Abstract: 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.

Key words: metro shield, portal steel ring, spatial shape parameters, singular value decomposition, variance ratio test