基于Copula函数的青藏铁路多年冻土区路基变形相关性分析

Correlation Analysis of Subgrade Deformation of Qinghai-Tibet Railway in Permafrost Regions Based on Copula Function

为解决青藏铁路多年冻土区路基两侧不规律变形问题,根据青藏高原多年冻土区全线铁路不同路基类型观测站点路基融沉的长期观测数据,利用箱线图查找异常值的原理分别对其进行异常值检验,再基于Copula理论给出了路基两侧变形相关性分析的建模步骤,确定路基两侧变形的相关性结构,并依据不同Copula族特征对其进行相关性分析,实现多年冻土区路基两侧变形的主侧方向判定。研究结果表明:(1)不同路基类型两侧高度的变形呈正相关且相关性极高,说明多年冻土区路基两侧高度变形基本满足一致性;(2)4组样本数据的最优相关结构为t-Copula,即多年冻土区路基两侧变形具有对称性且上、下尾部相关性较强的特点;(3)路基两侧的变形模式几乎均等性相依。本文研究成果可为路基进行状态监测和路基养护提供参考。

In order to solve the problem of irregular deformations on the two sides of the subgrade of Qinghai-Tibet Railway in the permafrost regions,according to the long-term observation data on the thawing settlement of the subgrade in the permafrost regions on Qinghai-Tibet Plateau from observation stations for different types of subgrade along the whole railway,abnormal values were checked according to the principle of using box plots to find abnormal values. Then,the modeling steps for correlation analysis of the deformations on the two sides of the subgrade were given based on Copula Theory to determine the correlation structure of the deformations on the two sides of the subgrade. The correlation analysis was carried out according to the characteristics of different Copula families to judge the main side direction of the deformations on the two sides of the subgrade in permafrost regions. The results show that:(1) The height deformations on the two sides of different types of subgrade are positively and highly correlated. This indicates the height deformations on the two sides of the subgrade in permafrost regions are basically consistent.(2) The optimal correlation structure of the 4groups of sample data is-Copula,that is,the deformations on the two sides of the subgrade in the permafrost area are symmetrical and the upper and lower tails are strongly correlated.(3) The deformation modes on the two sides of the subgrade are almost equally correlated. The research results of this paper can provide a reference for subgrade status monitoring and subgrade maintenance.