基于SVD的地铁盾构洞门钢环空间形态参数计算

Calculation of Spatial Shape Parameters of Portal Steel Rings in Metro Shields Based on Singular Value Decomposition

为解决现有地铁盾构隧道洞门钢环空间形态参数计算方法步骤繁琐、需要初始值等问题,在分析空间平面方程和球面方程求解系数特点的基础上,提出利用奇异值分解(SVD)法一次性解算出球面方程参数和洞门钢环所在空间平面单位法向量,再利用上述参数直接计算洞门钢环的中心位置、半径、平整度、圆度等空间形态参数。该过程无需初始值和迭代计算,更为便捷高效。为消除观测点中可能存在的粗差,进一步结合方差比值检验法实现粗差的探测。应用结果表明:SVD法计算结果与商业软件一致,即使存在粗差,利用方差比值检验法也可以准确定位粗差,二者结合具有较好的实用价值。

The existing calculation methods for determining the spatial shape parameters of steel portal rings in metro shields are tedious, and the initial input values degrade their applicability and performance. To address these problems, a singular value decomposition(SVD) method is proposed to obtain the spherical equation parameters and unit normal vector of the plane at the steel portal ring′s location based on the analysis of the solution coefficients for plane and spherical equations. The obtained parameters are used to calculate the spatial shape parameters, including the center position, radius, flatness, and roundness of the portal ring. This calculation does not require initial values or iterative calculations, and hence, it is convenient and efficient. To eliminate possible gross errors in the observed points, the method of variance ratio testing is further employed to detect gross errors. The results show that the SVD calculation results are consistent with those obtained using commercial software, and the variance ratio test accurately positions the gross errors, demonstrating the practicality of the recommended method.