Modeling CMM dynamic measuring error based on the 3B-spline orthogonal projection partial least squares
Date of Issue2012
School of Mechanical and Aerospace Engineering
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.
International journal on advances in information sciences and service sciences
© 2012 The International Association for Information, Culture, Human and Industry Technology (AICIT). This paper was published in International journal on advances in information sciences and service sciences and is made available as an electronic reprint (preprint) with permission of the International Association for Information, Culture, Human and Industry Technology (AICIT). The paper can be found at the following official DOI: http://dx.doi.org/10.4156/aiss.vol4.issue15.29. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.