海上风电单桩基础直线度测量最小二乘空间圆拟合法  

The method of least square 3D circle fitting in straightness surveying of offshore wind power pile

作　　者：吴昊[1,2,3] WU Hao(Tianjin Research Institute for Water Transport Engineering,M.O.T,Tianjin 300456,China;Tianjin Survey and Design Institute for Water Transport Engineering,Tianjin 300456,China;Tianjin Key Laboratory of Surveying and Mapping for Waterway Transport Engineering,Tianjin 300456,China)

机构地区：[1]交通运输部天津水运工程科学研究所,天津300456 [2]天津水运工程勘察设计院有限公司,天津300456 [3]天津市水运工程测绘技术企业重点实验室,天津300456

出　　处：《水道港口》2022年第5期683-688,共6页Journal of Waterway and Harbor

基　　金：交通运输部天津水运工程科学研院所科研创新基金项目(TKS20220303)。

摘　　要：海上风电单桩基础的直线度是评价其挠度变化的一项重要指标,其精度取决于截面圆心的拟合精度。利用最小二乘原理,推导了一种高精度的空间圆曲线拟合算法。根据空间圆两点之间弦长的中垂面均相交于圆心的特性,得出多观测点两点之间连线与其中垂线必定垂直的结论,以此为依据组建了向量乘积的矩阵方程。又根据圆心点必定位于多观测点拟合平面之上的特点,以此作为限制条件,利用附有限制条件间接平差理论,根据最小二乘法,构建解算方程,拟合解算出空间圆心坐标和半径,并计算出各观测点的平整度和圆度差,作为拟合优良的参考标准。将该算法在工程项目中进行了实际应用,与MATLAB数学计算软件中的拟合算法进行了比对,计算精度良好。The straightness of single pile foundation for offshore wind power is an important index to evaluate the variation of deflection and its accuracy depends on the fitting accuracy of the center of cross section.Based on the least square principle,a high precision space circle curve fitting method is derived.According to the property that the vertical planes of the chord length between two points of a space circle intersect at the center of the circle,the conclusion is drawn that the line between two points of multiple observation points must be perpendicular to its middle vertical line.On this basis,the matrix equation of vector product is established.According to the characteristic that the center of the circle must be located on the fitting plane of multiple observation points,this is taken as the limiting condition,and the indirect adjustment theory with the limiting condition is used to construct the solution equation according to the least square method.The coordinates and radius of the center of the space are calculated by fitting and solving,and the flatness and roundness difference of each observation point are calculated as the reference standard of good fitting.The algorithm is applied in engineering projects,and compared with the fitting method in MATLAB mathematical calculation software,the calculation accuracy is good.

关 键 词：海上风电 单桩 直线度 最小二乘 空间圆拟合 

分 类 号：U675[交通运输工程—船舶及航道工程]