Analysis and Comparison of Bayesian Methods for Measurement Uncertainty Evaluation

Abstract

Based on the Bayesian principle, the modern uncertainty evaluation methods can fully integrate prior and current sample information, determine the prior distribution according to historical information, and deduce the posterior distribution by integrating prior distribution and the current sample data with the Bayesian model. As such, it is possible to evaluate uncertainty, updating in real time the uncertainty of the measuring instrument according to regular measurement, and timely reflect the latest information on the accuracy of the measurement system. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The maximum entropy principle and the hill-climbing search optimization algorithm are introduced to determine the prior distribution probability density function and the sample information likelihood function. The probability density function of posterior distribution is obtained by the Bayesian formula to achieve the optimization estimation of uncertainty. Three methods of measurement uncertainty evaluation based on Bayesian analysis are introduced: the noninformative prior, the conjugate prior, and the maximum entropy prior distribution. The advantages and limitations of each method are discussed.

Optimisation estimation of uncertainty integrated with production information based on Bayesian fusion method

“…After obtaining the measurement sample , it integrates prior information and current sample information based on the Bayes formula to obtain posterior distribution, thus achieving statistical inference of . Where, is the prior density function of , is the posterior density function and is the sample likelihood function [9, 10].…”

Misjudgement probability estimation of product inspection based on uncertainty

“…According to (10), the posterior distribution standard uncertainty of the repeatability information of the integrated two products is: Considering it as a priori information, by integrating it with the follow‐up uncertainty assessment data of multiple products, the repetitive component which can fully reflect the accuracy level of the batch product inspection process can be obtained [8].…”

Evaluation and Optimization of Task-oriented Measurement Uncertainty for Coordinate Measuring Machines Based on Geometrical Product Specifications

“…Similarly, the uncertainty components caused by repeatability and reproducibility of position error measurements are Formula (6) and Formula (7). Substitute Formula (14)-Formula (17) into Formula (3) and a universal model can be obtained for evaluating the uncertainty of the CMM position measurement tasks.…”

“…As an important parameter to characterize the quality of the measurement results, measurement uncertainty reflects the credibility of measurement results. To give scientific and proper evaluation of measurement uncertainty is an important factor to guarantee the development of modern measuring science [7,8]. CMM can complete the measurement of spatial geometric elements (including size, geometrical error parameters) more conveniently, featuring a large measurement range, high measurement efficiency and strong measurement versatility.…”