基于中点弦测法的轨向高低数值算法研究

Research on Numerical Algorithm of the Track Alignment and Height Based on Midpoint Chord Measuring Method

轨道几何形位直接影响列车行车安全性,而桥梁结构刚度决定了轨道几何形位值的大小。为得到评判桥梁结构刚度的两个轨道几何形位参数(轨向和高低),基于中点弦测法的计算原理,对其数值算法进行了研究。提出了几何法和插值法两种算法,对比了二者的计算精度和效率:几何法的控制弦长为指定弦长,计算精度比插值法高,能准确输出中点弦测值,但需联立求解高阶方程组,计算效率比插值法低。插值法采用的弦长为近似值,计算精度较几何法低,但计算效率高。两种方法均满足计算精度要求,并可以实现计算结果的可视化输出。

The track geometry directly affects the safety of train operation,and the bridge structure stiffness determines the value of the track geometry.In order to obtain the two track geometric parameters(track direction and height)for evaluating the bridge structure stiffness,the numerical algorithm is studied based on the calculation principle of the midpoint chord measuring method.Two algorithms,geometric method and interpolation method,are proposed,and their calculation accuracy and efficiency are compared:the control chord length of geometric method is the specified chord length,and the calculation accuracy is higher than that of interpolation method.It can accurately output the midpoint chord measurement value,but it needs to solve the higher-order e-quations simultaneously,and the calculation efficiency is lower than that of interpolation method.The chord length of the interpolation method is an approximate value,and the calculation accuracy is lower than that of the geometric method,but the calculation efficiency is high.Both methods meet the calculation accuracy requirements and can realize the visual output of the calculation results.