首页|基于直接概率积分法的列车-轨道-桥梁系统随机分析

基于直接概率积分法的列车-轨道-桥梁系统随机分析

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由于施工和制造误差使得铁路工程结构参数不可避免地具有不确定性,同时作为系统主要自激励的轨道不平顺亦具有明显的随机性和时变性,因此,探明不确定因子对列车和轨道-桥梁结构动态性能的影响非常重要.为了高效地完成列车-轨道-桥梁系统随机性能分析,建立列车-轨道-桥梁空间振动分析模型,采用轨道不平顺概率模型和谱表达-随机函数的方式在有限随机变量空间中实现轨道不平顺随机过程的高效模拟.引入概率密度积分方程和直接概率积分法发展了列车-轨道-桥梁系统随机动力方程和相应的计算求解策略.基于MATLAB实现了列车-轨道-桥梁随机振动的直接概率积分法分析程序,计算了全概率不平顺激励和参数随机条件下车-轨-桥系统振动响应的均值、标准差和时变的概率密度信息.研究结果表明:与概率密度演化分析方法相比,直接概率积分法可较好地反映行车过程中系统响应的概率密度特征,然而其在系统响应随机后处理时更为高效,其效率可提高1～2个数量级.此外,考虑轨道不平顺全概率激励更能准确地反映行车过程系统响应的概率特征,平均概率谱可能使得计算结果偏于保守;行车速度对于列车和桥梁动态行为的影响是显著的,随着行车速度的增加系统响应的范围逐渐变大.研究结果进一步拓展了列车-轨道-桥梁随机系统的分析方法,可以高效地用于系统状态评估和设计优化.
Stochastic analysis of vehicle-track-bridge system based on direct probability integral method
The structural parameters of railway engineering structures inherently exhibit randomness due to construction and manufacturing processes.Additionally,the track irregularity,as the primary self-excitation source in the system,demonstrates apparent randomness and time-varying characteristics.Therefore,it is important to investigate the impact of uncertain factors on the dynamic performance of train and track-bridge structures.To efficiently fulfill the stochastic performance analysis of system,a three-dimensional train-track-bridge vibration model was established in this paper.The track irregularity probability model and spectral representation-stochastic function method were employed to efficiently achieve the simulation of track irregularity in the finite random variable space.The probability density integral equation(PDIE)and direct probability integration method(DPIM)were introduced to develop the stochastic dynamic equation of the train-track-bridge system and the corresponding calculation and solution strategy.The direct probability integration method analysis program of stochastic vibration for the train-track-bridge was compiled in MATLAB,and then the mean value,standard deviation and time-varying probability density of system responses subjected to the full-probability irregularity excitation and random parameter were obtained.The results indicate that the direct probability integration method can also better reflect the probability characteristics of the system response compared with the probability density evolution analysis method,and moreover,the DPIM is more efficient in random post-processing of the system response,and its efficiency can be improved by 1～2 orders of magnitude.In addition,considering the full probability excitation of track irregularity,which more accurately reflect the probabilistic characteristics of the system response,the average spectrum makes the calculation results conservative.The impact of speed on the dynamic behavior of train and bridge is significant,and the range of system response gradually increases as vehicle speed increases.The research results further expand the analysis method of the train-track-bridge stochastic systems,which could be employed for system state evaluation and design optimization effectively.

direct probability integral methodvehicle-track-bridge interactionstochastic analysisspectral representation-stochastic function method

刘虎兵、宋力、徐磊、蒋丽忠、余志武

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中南大学 土木工程学院,湖南 长沙 410075

高速铁路建造技术国家工程研究中心,湖南 长沙 410075

直接概率积分法 列车-轨道-桥梁相互作用 随机分析 谱表达-随机函数法

国家自然科学基金资助项目国家自然科学基金资助项目国家自然科学基金资助项目国家自然科学基金资助项目中南大学中央高校基本科研业务费专项资金资助项目中国科协青年人才托举工程项目中国中铁重大专项中国中铁重大专项

517786315207849252008404U19342172023ZZTS03772020-2022QNRC0022020-Special-022021-Special-04-2

2024

10.19713/j.cnki.43-1423/u.T20230440

铁道科学与工程学报
中南大学 中国铁道学会

铁道科学与工程学报

CSTPCD北大核心EI
影响因子：0.837
ISSN：1672-7029
年,卷(期)：2024.21(2)
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