| Abstract: | This work is devoted to constructing a stochastic analysis model for train–track? interaction. The fundamentals of the modelling framework in the establishment of the dynamic model, simulation of system uncertainties and randomness propagation process have been properly illustrated and unified in detail. For modelling train–track interaction, a matrix representation method is developed to depict the displacement compatibility and force equilibrium between the train and tracks. This dynamic model possesses advantages in computational stability and accuracy. Using uncertainty quantification approaches, the randomness of system geometries and longitudinal inhomogeneity of system properties can be simulated properly. Finally, the probabilistic transmission between the system inputs and response outputs are investigated from physical concepts, and a family of probability density evolution methods is introduced. Following the fundamental framework of train–track stochastic analysis, numerical examples are presented in detail to show the efficiency and accurateness of the proposed model. Moreover, the applications and advancements of this model in reliability assessment, response and frequency analysis, derailment, etc., are illustrated. |
