A method and system for evaluating measurement uncertainty of power frequency electric field calibration device

Abstract

The present invention discloses a method and system for evaluating the measurement uncertainty of an industrial frequency electric field calibration device, comprising: determining a measurement function for generating a nominal value of an industrial frequency electric field by the industrial frequency electric field calibration device; setting a probability density function for each input quantity of the measurement function, and determining the probability distribution of each input quantity according to the probability density function; generating a discrete distribution sample of a final output quantity based on Monte Carlo sampling according to the probability distribution of each input quantity, and determining the number of Monte Carlo samplings M based on the discrete distribution sample of the output quantity; performing Monte Carlo sampling to obtain M output quantities of the measurement function; performing non-decreasing sorting on the M output quantities of the measurement function to obtain the sorted M output quantities of the measurement function, and obtaining a discrete expression of the distribution function of the sorted M output quantities of the measurement function based on the sorted M output quantities of the measurement function; and calculating the inclusion interval of the M output quantities under a preset probability based on the discrete expression of the distribution function.

Description

Technical Field

[0001] The present invention relates to the technical field of electrical parameter testing, and more specifically, to a method and system for evaluating the measurement uncertainty of an industrial frequency electric field calibration device. Background Art

[0002] As an important environmental impact factor of power transmission and transformation projects, power frequency electric field parameters are indispensable in the environmental impact assessment of power transmission and transformation projects before and after their construction and operation. Its measurement results are directly applied to engineering design fields such as conductor selection, endpoint site selection, and path planning. It is also an important legal basis for alleviating public anxiety and judging environmental disputes. The accuracy of power frequency electric field measurement results will directly affect the difficulty of project cost control, the level of environmental ecological friendliness, and the quality of protection of the vital rights and interests of the people. At the same time, in the power industry, power frequency electric field measurement, as a very important technical means of studying and analyzing electric fields, is also widely used in electrical cable fault location, electrical insulation performance optimization, meteorological disaster warning, and electric field biological effects.

[0003] The accurate calibration of power frequency electric field parameters is a prerequisite for the practical application of the above-mentioned technologies. The quality of the measurement results of power frequency electric field parameters is directly determined to a large extent by the level of the calibration system with a higher metrology level in the traceability chain. The reasonably assessed uncertainty of the power frequency electric field calibration device is an important reference for judging the quality of the measurement results of power frequency electric field parameters, and has important scientific research significance and engineering value for the scientific, effective and correct use of measurement results.

[0004] Since the Uncertainty of Measurement-Part 3: Guide to the expression of uncertainty in measurement (1993) was published by the Working Group on Expression of Uncertainty in Measurement (WG3) of ISO Technical Advisory Working Group 4 (TAG4) in the name of 7 international organizations in 1993, after years of research and development, various countries and some international organizations in professional disciplines have successively published corresponding guidance documents on the evaluation of uncertainty in measurement based on the general rules of the guidelines. In the field of measurement uncertainty evaluation, a relatively unified and standardized evaluation method consensus has been formed internationally.

[0005] In my country, the National Institute of Metrology, China Legal Metrology Management Metrology Technical Committee and other organizations have also formulated and issued a series of measurement uncertainty guidelines and technical specification documents, including the Measurement Uncertainty Specification, JJF1059-2012 Measurement Uncertainty Evaluation and Expression, etc., based on the Uncertainty of Measurement Part 3: Guide to the Expression of Uncertainty in Measurement. These guidelines and technical specification documents constitute the framework for the evaluation of measurement uncertainty in my country, and also make the expression of measurement uncertainty in the field of metrology and testing in my country in line with international standards.

[0006] In the prior art, the uncertainty assessment of measurement results at home and abroad mainly includes the GUM method and the Monte Carlo method (MCM). The GUM method is based on the central limit theorem. It propagates the best estimate of the input quantity and its standard uncertainty by applying the uncertainty propagation law, and finally obtains the best estimate of the output quantity and its measurement uncertainty. The MCM method uses random sampling of probability distribution to finally determine the probability density function (PDF) of the output quantity by means of distribution propagation. At present, in public reports at home and abroad, the GUM method is usually used to assess the measurement uncertainty of the power frequency electric field calibration device, and no application methods and examples of the Monte Carlo method are found.

[0007] Therefore, a technique is needed to evaluate the measurement uncertainty of a power frequency electric field calibration device based on the Monte Carlo method. Summary of the invention

[0008] The technical solution of the present invention provides a method and system for evaluating the measurement uncertainty of an industrial frequency electric field calibration device, so as to solve the problem of how to evaluate the measurement uncertainty of the industrial frequency electric field calibration device based on the Monte Carlo method.

