Comparison of GUF and Monte Carlo methods to evaluate task-specific uncertainty in laser tracker measurement

YANG Jing-zhao(杨景照), LI Guo-xi(李国喜), WU Bao-zhong(吴宝中), GONG Jing-zhong(龚京忠), WANG Jie(王杰)

(College of Mechatronics and Automation, National University of Defense Technology, Changsha 410073, China)

Abstract:Measurement uncertainty plays an important role in laser tracking measurement analyses. In the present work, the guides to the expression of uncertainty in measurement (GUM) uncertainty framework (GUF) and its supplement, the Monte Carlo method, were used to estimate the uncertainty of task-specific laser tracker measurements. First, the sources of error in laser tracker measurement were analyzed in detail, including instruments, measuring network fusion, measurement strategies, measurement process factors (such as the operator), measurement environment, and task-specific data processing. Second, the GUM and Monte Carlo methods and their application to laser tracker measurement were presented. Finally, a case study involving the uncertainty estimation of a cylindricity measurement process using the GUF and Monte Carlo methods was illustrated. The expanded uncertainty results (at 95% confidence levels) obtained with the Monte Carlo method are 0.069 mm (least-squares criterion) and 0.062 mm (minimum zone criterion), respectively, while with the GUM uncertainty framework, none but the result of least-squares criterion can be got, which is 0.071 mm. Thus, the GUM uncertainty framework slightly underestimates the overall uncertainty by 10%. The results demonstrate that the two methods have different characteristics in task-specific uncertainty evaluations of laser tracker measurements. The results indicate that the Monte Carlo method is a practical tool for applying the principle of propagation of distributions and does not depend on the assumptions and limitations required by the law of propagation of uncertainties (GUF). These features of the Monte Carlo method reduce the risk of an unreliable measurement of uncertainty estimation, particularly in cases of complicated measurement models, without the need to evaluate partial derivatives. In addition, the impact of sampling strategy and evaluation method on the uncertainty of the measurement results can also be taken into account with Monte Carlo method, which plays a guiding role in measurement planning.

Key words:task-specific uncertainty; laser tracker; measurement uncertainty evaluation; Monte Carlo method; uncertainy framework (GUF)