Gaussian process method for form error assessment using coordinate measurements

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.