Metro Stray Current Leakage Zone Localization Method Considering Rail Resistance Uncertainty
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摘要:
现有地铁杂散电流泄漏定位方法通常将钢轨纵向电阻视为确定值，忽略了其因材料老化、接头电阻及环境因素导致的不确定性，从而影响定位精度与泛化性能. 为此，本文基于实测地铁钢轨纵向电阻数据，提出一种考虑其概率统计规律的杂散电流泄漏定位方法. 首先，利用核密度估计方法建立钢轨纵向电阻的概率分布模型，进而采用蒙特卡罗仿真方法模拟其不确定性，构建钢轨-大地电阻网络模型；在此基础上，采用遗传-粒子群优化算法提出钢轨对地过渡电阻或电导分布的计算方法，进而提出基于逐级定位的杂散电流泄漏位置定位策略；该策略首先通过粗定位确定杂散电流泄漏位置所在的车站区间，同时筛选最优适应度结果以估计钢轨纵向电阻分布，进一步在泄漏区间范围内利用逐级细分定位泄漏区域，并通过计算沿线钢轨对地过渡电导超过阈值的概率，实现泄漏位置的判定. 与模拟泄漏区域的对比结果表明：在钢轨纵向电阻非均匀分布、不同泄漏程度及不同泄漏范围下，所提方法均能准确定位到泄漏区域所在的车站区间，定位偏差小于30%；在考虑测量噪声影响时，钢轨纵向电阻估计结果的平均相对误差小于5%，表明所提方法有较强的鲁棒性和工程适用性.
Abstract:Existing metro stray-current leakage location methods often treat longitudinal rail resistance as deterministic and ignore its uncertainty caused by material aging, joint resistance, and environmental factors, which reduces location accuracy and generalization performance. Based on measured longitudinal rail resistance data from a metro system, a method that accounts for the probabilistic characteristics of longitudinal rail resistance was proposed for locating stray-current leakage. Kernel density estimation was used to establish the probability distribution model of longitudinal rail resistance. Monte Carlo methods were then used to simulate uncertainty in longitudinal rail resistance, and a rail-earth resistance network model was constructed. Building on this model, a method was proposed to calculate the distribution of rail-to-earth transition resistance or conductance using a hybrid genetic algorithm-particle swarm optimization algorithm, and a stepwise strategy was developed for locating stray-current leakage. The strategy first identified the inter-station section containing the leakage position through coarse localization and estimated the distribution of longitudinal rail resistance by selecting the solutions with the best fitness values. The leakage zone within the identified section was then determined through stepwise subdivision. During the location process, the leakage position was identified by calculating the probability that rail-to-earth transition conductance along the line exceeds a threshold. Comparisons of the location results with simulated leakage zones show that the proposed method can accurately identify the inter-station section containing the leakage zone when longitudinal rail resistance is nonuniformly distributed and leakage severity and range vary. The location deviation is less than 30%, and the average relative error in estimating longitudinal rail resistance is less than 5% in the presence of measurement noise, indicating strong robustness and practical engineering applicability.
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图 1 单位长度钢轨纵向电阻统计结果
Figure 1. Statistical results of longitudinal rail resistance per unit length
图 2 单位长度钢轨纵向电阻概率密度分布
Figure 2. Probability density distribution of longitudinal rail resistance per unit length
图 5 杂散电流泄漏位置逐级定位方法流程
Figure 5. Flowchart of stepwise localization method for stray-current leakage positions
图 7 地铁杂散电流泄漏区间定位流程
Figure 7. Inter-station section localization procedure for metro stray-current leakage
图 8 杂散电流泄漏区域逐级定位策略流程图
Figure 8. Flowchart of stepwise localization strategy for stray-current leakage zones
图 10 区间定位模型钢轨对地过渡电导计算结果
Figure 10. Calculated rail-to-earth transition conductance for inter-station section localization model
图 11 钢轨对地过渡电导（划分距离500 m）
Figure 11. Rail-to-earth transition conductance （500 m segment length）
图 12 钢轨对地过渡电导（划分距离25 m）
Figure 12. Rail-to-earth transition conductance （25 m segment length）
图 14 车站间单位长度钢轨纵向电阻统计
Figure 14. Statistical results of longitudinal rail resistance per unit length between stations
图 15 定位过程中钢轨对地过渡电导计算结果
Figure 15. Calculated rail-to-earth transition conductance during localization
表 1 模型关键参数
Table 1. Key model parameters
金属结构 参数 参数值 接触网 纵向电阻/（mΩ•km−1） 8 钢轨 纵向电阻/（mΩ•km−1） 38 钢轨绝缘涂层 电阻率/（Ω•m） 450000 厚度/mm 10 排流网 纵向电阻/（mΩ•km−1） 660 结构钢筋 纵向电阻/（mΩ•km−1） 320 
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表 2 工况A和B参数设置
Table 2. Parameter settings for operating conditions A and B
工况 起点/m 终点/m 绝缘涂层/（Ω•m） A 1500 2000 45000 B 8500 9000 45000
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表 3 工况A1参数设置
Table 3. Parameter settings for operating condition A1
钢轨位置/m 钢轨纵向电阻/（mΩ•km−1） [0, 1314 ]37 [ 9426 ,10730 ]39
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表 4 工况A2和A3参数
Table 4. Parameters for operating conditions A2 and A3
工况 泄漏位置/m 绝缘涂层/（Ω•m） A2 [ 1500 ,2000]4500 A3 [ 1500 ,1600 ]4500
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