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.

这项工作致力于构建火车-轨道交互的随机分析模型。建模框架在动态模型建立、系统不确定性模拟和随机性传播过程中的基本原理得到了适当的说明和统一。为了模拟火车-轨道相互作用，开发了一种矩阵表示方法来描述火车和轨道之间的位移兼容性和力平衡。这种动态模型在计算稳定性和准确性方面具有优势。使用不确定性量化方法，可以正确模拟系统几何形状的随机性和系统属性的纵向不均匀性。最后，从物理概念研究系统输入和响应输出之间的概率传输，并介绍了一系列概率密度演化方法。遵循列车-轨道随机分析的基本框架，详细介绍了数值例子，以证明所提出模型的效率和准确性。此外，还说明了该模型在可靠性评估、响应和频率分析、脱轨等方面的应用和进展。