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GB/T 18459-2001 English PDF (GBT18459-2001)

GB/T 18459-2001 English PDF (GBT18459-2001)

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GB/T 18459-2001: Methods for calculating the main static performance specifications of transducers

This Standard specifies the definitions and calculation methods of the main static performance specifications of general transducers. This Standard is applicable to the calculation of the main static performance specifications of transducers during the process of development, production and use. It is also applicable to the development and revision of product standards for various transducers.
GB/T 18459-2001
NATIONAL STANDARD OF THE
PEOPLE REPUBLIC OF CHINA
ICS 17.020
N 05
Methods for calculating the main static performance
specifications of transducers
ISSUED ON: OCTOBER 08, 2001
IMPLEMENTED ON: MAY 01, 2002
Issued by: General Administration of Quality Supervision, Inspection and Quarantine
Table of Contents
Foreword ... 3
1 Scope ... 4
2 Definitions ... 4
3 Calculation method for single static performance specification ... 10 4 Calculation methods for uncertainty and other comprehensive static
performance specifications ... 34
Annex A (Normative) General principle and calculation example of linearity calculation ... 41
Annex B (Normative) General principle and calculation example of conformity calculation ... 48
Annex C (Normative) Calculation examples for transducer sub-performance specifications and comprehensive performance specifications ... 56
Annex D (Normative) Calculation example for transmitter sub-item performance specifications and comprehensive performance specifications ... 69
Annex E (Normative) Inspection of transducer precision ... 73
Annex F (Informative) Pre-processing of raw data ... 75
Annex G (Informative) Basic principles for transducer uncertainty calculation ... 82
Annex H (Informative) Bibliography ... 85
Methods for calculating the main static performance
specifications of transducers
1 Scope
This Standard specifies the definitions and calculation methods of the main static performance specifications of general transducers.
This Standard is applicable to the calculation of the main static performance specifications of transducers during the process of development, production and use. It is also applicable to the development and revision of product standards for various transducers.
2 Definitions
For the purposes of this document, the following terms and definitions apply. 2.1 Basic terminologies
2.1.1 static characteristics
the relationship between output and input when measured under constant or slow-change conditions
NOTES:
1 The static characteristics of the transducer include a variety of performance indicators that can be determined by static calibration.
2 The static performance specifications of the transducer shall normally be marked with the applicable temperature range.
2.1.2 static calibration
the process of obtaining static characteristics under specified static test conditions
2.1.3 measuring range
the interval expressed by the maximum measured (measured upper limit) and the smallest measured (lower measured limit) under the premise of ensuring performance indicators
the transducer that working characteristics are represented by curve equation 2.2 Static calibration characteristics
2.2.1 up-travel actual average characteristics
the connection curve of the arithmetic mean point of a set of measured values at each calibration point of the up-travel
2.2.2 down-travel actual average characteristics
the connection curve of the arithmetic mean point of a set of measured values at each calibration point of the reverse stroke
2.2.3 up-travel and down-travel actual average characteristics
the connecting curve of the average point of the arithmetic mean of the positive and down-travel strokes of each calibration point, also called the actual characteristics (curve)
2.3 static performance specifications
2.3.1 resolution
the minimum input change that produces observable output changes over the entire input range
2.3.2 sensitivity
the ratio of output change to corresponding input change
2.3.3 hysteresis
the difference between the positive and down-travel stroke outputs of the transducer for the same input when the input is full-span
2.3.4 repeatability
the degree of dispersion between a set of measured outputs, in a short interval of time, under the same working conditions, when the input volume changes from the same direction to full scale, multiple times approaching and reaching the same calibration point
2.3.5 linearity
the maximum deviation of the actual average characteristic curve of the positive and down-travel strokes from the reference line, expressed as a percentage of full-span output
the linearity that the reference line is the front terminal-based line
NOTES:
1 The front terminal-based line passes through the front terminal point of the actual characteristics of the transducer. However, the maximum deviation of the transducer's actual characteristics shall be minimized by changing the slope.
