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Evaluation of Uncertainty in Resistance Measurement for Verificating Meter for pH Meters Based on MCM
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摘要: pH计检定仪作为检定校准pH（酸度）计、离子计、自动电位滴定仪等仪器电计部分的计量标准装置，在电化学计量领域中起到重要作用。随着JJG 919-2023《pH计检定仪检定规程》的发布，其规程一直未提供pH计检定仪高阻器电阻测量结果的不确定度的有关内容。通过运用国际通用的不确定度评定方法（GUM法）与蒙特卡洛方法（MCM法）对pH计检定仪高阻器的阻值测量结果进行不确定度评定。首先，采用GUM法对高阻器阻值的测量不确定度进行评定，通过采用MCM alchimia软件来对MCM法对其测量结果的不确定度评定。为了验证MCM alchimia软件对MCM法的有效性，使用运算和可视化更为完善的MATLAB软件对其MCM法以及自适应MCM法计算结果的比较，结果表明MCM alchimia软件计算得到的不确定度结果与MATLAB编程所得到的不确定度结果是一致的。另外，通过采用JJF1059.2-2012中用MCM法验证GUM法结果的方法，对GUM法评定pH计检定仪高阻器阻值测量结果不确定度的适用性，结果未能通过验证。因此，应用MCM法并通过MCM alchimia软件在pH计检定仪高阻器电阻测量不确定度评定方法的标准化提供参考。Abstract: The Verificating meter for pH meters serves as a metrological standard device for the verification and calibration of the electrical meter parts of instruments such as pH meters,ion meters,and automatic potentiometric titrators. It plays an important role in the field of electrochemical metrology.With the release of JJG 919-2023 "Verification Regulation of Verificating Meters for pH Meters",there has been no provision of content regarding the uncertainty of resistance measurement results of high-resistance devices in Verificating meters for pH meters.This article evaluates the uncertainty of resistance measurement results of high-resistance devices in Verificating meters for pH meters by applying the internationally recognized uncertainty evaluation methods:the Guide to the Expression of Uncertainty in Measurement(GUM) method and the Monte Carlo Method(MCM).Initially,we use the GUM method to assess the measurement uncertainty of high-resistance values,adopting MCM alchimia software to evaluate the uncertainty of its measurement results through the MCM method.To verify the effectiveness of MCM alchimia software for the MCM method,a comparison of the calculation results of the MCM method and the adaptive MCM method using MATLAB software with more comprehensive computation and visualization capabilities is conducted.The results indicate that the uncertainty outcomes calculated by MCM alchimia software are consistent with those obtained through MATLAB programming.Additionally, by employing the MCM method to validate the GUM method results as described in JJF1059.2-2012,the applicability of the GUM method for evaluating the uncertainty of resistance measurement results of high-resistance devices in Verificating meters for pH meters was assessed and failed to pass the validation.Therefore, applying the MCM method and utilizing MCM alchimia software provides a reference for the standardization of uncertainty assessment methods in resistance measurements of high-resistance devices in Verificating meters for pH meters.
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Key words:
- metrology /
- verificating meter for pH meters /
- Monte Carlo method /
- GUM /
- high-value resistor /
- MCM Alchimia /
- measurement uncertainty
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图 1 pH计检定仪高阻器阻值校准的接线图
Figure 1. Wiring diagram for high resistance value verificating meter for pH meters.
图 4 CORRELATION MATRIX界面显示
Figure 4. Wiring diagram for high resistance value calibration of pH meter verification instrument.
图 6 pH计检定仪高阻器1 GΩ阻值测量概率分布
Figure 6. The probability distribution of the resistance measurement of the 1GΩ high resistor in the verificating meter for pH meters
表 1 各分量标准不确定度汇总表
Table 1. Summary table of standard uncertainty of each component
不确定度分量 不确定度来源 u(xi)的值 灵敏系数ci ui(GΩ) $ u({\bar E_1}) $ 1000 mV测量值0.00225 mV0.0010 GΩ·mV2.3×10−6 $ u({\bar E_1}) $ 采样电压测量值 0.24 mV 0.034 GΩ·mV 0.0082 $ u({R_0}) $ 取样电阻不确定度 2.3×10−5 GΩ 32 0.0007 
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表 2 测量模型的输入量及其服从的PDF
Table 2. Input quantities of the measurement model and their corresponding probability density functions (PDF)
输入量 分布 参数 期望μ 标准偏差σ 期望(a+b)/2 半宽度(b-a)/2 E01 N(μ,σ2) 1000.001 mV0.00027 mV— — E02 R(a,b) — — 0 mV 0.0039 mVE11 N(μ,σ2) 29.885 mV 0.169 mV — — E12 R(a,b) — — 0 mV 0.000249 mVE13 N(μ,σ2) 0 mV 0.005 mV — — R0 N(μ,σ2) 0.029993 GΩ0.000022 GΩ— —
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表 3 MCM结果及扩展不确定度结果
Table 3. MCM results and expanded uncertainty results
/GΩ 高阻器阻值 测量结果 标准不确定度 扩展不确定度（k=2） R 0.974 0.006 0.011
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表 4 几种方法不确定度结果的比较
Table 4. Comparison of uncertainty results from several methods
/GΩ 不确定度评定方法
（运用软件）测量值 标准不确定度 95%包含区间 GUM 0.974 0.006 [0.962,0.986] GUM
(MCM Alchimia)0.974 0.006 [0.962,0.986] MCM
(MCM Alchimia)0.974 0.006 [0.962,0.985] MCM
(MATLAB)0.974 0.006 [0.962,0.985] 自适应MCM
(MATLAB)0.974 0.006 [0.962,0.985]
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表 5 GUM法的验证汇总表 /GΩ
Table 5. Summary table of validation for the GUM method
容差δ y Up dlow dhigh 是否通过验证 0.005 0.97 0.02 0.012 0.005 否 0.0005 0.974 0.012 0.00049 0.0012 否
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