Generation of numerical artefacts incorporating spatially correlated form error

Abstract

This paper is concerned with the generation of numerical artefacts, that is, reference data sets, for assessing the accuracy and fitness of purpose of software for computing minimum zone (MZ, Chebyshev) associated features. We describe an algorithm for generating datasets corresponding to a pre-specified best-fit surface and form error. We use a Gaussian process model to generate form errors that are spatially correlated. The form errors can be drawn from multivariate Gaussian or rectangular distributions. For the latter case a Gaussian copula is used to construct a multivariate multivariate distribution with the pre-assigned correlation. We illustrate the data generation on MZ circle fitting problems. We also describe an approximate MZ circle fitting problem that can be solved using linear programming.

Keywords

• Coordinate metrology
• Form error
• Minimum zone
• Numerical artefacts
• Spatial correlation