| 轨道不平顺概率模型 |
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| 引用本文： | 徐磊,翟婉明.轨道不平顺概率模型[J].交通运输工程学报,2018,18(3):56-63. |
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| 作者姓名： | 徐磊 翟婉明 |
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| 作者单位： | 1.西南交通大学 牵引动力国家重点实验室, 四川 成都 6100312.代尔夫特理工大学 道路与铁道工程系, 南荷兰 代尔夫特 2628 |
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| 基金项目： | 国家自然科学基金项目51678507西南交通大学轨道交通工程动力学创新引智基地项目B16041 |
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| 摘 要： | 为了高效选取轨道不平顺随机样本, 以满足车辆-轨道系统随机动力与可靠度分析中的激振源遍历性要求, 依据轨道随机不平顺的弱平稳与谱相似特征, 提出了一种轨道不平顺概率模型; 采用离散概率积分和统计方法, 在时域中将大量轨道不平顺检测信号分成若干个时程序列, 对每个序列采用谱分析法计算其统计功率谱密度分布; 采用矩阵法对轨道不平顺功率谱密度函数进行集合表征, 视每条谱线在不同频率点的功率谱密度概率具有累加性, 采用单一频率下的功率谱密度概率分布推知整条谱线的出现概率; 采用通用随机模拟方法选取代表性轨道谱, 并反演随机不平顺序列; 实测了某高速铁路约269km的轨道高低和方向不平顺, 基于车辆-轨道耦合动力学理论, 从轨道不平顺模拟幅值与车辆-轨道系统动力响应的概率密度分布出发, 对比了轨道不平顺概率模型与轨道不平顺随机模型的计算结果, 以验证轨道不平顺概率模型的正确性和高效性。计算结果表明: 以2种模型生成的轨道随机不平顺为激振源, 获得的车辆-轨道系统动力响应分布熵差异小于2%, 2种模型均能准确表达不平顺激扰特性; 为保证模拟与实测不平顺的概率密度分布一致, 采用随机模型和概率模型分别需要生成131和33个随机样本, 概率模型具有更高的分析效率; 在给定计算工况下, 轮轨力和车体加速度的幅值分别为38~152kN和-0.042g~0.043g (g为重力加速度), 均未超过《高速铁路设计规范》 (TB 10621—2014) 中的限值(轮轨力为170kN, 车体加速度为0.25g), 表明此高速铁路轨道不平顺状态较优, 行车安全性和舒适性可以得到保证。
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| 关 键 词： | 铁道工程 轨道不平顺 概率模型 随机振动 车辆-轨道耦合动力学 随机模型 |
| 收稿时间： | 2017-12-03 |
Track irregularity probabilistic model |
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| XU Lei,ZHAI Wan-ming.Track irregularity probabilistic model[J].Journal of Traffic and Transportation Engineering,2018,18(3):56-63. |
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| Authors: | XU Lei ZHAI Wan-ming |
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| Affiliation: | 1.State-Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, Sichuan, China2.Section of Road and Railway Engineering, Delft University of Technology, Delft 2628, Zuid-Holland, Netherlands |
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| Abstract: | To efficiently select track irregularity random samples for satisfying the ergodicity requirements of excitation sources in stochastic dynamics and reliability analysis in vehicle-track system, the weak-stationarity and similarity spectral of track irregularities were introduced to propose a track irregularity probabilistic model. Using the discrete probability integration and statistical approaches, the massively measured track irregularity time histories were divided into multiple time-domain sequences. The statistical power spectral density distribution of each sequence was calculated by the spectral analysis method. Then, using the matrix-based method, the set representation of the power spectral density function of track irregularities was obtained. It was assumed that the power spectral densities could be linearly accumulated at different frequencies, allowing the probabilities of entire spectra line to be obtained using the power spectral density probability distribution of a single frequency. The representative track irregularity spectra were selected through the commonly random simulation methods, and the track random irregularities were inversely simulated. The height and direction track irregularities of high-speed railway about 269 km were measured. Based on the vehicle-track coupled dynamics theory, the calculation results between the track irregularity probabilistic model and track irregularity stochastic model was compared from the aspects of the simulated amplitude of track irregularity and the probability density distribution for dynamic response in the vehicle-track system to verify the validity and high efficacy of the track irregularity probabilistic model. Calculation result shows that when taking the track random irregularities caused by the two models as excitation sources, the difference of the obtained probability entropies of vehicle-track system dynamic response between the two models is less than 2%. Both models can accurately express the excitation characteristics of track irregularities. The stochastic and probabilistic models need 131 and 33 random samples, respectively, to guarantee the consistent probability density distributions between the simulation and measurement, and the probabilistic model has higher computation efficiency. Under the presented computational condition, the wheel-rail forces and car body accelerations are 38-152 kN and-0.042 g-0.043 g, respectively, and are respectively less than the limits of wheel-rail forces (170 kN) and car body accelerations (0.25 g) in Code for High Speed Railway Design (TB 10621—2014). The track irregularity status of the investigated high-speed line is sufficient to guarantee the running safety and riding comfort of the vehicle. |
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