2 The front terminal-based line is called the zero-base line in some foreign standards and literature. 2.3.5.6 Independent linearity
the linearity that the reference line is the best straight line
NOTES:
1 The best straight line is the median line of two parallel lines that are closest to each other and can accommodate the up-travel and down-travel actual average characteristics of the transducer. 2 The best straight line guarantees that the actual deviation of the transducer?€?s actual characteristics is minimal.
2.3.5.7 least-squares linearity
the linearity that the reference line is the least square line
NOTE: The least-squares line shall ensure that the sum of the squares of the actual characteristics of the transducer is minimal.
2.3.6 conformity
the maximum deviation of the curve of the up-travel and down-travel actual average characteristics to the reference curve, expressed as a percentage of full-span output
NOTES:
1 There are multiple compliances that vary with the reference curve.
2 Conformity shall be limited. Conformity without qualifiers means independent conformity. 2.3.6.1 absolute conformity
the conformity that the reference curve is the specified curve, also known as theoretical conformity
NOTES:
1 The reference curve for absolute conformity is pre-defined. It reflects the conformity precision and is absolutely different from the properties of several other degrees of conformity. 2.3.8 uncertainty
an evaluation result that characterizes the measured true value in a certain range; it is a parameter that reasonably gives the dispersion of the measured value, and it is also a parameter associated with the measurement result NOTE: Uncertainty can more reasonably represent the nature of measurement results from both qualitative and quantitative aspects.
2.3.9 total uncertainty
also known as basic uncertainty, an uncertainty obtained by static calibration under specified conditions and according to the specified calculation method NOTE: In this Standard, the total uncertainty is combined linearity, hysteresis and repeatability. It reflects their joint role. It is not simply adding.
2.3.10 zero drift
zero output only changes with time within the specified time, usually expressed as a percentage of full-span output
2.3.11 drift of output span
full-span output changes only over time within the specified time, usually expressed as a percentage of full-span output
NOTE: If the prescribed assessment time is long, such as months to years, this indicator is often referred to as long term stability.
2.3.12 thermal zero shift
zero output change caused by changes in ambient temperature, usually
expressed as a percentage of the full-span output of the unit temperature 2.3.13 thermal shift of output span
full-span output change that is due to changes in ambient temperature, usually expressed as a percentage of the full-span output of the unit temperature 3 Calculation method for single static performance
specification
3.1 Establishment of static calibration characteristics
3.1.1 General requirements for static calibration
value of the difference between the maximum and minimum values of a set of n measured values at the ith calibration point;
dR - range coefficient; it depends on the number of calibration cycles n, i.e. the number of measurements at a calibration point or the sample size n. The relationship between the range coefficient dR and the number of calibration cycles is shown in Table 2.
Table 2
NOTES:
1 The range method is slightly simpler than the Bessel formula method. However, the calculated sample standard deviation S is generally slightly larger.
2 When calculating S, if not specified, it refers to Bessel formula method. In case of dispute, the Bessel formula shall prevail.
3.7.4 Selection of standard deviation of transducer sample
3.7.4.1 If the number of calibration points is m (usually m=5~11), 2m sample standard deviation S can be calculated. This Standard stipulates that the largest S (i.e. the maximum standard deviation Smax) is selected to participate in the calculation of Equation 10 so as to obtain the repeatability of the transducer as a single performance specification.
3.7.4.2 This Standard allows the user to perform an equal precision test on the transducer being tested as an option according to the method of Annex E. The variance at each measurement point of the equal precision transducer has the same mathematical expectation. Therefore, the average variance can be used instead of the variance at each measurement point. Therefore, if it is determined that the transducer is an equal-precision sensor, the maximum standard
deviation Smax shall not be taken. It shall take the average standard deviation Sav to calculate the repeatability. Sav is calculated as follow:
If the precision of the transducer being tested is not performed, or if the test fails, the requirements of 3. 7. 4. 1 shall still be applied. That is, calculate repeatability according to the requirements of unequal precision transducer. NOTES:
- maximum and minimum input values of the transducer.