[0009] In order to solve the above problems, the present invention provides a method for evaluating the measurement uncertainty of a power frequency electric field calibration device, the method comprising:

[0010] Based on the pre-established measurement model, determining the measurement function of the power frequency electric field calibration device to generate the nominal value of the power frequency electric field;

[0011] Setting a probability density function for each input quantity of the measurement function, and determining a probability distribution of each input quantity according to the probability density function;

[0012] According to the probability distribution of each input quantity, a discrete distribution sample of the final output quantity is generated based on Monte Carlo sampling, and the number of Monte Carlo sampling M is determined based on the discrete distribution sample of the output quantity;

[0013] Based on the Monte Carlo sampling number M, Monte Carlo sampling is performed to obtain M output quantities of the measurement function;

[0014] Sorting the M output quantities of the measurement function in a non-decreasing manner to obtain the sorted M output quantities of the measurement function, and obtaining a discrete expression of a distribution function of the sorted M output quantities of the measurement function based on the sorted M output quantities of the measurement function;

[0015] Based on the discrete expression of the distribution function, the inclusion intervals of the M output quantities under the preset probability are calculated.

[0016] Preferably, the measurement function is:

[0017]

[0018] D=D T [1+2α(T-T0)],

[0019] Where, E is the nominal value of the power frequency electric field generated by the power frequency electric field calibration device; N is the voltage transformer ratio; V is the voltage representation value; E0 is the background electric field; D is the parallel plate spacing at laboratory temperature; D T is the distance between parallel plates at the traceability temperature; rep is the measurement repeatability; T is the laboratory temperature; T0 is the temperature at the traceability time; α is the linear expansion coefficient of the parallel plate material.

[0020] Preferably, determining the Monte Carlo sampling number M comprises:

[0021] Make sure that the value of M1 is greater than or equal to 1 / (1-p) 10 4 Times:

[0022] M1≥1 / (1-p)×10 4 ,

[0023] Where M1 is the minimum number of sampling times to ensure that the uncertainty provides the expected inclusion interval, and p is the expected inclusion probability;

[0024] Make sure that the value of M2 is greater than or equal to the degrees of freedom required to maintain enough significant figures for the uncertainty:

[0025]

[0026] Where M2 is the minimum number of sampling times to ensure that the uncertainty retains sufficient significant figures, v is the required degree of freedom, u(y) is the standard uncertainty, and σ[u(y)] is the standard deviation of the standard uncertainty u(y);

[0027] Determine M to be the larger value of M1 and M2:

[0028] M≥MAX(M1,M2).

[0029] Preferably, the performing of Monte Carlo sampling based on the Monte Carlo sampling number M includes:

[0030] The measurement model is denoted as Y=f(X1,...X N ), from N input quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities by calculation. r =f(x r ), r = 1, ..., M, we can further obtain the estimated value of the simplified measurement model Y and standard uncertainty u(y), input matrix x r , the output matrix y r Respectively represent:

[0031]

[0032]

[0033] Among them, (X1,…X N ) are the N input quantities in the measurement model, ξ i To describe the input quantity X i A variable with possible values, (x 1,r ,…x N,r ) is the sample of input quantity, (y1,…,y M ).

[0034] Preferably, the preset probability is 50%, 90%, 95%, 99% or 99.73%.

[0035] According to another aspect of the present invention, the present invention provides a system for evaluating the measurement uncertainty of a power frequency electric field calibration device, the system comprising:

[0036] An initialization unit, for determining a measurement function for generating a nominal value of a power frequency electric field by a power frequency electric field calibration device based on a pre-established measurement model;

[0037] A first determining unit, configured to set a probability density function for each input quantity of the measurement function, and determine a probability distribution of each input quantity according to the probability density function;

[0038] A second determining unit is used to generate a discrete distribution sample of a final output based on Monte Carlo sampling according to the probability distribution of each input, and determine the number of Monte Carlo samplings M based on the discrete distribution sample of the output;

[0039] A first acquisition unit, configured to perform Monte Carlo sampling based on the Monte Carlo sampling number M, to acquire M output quantities of the measurement function;

[0040] A second acquisition unit is used to sort the M output quantities of the measurement function in a non-decreasing manner, obtain the sorted M output quantities of the measurement function, and obtain a discrete expression of a distribution function of the sorted M output quantities of the measurement function based on the sorted M output quantities of the measurement function;

[0041] A calculation unit is used to calculate the inclusion interval of M output quantities under a preset probability based on the discrete expression of the distribution function.

