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GB/T 18459-2001Methods for calculating the main staticperformance specifications of transducers (English PDF)

传感器主要静态性能指标计算方法

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Issued by

General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China

Level / Type

National · Recommended

Issue date

October 8, 2001

Implementation date

May 1, 2002

Scope

GB/T 18459-2001 is the English-translated version of 传感器主要静态性能指标计算方法.

GB/T 18459-2001 is the Chinese national standard on methods for calculating the main staticperformance specifications of transducers, in the field of metrology and measurement. The /T suffix marks it as a recommended standard: it is not compulsory by itself, but it becomes binding as soon as a contract, a tender or a customer specification calls it up - which in practice is how most foreign buyers meet it. It was issued on 8 October 2001 by the General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China, and has been in force since 1 May 2002. Classification: ICS 17.020, CCS N05. This page is published from the official record of the standard held by the Chinese standards administration: the identification, the dates, the classification and the issuing body are taken from there. The clause text, the tables and the numeric limits are in the document itself, which is delivered complete in English translation.

Document preview — GB/T 18459-2001

National Standard of the People's Republic of China

ICS: 17.020
Classification: N05

Issued by: General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China

1 Scope
2 Definitions
2.1 Basic terminologies
2.2 Static calibration characteristics
2.3 Static performance specifications
3 Calculation method for single static performance
3.1 Establishment of static calibration characteristics
3.7.4 Selection of standard deviation of transducer sample
4 Calculation methods for uncertainty and other
4.1 Linearity plus hysteresis
4.2.3.1 Selection and calculation principles
Annex A
Annex B

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.

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.

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; t

0.95 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;

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 the calculation method of the transducer's comprehensive static performance specifications, so only the calculation principle is proposed.

4.3.1 Single-travel fixed-point transducer For example, the fixed-point error of switches such as single-travel pressure switch and temperature switch is only repeatability, and the calculation method can refer to 4.2. At this time, the working characteristic of the transducer is a fixed point. The single stroke is taken as an up-travel or a down-travel. The working characteristics of the transducer shall be taken as the actual average point of the selected up-travel or the actual average point of the down-travel.

4.3.2 Dual-travel fixed-point transducer For example, the fixed-point error of a dual-travel pressure switch, temperature switch, etc. is only hysteresis plus repeatability. Refer to

4.2 for its calculation method. At this time, its working characteristics equation is: the measured number (Y) = the measured amount (x). The working characteristics is a fixed point, which shall be taken as the actual average point of the selected up-travel and down-travel.

4.3.3 Linearity plus hysteresis plus repeatability of transmitter The total uncertainty shall be calculated based on the straight line of its given working characteristics. Refer to

4.2 and Annex D for its calculation method.

4.3.4 Transducer or transmitter with measured digital display Its working characteristics equation is: the measured number (Y) = the measured amount (x). Refer to

4.2 and Annex C for the calculation method of its total uncertainty.

4.3.5 Utilization characteristics Utilization characteristics equation: the measured amount (x) = function of transducer output f (y). For linear transducer, the characteristics equation can be derived directly from the working characteristics equation. For non-linear transducer, generally only numerical solutions (such as Newton iteration) can be used to calculate the working characteristics.

Annex A

(Normative) General principle and calculation example of linearity calculation A

1 Calculation example for zero-based linearity Try to calculate the zero-based line and zero-based linearity of a set of static calibration test data (average of multiple measurements) listed in the table below. Table A1 A

1.1 General calculation principle The connection line between the desired theoretical zero point and the minimum center of gravity of the smallest positive and negative deviation points is not calculated at one time. It can only approach gradually. The so-called minimum largest positive and negative deviation points mean that each approximation shall produce a pair of largest positive and negative deviation points. What it needs is only a pair of the minimum positive and negative deviation points of a set of the largest positive and negative deviation points obtained by each approximation (the characteristic is that the absolute values of the largest positive and negative deviation of this pair of largest positive and negative deviation points are equal and minimum). A.1.2 Calculation of the first approximation line The theoretical zero point and the rear terminal point line are used as the first approximation line of the zero-based line. The equation is: The deviation of each calibration point calculated by it is: Table A

Annex B

(Normative) General principle and calculation example of conformity calculation B

1 General principle for conformity calculation The reference curve for conformity is calculated by using the Chebyshev interlaced point group principle. And use the improved Remez algorithm. The specific principle of calculating the reference curve according to this principle can be summarized into the following four parts. B

1.1 According to the shape of the curve formed by a set of test data points, the function form or the degree of the polynomial of the fitting curve is selected empirically or by other methods (for example, looking at the variation of the adjacent difference quotients). B

1.2 If the reference curve equation has n unknown coefficients, then n+1 interlaced points shall be selected. When the mandatory reference curve passes a specified point, the staggered point is reduced by one. But the total number of interlaced points cannot be less than two. B

1.3 Orderly select the required number of interlaced points on the x-axis. In the first approximation, n points can be selected substantially equidistantly, preferably including the first and last points, to find a curve passing through the n points. In the second and subsequent approximation, the interlaced point group shall be selected according to the deviation and size of the previous set of approximation curves. The deviation signal at each staggered point shall be positive and negative alternate. The more the absolute value is the deviation point, the more the priority shall be selected or swapped into the interlaced point group. Zero deviation point can be regarded as the smallest positive deviation point or negative deviation point. B

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Editions of GB/T 18459

Edition	Title	Revision	Status
GB/T 18459-2001	Methods for calculating the main staticperformance specifications of transducers	current edition	Current

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