Fourier series-based reliability analysis of train-bridge interaction under crosswind action using fuzzy random uncertainty

High-speed trains crossing long-span railway bridges under crosswind loads can lead to complex dynamic responses, posing risks to both running safety and structural serviceability. These scenarios involve non-stationary wind excitations, high-frequency train–bridge interactions due to wheel–rail contact forces, and uncertain bridge damping arising from limited experimental data. Traditional analysis methods, deterministic, probabilistic, or fuzzy, often isolate individual uncertainty sources and may fail to capture the coupled, nonlinear behaviour of such systems. To overcome these limitations, a hybrid Fourier–fuzzy–reliability framework is proposed. The Fourier series characterizes dominant frequency-domain features, such as cyclic wheel–rail forces. Fuzzy logic models’ epistemic uncertainties, including imprecise damping ratios and variable wind parameters, while inherent randomness is represented by stochastic variables. These elements are unified through reliability analysis to evaluate failure probabilities of the train–bridge system under crosswind conditions. The framework is applied to a case study involving a high-speed train traversing the Yibin Lingang Bridge in China, and the method is validated against a Monte Carlo simulation, reducing computation time by up to 97 %. Results demonstrate that, unlike traditional methods, the proposed approach reveals a more realistic and progressive transition in failure probability with increasing vibration amplitudes, offering enhanced reliability insights for wind-resilient railway bridge design and operation.