考虑非正定相关性的测量不确定度蒙特卡洛评定方法

doi:10.3969/j.issn.1000-1158.2022.06.19

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Abstract When the Monte Carlo method is used to evaluate the measurement uncertainty and the input quantities correlation is considered, it is necessary to generate relevant multi-dimensional random variables that obey any marginal probability distribution based on the Nataf inverse transformation. In order to solve the problem that the linear transformation matrix cannot be generated when the input correlation coefficient matrix is not positive definite in the Nataf inverse transformation process, an iterative correction algorithm based on the Barzilai-Borwein gradient method is proposed. Furthermore, it discusses the implementation steps of Monte Carlo method that the input quantities obey non-normal distribution. Finally, the iterative correction algorithm proposed and the Monte Carlo method based on Nataf inverse transformation are used to evaluate the uncertainty of the wheel-rail longitudinal creep rate of the high-speed wheel-rail system, which verifies the feasibility and effectiveness of the algorithm.

Key words： metrology uncertainty in measurement Monte Carlo method correlation non-positive definite iterative correction Nataf inverse transformation wheel-rail longitudinal creep rate

Received: 01 December 2021 Published: 30 June 2022

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	Articles by authors
	JU Yan-fei
	WANG Jun-biao
	CHANG Chong-yi
	ZHAO Ze-ping

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JU Yan-fei,WANG Jun-biao,CHANG Chong-yi, et al. Monte Carlo Method for the Measurement Uncertainty Evaluation Considering Non-positive Definite Correlation[J]. Acta Metrologica Sinica, 2022, 43(6): 830-836.

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http://jlxb.china-csm.org:81/Jwk_jlxb/EN/10.3969/j.issn.1000-1158.2022.06.19 OR http://jlxb.china-csm.org:81/Jwk_jlxb/EN/Y2022/V43/I6/830

［1］JCGM 100: 2008 Evaluation of measurement data—Guide to the expression of uncertainty in measurement ［S］.
［2］JJF 1059.1—2012测量不确定度评定与表示［S］.
［3］JCGM 101: 2008 Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement ”Propagation of distributions using a Monte Carlo method ［S］.
［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 Instrumentation, 2011, 25 (4): 301-308.
［5］王伟, 宋明顺, 陈意华, 等. 蒙特卡罗方法在复杂模型测量不确定度评定中的应用［J］. 仪器仪表学报, 2008, 29 (7): 1446-1449.
Wang W, Song M Sh, Chen Y H, et al. Application of Monte-Carlo method in measurement uncertainty evaluation of complicated model ［J］. Chinese Journal of Scientific Instrument, 2008, 29 (7): 1446-1449.
［6］张学仪, 何小妹, 刘峻峰, 等. 基于蒙特卡洛法的叶片型面参数测量不确定度分析［J］. 航空制造技术, 2021, 64 (12): 94-101.
Zhang X Y, He X M, Liu J F, et al. Evaluation of Uncertainty in Blade Parameter Measurement Based on Monte Carlo Method ［J］. Aeronautical Manufacturing Technology, 2021, 64 (12): 94-101.
［7］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.
［8］程银宝,陈晓怀,王中宇, 等. CMM形状测量任务的不确定度分析与评定［J］. 计量学报, 2020, 41(2): 134-138.
Cheng Y B, Chen X H, Wang Z Y,et al. Uncertainty Analysis and Evaluation of Form Measurement Task for CMM［J］. Acta Metrologica Sinica, 2020, 41(2): 134-138.
［9］王朋朋,程杰,张艳昆,等. 0.005级压力式水深测量仪器检定装置的测量不确定度评定［J］. 计量学报, 2021, 42(8): 1053-1060.
Wang P P, Cheng J, Zhang Y K, et al. Evaluation of Measurement Uncertainty of Level 0.005 Pressure Type Water Depth Measuring Instrument Verification Device［J］. Acta Metrologica Sinica, 2021, 42(8): 1053-1060.
［10］靳浩元,刘军. 测量不确定度的评定方法及应用研究［J］. 计量科学与技术, 2021, 65(5): 124-131.
Jin H Y, Liu J.The Evaluation Method and Application Research of Measurement Uncertainty［J］. Metrology Science and Technology, 2021, 65(5): 124-131.
［11］魏明明. 蒙特卡洛法与GUM评定测量不确定度对比分析［J］. 电子测量与仪器学报, 2018, 32 (11): 17-25.
Wei M M. Comparative analysis of measurement uncertainty evaluation with Monte Carlo method and GUM ［J］. Journal of Electronic Measurement and Instrumentation, 2018, 32 (11): 17-25.
［12］杨建. 蒙特卡罗法评定测量不确定度中相关随机变量的MATLAB实现［J］. 计测技术, 2012, 32 (4): 51-54.
Yang J. The MATLAB Realization of Correlated Random Variable in Evaluation of Measurement Uncertainty Based on Monte Carlo Method［J］. Metrology & Measurement Technology, 2012, 32 (4): 51-54.
［13］崔伟群, 杭晨哲. 基于蒙特卡罗方法评定不确定度中相关随机变量模拟［J］. 现代测量与实验室管理, 2010, 18 (4): 24-27.
Cui W Q, Hang C Z. Simulation of Correlated Random Variables in Uncertainty Evaluation Based on Monte Carlo Method ［J］. Modern Measurement and Laboratory Management, 2010, 18 (4): 24-27.
［14］文德智, 卓仁鸿, 丁大杰, 等. 蒙特卡罗模拟中相关变量随机数序列的产生方法［J］. 物理学报, 2012, 61 (22): 26-33.
Wen D Z, Zhuo R H, Ding D J, et al. Generation of correlated pseudorandom variables in Monte Carlo simulation ［J］. Acta Physica Sinica, 2012, 61 (22): 26-33.
［15］凌明祥, 李会敏, 黎启胜, 等. 含相关性的测量不确定度拟蒙特卡罗评定方法［J］. 仪器仪表学报, 2014, 35 (6): 1385-1393.
Ling M X, Li H M, Li Q S, et al. Quasi Monte Carlo method for the measurement uncertainty evaluation considering correlation ［J］. Chinese Journal of Scientific Instrument, 2014, 35 (6): 1385-1393.
［16］Barzilai J, Borwein J M. Two-Point Step Size Gradient Methods ［J］. Ima J. numer. anal, 1988, 8 (1): 141-148.
［17］Liu P L, Kiureghian A D. Multivariate distribution models with prescribed marginals and covariances ［J］. Probabilistic Engineering Mechanics, 1986, 1 (2): 105-112.
［18］Xiao Q. Evaluating correlation coefficient for Nataf transformation ［J］. Probabilistic Engineering Mecha-nics, 2014, 37: 1-6.
［19］叶德培. 测量不确定度理解评定与应用［M］. 北京: 中国质检出版社, 2013.
［20］罗仁, 石怀龙. 铁道车辆系统动力学及应用［M］. 成都: 西南交通大学出版社, 2018.