Abstract
In this paper, a probabilistic model devoted to investigating the dynamic behaviors of train-bridge systems subjected to random track irregularities is presented, in which a train-ballasted track-bridge coupled model with nonlinear wheel-rail contacts is introduced, and then a new approach for simulating a random field of track irregularities is developed; moreover, the probability density evolution method is used to describe the probability transmission from excitation inputs to response outputs; finally, extended analysis from three aspects, that is, stochastic analysis, reliability analysis, and correlation analysis, are conducted on the evaluation and application of the proposed model. Besides, compared to the Monte Carlo method, the high efficiency and the accuracy of this proposed model are validated. Numerical studies show that the ergodic properties of track irregularities on spectra, amplitudes, wavelengths, and phases should be taken into account in stochastic analysis of train-bridge interactions. Since the main contributive factors concerning different dynamic indices are rather different, different failure modes possess no obvious or only weak correlations from the probabilistic perspective, and the first-order reliability theory is suitable in achieving the system reliability.
Highlights
Random Field of Track IrregularitiesRising from the manufacturing faultiness and environmental loads, e.g., cyclic wheel-rail interactions, material fatigue, and track settlement, track irregularities are characterized by high-dimensional randomicity in both spatial and temporal domains
Xu and Zhai [11, 12] pointed out that the ergodic properties of PSD probabilities, amplitudes, and wavelengths of track irregularities should be taken into account in the stochastic analysis of vehicle-track interactions and presented a track irregularity probabilistic model
Conclusions is paper introduces a 3D train-track-bridge coupled system with nonlinear wheel-rail interactions first. en, a probabilistic model is proposed to represent both spatial and spectral randomness of track irregularities. By combining these two models and probability density evolution method (PDEM), extensive studies are conducted on stochastic analysis, reliability analysis, and correlation analysis. e following remarks can be drawn from the results thereby obtained: (1) e full probability characteristics of track irregularities should be considered when assessing the random vibrations of train-bridge systems
Summary
Rising from the manufacturing faultiness and environmental loads, e.g., cyclic wheel-rail interactions, material fatigue, and track settlement, track irregularities are characterized by high-dimensional randomicity in both spatial and temporal domains. Xu and Zhai [11, 12] pointed out that the ergodic properties of PSD probabilities, amplitudes, and wavelengths of track irregularities should be taken into account in the stochastic analysis of vehicle-track interactions and presented a track irregularity probabilistic model. E approach on the PSD probability distribution of track irregularities from big data of measurements proposed by Xu and Zhai [11, 12] can be reconsidered as follows. W, is the discrete frequency point and min[·] and max[·] denote the minimum and maximum operators, respectively. Let Tυ,Ui(x) be a onedimensional stationary random process to characterize the PSD of track irregularity at cumulative probability Ui, denoted by Pυ,U′i(ω). K 0 in which ωk kΔω where Δω is the frequency interval; u(ω) and v(ω) are two mutually orthogonal real processes with
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