基于保角变换法的不同地形对地面落雷分布的影响研究

Study on Influence of Different Terrain to Distribution of Ground Lightning Drop based on Conformal Transformation Method

针对高铁在地形复杂区域的落雷密度较难估算问题,提出了一种基于保角变换法与雷电先导发展理论相结合的方法求解不同地形条件下的落雷密度。首先对对称地形的保角变换函数进行拓展验证,使其满足实际复杂地形形状的需求,并得到地形参数与保角变换参数的数学对应关系;再结合雷电先导发展理论建立落雷分布计算仿真模型,在不同地形条件下进行落雷分布仿真,对仿真数据进行整理统计形成落雷分布概率密度函数曲线,通过对曲线进行对比得到落雷分布的差异性。该方法拓展了保角变换函数的应用范围,为估算复杂地形区域的落雷密度问题提供了一种新思路、新方法。

With regard to the problem that it is difficult to estimate the lightning density of high-speed railway in complex terrain area,a method based on conformal transformation and lightning leader development theory is proposed to solve the lightning density under different terrain conditions.Firstly,the conformal transformation function of symmetrical terrain is extended and verified to meet the requirements of actual complex terrain shape,and the mathematical correspondence between terrain parameters and conformal transformation parameters is obtained.Then combined with the lightning leader development theory,the calculation and simulation model of lightning drop distribution is established.The lightning drop distribution simulation is carried out under different terrain conditions.The simulation data are sorted and counted to form the probability density function curve of lightning drop distribution.The difference of lightning drop distribution is obtained by comparing the curves.This method expands the application range of conformal transformation function,and provides a new idea and method for estimating the lightning density in complex terrain area.