[0042] Preferably, the measurement function is:

[0043]

[0044] D=D T [1+2α(T-T0)],

[0045] Where, E is the nominal value of the power frequency electric field generated by the power frequency electric field calibration device; N is the voltage transformer ratio; V is the voltage representation value; E0 is the background electric field; D is the parallel plate spacing at laboratory temperature; D T is the distance between parallel plates at the traceability temperature; rep is the measurement repeatability; T is the laboratory temperature; T0 is the temperature at the traceability time; α is the linear expansion coefficient of the parallel plate material.

[0046] Preferably, determining the Monte Carlo sampling number M comprises:

[0047] Make sure that the value of M1 is greater than or equal to 1 / (1-p) 10 4 Times:

[0048] M1≥1 / (1-p)×10 4 ,

[0049] Where M1 is the minimum number of sampling times to ensure that the uncertainty provides the expected inclusion interval, and p is the expected inclusion probability;

[0050] Make sure that the value of M2 is greater than or equal to the degrees of freedom required to maintain enough significant figures for the uncertainty:

[0051]

[0052] Where M2 is the minimum number of sampling times to ensure that the uncertainty retains sufficient significant figures, v is the required degree of freedom, u(y) is the standard uncertainty, and σ[u(y)] is the standard deviation of the standard uncertainty u(y);

[0053] Determine M to be the larger value of M1 and M2:

[0054] M≥MAX(M1,M2).

[0055] Preferably, the

[0056] Based on the Monte Carlo sampling number M, Monte Carlo sampling is performed, including:

[0057] The measurement model is denoted as Y=f(X1,...X N ), from N input quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities by calculation. r =f(x r ), r = 1, ..., M, we can further obtain the estimated value of the simplified measurement model Y and standard uncertainty u(y), input matrix x r , the output matrix y r Respectively represent:

[0058]

[0059]

[0060] Among them, (X1,…X N ) are the N input quantities in the measurement model, ξ i To describe the input quantity X i A variable with possible values, (x 1,r ,…x N,r ) is the sample of input quantity, (y1,…,y M ).

[0061] Preferably, the preset probability is 50%, 90%, 95%, 99% or 99.73%.

[0062] The technical solution of the present invention provides a method and system for evaluating the measurement uncertainty of a power frequency electric field calibration device. A measurement model is established according to the implementation process of the power frequency electric field calibration, a probability density function is set for the input quantity based on the available information, and then the probability density of the input quantity is discretely sampled, and the distribution of the input quantity is propagated through the measurement model of uncertainty evaluation to obtain a discrete expression of the output quantity distribution function; based on the discrete expression of the distribution function, the inclusion interval of the M output quantities under the preset probability is calculated. The technical solution of the present invention proposes a method for evaluating the measurement uncertainty of a power frequency electric field calibration device based on the Monte Carlo method, which has more advantages than the existing methods in terms of accuracy, reliability and calculation efficiency, and can produce certain theoretical significance and social and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] A more complete understanding of exemplary embodiments of the present invention may be obtained by referring to the following drawings:

[0064] Figure 1 It is a flow chart of a method 100 for evaluating measurement uncertainty of a power frequency electric field calibration device according to a preferred embodiment of the present invention;

[0065] Figure 2 It is a schematic structural diagram of a power frequency electric field calibration device according to a preferred embodiment of the present invention;

[0066] Figure 3 It is an assessment flow chart according to a preferred embodiment of the present invention;

[0067] Figure 4 A schematic diagram of probability distribution propagation of input quantity according to a preferred embodiment of the present invention;

[0068] Figure 5 A probability distribution histogram of each input quantity according to a preferred embodiment of the present invention;

[0069] Figure 6 A probability distribution histogram of the output according to a preferred embodiment of the present invention;

[0070] Figure 7 Schematic diagram of the inclusion interval of the output quantity at 95% inclusion probability according to a preferred embodiment of the present invention;

[0071] Figure 8 Schematic diagram of the structure of a system 800 for evaluating measurement uncertainty of a power frequency electric field calibration device according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0072] Now, exemplary embodiments of the present invention are described with reference to the accompanying drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to disclose the present invention in detail and completely and to fully convey the scope of the present invention to those skilled in the art. The terms used in the exemplary embodiments shown in the accompanying drawings are not intended to limit the present invention. In the accompanying drawings, the same units / elements are marked with the same reference numerals.

