CN113761712A - Method and system for evaluating measurement uncertainty of calibration system - Google Patents
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Abstract
The invention discloses a method and a system for evaluating the measurement uncertainty of a calibration system, and belongs to the technical field of electrical parameter testing and metering. The method comprises the following steps: establishing a measurement model of a direct current synthetic electric field calibration system; setting a probability density distribution function for the input quantity of the measurement model, and determining the Monte Carlo sampling times through the probability density distribution function; acquiring an output matrix of the measurement model; according to the simplified model and the output matrix, performing non-decreasing ordering on the output quantity; and evaluating the measurement uncertainty of the direct current synthetic electric field calibration system. The method effectively solves the problems that the measurement model is poor in regularity and remarkable in nonlinearity due to more influence factors of the measurement result of the direct current synthetic electric field calibration system, and the result is unreliable when the GUM method is used for evaluating the measurement uncertainty.
Description
Technical Field
The present invention relates to the field of electrical parameter testing and metering, and more particularly, to a method and system for assessing measurement uncertainty of a calibration system.
Background
The direct current synthetic electric field parameters are used as important environmental influence factors of the power transmission and transformation project, and are indispensable in project environmental influence evaluation before and after construction and operation of the power transmission and transformation project. The measurement result is directly applied to the engineering design fields of wire type selection, end point site selection, path planning and the like, and is also an important legal basis for relieving public anxiety and judging environmental disputes, and whether the measurement result of the direct current synthetic electric field is accurate or not directly influences the difficulty degree of engineering cost control, the environment-friendly level and the quality guarantee of the vital interests of people. Meanwhile, in the power industry, direct current synthetic electric field measurement is taken as an important technical means for researching and analyzing the direct current synthetic electric field, and the method has a great deal of application in the aspects of electrical equipment pollution accumulation improvement, geophysical exploration, atmosphere lightning early warning, industrial crystal processing and the like.
The accurate calibration of the direct current synthesis electric field parameters is a precondition for the practical application of the technology, and the quality of the measurement result of the direct current synthesis electric field parameters is directly determined by the level of a calibration system with higher metrological grade on a tracing chain to a great extent.
The reasonably evaluated uncertainty of the direct current synthetic electric field calibration system is an important reference basis for judging the quality of the measurement result of the direct current synthetic electric field parameters, and has important scientific research significance and engineering value for scientifically, effectively and correctly utilizing the measurement result.
Disclosure of Invention
The invention aims at the defects of the prior art and provides a method for evaluating the measurement uncertainty of a calibration system, which comprises the following steps:
aiming at the state that the ion current density of the direct current synthetic electric field reaches saturation, a measurement model of the direct current synthetic electric field calibration system is established;
setting a probability density distribution function for the input quantity of the measurement model, and determining the Monte Carlo sampling times through the probability density distribution function;
simplifying the measurement model, carrying out Monte Carlo sampling according to the determined Monte Carlo sampling times, determining that the estimation value and the standard of the measurement model are uncertain, and acquiring an output matrix of the measurement model;
according to the simplified model and the output matrix, non-descending sorting is carried out on the output quantity, after sorting is completed, discrete expression of a distribution function of the output quantity is determined, and an inclusion interval of the output quantity under the condition of an appointed inclusion probability is calculated through the discrete expression;
and evaluating the measurement uncertainty of the direct current synthesis electric field calibration system according to the estimated value, the standard uncertainty and the contained interval of the measurement model.
Optionally, the measurement model specifically includes:
wherein E is the nominal value of the DC synthesized electric field generated by the calibration system, UTIs a voltage representation value of a high-voltage polar plate, N is a transformation ratio of a voltage transformer, E0For background DC field, T is laboratory temperature, T0The temperature during tracing, alpha is the linear expansion coefficient of the material of the parallel polar plate in the calibration zone, and dTThe distance between parallel polar plates in a calibration area at a tracing temperature is adopted, and rep is measurement repeatability;
optionally, the input quantity includes a plurality of input quantities, and each input quantity sets a probability density function;
the input quantity includes: the device comprises a voltage representation value, a voltage transformer transformation ratio, a parallel polar plate distance of a calibration area, a linear expansion coefficient of a parallel polar plate material, laboratory temperature, temperature during tracing, a background direct current electric field and measurement repeatability.
