北京航空航天大学学报 ›› 2008, Vol. 34 ›› Issue (06): 729-733.

• 论文 • 上一篇    下一篇

Gram-Schmidt回归及在刀具磨损预报中的应用

王惠文1, 陈梅玲2, Gilbert Saporta3   

  1. 1. 北京航空航天大学 经济管理学院, 北京 100191;
    2. 北京航空航天大学 理学院, 北京 100191;
    3. 国立巴黎工艺技术学院, 巴黎 75141
  • 收稿日期:2007-06-05 出版日期:2008-06-30 发布日期:2010-09-17
  • 作者简介:王惠文(1957-),女,辽宁大连人,教授,wanghw@vip.sina.com.

Gram-Schmidt regression and application in cutting tool abrasion prediction

Wang Huiwen1, Chen Meiling2, Gilbert Saporta3   

  1. 1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    3. Conservatoire National Des Arts et Métier, Paris 75141, France
  • Received:2007-06-05 Online:2008-06-30 Published:2010-09-17

摘要: 多元线性回归是一种应用广泛的统计分析方法.在实际应用中,当自变量集合存在严重多重相关性时,普通最小二乘方法就会失效.为解决这一问题,利用Gram-Schmidt 正交变换,提出一种新的多元线性回归建模方法——Gram-Schmidt回归.该方法可实现多元线性回归中的变量筛选,同时也解决了自变量多重相关条件下的有效建模问题.将该方法应用于机械加工过程中刀具磨损的预报分析,有效地进行了变量筛选,并得到了解释性强同时拟合优度也很高的模型结果.

Abstract: Multiple linear regression is one of the most widely applied statistical methods in scientific research fields. However, the ordinary least squares method will be invalid when the independent variables set exists server multicolinearity problem. A new multiple linear regression method, named Gram-Schmidt regression, was proposed by the use of Gram-Schmidt orthogonal transformation in the modeling process. Not only can it screen the variables in multiple linear regression, but also provide a valid modeling approach under the condition of server multicolinearity. The method was applied to the prediction of the flank wear of cutting tool in the turning operation. The results demonstrate that the variable screening is reasonable and the model is highly fitted.

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