[0073] Unless otherwise specified, the terms (including technical terms) used herein have the commonly understood meanings to those skilled in the art. In addition, it is understood that the terms defined in commonly used dictionaries should be understood to have the same meanings as those in the context of the relevant fields, and should not be understood as idealized or overly formal meanings.

[0074] Figure 1 The present invention is a flowchart of a method 100 for evaluating the measurement uncertainty of a power frequency electric field calibration device according to a preferred embodiment of the present invention. The present invention relates to the metrological level assessment of power frequency electric field parameters, and specifically to a method for evaluating the measurement uncertainty of a power frequency electric field calibration device based on the Monte Carlo method. The present invention proposes a method for evaluating the measurement uncertainty of a power frequency electric field calibration device based on the Monte Carlo method. The method establishes a measurement model according to the implementation process of power frequency electric field calibration, sets a probability density function for the input quantity based on the available information, and then discretely samples the probability density of the input quantity, and propagates the distribution of the input quantity through the measurement model for uncertainty assessment, and obtains a discrete expression of the output quantity distribution function and its characteristic value, which is more advantageous than the existing methods in terms of accuracy, reliability and computational efficiency.

[0075] like Figure 1 As shown, the method 100 for evaluating the measurement uncertainty of the power frequency electric field calibration device provided by the present invention comprises:

[0076] Step 101: Based on a pre-established measurement model, a measurement function for generating a nominal value of a power frequency electric field by a power frequency electric field calibration device is determined.

[0077] Preferably, the measurement function is:

[0078]

[0079] D=D T [1+2α(T-T0)],

[0080] Where, E is the nominal value of the power frequency electric field generated by the power frequency electric field calibration device; N is the voltage transformer ratio; V is the voltage representation value; E0 is the background electric field; D is the parallel plate spacing at laboratory temperature; D Tis the distance between parallel plates at the traceability temperature; rep is the measurement repeatability; T is the laboratory temperature; T0 is the temperature at the traceability time; α is the linear expansion coefficient of the parallel plate material.

[0081] The present invention first establishes a measurement model. During the implementation of the power frequency electric field calibration, the power frequency electric field probe is placed at the geometric center of the parallel plate structure, and a certain voltage is applied to the upper plate, which can generate a corresponding power frequency electric field strength level between the parallel plates. At the same time, the voltage signal is transmitted to the voltmeter via the voltage transformer, and the voltage value is recorded, so that the nominal value of the power frequency electric field generated by the calibration device can be calculated. Among them, the system of power frequency electric field calibration is as follows Figure 2 shown.

[0082] It can be seen that the power frequency electric field strength level depends on the input voltage, the voltage transformer ratio, and the parallel plate spacing.

[0083]

[0084] Among them, E is the nominal value of the power frequency electric field generated by the calibration system, in V / m; V is the voltage representation value, in V; N is the voltage transformer ratio, dimensionless; D is the parallel plate spacing, in m.

[0085] Due to the existence of the background electric field in the experimental environment, equation (1) becomes

[0086]

[0087] Where E0 is the background electric field, in V / m.

[0088] Introducing the measurement repeatability of the calibration process, equation (2) becomes

[0089]

[0090] Where rep is the measurement repeatability, and its estimated value is rep=1.0.

[0091] Some input quantities in the measurement function are themselves functions of other quantities and should be expressed as consisting of basic quantities. Furthermore, the parallel plate spacing D is a function related to the laboratory ambient temperature:

[0092] D=D T [1+2α(T-T0)] (4)

[0093] Where T is the laboratory temperature, in °C; T0 is the temperature at the time of tracing, in °C; α is the linear expansion coefficient of the parallel plate material, in °C -1 .

[0094] Finally, the measurement function of the power frequency electric field calibration device becomes:

[0095]

[0096] Step 102: Set a probability density function for each input quantity of the measurement function, and determine the probability distribution of each input quantity based on the probability density function.

[0097] The present invention sets a probability density function of the input quantity. For each input quantity of the above measurement function, an appropriate probability density function is set, and the probability density function is derived based on the available information. The input quantities include voltage transformer ratio, voltage representation value, parallel plate spacing, linear expansion coefficient of parallel plate material, laboratory temperature, temperature during tracing, background electric field, and measurement repeatability.

[0098] Step 103: Generate a discrete distribution sample of the final output based on Monte Carlo sampling according to the probability distribution of each input, and determine the number of Monte Carlo sampling M based on the discrete distribution sample of the output.

