非均匀采样加权最小二乘圆拟合的潜艇承压检测数据处理方法  

Survey Data Processing Method of Submarine Pressure Resistance Based on Non-uniform Sampling Weighted Least Square Circle Fitting

作　　者：王中[1] 彭飞[1] 韩玉超 孟庆旭 邓为耀 WANG Zhong;PENG Fei;HAN Yuchao;MENG Qingxu;DENG Weiyao(College of Naval Architecture and Ocean Engineering,Naval University of Engineering,Wuhan430033,China)

机构地区：[1]海军工程大学舰船与海洋学院,湖北武汉430033

出　　处：《武汉大学学报（信息科学版）》2024年第6期970-976,共7页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(51609253)。

摘　　要：为了最大程度抵抗深水压力,潜艇耐压壳体常采用柱锥结构形式,在建造和修理时需要检测各肋骨剖面圆度。因现场条件限制或融合使用多种不同测量手段获取数据,测量采样点常呈现非均匀性,导致经典最小二乘圆拟合的结果与实际情况存在偏差,尤其对用作圆度判定条件的最大挠度影响显著。基于经典Pratt圆拟合方法,运用先直接拟合,再根据对应圆心角定权、最后加权拟合的三步走策略,提出一种新的非均匀采样加权最小二乘圆拟合方法及其定权规则,用于潜艇承压检测数据处理。对标准椭圆采样分析数值实验表明,所提方法能够较好地消除非均匀采样对圆拟合的影响,拟合计算得到的最大挠度更加准确,具有较好的精度和工程实用价值,可以用于潜艇耐压壳体圆度测量非均匀采样点的圆拟合计算。Objectives In order to withstand the deep water pressure,the cylindrical structure and the conical structure are often used as the submarine pressure hull.The section roundness of the submarine pressure hull needs to be measured during construction and repair.Due to the limitation of environment conditions and the fusion of different survey methods to obtain data,the survey points are often non-uniform.This case would result in the deviation between the results of classical least square circle fitting method and the actual situation,especially to the maximum deflection which is used as the judgment condition of roundness.Therefore,it is necessary to adopt a method to eliminate the influence of non-uniform distribution of the survey points.Methods A non-uniform sampling weighted least squares circle fitting method and its weighting rules are proposed based on the classical Pratt circle fitting method.There are three steps in the proposed method.First,the survey points are fitted by the classical Pratt method.Then,the weight of point is calculated according to the corresponding center angle.Finally,the survey points with weight are fitted.Results Numerical experiments on standard ellipse sampling analysis are carried out.The results show that the maximum deflection is more affected than the fitted center and radius by the non-uniformity of the sampling points.Because the roundness evaluation judgment of the submarine pressure hull is based on the maximum deflection,the fitting results of the proposed method are more accurate and reliable than the classical circle fitting method.Conclusions The proposed method can eliminate the influence of non-uniform sampling on circle fitting better,and has good accuracy and engineering practical value.

关 键 词：潜艇 耐压壳体 圆拟合 非均匀采样 加权最小二乘法 

分 类 号：P258[天文地球—测绘科学与技术]