Research and Implementation of Geometric Element Fitting Algorithm Based on Least-Squares

杜福洲; 王小强; 段桂江

doi:10.16080/j.issn1671-833x.2011.21.001

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Research and Implementation of Geometric Element Fitting Algorithm Based on Least-Squares

更新时间：2026-04-23

- Research and Implementation of Geometric Element Fitting Algorithm Based on Least-Squares
- Aeronautical Manufacturing Technology Vol. 54, Issue 21, Pages: 65-68(2011)
- 作者机构：
  
  北京航空航天大学机械工程及自动化学院
- 作者简介：
- 基金信息：
- DOI：10.16080/j.issn1671-833x.2011.21.001
  CLC：
- Published：2011
- 稿件说明：
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杜福洲，王小强，段桂江. 基于最小二乘法的几何元素拟合算法研究[J]. 航空制造技术, 2011, 54(21): 65-68.

杜福洲, 王小强, 段桂江. Research and Implementation of Geometric Element Fitting Algorithm Based on Least-Squares[J]. Aeronautical Manufacturing Technology, 2011, 54(21): 65-68.
杜福洲，王小强，段桂江. 基于最小二乘法的几何元素拟合算法研究[J]. 航空制造技术, 2011, 54(21): 65-68. DOI： 10.16080/j.issn1671-833x.2011.21.001.

杜福洲, 王小强, 段桂江. Research and Implementation of Geometric Element Fitting Algorithm Based on Least-Squares[J]. Aeronautical Manufacturing Technology, 2011, 54(21): 65-68. DOI： 10.16080/j.issn1671-833x.2011.21.001.

摘要

误差评定是零件检测环节中的重要检验项目之一，几何元素拟合是基于坐标测量法评定误差的核心内容。在对常见几何元素分析研究的基础之上，构建了其参数化数学模型，基于最小二乘法提出其拟合算法的整体框架，对具体的算法进行了研究并给出了优化算法初始值的计算过程，基于 MATLAB 平台对拟合算法进行了实现，并将其拟合结果与 NIST 的结果进行比较分析，结果验证了该算法的可行性。

Abstract

Error evaluation is one of the important tests in the process of part inspection. Geometric fi tting is the core content in the error evaluation based on the coordinate measuring. Based on the analysis of the common geometric elements

the parameterized mathematic model of geometric elements is constructed and the frame of the fi tting algorithms is proposed. Meanwhile the detail of fitting algorithms and the initial value of the optimization algorithms are illustrated. Then algorithms are carried out on the MATLAB platform and the fitting results are compared with the results of NIST. The comparision shows that the fi tting algorithms are feasible.

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