Optionally, the number of sampling M is at least M1And M2The larger of (a), the formula is as follows:
M≥MAX(M1,M2)
M1should be greater than or equal to 10 of 1/(1-p)4The formula is as follows:
M1≥1/(1-p)×104
wherein M is1P is the expected inclusion probability for the minimum number of samples when providing the expected inclusion interval with guaranteed uncertainty;
M2should be equal to or greater than the degree of freedom required to retain sufficient significant figures for uncertainty, the formula is as follows:
wherein M is2Minimum number of samples to retain sufficient number of significant digits to ensure uncertainty, v is the degree of freedom required, u (y) is the standard uncertainty, σ [ u (y)]Is the standard deviation of the standard uncertainty u (y).
Optionally, the simplified measurement model is denoted as Y ═ f (X)1,…XN)，X1～XNIs N input quantities.
Optionally, the monte carlo sampling is performed according to the determined monte carlo sampling times, which specifically includes:
from X of N input quantitiesiProbability density function gxi(ξi) Extract M vectors xr＝(x1,r,…xN,r) Determining M output quantities yr＝f(xr) R 1, …, M, constructing an input matrix x from the output quantitiesrAnd an output matrix yr；
Input matrix xrComprises the following steps:
output matrix yrComprises the following steps:
the present invention also proposes a system for assessing the uncertainty of a measurement of a calibration system, said system comprising:
the model building module is used for building a measurement model of the direct current synthetic electric field calibration system aiming at the state that the ion current density of the direct current synthetic electric field reaches saturation;
the sampling frequency determining module is used for setting a probability density distribution function for the input quantity of the measurement model and determining the Monte Carlo sampling frequency through the probability density distribution function;
the sampling module is used for simplifying the measurement model, carrying out Monte Carlo sampling according to the determined Monte Carlo sampling times, determining that the estimation value and the standard of the measurement model are uncertain, and acquiring an output matrix of the measurement model;
the calculation module performs non-descending sequencing on the output quantity according to the simplified model and the output matrix, determines the discrete expression of the distribution function of the output quantity after the sequencing is completed, and calculates the inclusion interval of the output quantity under the appointed inclusion probability through the discrete expression;
and the output module is used for evaluating the measurement uncertainty of the direct current synthesis electric field calibration system according to the estimated value, the standard uncertainty and the contained interval of the measurement model.
Optionally, the measurement model specifically includes:
wherein E is the nominal value of the DC synthesized electric field generated by the calibration system, UTIs a voltage representation value of a high-voltage polar plate, N is a transformation ratio of a voltage transformer, E0For background DC field, T is laboratory temperature, T0The temperature during tracing, alpha is the linear expansion coefficient of the material of the parallel polar plate in the calibration zone, and dTThe distance between parallel polar plates in a calibration area at a tracing temperature is adopted, and rep is measurement repeatability;
optionally, the input quantity includes a plurality of input quantities, and each input quantity sets a probability density function;
the input quantity includes: the device comprises a voltage representation value, a voltage transformer transformation ratio, a parallel polar plate distance of a calibration area, a linear expansion coefficient of a parallel polar plate material, laboratory temperature, temperature during tracing, a background direct current electric field and measurement repeatability.
Optionally, the number of sampling M is at least M1And M2The larger of (a), the formula is as follows:
M≥MAX(M1,M2)
M1should be greater than or equal to 10 of 1/(1-p)4The formula is as follows:
M1≥1/(1-p)×104
wherein M is1P is the expected inclusion probability for the minimum number of samples when providing the expected inclusion interval with guaranteed uncertainty;
M2should be equal to or greater than the degree of freedom required to retain sufficient significant figures for uncertainty, the formula is as follows:
wherein M is2Keeping sufficient number of digits for uncertaintyV is the desired degree of freedom, u (y) is the standard uncertainty, σ [ u (y)]Is the standard deviation of the standard uncertainty u (y).
