基于混合Copula函数的风雨联合概率分布模型

Joint Probability Distribution Model of Wind Velocity and Rainfall with Mixed Copula Function

特殊地区风雨联合作用下高速铁路桥梁和车辆的气动特性会发生改变,进而影响列车安全舒适运行。为了全面描述风雨联合分布规律和时空关联特征,基于兰新高铁自然灾害监测系统的长时气象监测数据,提出基于混合Copula函数的风雨联合概率分布模型。首先选取Gumbel、Clayton和Frank Copula函数建立混合Copula函数。然后采用非参数核密度估计方法估计出日极值风速和日极值雨强的边缘分布函数;根据贝叶斯模型加权平均方法以及离差平方和最小准则分别估算出混合Copula函数的权重参数和相依参数;利用K-S法以及最小距离法对混合Copula函数进行拟合优度检验。最后以兰新高铁沿线日极值风速和日极值雨强的监测数据为例,建立基于不同Copula函数的风雨联合概率分布模型,并比较不同模型的拟合优度。研究结果表明:基于混合Copula函数的风雨联合概率分布模型能够更加准确地描述日极值风速和日极值雨强之间的多种相关关系;基于Gumbel、Clayton和Frank三种混合Copula函数的风雨联合概率分布模型是描述日极值风速和日极值雨强联合分布规律的最优模型;兰新高铁沿线基站监测的日极值风速和日极值雨强之间存在下尾相关为主、上尾相关和对称相关为辅的相关关系。

The aerodynamic characteristics of high-speed railway bridges and vehicles vary under wind and rain in special areas,then affecting the operation safety and comfort of trains.To comprehensively describe the joint distribution law and spatiotemporal correlation features of wind velocity and rainfall,this paper presents a joint probability distribution model of wind velocity and rainfall with mixed Copula function based on monitoring data from the natural disaster monitoring system of the Lanzhou-Xinjiang high-speed railway.The mixed Copula function was constructed using the Gumbel,Clayton,and Frank Copula functions.The marginal distribution functions of extreme wind velocity and rainfall were then estimated using the nonparametric kernel density estimation method.The weight and dependence parameters of mixed Copula function were estimated according to the Bayesian weighted average method and minimum of sum square variation.The goodness of fit of mixed Copula function was tested using the K-S and minimum distance methods.Finally,taking the monitoring data of the extreme wind velocity and rainfall along the Lanzhou-Xinjiang high-speed railway as an example,the joint probability distribution models of wind velocity and rainfall with different copula functions were established and compared.The results show that the joint probability distribution models of wind velocity and rainfall with mixed Copula function can more accurately describe the various correlations between the extreme wind velocity and rainfall.The joint probability distribution model of wind velocity and rainfall with three mixed Copula functions is the best model to describe the joint distribution law of the extreme wind velocity and rainfall.The correlations between the extreme wind velocity and rainfall monitored by the base station along the Lanzhou-Xinjiang high-speed railway are main left tail,secondary right tail,and secondary symmetry.