Algorithmic iterative sampling in coordinate metrology plan for coordinate metrology using dynamic uncertainty analysis

Coordinate metrology is inherently subject to a source of uncertainty due to an attempt to inspect an unknown surface based on a limited number of discrete observations called sampling points. The computation tasks required for this evaluation need to be designed and conducted to minimize the uncertainty factors during the inspection process. This work presents a novel sampling planning approach based on a probabilistic framework to estimate the uncertainty in reconstruction of the measured surface. The goal is to minimize the required number of sample points to inspect a surface flatness within an acceptable level of uncertainty. The developed methodology models the deviation from the ideal geometry is modeled as a linear combination of shape functions. Then a Probability Density Function (PDF) is created based on a prior model of the expected surface´s deviation characteristics. By combining the prior probability density function and the current set of measurements, a new PDF for the reconstructed deviation is updated during the measurement process which which combines their expected values and their uncertainties. This PDF in turn can be used to estimate critical points for flatness measurement. Those critical points are in turn elected to be sampled at the next measurements. The proposed adaptive sampling is evaluated using virtual sampling of a machined surface. Results show important improvement over the commonly used random sampling approaches.