在役潜艇的建造和修理需要检测其耐压壳体的截面圆度，因现场条件限制或多设备融合测量，测量采样点经常呈现非均匀性，导致最小二乘圆拟合的结果与实际情况不符，研究旨在减小非均匀采样带来的影响，提高拟合圆的精度。基于非均匀采样定权提出一种非均匀采样加权总体最小二乘圆拟合方法，同时考虑观测向量和系数矩阵都有扰动，用于潜艇耐压壳体测量数据的处理。通过对4种不同预设形状的采样分析数值实验表明，该方法能提高非均匀采样情况下圆拟合的精度，但当随机误差加大至1.5 mm，该方法不能完全优于最小二乘法。非均匀采样加权总体最小二乘圆拟合法计算得到的圆心偏差及半径偏差都比最小二乘法的结果更小，具有较好的工程实用价值，可用于在役潜艇耐压壳体圆度测量非均匀采样时的圆拟合计算。
The maintenance and repair of in-service submarines need to detect the roundness of the section of the pressure hull. Due to site conditions or multi-equipment fusion measurement, the measurement sampling points often show non-uniformity, resulting in the result of least squares circle fitting and the actual situation. The research aims to reduce the influence of non-uniform sampling and improve the accuracy of fitting circles.Based on non-uniform sampling weighting, a non-uniform sampling weighted overall least squares circle fitting method is proposed, which also considers the disturbance of observation vector and coefficient matrix, which is used for the processing of submarine pressure hull measurement data. Numerical experiments of sampling analysis of four different preset shapes show that this method can improve the accuracy of circle fitting in the case of non-uniform sampling, but when the random error increases to 1.5 mm, this method cannot be completely better than the least squares method. The center deviation and radius deviation calculated by the non-uniform sampling weighted overall least squares circle fitting method are smaller than the results of the least squares method, which has good engineering practical value, and can be used for the measurement of the roundness of the in-service submarine pressure hull. Circle fit calculation when uniformly sampled.
2023,45(18): 51-57 收稿日期：2022-08-24
DOI：10.3404/j.issn.1672-7649.2023.18.009
分类号：U662.2
基金项目：国家自然科学基金资助项目(51609253)
作者简介：邓为耀(1997-),男,硕士研究生,研究方向为船舶设计制造维修工程
参考文献：
[1] IMRAN M, SHI D Y, TONG L L. Multi-objective design optimization of composite submerged cylindrical pressure hull for minimum buoyancy and maximum buckling load capacity[J]. Defence Technology, 2021, 17(4): 1190–1206
[2] 王晓天, 梁学先. 崔洪斌. 潜艇耐压液舱壳板强度的计算方法研究[J]. 哈尔滨工程大学学报, 2006, 27(5): 690–692.
[3] 白旭, 王晓天, 孙丽萍. 单壳体潜艇球柱组合壳结构边缘效应分析[J]. 哈尔滨工程大学学报, 2013, 34(4): 409–414.
[4] 胡剑. 潜艇耐压壳体测量方法比较研究[J]. 中国水运(下半月), 2016, 16(2): 112–115.
[5] 王海霖, 黄祥兵, 彭飞. 基于三维点云的加筋圆柱壳体圆度测量及初挠度计算[J]. 中国舰船研究, 2016, 11(6): 65–69+82.
[6] 王鹏, 朱晓军. 赵剑飞. 潜艇耐压壳体径向初挠度评定方法研究[J]. 武汉理工大学学报(交通科学与工程版), 2013, 37(1): 149–152+157.
[7] 王中, 彭飞, 朱志洁, 等. 耐压体激光圆度测量分析系统[C]//2016年MIS/S&A学术交流会议论文集, 4016: 238–245
[8] 陈明晶, 方源敏. 陈杰. 最小二乘法和迭代法圆曲线拟合[J]. 测绘科学, 2016, 41(1): 194–197+202
CHEN M J, FANG Y M. CHEN J. Circular curve fitting by least squares method and iterative method[J]. Science of Surveying and Mapping, 2016, 41(1): 194–197+202
[9] 黄力峰, 汪伟. 吴南星. 基于最小二乘原理的圆拟合及误差评定算法研究[J]. 机械工程与自动化, 2020, 2(2): 4–6
HUANG L F, WANG W. WU N X. Research on circle fitting and error evaluation algorithm based on least squares Principle[J]. Mechanical Engineering and Automation, 2020, 2(2): 4–6
[10] KUZMENKO Y, SAMOYLENKO O. Processing by Least Square Method of the Measurements Results for Key, Regional and Supplementary Comparison of the Measurement Standards[J]. Метрологiя та прилади, 2018(2): 2180–2307
[11] 鲁铁定. 周世健. 总体最小二乘的迭代解法[J]. 武汉大学学报(信息科学版), 2010, 35(11): 1351–1354.
[12] 张明, 陶延林. 山中雪. 总体最小二乘算法在矿山测量数据中的应用[J]. 中国锰业, 2019, 37(5): 116–119+123.
[13] 苍桂华. 岳建平. 基于加权总体最小二乘法的点云平面拟合[J]. 激光技术, 2014, 38(3): 307–310.
[14] 袁豹. 岳东杰. 加权总体最小二乘法及其在GPS高程拟合中的应用[J]. 勘察科学技术, 2013(2): 43–45+64
YUAN B. YUE D J. Weighted overall least squares method and its application in GPS elevation fitting[J]. Survey Science and Technology, 2013(2): 43–45+64. (in Chinese)
[15] 袁豹, 岳东杰, 许义. 加权总体最小二乘在曲面拟合中的应用[J]. 勘察科学技术, 2013, (3): 47–50.
[16] TANG L W, LU Y Y. Study of the grey Verhulst model based on the weighted least square method[J]. Physica A:Statistical Mechanics and its Applications, 2020, 545: 378–4371
[17] 李全信. 圆曲线的拟合方法与精度分析[J]. 北京测绘, 2001, (3): 29–33+41.
[18] MAROPOULOS P G, GUO Y, JAMSHIDI J. Large volume metrology process models: A framework for integrating measurement with assembly planning[J]. CIRP Annals - Manufacturing Technology, 2008, 57(1): 7–85
[19] 孟飙. 曲学军. 大尺寸复杂形状组合测量系统的全局标定与多视数据融合[J]. 自动化学报, 2017, 43(11): 2051–2060.
[20] 曹雷. 潜艇建造工艺[M]. 武汉: 海军工程大学, 2003: 148–153.
[21] 鲁铁定, 邓小渊, 常晓涛. 圆曲线拟合的总体最小二乘算法分析[J]. 测绘科学, 2019, 44(2): 33–37.
