Stochastic vibration analysis of high-speed vehicle–bridge system under crosswind action based on probability density evolution method

Abstract

Crosswind is one of the key factors threatening the safety and stability of high-speed train operations. Due to the highly stochastic nature of natural wind fluctuations, traditional analysis methods struggle to accurately capture the full probabilistic information of system responses. This paper introduces the probability density evolution method (PDEM) to conduct an in-depth study on the stochastic vibration response of a high-speed vehicle–bridge coupled system under crosswind. First, a dynamic analysis model for the vehicle–bridge coupling system considering the randomness of aerodynamic loads is established. The stochastic wind load acting on the vehicle–bridge system is simulated using a non-stationary assumption, where the wind speed process is described as a spatially varying stationary Gaussian random field. Based on this, the probability density evolution method is applied by introducing random variables that characterize the essential randomness of the wind field, and a generalized probability density evolution equation is constructed to relate the system state quantities to these random variables. Using the multiple-distribution point selection method, a representative set of points is selected, ultimately obtaining the probability density function (PDF) and its evolution process of the stochastic dynamic response of the system. Taking a long-span cable-stayed bridge as an example, numerical simulations accurately reveal the complete evolution of the PDF of the system response in the time domain under crosswind. This method provides a more comprehensive and accurate theoretical tool and analytical approach for assessing the operational safety risks of high-speed trains crossing long-span bridges in crosswind environments.

Keywords

Crosswind / Stochastic vibration / Vehicle–bridge model / Probability density evolution theory

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Funding

National Natural Science Foundation of China(52478321)

Science and Technology Innovation Program of Hunan Province(2025RC3028)

China State Railway Group Co., Ltd. Science and Technology Research and Development Program Project(L2024G007)

Natural Science Foundation of Hunan Province(2024JJ5427)

Science and Technology Research and Development Program Project of China Railway Group Limited(No. 2022-Special-09)

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