A Bayesian methodology for detection of railway ballast damage using the modified Ludwik nonlinear model

In this paper, an improved nonlinear model of railway ballast is proposed based on the modified Ludwik model. The accuracy of model-based structural damage detection relies on the correct representation of the mechanical behavior of the system, hence the need for incorporating nonlinearity into track models. The modified form of the Ludwik model is proposed for describing the stress–strain relationship of the ballast layer during its loading and unloading. In this study, a section of ballasted track across a single sleeper is modeled using the beam on elastic foundation theory. In the finite element model of the track system, the concrete sleeper and the underlaying ballast are modeled by Timoshenko beam elements and a series of nonlinear springs, respectively. The elastoplasticity of these springs during the vertical vibration of the track system can be effectively captured using the proposed model, which can be easily integrated into the Bayesian statistical framework. For correct identification of the scaling factors of the system properties, as well as quantification of the inherent uncertainties, a time-domain Markov chain Monte Carlo-based Bayesian model updating method with a novel stopping criteria is developed. The efficacy of the proposed methodology is demonstrated using in-situ measurements obtained during impact hammer tests on an indoor full-scale track segment under laboratory conditions, with artificially simulated ballast damage. A series of impact hammer tests are carried out to study the effects of impact locations and sensor sparsity on the performance of the proposed methodology. The methodology exhibits very high accuracy in identifying the simulated ballast damage under the target sleeper, even with different impact and sensor configurations.