留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

测量误差理论的真值中心论和测得值中心论

叶晓明 丁士俊 师会生

【引用本文】 叶晓明,丁士俊,师会生. 测量误差理论的真值中心论和测得值中心论[J]. 计量科学与技术,2021, 65(3):19-27 doi: 10.3969/j.issn.2096-9015.2021.03.04
引用本文: 【引用本文】 叶晓明,丁士俊,师会生. 测量误差理论的真值中心论和测得值中心论[J]. 计量科学与技术,2021, 65(3):19-27 doi: 10.3969/j.issn.2096-9015.2021.03.04
YE Xiaoming, DING Shijun, SHI Huisheng. True-Value Centered Theory and Measured-Value Centered Theory in Measurement Error Theories[J]. Metrology Science and Technology, 2021, 65(3): 19-27. doi: 10.3969/j.issn.2096-9015.2021.03.04
Citation: YE Xiaoming, DING Shijun, SHI Huisheng. True-Value Centered Theory and Measured-Value Centered Theory in Measurement Error Theories[J]. Metrology Science and Technology, 2021, 65(3): 19-27. doi: 10.3969/j.issn.2096-9015.2021.03.04

测量误差理论的真值中心论和测得值中心论

doi: 10.3969/j.issn.2096-9015.2021.03.04
详细信息
    作者简介:

    叶晓明(1963-),武汉大学测绘学院副教授,研究方向:测量仪器及误差理论,邮箱:xmye@sgg.whu.edu.cn

True-Value Centered Theory and Measured-Value Centered Theory in Measurement Error Theories

  • 摘要: 传统经典测量误差理论认为测得值(观测值)是随机变量,真值是常量;但新概念测量理论认为测得值(观测值)是常量,真值是随机变量。本文通过概率论概念的回顾,对二种不同的常量和随机变量概念解释进行对比分析,指出传统测量理论对基本数学概念的曲解以及由此导致的诸多概念逻辑困境,并阐明新概念测量理论的基本概念逻辑和误差评价原理。
  • 图  1  传统测量误差理论的概念示意图

    Figure  1.  Conceptual diagram of the traditional measurement error theory

    图  2  新概念理论的概念原理示意图

    Figure  2.  Schematic diagram of concepts in the new theory

    图  3  测距仪周期误差的规律性和随机性

    Figure  3.  Regularity and randomness in the periodic error of a rangefinder

    图  4  四舍五入误差的规律性和随机性

    Figure  4.  Regularity and randomness in the rounding error

    图  5  直流电压测量中交流电干扰误差的规律性和随机性

    Figure  5.  Regularity and randomness in the AC interference error in DC voltage measurements

    图  6  电子噪声误差的规律性和随机性

    Figure  6.  Regularity and randomness in an electronic noise error

    图  7  三段基线

    Figure  7.  Three-section baselines

    表  1  概率论教科书对离散型随机变量概念的描述

    Table  1.   The concept of a discrete random variable in the probability theory

    $ X $$ {x}_{1} $$ {x}_{2} $$ {x}_{i} $
    $ P $$ {p}_{1} $$ {p}_{2} $$ {p}_{i} $
    下载: 导出CSV

    表  2  公式(10)(11)(12)中的概念类别比较

    Table  2.   Comparison of concept categories in Formulas (10), (11), and (12)

    观测值${q_k}$观测值${q_j}$测得值$\bar q $
    公式(10)常数——常数
    公式(11)随机变量常数常数
    公式(12)随机变量——随机变量
    下载: 导出CSV

    表  3  传统测量误差理论中的数学期望缺失问题

    Table  3.   Lack of mathematical expectation in the traditional measurement error theory

    测得值$ x $随机误差$ r=x-E\left(x\right) $系统误差$ s=E\left(x\right)-{x}_{T} $真值$ {x}_{T} $
    $\left\{ {\begin{array}{*{20}{l}} {E(x) = ???} \\ {{u^2}(x) = E{{[x - E(x)]}^2}} \end{array} } \right.$$\left\{ {\begin{array}{*{20}{l}} {E(r) = 0} \\ {{u^2}(r) = {u^2}(x)} \end{array} } \right.$$\left\{ {\begin{array}{*{20}{l}} {E(s) = ???} \\ {{u^2}(s) = 0} \end{array} } \right.$$\left\{ {\begin{array}{*{20}{l}} {E({x_T}) = ???} \\ {{u^2}({x_T}) = 0} \end{array} } \right.$
    下载: 导出CSV

