加速度计校准的贝叶斯不确定度评估

胡红波; 刘爱东; 左爱斌; 杨丽峰

doi:10.12338/j.issn.2096-9015.2020.9051

加速度计校准的贝叶斯不确定度评估

doi: 10.12338/j.issn.2096-9015.2020.9051

中国计量科学研究院，北京 100029

详细信息

作者简介:
胡红波（1980-），中国计量科学研究院副研究员，研究方向：振动冲击基标准装置、测试技术及测量数据分析处理，邮箱：huhb@nim.ac.cn

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出版历程
- 网络出版日期: 2021-05-17
- 刊出日期: 2021-06-24

Bayesian Uncertainty Evaluation for Accelerometer Calibration

National Institute of Metrology, Beijing 100029, China

摘要

摘要: 主要论述了贝叶斯统计用于加速度计校准结果的分析。首先介绍了对于线性测量模型，GUM、GUM S1以及基于贝叶斯统计分析测量不确定度的过程，说明三种方法分析的不同之处。然后结合实际工作中振动与冲击校准加速度计的数据，利用不同先验分布的贝叶斯统计和GUM系列方法进行了分析并对结果进行了比较。针对冲击加速度国际关键比对的部分数据建立了贝叶斯独立和层次两种不同的数据统计模型，在此基础之上结合马尔科夫链蒙特卡罗法（MCMC）对比对参考值和相应不确定度的计算，并且与通用方法的计算结果进行了比较。通过不同方法得到结果的一致性与差异性说明了贝叶斯统计用于不确定度评估的优缺点。
- 计量学 /
- 不确定度评估 /
- 贝叶斯统计 /
- 加速度计校准 /
- 冲击比对
Abstract: In this paper, Bayesian statistics is applied for the uncertainty evaluation of accelerometer calibration results. The process of analyzing measurement uncertainty based on GUM, GUM S1, and Bayesian statistics for linear measurement models is first presented to illustrate the differences in the analysis of the three methods. Combined with the vibration and shock calibration accelerometer data in actual work, the Bayesian statistics and GUM series methods with different prior distributions were used to analyze and compare the results. For the estimation of the reference value and its uncertainty for the key comparison in the field of shock acceleration, two different statistical models were developed using the Bayesian unpooled method and numerical method, on which the reference values and the corresponding uncertainties were calculated in combination with the Markov chain Monte Carlo method (MCMC) comparison, and the results were compared with those of the general method. The advantages and disadvantages of Bayesian statistics for uncertainty assessment are illustrated by the consistency and variability of the results obtained by the different methods.
- metrology /
- uncertainty evaluation /
- bayesian statistics /
- accelerometer calibration /
- shock comparison

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图 1 两种方法的比较（黑实线为GUM，浅绿色阴影为GUM S1）

Figure 1. Comparison of the two methods (Solid black line represents GUM, and light green shadow represents GUM S1)

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图 2 无信息先验被测量后验分布样本及概率分布

Figure 2. Simulations and probability density function of posterior distribution with noninformative prior

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图 3 先验分布取正态分布

Figure 3. Taking normal distribution as prior distribution

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图 4 先验分布取截断的正态分布

Figure 4. Taking truncated normal distribution as prior distribution

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图 5 独立模型

Figure 5. The unpooled model

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图 6 分层模型

Figure 6. The hierarchical model

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图 7 两种模型计算结果

Figure 7. Results of the two different models

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图 8 三种方式计算的结果

Figure 8. Results of the three different methods

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