泰勒级数准则的船体分段测量数据配准解析解  

Analytical solution of measurement data registration for hull blocks based on Taylor series criterion

作　　者：杨贵强 王炬成[1] 李瑞[2] YANG Guiqiang;WANG Jucheng;LI Rui(College of Naval Architecture and Ocean Engineering,Jiangsu University of Science and Technology,Zhenjiang 212100,China;School of Naval Architecture and Ocean Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]江苏科技大学船舶与海洋工程学院,江苏镇江212100 [2]大连理工大学船舶工程学院,辽宁大连116024

出　　处：《哈尔滨工程大学学报》2024年第11期2094-2099,共6页Journal of Harbin Engineering University

基　　金：工业和信息部高技术船舶项目(MC-201917-C09).

摘　　要：为提高船体分段测量数据与CAD模型间的配准定位效率,本文给出了一个基于泰勒级数准则的点集配准解析解,直接求解配准变换参数。通过分析最小二乘解析解的求解特点,考虑到配准变换参数的齐次表示问题,引入特征因子构建新的齐次变换矩阵,建立配准齐次表示模型。利用泰勒级数展开齐次变换矩阵的最近正交矩阵,得到齐次变换矩阵的无限次估计解。在此基础上,根据配准齐次表示模型的最大化,计算旋转矩阵的近似解析最优解。以理论模型和甲板分段实测数据为例子验证。本文算法的有效性及实用性,为船体分段快速测量分析提供算法依据。To enhance the registration positioning efficiency between segmented hull measurement data and CAD models,this paper presents an analytical solution for point set registration using the Taylor series criterion.This method directly determines the registration transformation parameters.First,it analyzes the characteristics of the least squares analytical solution,addressing the homogeneous representation issue of registration transformation parameters.To tackle this,feature factors are introduced to construct a new homogeneous transformation matrix,establishing a registration homogeneous representation model.Subsequently,an infinite estimation solution for the homogeneous transformation matrix is derived by expanding it into the nearest orthogonal matrix using the Taylor series.On this basis,an approximate analytical optimal solution for the rotation matrix is calculated by maximizing the representation within the registration homogeneous model.The effectiveness and practicality of the proposed algorithm are validated through theoretical models and actual measured data of deck segments.The proposed algorithm provides a robust algorithmic foundation for rapid measurement and analysis of hull segments.

关 键 词：船体分段 精度控制 齐次坐标 泰勒级数 点集配准 解析解 最小二乘 特征因子 最近正交矩阵 

分 类 号：U671.99[交通运输工程—船舶及航道工程]