一种稳健空间圆拟合方法及其在地铁洞门环检测中的应用  

A Robust 3D Circle Fitting Method and Its Application in Tunnel Ring Detection of Subway Tunnel

作　　者：曾豆豆 徐小左[1] 武瑞宏[1] 常航 ZENG Doudou;XU Xiaozuo;WU Ruihong;CHANG Hang(China Railway First Survey and Design Institute Group Co.,Ltd.,Xi'an 710043,China)

机构地区：[1]中铁第一勘察设计院集团有限公司,西安710043

出　　处：《铁道勘察》2024年第2期22-27,共6页Railway Investigation and Surveying

基　　金：中铁第一勘察设计院集团有限公司科研项目重点课题[(2022KY49ZD(ZNGZ)-01,2021KY73ZD(ZDZX)-01,2022KY56(ZDZX)-02)]。

摘　　要：空间圆拟合在点云数据处理、地铁建设、工业检测中应用广泛,但存在计算步骤繁琐、拟合精度易受异常值影响等不足。针对这些问题,提出一种基于结合改进的主成分分析和罗德里格投影的空间圆拟合方法。首先提出改进的主成分分析法在拟合空间圆所在最佳平面的同时也可以剔除测量中的粗差,该剔除粗差步骤简单、高效,也提升了算法稳健性;接着利用罗德里格投影将三维坐标投影到拟合的平面上进行平面圆的拟合,拟合后再投影至三维坐标系,该步骤进一步提高了算法便捷性;最后利用深圳某地铁车站洞门钢环实际测量数据和几种常见的空间圆拟合算法进行对比实验,分析改进算法的普适性和剔除粗差的能力。实验结果表明,提出的空间圆拟合方法拟合结果可靠,能够有效地剔除观测带来的粗差,提升空间圆的拟合精度和工作效率。在有粗差的情况下拟合的平均圆度为4.8 mm,较对比方法拟合平均圆度提高约50%。3D circle fitting is widely used in point cloud processing,subway construction and industrial inspection.However,current 3D circle algorithms face challenges such as cumbersome calculation steps and the susceptibility of fitting accuracy to outliers.To solve these problems,a 3D circle fitting method which combines improved principal component analysis and Rodrigues projection was proposed in this paper.First,it was proposed that the improved principal component analysis method can eliminate the gross errors in the measurement while fitting the optimal plane of the spatial circle,this procedure was both simple and efficient,and it improved the robustness of the algorithm.Then Rodrigues projection was used to project the three-dimensional coordinates onto the fitted plane for the fitting of the plane circle,and then the fitting was projected to the three dimensions,which further improved the convenience of the algorithm.Finally,a comparative experiment was carried out between the actual measurement data of the tunnel ring in a metro station in Shenzhen and several common 3D circles fitting methods to analyze the universality of the improved algorithm and the ability of eliminating outliers.The experimental results show that the fitting accuracy of the 3D circle fitting method in this paper is reliable,which can effectively eliminate the gross error caused by the observation,improve fitting accuracy and work efficiency of the 3D circle.The average roundness is 4.8 mm in the presence of gross errors,which is nearly 50%higher than the comparison method.

关 键 词：地铁 空间圆 主成分分析 罗德里格变换 洞门环 

分 类 号：U231[交通运输工程—道路与铁道工程] P258[天文地球—测绘科学与技术] P224