[0099] Preferably, determining the number of Monte Carlo sampling times M includes:

[0100] Make sure that the value of M1 is greater than or equal to 1 / (1-p) 10 4 Times:

[0101] M1≥1 / (1-p)×10 4 ,

[0102] Where M1 is the minimum number of sampling times to ensure that the uncertainty provides the expected inclusion interval, and p is the expected inclusion probability;

[0103] Make sure that the value of M2 is greater than or equal to the degrees of freedom required to maintain enough significant figures for the uncertainty:

[0104]

[0105] Where M2 is the minimum number of sampling times to ensure that the uncertainty retains sufficient significant figures, v is the required degree of freedom, u(y) is the standard uncertainty, and σ[u(y)] is the standard deviation of the standard uncertainty u(y);

[0106] Determine M to be the larger value of M1 and M2:

[0107] M≥MAX(M1,M2).

[0108] The present invention determines the number of Monte Carlo samplings, and according to the probability distribution set for the input quantity in the second step, the Monte Carlo sampling can be used to generate a discrete distribution sample of the final output quantity, and the degree of closeness of the distribution sample to the actual sample distribution depends on the number of Monte Carlo samplings M, that is, the sample size M. The more sampling times, the larger the sample size, the closer the statistical law is to the actual situation of the output quantity, but the longer the required calculation time is. The fewer sampling times, the smaller the sample size, and the farther the statistical law is from the actual situation of the output quantity. Therefore, the value of M is very critical for the measurement uncertainty assessment of the power frequency electric field.

[0109] The specific steps to determine are as follows:

[0110] 1) The value of M1 should be greater than or equal to 1 / (1-p) 10 4 times, that is:

[0111] M1≥1 / (1-p)×10 4 (6)

[0112] 2) The value of M2 should be greater than or equal to the degrees of freedom required to retain sufficient significant figures for uncertainty, that is:

[0113]

[0114] 3) M takes at least the larger value of M1 and M2, that is:

[0115] M≥MAX(M1,M2) (8)

[0116] Step 104: Based on the Monte Carlo sampling number M, Monte Carlo sampling is performed to obtain M output quantities of the measurement function.

[0117] Preferably, based on the Monte Carlo sampling number M, Monte Carlo sampling is performed, including:

[0118] The measurement model is denoted as Y=f(X1,...X N ), from N input quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities by calculation. r =f(x r ), r = 1, ..., M, we can further obtain the estimated value of the simplified measurement model Y and standard uncertainty u(y), input matrix x r , the output matrix y r Respectively represent:

[0119]

[0120]

[0121] Among them, (X1,…X N ) are the N input quantities in the measurement model, ξ i To describe the input quantity X i A variable with possible values, (x 1,r ,…x N,r ) is the sample of input quantity, (y1,…,y M ).

[0122] Step 4: Monte Carlo sampling

[0123] The simplified measurement model is recorded as Y = f(X1,…X N ), from N output quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities y by calculation r =f(x r ), r = 1, ..., M, we can further get the estimated value of the measurement model Y and standard uncertainty u(y). Input matrix x r , the output matrix y r They are expressed as formula (9) and formula (10) respectively:

[0124]

[0125]

[0126] Step 105: sort the M output quantities of the measurement function in a non-decreasing manner to obtain the sorted M output quantities of the measurement function, and based on the sorted M output quantities of the measurement function, obtain a discrete expression of the distribution function of the sorted M output quantities of the measurement function.

[0127] The present invention performs non-decreasing sorting on the output quantity, and sorts the y in the fourth step r =f(x r ), r = 1, ..., M are sorted in non-decreasing order to obtain the sorted output y (r) , r = 1, ..., M, we can further get the output distribution function G Y (η) Discrete expression G.

[0128] Step 106: Based on the discrete expression of the distribution function, calculate the inclusion interval of the M output quantities under the preset probability.

[0129] Preferably, the preset probability is 50%, 90%, 95%, 99% or 99.73%.

[0130] The present invention determines the inclusion interval and uses the discrete expression G to calculate the inclusion interval of the output quantity Y under the agreed inclusion probability. like Figure 3 shown.

[0131] The present invention effectively solves the problem that the measurement results of the power frequency electric field calibration device are due to many influencing factors, resulting in poor regularity and significant nonlinearity of the measurement model, and thus unreliable results when the GUM method is used to evaluate the measurement uncertainty.

[0132] The present invention effectively solves the problem of difficulty in derivation calculation in existing methods when facing the nonlinear model of the power frequency electric field calibration device. At the same time, there is no approximate conversion of the model function, thus achieving more accurate measurement uncertainty assessment.

