Computational study demonstrates efficient stochastic dynamic analysis in partitioned vehicle-rail-bridge systems, highlighting accurate response prediction under high-dimensional uncertainties.
Stochastic dynamic response analysis of three-dimensional (3D) vehicle-rail-bridge (VRB) systems is challenging due to time-varying coupling, high-dimensional uncertainties, and strongly nonstationary and non-Gaussian response characteristics. This study develops an efficient stochastic dynamic analysis framework by introducing the dimension-reduced probability density evolution equation (DR-PDEE) into a non-iterative partitioned VRB model. The vehicle, rail, and bridge subsystems are formulated as time-invariant stochastic subsystems connected through time-dependent wheel-rail and time-independent rail-bridge interfaces, thereby avoiding repeated assembly and factorization of global time-varying system matrices. Based on this deterministic backbone, the DR-PDEE is used to characterize the time-varying probability density evolution of selected displacement responses under random system parameters and stochastic track irregularities. To improve numerical robustness for highly nonstationary and non-Gaussian VRB responses, a dimension-reduced Monte Carlo solution strategy is adopted for solving the DR-PDEE and compared with the classical path-integration scheme. Numerical results are validated against Monte Carlo simulations with 10,000 realizations. The proposed framework accurately captures nonstationary and non-Gaussian response distributions using a limited number of samples, demonstrating its efficiency and potential for stochastic analysis of complex coupled railway systems.
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Yuan et al. (2026) studied this question.
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