铁路既有线曲线复测计算方法

Calculation Method for Curve Re-Surveying of the Existing Railway Line

为提高计算精度和速度,研究利用坐标法和最小二乘法进行铁路既有线曲线复测的计算。首先利用坐标法计算各测点的坐标,再计算正矢,然后根据正矢的变化规律选定圆曲线上的测点,用最小二乘法拟合出既有线圆曲线的半径和圆心坐标,并以拨正量最小为优化目标,优化圆曲线半径及圆心,进而计算出缓和曲线的长度、各测点的拨正量、特征点的里程和坐标等。实例计算表明:在铁路既有线曲线复测计算中,坐标法和最小二乘法结合使用,不仅克服了基于渐伸线原理的传统近似计算方法存在的误差问题,提高了计算精度,拨正量小,而且能够实现一次性利用圆曲线上所有测点的坐标拟合出圆曲线的半径和圆心坐标。

In order to improve the calculation precision and speed, the calculation method for curve re-surveying of the existing railway line was studied based on coordinate method and least square fitting method. The coordinates and the calculation versine of each measured point were first obtained by coordinate meth- od. Then the measured points on the circular curve were selected according to the change law of versine. The circular curve radius and the circle center coordinates were then fitted by the least square method. With minimizing the move distance as the optimization objective, the circular curve radius and circle center coordinate were then optimized, the transition curve length, the move distance of each measured points, the mileages and the coordinates of the feature points and so on were further computed. Example calculation shows that the combined use of the coordinate method and the least-square fitting method in the calcu- lation of re-surveying the existing railway curve line not only can overcome error problem of the traditional approximate method based on the theory of involute, improve the calculation precision, minimize the move distance, but also can realize fitting out the circular curve radius and circle center coordinate by using all coordinates of the measured points in circular curve for one time.