有砟轨道高低不平顺概率分布的时空特征

为研究有砟轨道不同线形区段上高低不平顺标准差所服从的最优概率分布函数及其时空特征, 采用三参数概率分布函数拟合有砟轨道高低不平顺标准差峰值及尾部特性, 选取了5种三参数理论分布函数, 并确定了最优概率分布函数的选择原则; 以既有沪昆线为例, 拟合了有砟轨道上6种不同线形区段上高低不平顺标准差服从的最优概率分布函数; 分析了高低不平顺标准差的时间特征, 采用非线性函数拟合了分布函数参数随时间的变化情况; 分析了高低不平顺标准差的空间特征, 比较了轨道质量状态在空间维度上的不同。分析结果表明: 在高低不平顺标准差大值区域, 三参数Lognormal分布理论值与实际值的相对误差小于5%, 而正态分布理论值与实际值的相对误差则大于50%, 因此, 采用三参数概率分布函数能有效解决两参数概率分布函数理论值在此区域与实际值发生偏离的问题; 在描述线形区段的统计分布特性时, 不同线形区段应选择不同的分布函数, 同一线形区段宜选取同一种分布函数; 既有沪昆线桥隧区段上, Burr分布有5次是最优概率分布, 且P值之差的均值和标准差分别为0.09和0.12;各区段高低不平顺标准差所服从分布的3个参数用非线性函数拟合的优度均大于0.6, 因此, 采用非线性函数可有效拟合3个参数随时间的变化规律; 维修与养护作业前后桥隧区段高低不平顺标准差的超限百分比都小于3%, 圆曲线、缓和曲线和直线区段上高低不平顺标准差的超限百分比为3.5%~12.8%, 而限速区段和道岔区段上均大于25%。确定的最优概率分布函数选择原则可应用于轨道不平顺概率分布特征研究。 

Temporal-spatial features of probability distribution of vertical irregularity in ballasted track

To study the optimum probability distribution function and the temporal-spatial features of vertical irregularity standard deviations on different sections of ballasted track, the three-parameter probability distribution function was used to fit the features of peak value and the tail of vertical irregularity standard deviations of ballasted track. Five three-parameter theoretical distribution functions were selected, and the selection principle of the optimum probability distribution function was determined. Taking the existing Shanghai-Kunming Line as an example, the optimum probability distribution functions of vertical irregularity standard deviations on six different linear sections of ballasted track were fitted. The temporal feature of vertical irregularity standard deviation was analyzed. The variations of distribution function parameters with time were fitted by non-linear functions. The spatial feature of vertical irregularity standard deviation was analyzed. The differences of track quality statuses in spatial dimension were compared. Analysis result shows that in the large value region of vertical irregularity standard deviations, the relative error between the theoretical value obtained from the three-parameter Lognormal distribution and the actual value is less than 5%, while the relative error between the theoretical value obtained from the normal distribution and the actual value is more than 50%. Therefore, the three-parameter probability distribution function can effectively solve the deviated problem between the theoretical value of two-parameter probability distribution function and the actual value in this region. When describing the statistical distribution features of linear sections, different distribution functions should be selected on different linear sections, and the same distribution function should be selected on the same linear section. On the bridge and tunnel sections of existing Shanghai-Kunming Line, the Burr distribution obtains the optimum probability distribution for five times, and the mean and standard deviation of difference of P values are 0.09 and 0.12, respectively. When using the non-linear function to fit the parameters of the distribution obeyed by the vertical irregularity standard deviation on each section, the fitting goodnesses of three parameters are all greater than 0.6. Therefore, the non-linear function can be used to fit the variations of three parameters with time. Both the over-range percentages of vertical irregularity standard deviations on bridge and tunnel sections before and after the repair and maintenance operations are less than 3%. The over-range percentages of vertical irregularity standard deviations on circular, transition and straight line sections are 3.5%-12.8%, while the values on the speed-limit and switch sections are greater than 25%. Therefore, the determined selection principle of the optimum probability distribution function can be used to study the probability distribution feature of track irregularity.