Optionally, the simplified measurement model is denoted as Y ═ f (X)1,…XN)，X1～XNIs N input quantities.
Optionally, the monte carlo sampling is performed according to the determined monte carlo sampling times, which specifically includes:
from X of N input quantitiesiProbability density function gxi(ξi) Extract M vectors xr＝(x1,r,…xN,r) Determining M output quantities yr＝f(xr) R 1, …, M, constructing an input matrix x from the output quantitiesrAnd an output matrix yr；
Input matrix xrComprises the following steps:
output matrix yrComprises the following steps:
the method effectively solves the problems that the measurement model is poor in regularity and remarkable in nonlinearity due to more influence factors of the measurement result of the direct current synthetic electric field calibration system, and the result is unreliable when the GUM method is used for evaluating the measurement uncertainty.
The method effectively solves the problem that the derivation calculation is difficult when the existing method faces the nonlinear model of the direct current synthetic electric field calibration system, and meanwhile, the approximate conversion of the model function does not exist, so that more accurate measurement uncertainty evaluation is realized.
The calculation processing process of the invention is clear, avoids the introduction of subjective hypothesis conditions in the prior method, is convenient to be executed by using computer language, and provides a new method and certain beneficial reference for the DC synthetic electric field calibration system to realize high-precision, high-efficiency and high-reliability measurement uncertainty evaluation work.
Drawings
Fig. 1 is a schematic diagram of a dc synthesized electric field calibration system according to the present invention.
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a schematic illustration of a probability distribution propagation of an input quantity according to the present invention;
FIG. 4 is a histogram of probability distributions of various input quantities in an embodiment of the present invention;
FIG. 5 is a histogram of a probability distribution of an output quantity in an embodiment of the present invention;
FIG. 6 is a graph of an inclusion interval of output at a 95% inclusion probability in accordance with an embodiment of the present invention;
fig. 7 is a block diagram of the system of the present invention.
Detailed Description
The exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the embodiments described herein, which are provided for complete and complete disclosure of the present invention and to fully convey the scope of the present invention to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention. In the drawings, the same units/elements are denoted by the same reference numerals.
Unless otherwise defined, terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Further, it will be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense.
The direct current resultant electric field calibration can be divided into the case where the ion current density does not reach saturation and the case where the ion current density reaches saturation, and the patent is directed only to the latter.
The DC synthesized electric field calibrating device consists of corona area, control area and calibrating area comprising corona starting electrode, control polar plate, high voltage polar plate and earthing polar plate. In the implementation process of the calibration of the direct current synthetic electric field, the direct current synthetic electric field probe is placed below the grounding polar plate, and voltages are applied to the corona-starting electrode, the control polar plate and the high-voltage polar plate, so that the functions of manufacturing space ions, controlling ion current density and generating the direct current synthetic electric field are respectively achieved. Meanwhile, the voltage signal is transmitted to the voltmeter through the voltage transformer, and the nominal value of the direct-current combined electric field generated by the calibration device can be calculated and obtained by recording the voltage value, and a system schematic diagram of the direct-current combined electric field calibration is shown in fig. 1.
The invention proposes a method for assessing the uncertainty of a measurement of a calibration system, as shown in fig. 2, comprising:
the first step is as follows: establishing a measurement model
The level of the field intensity of the direct current composite electric field depends on the input voltage of the high-voltage polar plate, the transformation ratio of the voltage transformer and the distance between the parallel polar plates of the calibration area, so that:
due to the existence of the experimental environment background direct current electric field, the formula (1) becomes:
introducing measurement repeatability of the calibration process, equation (2) becomes:
some of the input quantities in the measurement function are themselves functions of other quantities and should be represented as consisting of basic quantities.
