Gram-Schmidt regression and application in cutting tool abrasion prediction
Wang Huiwen1, Chen Meiling2, Gilbert Saporta3*
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
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.