A Monte Carlo Markov Chain method to model pavement distress deterioration

This paper investigates a new statistical approach to identify the road propagation models and their explanatory. It applies a two-phase Monte Carlo Markov Chain (MCMC) method, which was previously developed for image processing and vehicles trajectory modelling. In the first phase, a specific equation is selected to model the distress propagation (sigmoid, exponential). This equation is governed by a set of internal and external (explanatory variables) parameters. Some initial realistic values are allocated to these parameters by a standard regression. In the second phase, the MCMC method itself is applied in an iterative approach. It is assumed that the probability distribution of each parameter is known. Each iteration starts with the substitution of the value of one of the parameters with another value generated by a random process exploiting the distribution of this parameter. A new model is thus built and compared to the former one, using the Metropolis-Hasting criteria. An “acceptance ratio” is calculated for the new model, which is equal to the weight of this model, divided by the weight of the previous one, multiplied by a coefficient which depends on the random distribution curve. The weight of a model is the mean quadratic distance between the distress real observations and the model predictions. The new equation belongs to the chain if the acceptance ratio is higher than 1. Else, a bigger ratio yields a bigger probability to keep it in the chain. As a first assessment, this method was tested and compared to other methods on simulated data, and then the results were confirmed on real data