Uncertainty Calculation of Roundness by Automatic Differentiation
According to the Guide to the Expression of Uncertainty in Measurement (GUM), all measurement results must have a stated uncertainty associated to them. But in most cases of roundness measurement either no uncertainty value is given, or the calculation is not based on the model of the respective association criterion for the geometrical feature, because no suitable measurement uncertainty calculation procedure does exist. For the case of roundness measurement in coordinate metrology, this paper will suggest algorithms for the calculation of the measurement uncertainty of the roundness deviation based on the two mainly used association criteria LSC and MZC. The calculation of the sensitivity coefficients for the uncertainty calculation can be done by automatic differentiation, in order to avoid introducing additional errors by the traditional difference quotient approximations. The proposed methods are exact and need as input data only the measured co-ordinates of the data points and their associated uncertainties.
Yuri Chugui, Yongsheng Gao, Kuang-Chao Fan, Roald Taymanov and Ksenia Sapozhnikova
J. C. Lin et al., "Uncertainty Calculation of Roundness by Automatic Differentiation", Key Engineering Materials, Vol. 437, pp. 217-221, 2010