Markovian Degradation Modeling of Rails

Rail defects pose a significant threat to railway safety and efficiency. Probabilistic modeling of defect propagation has the potential of improving decision-making for circumvention of dangerous rail degradation.

We propose a continuous-time Markov chain with transition rates regressed on location-dependent covariates to model discretely observed degradation trajectories discovered at the Norwegian rail network. We propose two estimation approaches. The first approach obtains the full data log-likelihood by Monte Carlo simulation of full data defect trajectories, which informs the Excectaion-Maximization algorithm. The second approach maximizes the discrete data log-likelihood informed by analytical gradient information.