    表  4  新概念测量误差理论中的概念解释

    Table  4.   Concepts in the new measurement error theory

    测得值$ {x}_{0} $误差$ \varDelta $真值$ {X}_{T} $
    $\left\{ {\begin{array}{*{20}{l}} {E({x_0}) = {x_0}} \\ {{u^2}({x_0}) = 0} \end{array} } \right.$$\left\{ {\begin{array}{*{20}{l}} {E(\varDelta ) = 0} \\ {{u^2}(\varDelta ) = E({\varDelta ^2})} \end{array} } \right.$$\left\{ {\begin{array}{*{20}{l}} {E({X_T}) = {x_0}} \\ {{u^2}({X_T}) = {u^2}(\varDelta )} \end{array} } \right.$
    下载: 导出CSV

    表  5  三段基线的全组合观测值

    Table  5.   Combination of all observations of three-section baselines

    线段ABBCCDACBDAD
    观测值$ {x}_{1} $$ {x}_{2} $$ {x}_{3} $$ {x}_{4} $$ {x}_{5} $$ {x}_{6} $
    下载: 导出CSV
  • [1] 叶晓明, 凌模, 周强, 等. 误差理论的新哲学观[J]. 计量学报, 2015, 36(6): 666-670. doi: 10.3969/j.issn.1000-1158.2015.06.25
    [2] Ye Xiao-ming, Xiao Xue-bin, Shi Jun-bo, et al. The new concepts of measurement error theory[J]. Measurement, 2016, 83(4): 96-105.
    [3] Ye Xiao-ming, Liu Hai-bo, Ling Mo, et al. The new concepts of measurement error's regularities and effect characteristics[J]. Measurement, 2018, 126(10): 65-71.
    [4] Ye Xiao-ming, Ding Shi-jun. Comparison of variance concepts interpreted by two measurement theories[J]. Journal of Nonlinear and Convex Analysis, 2019, 20(7): 1307-1316.
    [5] Shi Huisheng, Ye Xiaoming, Xing Cheng, et al. Originand Evolution of Conceptual Differences between Two Measurement Theories[J]. Fuzzy Systems and Data MiningVI, 2020(1): 66-77.
    [6] Shi Huisheng, Ye Xiaoming, Xing Cheng, et al. A New Theoretical Interpretation of Measurement Error and Its Uncertainty[J]. Discrete Dynamics in Nature and Society, 2020(2020):1-14.
    [7] 叶晓明. 新概念测量误差理论[M]. 武汉: 湖北科学技术出版社, 2017.
    [8] 叶晓明. 测量误差及其不确定性的普适理论(共享版)[EB/OL].http://blog.sciencenet.cn/home.php?mod=space&uid=630565&do=blog&view=me&from=space.
    [9] 齐民友, 刘禄勤, 王文祥, 等. 概率论与数理统计[M]. 高等教育出版社, 2011: 44-46.
    [10] 盛骤, 谢式千, 潘承毅. 概率论与数理统计[M]. 高等教育出版社, 2008: 32-33.
    [11] JCGM 200: 2012, International vocabulary of metrology — Basic and general concepts and associated terms (VIM)[S]. BIPM, S´evres, France, 2012.
    [12] 国家质量监督检验检疫总局.通用计量术语及其定义: JJF1001-2011[S]. 中国质检出版社, 2011.
    [13] 国家质量监督检验检疫总局. 测绘学基本术语: GB/T14911-2008[S]. 中国标准出版社, 2008.
    [14] 武汉大学测绘学院. 误差理论与测量平差基础[M]. 武汉大学出版社, 2016.
    [15] 费业泰. 误差理论与数据处理[M]. 机械工业出版社, 2016.
    [16] JCGM 100: 2008, Guide to the Expression of Uncertainty in Measurement(GUM)[S]. BIPM, S´evres, France. 2008.
    [17] 国家质量监督检验检疫总局. 测量不确定度评定与表示: JJF1059-2012[S]. 中国质检出版社, 2011.
    [18] Churchill Eisenhart. Expression of the Uncertainties of Final Results[J] Science, 1968, 14(6): 1201-1204.
    [19] 叶德培. 测量不确定度理解、评定与应用[M]. 中国计量出版社, 2007.
    [20] ISO 17123-4: 2012, Optics and optical instruments -- Field procedures for testing geodetic and surveying instruments -- Part 4: Electro-optical distance meters (EDM measurements to reflectors)[S]. ISO, Geneva, Switzerland, 2012.
  • 加载中
图(7) / 表(5)
计量
  • 文章访问数:  721
  • HTML全文浏览量:  228
  • PDF下载量:  78
  • 被引次数: 0
出版历程
  • 网络出版日期:  2021-04-13
  • 刊出日期:  2021-03-12

目录

    /

    返回文章
    返回