, S.H., "Pavement Performance Prediction Model using the Markov Process", Transportation Research Record 1123, Transportation Research Board, Washington, D.C., 12-19, 1987.

2

Ortiz-García, J.J., Costello, S.B., Snaith, M.S. "Derivation of Markov Transition Probability Matrices from Deterministic Models", submitted for publication, 2004.

3

Fylstra, D., Lasdon, L., Watson, J., Warren, A., "Design and use of the Microsoft Excel Solver", Interfaces, 28(5), 29-55, 1998. doi:10.1287/inte.28.5.29

4

Karan, M.A., Christison, T.S., Cheetham, A., Berdahl, G., "Development and Implementation of Alberta's Pavement Information and Needs System", Transportation Research Record 938, Transportation Research Board, Washington, D.C., 11-20, 1983.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)