基于PTC法的既有铁路纵断面调整优化方法

Optimization Method for Adjusting the Longitudinal Section of Existing Railways Based on PTC Method

以整体优化抬落道量最小为目标进行纵断面重构时,由于纵断面整体优化中各线元数学模型不同,拟合后的线元连接处会存在错位现象,不满足相邻线元首尾相接的平顺性条件。因此,本文提出了利用引入相切条件的方向加速(Powell with Tangent Condition,PTC)法来重构纵断面线形。首先利用方向加速(Powell)法进行各线元拟合优化,然后对竖曲线圆心坐标进行调整,通过调整后的圆心坐标重新计算纵断面竖曲线半径及直圆点和圆直点坐标,使竖曲线与左右两侧相邻直线坡段相切。对比利用PTC法与传统的曲率分段结合最小二乘法重构线形的抬落道量,结果表明,PTC法对线路重构的扰动更小,优化效果更好,在减小抬落道方面有显著优势。通过动力学仿真对比Powell法和PTC法优化线形后的车体动力学指标,结果表明,PTC法重构纵断面所得的线元连接处平顺性显著提高,各车体动力学性能指标明显减小,车辆运行的安全性和舒适性得到明显改善。

When reconstructing the longitudinal section with the goal of minimizing the overall optimization of the lifting and falling tracks volume,due to the different mathematical models of each line element in the overall optimization of the longitudinal section,there will be misalignment at the connection of the fitted line elements,which does not meet the smoothness condition of adjacent line elements being connected from the beginning to the end.Therefore,this article proposed the use of Powell with Tangent Condition(PTC)method to reconstruct the longitudinal section alignment by introducing tangent conditions.Firstly,the Powell method was used to optimize the fitting of each line element.Then,the center coordinates of the vertical curve were adjusted,and the radius of the vertical curve and the coordinates of the straight circle and the straight point of the circle were recalculated based on the adjusted center coordinates,so that the vertical curve is tangent to the adjacent straight slope segments on both sides.The comparison between the PTC method and the traditional curvature segmentation combined with the least squares method for reconstructing the amount of lifting and falling tracks shows that the PTC method has less disturbance to the line reconstruction,better optimization effect,and significant advantages in reducing lifting and falling tracks.By comparing the dynamic simulation results of Powell method and PTC method after optimizing the alignment,the results show that the smoothness of the line element connection obtained by PTC method for the longitudinal section reconstruction is significantly improved,and the dynamic performance indicators of each vehicle body are significantly reduced.The safety and comfort of vehicle operation are significantly improved.