基于证据理论的测量不确定度评定与分析

Evaluating and Analyzing Measurement Uncertainty Based on the Theory of Evidence

针对GUM推荐的基于概率统计理论的不确定度表达方法存在的局限性,提出了一种更为通用的基于证据理论的随机模糊变量(RFV)方法,实现对测量结果及其不确定度的评定。根据有效测量信息构建了RFV隶属函数以及相应的数学理论框架,通过简单的例子给出了如何运用RFV进行不确定度评定的流程。实验结果表明,该方法既可以提供测量结果的置信区间也可以给出不确定度分量的贡献程度。通过与GUM方法的比较,当存在不可忽略的非随机分量影响时,该方法比概率统计方法能更客观地描述测量结果离散程度。

Deal with the limitations of GUM recommendations to express the measurement uncertainty based on a probabilistic and statistical theory, a more general approach which framed within the theory of the evidence was proposed. The method can represent the measurement result and its associated uncertainty in terms of random-fuzzy variables. An exhaustive mathematical framework and RFV membership functions was established according to the available information. The procedure for expressing the measurement uncertainty in terms of RFV was given by simple examples. The experimental results reported show that RFV are capable of both providing all the intervals of confidence and representing the different contributions to uncertainty. By compared with the approach of the GUM, the RFV method allows representing the dispersion of the values that could reasonably be attributed to the measured in a more suitable way than the probability theory, especially when no negligible nonrandom effects are present.