基于线性回归和遗传算法的既有铁路纵断面拟合探讨

Discussion on Existing Railway Profile Fitting Based on Linear Regression and Genetic Algorithm

基于最小二乘原理对既有线纵断面进行回归分析,提出变坡点渐进识别方法输出可能变坡点的里程集合,以此为基础对连续纵坡段和竖圆曲线段逐一进行计算。充分考虑抬、落道量、最小坡段长度、竖缓(岔)重叠、最大坡度值、最大坡度代数差等约束,以最小化线路的抬、落道绝对值为拟合目标,建立既有铁路纵断面拟合数学规划模型,并针对问题特征设计遗传算法求解模型。通过实例分析了优化算法与人工拟合结果的差异,优化算法拟合结果符合设计规范,抬、落道量比人工拟合结果减少了8.7%,表明本文的拟合方法具有较好的工程适用价值。

Based on the principle of least squares,the regression analysis of the existing line profile was carried out and a method for identifying knick-point gradually was proposed to calculate the mileage set of the possible knick-points,with which the continuous slopes and the vertical circular curves were calculated in a row.In order to minimize the absolute value of lifting and falling tracks of the fitting line,the mathematical model of profile fitting was established with consideration of absolute value of lifting and falling tracks,minimum slope length,overlap of plane and profile,maximum gradient,maximum algebraic difference of gradient,etc.The genetic algorithm was designed to solve the model according to the characteristics of the problem.The running process of the algorithm was analyzed with a real case,and the optimized fitting result was reduced by 8.7%compared with the manual fitting result,which shows that the fitting method in this paper has good engineering application value.