The Bayesian methodology for the detection of railway ballast damage under a concrete sleeper

In this paper, a model-based method is proposed to address the problem of detecting railway ballast damage under a concrete sleeper. The rail-sleeper-ballast system is modelled as a Timoshenko beam on an elastic foundation with two masses representing the two rails. The uncertainties induced by modelling error and measurement noise are the major difficulties for vibration-based damage detection methods, and therefore, a probabilistic approach is adopted in this study for addressing the uncertainty problem. The proposed ballast damage detection methodology is conceptually divided into two phases. In the first phase, the Bayesian model class selection method is used to select the most plausible model class from a list of predefined candidates based on a given set of measurements. In the second phase, Bayesian model updating is adopted to calculate the posterior PDF of uncertain model parameters using the selected model class from the first phase. Damage to the ballast decreases its stiffness in supporting the sleeper, and it can be detected via the marginal posterior PDF of the ballast stiffness at different regions under the sleeper. A segment of full-scale ballasted track was constructed indoors and tested under laboratory conditions to demonstrate and verify the proposed methodology. Discussions related to the limitations of the proposed methodology in real application are given at the end of this paper.