摘要分析了自适应蒙特卡洛法(Mote Carlo method,MCM)评定测量不确定度时的规律,将其应用于实践领域。首先介绍了MCM基本原理和自适应MCM评定的具体流程、步骤及程序实现;然后根据自适应MCM需进行稳定性判定等特性,提出了自适应MCM波动性指标的概念;最后通过具有代表性的线性模型(铂电阻气温传感器测量误差值的关系模型)和非线性模型(电阻-温度关系模型)的仿真试验,得出自适应MCM波动性指标收敛趋势的一般性规律。最终为自适应MCM在评定测量不确定度时提供了一定的技术参考。
Abstract：The rule of adaptive Monte Carlo method(MCM) for measurement uncertainty evaluation is analyzed and apply it to practise areas. Firstly, the basic principles of MCM, the detailed process, steps and program implementation on the evaluation of adaptive MCM are introduced. Secondly, combined with the characteristics that the stability of adaptive MCM needs to be analyzed, the concept of adaptive MCM volatility index is proposed. Finally, the general law of convergence trend of adaptive MCM volatility index is concluded by means of simulation experiments, which use representative linear model (relational model of measuring error value by using platinum resistance air temperature sensor) and non-linear model (resistance-temperature relationship model). Ultimately, a technical reference for the measurement uncertainty evaluation by adaptive MCM is provided.
［1］ISO/IEC.Guide 98-3(2008)Uncertainty of Measurement-Part 3: Guide to the Expression of Uncertainty in Measurement［S］. 2008.
［2］ISO/IEC. GUIDE98-3 Supplement1-2008 Uncertainty of measurement-Part3/Supplement 1: Propagation of distributions using a Monte Carlo method［S］. 2008.
［3］陈怀艳, 曹芸, 韩洁. 测量不确定度的发展和应用研究［J］. 宇航计测技术, 2014, 32(5): 65-70.
Chen H Y, Cao Y, Han J. Research on Development and Application of Measurement Uncertainty［J］. Journal of Astronautic Metrology and Measurement, 2014, 32(5): 65-70.
［4］陈怀艳, 曹芸,韩洁.基于蒙特卡罗法的测量不确定度评定［J］.电子测量与仪器学报,2011,25(4):301-308.
Chen H Y, Cao Y, Han J. Evaluation of uncertainty in measurement based on a Monte Carlo method［J］. Journal of Electronic Measurement and Instrument, 2011, 25(4): 301-308.
［5］黄美发, 景晖, 匡兵, 等. 基于拟蒙特卡罗方法的测量不确定度评定［J］. 仪器仪表学报, 2009, 30(1): 120-125.
Huang M F, Jing H, Kuang B, et al. Measurement uncertainty evaluation based on quasi Monte-Carlo method［J］. Chinese Journal of Scientific Instrument, 2009, 30(1): 120-125.
［6］张婉洁, 赵轶. 蒙特卡洛法测量不确定度评定中测量模型的建立［J］. 计量与测试技术, 2017, 44(9): 56-57.
Zhang W J, Zhao Y. Discussion on the Establishment of Measurement Model in the Uncertainty Evaluation by the Monte Carlo Method［J］. Metrology & Measurement Technique, 2017, 44(9): 56-57.
［7］宋明顺, 张俊亮, 方兴华, 等. 基于蒙特卡罗方法的模型质量控制图［J］. 系统科学与数学, 2015, 35(11): 1291-1303.
Song M S, Zhang J L, Fang X H, et al. The model control chart based on Monte Carlo method［J］. Journal of Systems Science and Mathematical Sciences, 2015, 35(11): 1291-1303.
［8］宋明顺, 王伟. Monte Carlo方法评定测量不确定度中模拟样本数M的确定［J］. 计量学报, 2010, 31(1): 91-96.
Song M S, Wang W. Assignment of Simulation Sample Capability M in Uncertainty Evaluation by Monte Carlo Method［J］. Acta Metrologica Sinica, 2010, 31(1): 91-96.
［9］张海滨, 王中宇, 刘智敏. 测量不确定度评定的验证研究［J］. 计量学报, 2007, 28(3): 193-197.
Zhang H B, Wang Z Y, Liu Z M. Study on the Verification of Measurement Uncertainty［J］. Acta Metrologica Sinica, 2007, 28(3): 193-197.
［10］王瑞宝. 基于蒙特卡洛法的微波功率测量不确定度评定［J］. 国外电子测量技术, 2015, 34(7): 28-31.
Wang R B. Evaluation of measurement uncertainty of micowave power based on Monte Carlo method［J］. Foreign Electronic Measurement Technology, 2015, 34(7): 28-31.
［11］杭晨哲, 徐定华, 马国远, 等. 空气焓值法测量全年能源消耗效率不确定度评定方法研究［J］. 计量学报, 2017, 38(1): 34-39.
Hang C Z, Xu D H, Ma G Y, et al. Study on Uncertainty Evaluation of Annual Performance Factor Based on Air-enthalpy Method［J］. Acta Metrologica Sinica, 2017, 38(1): 34-39.
［12］胡佳豪, 林勇, 蔡广林, 等. 基于自适应蒙特卡罗法的导线载流量不确定度分析［J］. 华东电力, 2013, 41(11): 2241-2245.
Hu J H, Lin Y, Cai G L, et al. Conductor carrying capacity uncertainty analysis based on adaptive Monte Carlo method［J］. East China Electric Power, 2013, 41(11): 2241-2245.
［13］曹芸, 陈怀艳, 韩洁. 采用MCM对GUM法测量不确定度评定的验证方法研究［J］. 宇航计测技术, 2012, 32(2): 75-78.
Cao Y, Chen H Y, Han J. Research about Validating GUM Uncertainty Evaluation Using MCM［J］. Journal of Astronautic Metrology and Measurement, 2012, 32(2): 75-78.
［14］Andolfatto L, Mayer J R, Lavernhe S. Adaptive Monte Carlo applied to uncertainty estimation in five axis machine tool link errors identification with thermal disturbance［J］. International Journal of Machine Tools & Manufacture, 2011, 51(7-8): 618-627.
［15］刘园园, 杨健, 赵希勇, 等. GUM法和MCM法评定测量不确定度对比分析［J］. 计量学报, 2018, 39(1): 135-139.
Liu Y Y, Yang J, Zhao X Y, et al. Comparative Analysis of Uncertainty Measurement Evaluation with GUM and MCM［J］. Acta Metrologica Sinica, 2018, 39(1): 135-139.
［16］Wen X L, Zhao Y B, Wang D X, et al. Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error［J］. Precision Engineering, 2013, 37(4): 856-864.
［17］方兴华, 宋明顺, 顾龙芳, 等. 基于自适应蒙特卡罗方法的测量不确定度评定［J］. 计量学报, 2016, 37(4): 452-456.
Fang X H, Song M S, Gu L F, et al. Application of adaptive Monte Carlo method on measurement uncertainty evaluation［J］. Acta Metrologica Sinica, 2016, 37(4): 452-456.
［18］国家质量监督检验检疫总局. JJF1059.2-2012用蒙特卡洛法评定测量不确定度［S］. 北京:中国质检出版社, 2013.
2019, Vol. 40 
