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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 94
Development of the Transition Matrix Calculator S.B. Costello+, J.J. Ortiz-García* and M.S. Snaith$
+Department of Civil and Environmental Engineering, University of Auckland, New Zealand
Full Bibliographic Reference for this paper
, "Development of the Transition Matrix Calculator", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 94, 2005. doi:10.4203/ccp.81.94
Keywords: Markov theory, optimisation, pavement deterioration, pavement management, probabilistic models, transition matrices.
Summary
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,
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, 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. References
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