[0133] The calculation process of the present invention is clear, which avoids the introduction of subjective assumptions in the existing methods and is easy to execute using computer language. It provides a new method and certain beneficial reference for the measurement uncertainty evaluation work of the power frequency electric field calibration device to achieve high precision, high efficiency and high reliability.

[0134] In an embodiment of the present invention, the present invention provides a method for evaluating the measurement uncertainty of a power frequency electric field calibration device based on the Monte Carlo method, wherein the power frequency electric field calibration is performed at T = 23.0 ° C, and the calibration power frequency electric field point is 1000V / m, comprising the following steps:

[0135] Step 1: Build a measurement model

[0136] The measurement function of the power frequency electric field calibration device is given by formula (5):

[0137]

[0138] Step 2: Set the probability density function of the input

[0139] Based on the available information, an appropriate probability density function is set for each input quantity of the above measurement function. The input quantities are voltage transformer ratio N, voltage representation value V, parallel plate spacing D T , linear expansion coefficient α of the parallel plate material, laboratory temperature T, temperature T0 during traceability, background electric field E0, and measurement repeatability rep. Table 1 will list this information.

[0140] Table 1 Probability density function of input quantity for power frequency electric field calibration uncertainty setting

[0141]

[0142] Step 3: Determine the number of Monte Carlo sampling

[0143] Here we take p = 0.95, which means that the actual sample distribution is included with a probability of 95%, which can be calculated by the following formula:

[0144] M1≥1 / (1-p)×10 4 =2.0×10 5 ,

[0145] The selected inclusive interval length is retained to 2 significant figures, which can be calculated by the following formula:

[0146]

[0147] The number of Monte Carlo sampling M is at least the larger value of M1 and M2. In order to facilitate description and leave a certain redundancy for the sampling results, M is set to 1.0×10 6 .

[0148] Step 4: Monte Carlo sampling

[0149] Based on the voltage transformer ratio N, voltage indication value V, parallel plate spacing D T , the linear expansion coefficient α of the parallel plate material, the laboratory temperature T, the temperature T0 during tracing, the background electric field E0, and the probability density function of the measurement repeatability rep are respectively calculated as M = 1.0 × 10 6 After discrete sampling, the probability distribution histogram of each input quantity is as follows: Figure 4 As shown, M = 1.0 × 10 6 The input matrix and output matrix of vectors.

[0150]

[0151]

[0152] The estimated value of the measurement model Y is further calculated and the standard uncertainty u(y),

[0153]

[0154] u(y)=22.82V / m.

[0155] Step 5: Sort the output in non-decreasing order

[0156] Replace y in the fourth step r Sort in non-decreasing order to get the sorted output y (r) Probability distribution, further we can get the distribution function G of the output Y The discrete expression G of (η) is as follows Figure 6 shown.

[0157] Step 6: Determine the inclusion interval

[0158] Apply the discrete expression G to calculate the inclusion interval of the output quantity Y at 95% inclusion probability like Figure 7 shown.

[0159] Figure 8 This is a structural diagram of a measurement uncertainty assessment system for a power frequency electric field calibration device according to a preferred embodiment of the present invention. Figure 8 As shown, the present invention provides a system for evaluating the measurement uncertainty of a power frequency electric field calibration device, the system comprising:

[0160] The initialization unit 801 is used to determine the measurement function of the power frequency electric field nominal value generated by the power frequency electric field calibration device based on a pre-established measurement model.

[0161] Preferably, the measurement function is:

[0162]

[0163] D=D T [1+2α(T-T0)],

[0164] Where, E is the nominal value of the power frequency electric field generated by the power frequency electric field calibration device; N is the voltage transformer ratio; V is the voltage representation value; E0 is the background electric field; D is the parallel plate spacing at laboratory temperature; D T is the distance between parallel plates at the traceability temperature; rep is the measurement repeatability; T is the laboratory temperature; T0 is the temperature at the traceability time; α is the linear expansion coefficient of the parallel plate material.

[0165] The first determining unit 802 is used to set a probability density function for each input quantity of the measurement function, and determine the probability distribution of each input quantity according to the probability density function.

[0166] The second determining unit 803 is used to generate discrete distribution samples of the final output quantity based on Monte Carlo sampling according to the probability distribution of each input quantity, and determine the number of Monte Carlo sampling M based on the discrete distribution samples of the output quantity.

