Modeling CMM dynamic measuring error based on the 3B-spline orthogonal projection partial least squares - Zhang, Mei (2013)
It’s difficult to predict the dynamic error for coordinate measurement machine (CMM) by analyzing the error sources, because they are very complicated and have unknown interaction. In this paper an innovative modeling method is proposed by integrating 3B spline (3BS) transformation and orthogonal projection partial least squares (OPPLS). Three dimensional coordinates and direct computer control (DCC) parameters including positioning velocity, approaching distance and contacting velocity are used as the original independent variables of the model. The nonlinear relationship between the original independent variables and the CMM dynamic measurement errors is worked out by 3B spline transform. Then the orthogonal projection is used to build a new explanatory matrix by eliminating the components which are irrelative to the dependent variables. Finally, the operation of partial least-squares regression can be used to reduce the dimension and estimate the model parameters. With the proposed modeling method the nonlinear relationship between the independent variables and the dynamic measurement errors can be worked out without analyzing the error sources and their interactions. Besides, the problem of multi-collinearity caused by too many explanatory variables can also be overcome. The experimental results show that the mean square error of 3BS-OPPLS model is smaller than the 3B spline-partial least squares (3BS-PLS) model without the orthogonal projection, and the prediction accuracy of the model is notably improved.