Gram-Schmidt回归及在刀具磨损预报中的应用  

Gram-Schmidt regression and application in cutting tool abrasion prediction

作　　者：王惠文[1] 陈梅玲[2] Gilbert Saporta 

机构地区：[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

出　　处：《北京航空航天大学学报》2008年第6期729-733,共5页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金资助项目(70371007,70521001,70531010);北京市自然科学基金资助项目(9052006)

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.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 muhicolinearity. 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.

关 键 词：Gram-Schmidt正交变换 多元线性回归 多重相关性 刀具磨损 预测 

分 类 号：O212.4[理学—概率论与数理统计]