基于坐标测量的既有曲线整正算法设计与实现
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摘要
既有曲线整正需要与最新的勘测技术相结合,进行简洁高效的线路坐标测量并设计相应的曲线整正算法是研究的关键所在。以实测线路坐标数据为基础,采用几何重心法求算曲线中心区域点位对应的初始圆心坐标及对应半径,利用圆心到切线垂距与初始半径的差值估算初始缓和曲线长度。以拨道量平方和最小为目标函数,设计相应的半径及缓和曲线长度优化算法,并结合现场实测数据,采用计算机程序实现设计的算法,取得较为满意的计算结果。
Track geometry misalignment inevitably occurs, especially in curves. Modification of existing railway curves shall incorporate the latest surveying technology, the key to research lies in measuring coordinates with efficiency and in designing corresponding curve correction algorithm. The initial coordinate of the center and the radius of the curve with geometrical-centering method were calculated based on the measured coordinate data, the author also estimated the initial length of the transition curve using the difference between the initial radius and the vertical distance from curve center to tangent. Taking the quadratic sum of the modification volume of the track as objective function, an algorithm was designed to optimize the design of the length of transition curves and the corresponding radii. The algorithm was realized via computer program associated with the field measured data,and the satisfactory results was obtained.
Track geometry misalignment inevitably occurs, especially in curves. Modification of existing railway curves shall incorporate the latest surveying technology, the key to research lies in measuring coordinates with efficiency and in designing corresponding curve correction algorithm. The initial coordinate of the center and the radius of the curve with geometrical-centering method were calculated based on the measured coordinate data, the author also estimated the initial length of the transition curve using the difference between the initial radius and the vertical distance from curve center to tangent. Taking the quadratic sum of the modification volume of the track as objective function, an algorithm was designed to optimize the design of the length of transition curves and the corresponding radii. The algorithm was realized via computer program associated with the field measured data,and the satisfactory results was obtained.
引文
[1]全志强,杨育林.既有铁路曲线整正测量[J].测绘科学,2015,40(4):147-150.QUAN Zhiqiang,YANG Yulin.Realignment and survey of exiting line[J].Science of Surveying and Mapping,2015,40(4):147-150.
[2]张金良.偏角法和坐标法在既有铁路线路整正中的拓展研究及应用[D].南昌:华东交通大学,2017.ZHANG Jinliang.Study and application of deflection angle method and coordinate method based on existing railway lines[D].Nanchang:East China Jiaotong University,2017.
[3]YANG H,LI Long.Existing railway curve realignment constrained optimization algorithm research based on coordinates[J].Mathematics in Practice&Theory,2009,39(24):166-171.
[4]段晓峰,韩峰,李建强.基于点云信息的既有线整正方法研究[J].铁道标准设计,2013(8):15-18.DUAN Xiaofeng,HAN Feng,LI Jianqiang.Method study on curve realignment of existing railway based on point cloud data[J].Railway Standard Design,2013(8):15-18.
[5]Birkholz A B,Schlegel H B.Path optimization by a variational reaction coordinate method.I.Development of formalism and algorithms[J].Journal of Chemical Physics,2015,143(24):363-368
[6]于庆乐.全站仪在铁路曲线测量上的应用[J].煤炭技术,2012,31(4):152-153.YU Qingle.Aplication of whole station railway curve[J].Coal Technology,2012,31(4):152-153.
[7]孔晨辉,翁呷.线路曲线的测设[J].测绘地理信息,2017,42(6):69-72.KONG Chenhui,WENG Xia.Surveying of the line curve[J].Journal of Geomatics,2017,42(6):69-72.
[8]刘文涛.基于坐标算法的铁路线路整正系统研究[D].兰州:兰州交通大学,2013.LIU Wentao.Research the railway realignment system based on the coordinate algorithm[D].Lanzhou:Lanzhou Jiaotong University,2013.
[9]HOU M S,LIU Y X.Research on constrained optimization of coordinate method in railway curve realignment[J].Journal of Lanzhou Institute of Technology,2014,21(4):38-41.
[10]候茂盛.基于最优化理论的既有铁路曲线整正方法研究及应用[D].兰州:兰州交通大学,2015.HOU Maosheng.Research on calculation method in existing railway curve realignment by optimization theory and its application[D].Lanzhou:Lanzhou Jiaotong University,2015.
[11]全志强,杨育林.既有铁路曲线整正测量[J].测绘科学,2015,40(4):147-150.QUAN Zhiqiang,YANG Yulin.Realignment and survey of exiting line[J].Survey Science of Surveying and Mapping,2015,40(4):147-150.