NOTES:
1 The calculation method for terminal-based line is simple and easy to implement with the bridge detection circuit.
2 Compared with other linearities, the calculation results of terminal-based linearity is generally larger. 3.8.4 Shifted terminal-based linearity
See equation (16) for calculation.
As the shifted terminal-based equation of reference characteristics, see 3.8.3 for the calculation method of its terminal-based linear equation. See A.2.2.1 of Annex A for the translation method.
NOTE: The shifted terminal-based linearity can be used to replace the independent linearity in some occasions where the requirements are not too high.
3.8.5 Zero-based linearity
The principle of calculation method is shown in Figure 2. The calculation formula is shown in equation (16).
By definition, a zero-based linear equation can be written as reference characteristics:
where,
b - zero-base linear slope, i.e. the theoretical zero point of the transducer (x = 0, y = 0) and the slope of the line connecting the center of gravity of the smallest maximum positive and negative deviation points.
For the calculation of the zero-based line, see Annex A, A1.
NOTE: The working characteristics of the transducer can be represented by a zero-based line. Its equation is simple and easy to use.
3 The front terminal-based linearity is generally better than zero-based linearity. And it can make the deviation near the zero point of the transducer smaller.
3.8.7 Independent linearity
The principle of calculation method is shown in Figure 4. The calculation formula is shown in equation (16).
The calculation method of the best straight line is shown in Annex A, A2. NOTES:
1 Independent linearity value is the smallest among various linearities. Independent linearity is used whenever possible to accurately measure linearity.
2 If the transmitter has an adjustment means, it can adjust the translation and adjust the slope. Adjust the best straight line to the specified straight line for the highest absolute linearity. 3 Linearity shall be added with qualifier. Linearity without qualifiers means independent linearity. 3.8.8 Least-squares linearity
See equation (16) for the calculation formula.
As the least-squares line of the reference characteristic, the sum of the squares of the deviation of the actual characteristics of the transducer shall be minimized. The least-squares linear equation is:
where,
Yls - theoretical output of the transducer;
a, b - intercept and slope of the least-squares line, respectively;
x - actual input of the transducer.
The intercept and slope of the least-squares line can be obtained by straight line fitting of the actual characteristics of the transducer. The calculation formula is as follow:
where,
- the maximum deviation of the actual characteristics curve of the
transducer from the reference curve;
- the total average characteristics value of the transducer at the ith
calibration point;
Yi - the reference characteristics value of the transducer at the ith calibration point;
YFS - the full-span output of the transducer.
NOTES:
1 Example for calculation of :
(1) According to up-travel and down-travel actual average characteristics , use the best curve as the reference curve to calculate the independent conformity.
(2) According to up-travel and down-travel actual average characteristics , use the working characteristics curve as the reference curve to calculate the absolute conformity. 2 The results calculated by the second method described above shall contain the components of the hysteresis and repeatability to varying degrees. Strictly speaking, it is not conformity. 3 If not stated, the conformity refers to the result of calculated according to the first method above, that is, independent conformity.
4 In some applications, if necessary, it can also use a set of calibration data to calculate the conformity without .
3.9.2 Absolute conformity
The calculation formula is shown in equation (23).
NOTES:
1 In several conformities, the absolute conformity requirement is the strictest. 2 If non-linear transducer is required to be interchangeable, absolute conformity shall be used. 3.9.3 Terminal-based conformity
See Figure 5 for the principle of calculation method. See equation (23) for calculation formula.
If the thermal full-span output shift of the transducer is not linear with the temperature interval, then ( T2 - T1 ) shall be divided into several small intervals. And use equation (28) to calculate the ?? of each interval. Take the largest absolute value of ??.
