Infrastructure Deterioration Prediction with a Poisson Hidden Markov Model on Time Series Data

The deterioration of a pavement surface can be described in terms of the presence and severity of distinct distresses, like potholes, cracking, and rutting. Each deterioration process is ordinarily described by a set of pavement indicators (e.g., number of potholes, percentage of cracks, international roughness index) that are measured during monitoring and inspection activities. Manifestly, there exist statistical correlations among the deterioration processes. For instance, cracks appearing on a road section may contribute to an increase in pothole occurrence, and vice versa. In order to mathematically formulate the statistical interdependency among deterioration processes, a Poisson hidden Markov model is proposed in this paper. The model describes the complex process of pavement deterioration, which includes the frequent occurrence of local damage (e.g., potholes) as well as the degradation of other pavement indicators (e.g., cracks, roughness). To model the concurrent frequency of local damage, a stochastic Poisson process is used. At the same time, a Markov chain model is used to depict the degradation of other pavement indicators. A numerical estimation approach using Bayesian statistics with a Markov chain Monte Carlo simulation is developed to derive the values of the model’s parameters based on historical information. The applicability of the model was demonstrated through an empirical example using data from a Japanese highway road link.