[0167] Preferably, determining the number of Monte Carlo sampling times M includes:

[0168] Make sure that the value of M1 is greater than or equal to 1 / (1-p) 10 4 Times:

[0169] M1≥1 / (1-p)×10 4 ,

[0170] Where M1 is the minimum number of sampling times to ensure that the uncertainty provides the expected inclusion interval, and p is the expected inclusion probability;

[0171] Make sure that the value of M2 is greater than or equal to the degrees of freedom required to maintain enough significant figures for the uncertainty:

[0172]

[0173] Where M2 is the minimum number of sampling times to ensure that the uncertainty retains sufficient significant figures, v is the required degree of freedom, u(y) is the standard uncertainty, and σ[u(y)] is the standard deviation of the standard uncertainty u(y);

[0174] Determine M to be the larger value of M1 and M2:

[0175] M≥MAX(M1,M2).

[0176] The first acquisition unit 804 is used to perform Monte Carlo sampling based on the Monte Carlo sampling number M to acquire M output quantities of the measurement function.

[0177] Preferably,

[0178] Based on the Monte Carlo sampling number M, Monte Carlo sampling is performed, including:

[0179] The measurement model is denoted as Y=f(X1,...X N ), from N input quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities y by calculation r =f(x r ), r = 1, ..., M, we can further obtain the estimated value of the simplified measurement model Y and standard uncertainty u(y), input matrix x r , the output matrix y r Respectively represent:

[0180]

[0181]

[0182] Among them, (X1,…X N ) are the N input quantities in the measurement model, ξ i To describe the input quantity X i A variable with possible values, (x 1,r ,…x N,r) is the sample of input quantity, (y1,…,y M ).

[0183] The second acquisition unit 805 is used to sort the M output quantities of the measurement function in non-decreasing order, obtain the sorted M output quantities of the measurement function, and based on the sorted M output quantities of the measurement function, obtain a discrete expression of the distribution function of the sorted M output quantities of the measurement function.

[0184] The calculation unit 806 is used to calculate the inclusion interval of the M output quantities under a preset probability based on the discrete expression of the distribution function.

[0185] Preferably, the preset probability is 50%, 90%, 95%, 99% or 99.73%.

[0186] A system 800 for evaluating measurement uncertainty of a power frequency electric field calibration device according to a preferred embodiment of the present invention corresponds to a method 100 for evaluating measurement uncertainty of a power frequency electric field calibration device according to a preferred embodiment of the present invention, and will not be described in detail herein.

[0187] The invention has been described above with reference to a few embodiments. However, it is readily apparent to a person skilled in the art that other embodiments than the ones disclosed above are equally within the scope of the invention, as defined by the appended patent claims.

[0188] Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a / said / the [means, components, etc.]" are to be openly interpreted as at least one instance of the means, components, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not necessarily have to be performed in the exact order disclosed, unless explicitly stated otherwise.

Claims

1. A method for evaluating the measurement uncertainty of a power frequency electric field calibration device, characterized in that: The method comprises: Based on the pre-established measurement model, determining the measurement function of the power frequency electric field calibration device to generate the nominal value of the power frequency electric field; Setting a probability density function for each input quantity of the measurement function, and determining a probability distribution of each input quantity according to the probability density function; According to the probability distribution of each input quantity, a discrete distribution sample of the final output quantity is generated based on Monte Carlo sampling, and the number of Monte Carlo sampling M is determined based on the discrete distribution sample of the output quantity; Based on the Monte Carlo sampling number M, Monte Carlo sampling is performed to obtain M output quantities of the measurement function; Sorting the M output quantities of the measurement function in a non-decreasing manner to obtain the sorted M output quantities of the measurement function, and obtaining a discrete expression of a distribution function of the sorted M output quantities of the measurement function based on the sorted M output quantities of the measurement function; Based on the discrete expression of the distribution function, calculating the inclusion interval of M output quantities under a preset probability; Wherein, the measurement function is: D=D T [1+2α(T-T0], Where, E is the nominal value of the power frequency electric field generated by the power frequency electric field calibration device; N is the voltage transformer ratio; V is the voltage representation value; E0 is the background electric field; D is the parallel plate spacing at laboratory temperature; D T is the distance between parallel plates at the traceability temperature; rep is the measurement repeatability; T is the laboratory temperature; T0 is the temperature at the traceability time; α is the linear expansion coefficient of the parallel plate material; Wherein, determining the number of Monte Carlo sampling times M includes: Make sure that the value of M1 is greater than or equal to 1 / (1-p) 10 4 Times: M1≥1 / (1-p)×10 4 , Where M1 is the minimum number of sampling times to ensure that the uncertainty provides the expected inclusion interval, and p is the expected inclusion probability; Make sure that the value of M2 is greater than or equal to the degrees of freedom required to maintain enough significant figures for the uncertainty: Where M2 is the minimum number of sampling times to ensure that the uncertainty retains sufficient significant figures, v is the required degree of freedom, u(y) is the standard uncertainty, and σ[u(y)] is the standard deviation of the standard uncertainty u(y); Determine M to be the larger value of M1 and M2: M≥MAX(M1,M2).