4 Calculation methods for uncertainty and other
comprehensive static performance specifications
In static operation, linearity (conformity), hysteresis, and repeatability are often referred to as transducer's sub-performance or individual performance
specification. And the different combinations of these specifications constitute various comprehensive performance specifications. There is no mathematically defined link between comprehensive performance specifications (such as total uncertainty) and performance specifications for each sub-performance.
Take a linear transducer as an example (the algorithm of a non-linear
transducer is the same as that of a linear transducer). And it is based on the principle of measuring the performance specification of the transducer by the limit deviation. This Standard specifies the calculation methods for the following comprehensive performance specifications.
4.1 Linearity plus hysteresis
4.1.1 General form of calculation formula
Linearity plus hysteresis is the limit of transducer system error. It is calculated as follow:
where,
- the maximum deviation of up-travel actual average characteristics
and down-travel actual average characteristics to reference
line.
NOTES:
1 If not stated, the linearity plus hysteresis shall refer to the calculated results based on the up-travel actual average characteristics and down-travel actual average characteristics of the transducer to its reference line. Otherwise it shall indicate the type of reference line. 2 If the reference line is taken as transducer?€?s working characteristics line, the result of shall contain repetitive components to varying degrees. It is not linearity plus hysteresis strictly speaking. 3 For non-linear transducer, refer to this section for calculation of conformity plus hysteresis based on the same calculation principle.
4.1.2 Calculation of reference line
Use a best straight line to perform straight line fitting of transducer?€?s up-travel actual average characteristics and down-travel actual average characteristics. For specific practices, please refer to the relevant parts of Annex A, Annex B and Annex C of this Standard.
4.2 Linearity plus hysteresis plus repeatability
In this Standard, it is also called the total uncertainty of the transducer (corresponding to the original total precision, or the total error). It is to make that under reference working conditions, the deviation of the actual characteristics from its working characteristics is not exceeded by a specified confidence level. When expressed as a percentage of the transducer's full-span output YFS, it is called the relative total uncertainty of the transducer, which is often referred to as total uncertainty.
4.2.1 General form of calculation formula
where,
Bi - limit of total system error at the ith calibration point, which can be obtained separately by conventional non-statistical methods;
t0.95Si - limit of total accidental error at the ith calibration point; t0.95 is the inclusion factor of 95% confidence in the t distribution; Si is the standard deviation of the sample at the ith calibration point.
Equation (30) can also be expressed as:
where,
1 here is corresponding to Ur in Annex G;
2 If the limit-point envelope method of 4.2.3.2 is used to calculate , it shall be greatly simplified both in terms of concept and calculation process.
3 For non-linear transducer, refer to this section and calculate the conformity plus hysteresis plus repeatability according to the same calculation principle.
4.2.3 Calculation method for working characteristics
When calculating the linearity plus the hysteresis plus repeatability of the transducer, the reference line shall be taken as the straight line of the working characteristics of the transducer.
4.2.3.1 Selection and calculation principles
a) Consider the working characteristics of transducer.
b) It shall be beneficial to the use of transducer.
c) It shall help to reduce the value of the total uncertainty.
4.2.3.2 L(C)HR limit-point envelope method
In general, the total uncertainty of linear transducer depends on the combined effects of linearity, hysteresis and repeatability. As shown in Fig. 9, at the xi-th calibration point, the up-travel average point and the down-travel average point are respectively determined. Then, according to 3.7.3, the sub-
sample standard deviation Su,i at the ith calibration point of the up-travel and the sub-sample standard deviation Sd, i of the down-travel at the ith calibration point are obtained. Subtract cSu,i from the average of the up-travel. Add cSd, i to the average of the down-travel. Thus, two limit-points can be obtained at the xi-th calibration point. The calculation formulae are as follow:
uncertainty of the transducer.
4.3 Other comprehensive static performance specifications and
characteristics
The following comprehensive static performance specifications are special cases of transducer?€?s comprehensive static performance specifications. The calculation method is simpler than th...

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