[12]任少伟,胡欣明.运用坐标法进行既有复曲线拨距计算[J].铁道运营技术,2011,17(3):58-60.REN Shaowei,HU Xinming.Coordinate method is used to calculate existing complex curve adjustment[J].Railway Operation Technology,2011,17(3):58-60.
[13]覃乃轩,孙和金.坐标法曲线整正计算方法探讨[J].铁道运营技术,2013,19(3):49-51,54.TAN Naixuan,SUN Hejin.Discussion on the method of existing railway curve correction by coordinate method[J].Railway Operation Technology,2013,19(3):49-51,54.
[14]TB10098-2017,铁路线路设计规范[S].TB10098-2017,Code for design of railway line[S].
[15]WANG B C,HAN F.Research on optimization method for the existing railway curve realignment based on coordinate measurement[J].Journal of Lanzhou Jiaotong University,2008,1(1):11-13.
[16]赵长石,韩峰.铁路中桩坐标统一计算模型[J].兰州交通大学学报,2009,28(1):49-51.ZHAO Changshi,HAN Feng.Unified calculation model of railway curve coordinate[J].Journal of Lanzhou Jiaotong University,2009,28(1):49-51.
[2]张金良.偏角法和坐标法在既有铁路线路整正中的拓展研究及应用[D].南昌:华东交通大学,2017.ZHANG Jinliang.Study and application of deflection angle method and coordinate method based on existing railway lines[D].Nanchang:East China Jiaotong University,2017.
[3]YANG H,LI Long.Existing railway curve realignment constrained optimization algorithm research based on coordinates[J].Mathematics in Practice&Theory,2009,39(24):166-171.
[4]段晓峰,韩峰,李建强.基于点云信息的既有线整正方法研究[J].铁道标准设计,2013(8):15-18.DUAN Xiaofeng,HAN Feng,LI Jianqiang.Method study on curve realignment of existing railway based on point cloud data[J].Railway Standard Design,2013(8):15-18.
[5]Birkholz A B,Schlegel H B.Path optimization by a variational reaction coordinate method.I.Development of formalism and algorithms[J].Journal of Chemical Physics,2015,143(24):363-368
[6]于庆乐.全站仪在铁路曲线测量上的应用[J].煤炭技术,2012,31(4):152-153.YU Qingle.Aplication of whole station railway curve[J].Coal Technology,2012,31(4):152-153.
[7]孔晨辉,翁呷.线路曲线的测设[J].测绘地理信息,2017,42(6):69-72.KONG Chenhui,WENG Xia.Surveying of the line curve[J].Journal of Geomatics,2017,42(6):69-72.
[8]刘文涛.基于坐标算法的铁路线路整正系统研究[D].兰州:兰州交通大学,2013.LIU Wentao.Research the railway realignment system based on the coordinate algorithm[D].Lanzhou:Lanzhou Jiaotong University,2013.
[9]HOU M S,LIU Y X.Research on constrained optimization of coordinate method in railway curve realignment[J].Journal of Lanzhou Institute of Technology,2014,21(4):38-41.
[10]候茂盛.基于最优化理论的既有铁路曲线整正方法研究及应用[D].兰州:兰州交通大学,2015.HOU Maosheng.Research on calculation method in existing railway curve realignment by optimization theory and its application[D].Lanzhou:Lanzhou Jiaotong University,2015.
[11]全志强,杨育林.既有铁路曲线整正测量[J].测绘科学,2015,40(4):147-150.QUAN Zhiqiang,YANG Yulin.Realignment and survey of exiting line[J].Survey Science of Surveying and Mapping,2015,40(4):147-150.
[12]任少伟,胡欣明.运用坐标法进行既有复曲线拨距计算[J].铁道运营技术,2011,17(3):58-60.REN Shaowei,HU Xinming.Coordinate method is used to calculate existing complex curve adjustment[J].Railway Operation Technology,2011,17(3):58-60.
[13]覃乃轩,孙和金.坐标法曲线整正计算方法探讨[J].铁道运营技术,2013,19(3):49-51,54.TAN Naixuan,SUN Hejin.Discussion on the method of existing railway curve correction by coordinate method[J].Railway Operation Technology,2013,19(3):49-51,54.
[14]TB10098-2017,铁路线路设计规范[S].TB10098-2017,Code for design of railway line[S].
[15]WANG B C,HAN F.Research on optimization method for the existing railway curve realignment based on coordinate measurement[J].Journal of Lanzhou Jiaotong University,2008,1(1):11-13.
[16]赵长石,韩峰.铁路中桩坐标统一计算模型[J].兰州交通大学学报,2009,28(1):49-51.ZHAO Changshi,HAN Feng.Unified calculation model of railway curve coordinate[J].Journal of Lanzhou Jiaotong University,2009,28(1):49-51.