2. The method according to claim 1, characterized in that The performing of Monte Carlo sampling based on the Monte Carlo sampling number M includes: The measurement model is denoted as Y=f(X1,...X N ), from N input quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities by calculation. r =f(x r ), r = 1, ..., M, we can further obtain the estimated value of the simplified measurement model Y and standard uncertainty u(y), input matrix x r , the output matrix y r Respectively represent: Among them, (X1,…X N ) are the N input quantities in the measurement model, ξ i To describe the input quantity X i A variable with possible values, (x 1,r ,…x N,r ) is the sample of input quantity, (y1,…,y M ).

3. The method according to claim 1, characterized in that: The preset probability is 50%, 90%, 95%, 99% or 99.73%.

4. A system for evaluating the measurement uncertainty of a power frequency electric field calibration device, characterized in that: The system comprises: An initialization unit, for determining a measurement function for generating a nominal value of a power frequency electric field by a power frequency electric field calibration device based on a pre-established measurement model; A first determining unit, configured to set a probability density function for each input quantity of the measurement function, and determine a probability distribution of each input quantity according to the probability density function; A second determining unit is used to generate a discrete distribution sample of a final output based on Monte Carlo sampling according to the probability distribution of each input, and determine the number of Monte Carlo samplings M based on the discrete distribution sample of the output; A first acquisition unit, configured to perform Monte Carlo sampling based on the Monte Carlo sampling number M, to acquire M output quantities of the measurement function; A second acquisition unit is used to sort the M output quantities of the measurement function in a non-decreasing manner, obtain the sorted M output quantities of the measurement function, and obtain a discrete expression of a distribution function of the sorted M output quantities of the measurement function based on the sorted M output quantities of the measurement function; A calculation unit, used for calculating the inclusion interval of M output quantities under a preset probability based on the discrete expression of the distribution function; Wherein, the measurement function is: D=D T [1+2α(T-T0)], Where, E is the nominal value of the power frequency electric field generated by the power frequency electric field calibration device; N is the voltage transformer ratio; V is the voltage representation value; E0 is the background electric field; D is the parallel plate spacing at laboratory temperature; D T is the distance between parallel plates at the traceability temperature; rep is the measurement repeatability; T is the laboratory temperature; T0 is the temperature at the traceability time; α is the linear expansion coefficient of the parallel plate material; Wherein, determining the number of Monte Carlo sampling times M includes: Make sure that the value of M1 is greater than or equal to 1 / (1-p) 10 4 Times: M1≥1 / (1-p)×10 4 , Where M1 is the minimum number of sampling times to ensure that the uncertainty provides the expected inclusion interval, and p is the expected inclusion probability; Make sure that the value of M2 is greater than or equal to the degrees of freedom required to maintain enough significant figures for the uncertainty: Where M2 is the minimum number of sampling times to ensure that the uncertainty retains sufficient significant figures, v is the required degree of freedom, u(y) is the standard uncertainty, and σ[u(y)] is the standard deviation of the standard uncertainty u(y); Determine M to be the larger value of M1 and M2: M≥MAX(M1,M2).

5. The system according to claim 4, characterized in that Said Based on the Monte Carlo sampling number M, Monte Carlo sampling is performed, including: The measurement model is denoted as Y=f(X1,...X N ), from N input quantities X i The probability density function gx i (ξ i ) extract M vectors x r =(x 1,r ,…x N,r ), and obtain M output quantities by calculation. r =f(x r ), r = 1, ..., M, we can further obtain the estimated value of the simplified measurement model Y and standard uncertainty u(y), input matrix x r , the output matrix y r Respectively represent: Among them, (X1,…X N ) are the N input quantities in the measurement model, ξ i To describe the input quantity X i A variable with possible values, (x 1,r ,…x N,r ) is the sample of input quantity, (y1,…,y M ).

6. The system according to claim 4, characterized in that The preset probability is 50%, 90%, 95%, 99% or 99.73%.

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