Research on Consistency Judgement of Indication Error for Calibration Result of Humidity Sensor in Meteorology

In order to solve the lack of relevant evaluation research on the accuracy of HMP155A humidity sensor calibration results in the past, this paper designs the corresponding experimental scheme, and obtains the corresponding calibration results according to the experimental scheme; Then the measurement uncertainty of the indication error in the calibration results is evaluated by GUM, and the corresponding extended uncertainty U 95 is obtained. Finally, according to the requirements of JJF1094-2016 characteristic evaluation of measuring instruments, combined with the calibration results and the actual situation of U 95 , the conformity of the indication error of calibration is determined. The result is that each calibration point of the sensor meets the requirements of conformity determination and is within the qualified range. This research effectively makes up for the blank of the previous research on the conformity determination of the indication error of the calibration results and has strong theoretical and practical significance.

ensure the accuracy of the detection data of HMP155A humidity sensor, it is necessary to trace the quantity value regularly [1]. The quantity value tracing is generally in the way of calibration. The calibration method is reflected in the form of indication error and corresponding measurement uncertainty by comparing the humidity with the previous measurement standard. In order to ensure that the performance of the calibration results meets the standard, it is necessary to judge the conformity of the indication error of the measurement results according to the requirements of JJF1094-2016 characteristic evaluation of measuring instruments.
HMP155A humidity sensor is usually calibrated according to the humidity verification regulation. Since the verification regulation has made provisions on the evaluation method, measurement standard and environmental conditions, when the evaluated measuring instrument is in normal state, it is not necessary to judge the conformity of indication error according to the requirements of JJF1094-2016 evaluation of measuring instrument characteristics. However, further attention needs to be paid to whether the regulations in the meteorological department industry meet the relevant requirements. For example, the "verification regulation of meteorological platinum resistance temperature sensor in 2015" does not meet the requirements of instrument compliance assessment due to the accuracy grade of measuring instruments in the "verification regulation of meteorological platinum resistance temperature sensor in 2011". Therefore, in view of this situation, even if the verification regulation is used for calibration, it is still necessary to further determine and verify the compliance of indication error. In addition, the premise of instrument conformity determination is that the measuring instrument is in a normal state. However, during work, when the working state of the measuring instrument is unstable, the change is often very small, which is difficult for the staff to detect, which may also cause the results to fail to meet the requirements, At this time, the conformity judgment of the indication error of the calibration results can prompt whether the measuring instrument has faults that are difficult to detect. Lu T., et al. [2] and Zhang C., et al. [3] evaluated the uncertainty of humidity sensor. Yu Yanan, et al. [4], Sharma H., et al. [5], Martins L. L., et al. [6] and Hans I., et al. [7] analyzed the working principle of humidity sensor and calibration equipment, and Yang Z., et al. [8] and Wei, M., et al. [9] [10] evaluated the uncertainty of wind speed sensor, The above researchers either innovated the gum evaluation method or added the correlation analysis of different inputs in the U 95 uncertainty evaluation, which provides a good foundation for the follow-up research of this paper. This paper will first calibrate HMP155A humidity sensor, then evaluate the measurement uncertainty of the indication error in the calibration results, and finally judge the conformity of the indication error of the calibration results according to the requirements of JJF1094-2016 evaluation of measuring instrument characteristics.

Calibration Test
The calibration method is generally based on the requirements of JJG (meteor-  Table 2 for fluctuation, uniformity and correlation coefficient of temperature and humidity regulation box.

Evaluation of Measurement Uncertainty
Measurement uncertainty, referred to as uncertainty, is an important index to measure the reliability of measurement results. Only when the measured value is

Establishment of Measurement Model
According to the calibration experiment, the corresponding theoretical measurement model is established as follows: Considering that the measurement results are affected by some factors, combined with the actual measurement, the corresponding actual measurement model is established as follows:

Evaluation of Uncertainty Component
The relevant information of type A standard uncertainty of each calibration point obtained through calculation is shown in Table 3. The degree of freedom is the number of independent repeated measurements minus 1, so the degree of freedom corresponding to type A uncertainty is 9.

Type B Standard Uncertainty
According to the requirements of gum, the method of type B uncertainty is to  and the required probability p, the type B standard uncertainty can be obtained by the formula: u B = a/k. The corresponding relationship between the common distribution type probability p and the inclusion factor k is shown in Table 4.
When evaluating type B standard uncertainty, the degree of freedom [1] is:

1) Resolution introduction
In Formula (3), H 1 and H 5 correspond to the resolution of humidity standard and humidity sensor respectively, and the values are 0.01% RH. The influence range of the measured value is −0.005% RH -0.005% RH, so a = 0.005% RH, and meets the uniformity distribution characteristics, so k = 1.732. Since the value of the resolution does not change except for the failure of software and hardware, the reliability is estimated to be 100%.

2) Uncertainty of standard instrument value
The uncertainty of the humidity standard corresponding to H 2 in Formula (3) is obtained by querying the traceability certificate of the humidity standard. The corresponding measurement uncertainty at each measurement point is U = 0.5% RH, k = 2, which meets the normal distribution. The influence range of the measured value is −0.5% RH -0.5% RH, so a = 0.5% RH, and the reliability is estimated to be 80%.

