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| 车-轨-桥耦合系统随机动力学高效分析的直接概率积分法 |
| DPIM for uncertainty propagation analysis of train-track-bridge coupling stochastic system |
| 投稿时间：2024-10-09 修订日期：2024-11-18 |
| DOI： |
| 中文关键词: 车-轨-桥耦合系统 多源随机性 随机过程 动力可靠度 脱轨概率 直接概率积分法 |
| 英文关键词:train-track-bridge coupling system, multi-source randomness, stochastic process, dynamic reliability, derailment probability, direct probability integral method |
| 基金项目:国家自然科学基金项目（青年项目，重点项目），中央高校基本科研业务费 |
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| 中文摘要: |
| 在桥梁上行驶的列车与轨道共同构成车-轨-桥耦合系统，会受到轨道不平顺和极端地震荷载等随机源的影响，导致列车存在脱轨风险。本文考虑轨道不平顺和地震动的随机不确定性，提出了车-轨-桥耦合系统随机动力学高效分析的直接概率积分法，实现车-轨-桥系统随机动力响应和行车安全概率安全评定。首先，建立三维车-轨-桥耦合系统随机动力学模型，开展轨道不平顺和近断层随机地震动不确定性量化与表征。其次，基于概率守恒原理的积分表述，导出了刻画随机不确定性在耦合系统中传播的概率密度积分方程。通过联立耦合系统动力学方程和概率密度积分方程，发展了三维车-轨-桥耦合系统随机动力学高效分析的直接概率积分法。将脱轨系数作为行车安全评价准则，建立列车过桥安全极限状态函数，实现了列车过桥可靠性评定。最后，通过数值算例论证了提出方法的精度和效率，揭示了列车脱轨概率与地震动强度之前的非线性关系，并探究了近断层地震动速度脉冲对列车脱轨概率的影响规律。 |
| 英文摘要: |
| Trains running on bridges and track form a train-track-bridge coupling system, which is subject to the excitations of random sources excitation, such as track irregularities and extreme seismic ground motions, leading to the risk of train derailment. This study considers the multiple sources randomness from track irregularity and seismic ground motions, and proposes the direct probability integration method (DPIM) for highly efficient stochastic analysis of the train-track-bridge coupling system (TTBCS). Firstly, a three-dimensional stochastic dynamic model of TTBCS is established, and the randomness of track irregularity and near-fault random ground motions are quantified and characterized. Secondly, probability density integral equation (PDIE) that illustrates the propagation of random uncertainty in the coupling system is derived based on the integral description of the principle of probability conservation. By combining the dynamic equations of the TTBCS with the PDIE, the efficient DPIM is then developed for stochastic dynamic response analysis of TTBCS. The derailment coefficient is taken as the evaluation criterion of train running safety, the limit state function of train crossing bridge safety is established, and the probabilistic safety evaluation of train crossing bridge safety is achieved. Finally, the accuracy and efficiency of the proposed method are demonstrated by numerical examples, revealing the nonlinear relationship between derailment probability and seismic intensity, and exploring the effect of velocity pulses of near-fault seismic on derailment probability of trains. |
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