盾构隧道洞门钢环空间三维坐标及形态拟合算法

The Three-Dimensional Coordinate And Shape Fitting Algorithm of Steel Ring of Shield Tunnel Gate

为实现对盾构隧道洞门钢环的快速测量,介绍一种根据观测点拟合空间圆形,来得到洞门钢环“圆心三维坐标、半径、圆度、平整度、垂直度”等位置和姿态信息等的算法。利用洞门钢环为标准圆形的特性,根据“空间圆形弦长的中垂面相交于圆心点”的几何关系,推导多观测点拟合空间圆形的算法公式。通过“最小二乘法”和“附有限制条件的平差模型”理论,将公式方程进行线性化联立,组成矩阵方程;再使用计算机编程,将矩阵方程具体化,并介绍“弦长组合方式、平面拟合方法、限制条件联立、最小二乘解算形式”等各个计算步骤;最后,通过天津地铁Z2线工程的洞门钢环安装案例,将本文算法与商业隧道测量软件的计算结果进行对比,验证了该算法的可靠性。

In order to solve the problem of accurate and rapid measurement of steel ring of shield tunnel,an algorithm was introduced to obtain the position and attitude information of“three-dimensional coordinates,radius,roundness,flatness,verticality”of steel ring of tunnel door by fitting space circle according to the observation point.Based on the characteristics that the steel ring of the tunnel gate is a standard circle and the geometric relation that the vertical plane of the chord length of the space circle intersects the center of the circle,the algorithm formula of fitting the space circle with multiple observation points was derived.Through the theory of“least square method”and“adjustment model with restriction conditions”,the formula equations were linearized and combined to form matrix equations.By using computer programming,the form of matrix equation was specified,and the calculation steps such as“string length combination method”,“plane fitting method”,“confluence of constraints”and“least squares solution form”were introduced.The reliability of the proposed algorithm was verified by comparing the calculation results of commercial tunnel measurement software with the installation case of tunnel door steel ring in a subway project.