3) Introduction of temperature and humidity control box
In Formula (3), the fluctuation and uniformity of the temperature regulation and commissioning box corresponding to H 3 and H 4 are shown in Table 2.
Taking the 55% RH calibration point as an example, its volatility is ±0.74% RH, and the influence range of the measured value is corresponding to −0.74% RH -0.74% RH, so a = 0.74% RH, and meets the arcsine distribution characteristics, with the corresponding k = 1.414; The uniformity is [−0.42, 0.42], and the influence range of the measured value is corresponding to −0.42% RH -0.42% RH, so a = 0.5% RH, and meets the uniformity distribution characteristics, so k = 1.732. The reliability estimates corresponding to volatility and uniformity are both 80%.

4) Introduction of collector channel error
According to the error introduced by the internal acquisition channel of the 3 MS device corresponding to H 6 in Formula (3), the humidity reading device of the 3 MS system uses a multimeter to read the voltage value of the temperature sensor, and then converts it into the humidity value. By querying the traceability certificate of the corresponding multimeter, the corresponding uncertainty in Table 4. Correspondence between p and k of common probability distributions. the range range is: U = 0.0005 V, k = 2. Because the voltage of (0 -1)V corresponds to the humidity of (0 -100)% RH, The corresponding conversion relationship is: 0.0005V/100V(% RH) −1 = 0.05% RH, the influence range of the measured value is −0.05% RH~0.05% RH, so a = 0.05% RH, which meets the normal distribution, and the reliability is estimated to be 90%.

5) Rounding error introduction
The rounding error corresponding to H 7 in Formula (3) is introduced. According to previous experience, the rounding error is 0.1% RH, the error range is-0.05% RH -0.05% RH, a = 0.05% RH, which meets the uniformity distribution, and the reliability is estimated to be 90%.  Table 5.

Uncertainty Evaluation of Combined Standard
According to the requirements of GUM, the synthetic standard uncertainty is expressed in u c . When the measurement model is linear equation, its calculation formula [1] is: In combination with the actual situation of formula (3) of the measurement model,

X S
H H − corresponds to Type A standard uncertainty u A , H 1 -H 7 corresponds to type B standard uncertainty u 1 -u 7 respectively, and because the corresponding uniformity of the temperature and humidity control box will be affected when it fluctuates, there is a certain correlation between the fluctuation and uniformity of the temperature and humidity control box, and the corresponding correlation coefficient is r 34 = 0.51 (Table 2), Then the synthetic standard In addition, due to the mutual inclusiveness between the uncertainty component introduced by repeatability measurement and the uncertainty component introduced by resolution, it is necessary to compare the corresponding magnitude and discard the components with a small magnitude.
Since the magnitude of type a standard uncertainty is greater than the standard uncertainty measurement introduced by resolution, the values of u 1 and u 5 are discarded in the calculation of u c . Formula (7) is transformed into the corresponding calculation formula:

Expanded Uncertainty and Measurement Results
The expanded uncertainty is generally expressed by U, and its value calculation formula is U = k × u c , k = 2 is generally selected without special instructions, and the corresponding inclusion probability is p = 95.45%. Since the expanded uncertainty (represented by U 95 ) when p = 95% is required for compliance determination in this study, the corresponding inclusion factor k 95 needs to be calculated separately, which needs to be obtained by querying the t-value distribution table according to the value of the effective degree of freedom eff υ (k 95 = 1.96, only when eff υ = ∞ ). The uncertainty evaluation results and relevant information obtained through calculation are shown in Table 6.

Determination of Conformity of Indication Error
According to the requirements of JJF1094-2016 characteristic evaluation of measuring instruments, when judging the conformity of indication error in calibration results, there are the following four situations: 1) When U 95 ≤ MPEV/3 (MPEV is the maximum allowable error), it meets the compliance judgment requirements of indication error |δ| < MPEV is qualified (δ Is the indication error), otherwise it is judged as unqualified.
2) When U 95 > MPEV/3, whether it meets the compliance determination requirements of indication error is divided into two cases. The first is when: |δ| >   (9), k 95 is obtained by querying the T value distribution table of the effective degree of freedom, u c is obtained by formula (8), and the final U 95 is obtained by the product of k 95 and u c . The final U 95 value is to prepare for the subsequent determination of the conformity of indication error. 3) When U 95 > MPEV/3, MPEV − U 95 < δ < MPEV + U 95 , to be determined. In this case, it is generally recommended to recheck the equipment, observe whether there are abnormalities, and then calibrate again. Table 7 shows the relevant information of value error determination.
According to the above criteria, we can conclude that no matter how large the value of u95 is, as long as |δ| ≤ MPEV − U 95 , then they all meet the compliance determination requirements and are determined as qualified. It can be seen from Table 7 that all calibration points meet the requirements |δ| ≤ MPEV − U 95 , so the judgment results are qualified.

Conclusion
In this paper, a HMP155A humidity sensor is selected for calibration experiment