Gaussian process method for form error assessment using coordinate measurements

Abstract

A Gaussian process method for modeling and assessing form errors is presented. The Gaussian process method decomposes a geometric feature into three components: designed geometric form, systematic manufacturing errors and random manufacturing errors. It models the systematic manufacturing errors as a spatial model using a Gaussian correlation function and models the random manufacturing errors as independent identically distributed noises. Based on a handful of coordinate measurements, the Gaussian process model reconstructs the part surface and assesses the form error better than traditional methods. The Gaussian process method also provides an empirical distribution of the form error, allowing engineers to quantify the decision risk on part acceptance. This method works for generic geometric features. The method is implemented on two common features: a straight and a round feature. Simulated datasets as well as actual coordinate measuring machine data are used to demonstrate the improvement achieved by the proposed method over the traditional approaches.

Keywords:

• Spatial model
• Gaussian process
• form tolerance
• systematic manufacturing error
• random manufacturing error

Acknowledgments

The authors gratefully acknowledge financial support from the NSF under grant CMMI-0348150 and from the State of Texas Advanced Technology Program under grant 000512-0237-2003. The authors also appreciate the editor and the referees for their valuable comments and suggestions.