Wherein the parallel plate spacing d of the calibration zone is a function related to the ambient temperature of the laboratory:
d＝dT[1+2α(T-T0)] (4)
the measurement function of the final dc-synthesized electric field calibration system becomes:
in the above (1-5), E is a nominal value of a DC synthesized electric field generated by the calibration system, and the unit is kV/m; n is the transformation ratio of the voltage transformer and is dimensionless; u shapeTIs a voltage representation value of the high-voltage polar plate, and the unit is V; d is the parallel polar plate distance of the calibration area, and the unit is m; t is laboratory temperature in units of; t is0The temperature is the temperature during tracing and the unit is; alpha is the linear expansion coefficient of the material of the parallel polar plate of the calibration area and has the unit of DEG C-1；E0A background direct current electric field with the unit of kV/m; rep is the repeatability of the measurement, and its estimated value rep is 1.0.
The second step is as follows: setting a probability density function of the input quantity;
an appropriate probability density function is set for each input quantity of the above-mentioned measurement functions, and the probability density function is derived based on available information. The input quantity comprises a voltage representation value, a voltage transformer transformation ratio, a calibration area parallel polar plate distance, a linear expansion coefficient of a parallel polar plate material, laboratory temperature, temperature during tracing, a background direct current electric field and measurement repeatability.
The third step: determining the Monte Carlo sampling times;
according to the probability distribution set for the input quantity in the second step, a discrete distribution sample of the final output quantity can be generated by using Monte Carlo sampling, and the closeness degree of the distribution sample and the actual sample distribution depends on the Monte Carlo sampling frequency M, namely the sample capacity M. The more sampling times and the larger sample capacity, the closer the statistical law is to the real situation of the output quantity, but the longer the required calculation time is. The smaller the sampling times, the smaller the sample capacity, and the farther the statistical law is from the real situation of the output quantity. Therefore, the value of M is very critical to the measurement uncertainty evaluation of the direct current composite electric field.
The specific steps of the determination are as follows:
M1should be greater than or equal to 10 of 1/(1-p)4Double, i.e.
M1≥1/(1-p)×104 (6)
M2Should be greater than or equal to the degree of freedom required to preserve sufficient significant figures for uncertainty, i.e.
M is at least M1And M2Of greater value, i.e.
M≥MAX(M1,M2) (8)
The fourth step: performing Monte Carlo sampling;
simplified notation of the measurement model as Y ═ f (X)1,…XN) From N input quantities of XiProbability density function gxi(ξi) Extract M vectors xr＝(x1,r,…xN,r) M output quantities y obtained by calculation, as shown in FIG. 3r＝f(xr) R is 1, …, M, further obtaining an estimated value of the measurement model Y
And standard uncertainty u (y). Input matrix xrOutput matrix yrRespectively expressed by formula (9) and formula (10):
the fifth step: non-decreasing sorting is carried out on the output quantity;
mixing y in the fourth stepr＝f(xr) R is 1, …, M is sorted in a non-decreasing order to obtain sorted output quantity y(r)R is 1, …, M, and further the distribution function G of the output quantity can be obtainedY(η) discrete expression G.
A sixth step: determining an inclusion interval
Calculating the inclusion interval [ Y ] of the output quantity Y under the inclusion probability by using the discrete expression Glow，yhigh]。
The method is described by combining specific calculation examples, the calibration of the direct current synthesis electric field is carried out at the temperature T of 25.0 ℃, the point position of the calibration direct current synthesis electric field is 10kV/m, and the method specifically comprises the following steps:
the first step is as follows: establishing a measurement model
The measurement function of the DC-synthetic electric field calibration system is given by equation (5)
The second step is as follows: setting probability density function of input quantity
Deriving, based on available information, a suitable probability density function for each input of said measurement function, said input having a voltage representative value UTVoltage transformer transformation ratio N and calibration zone parallel polar plate distance dTLinear expansion coefficient alpha of parallel polar plate material, laboratory temperature T and temperature T in tracing0And a background DC electric field E0Measuring the repetitive rep, table 1 will list this information.
TABLE 1
The third step: determining Monte Carlo sample times
Here, p is 0.95, i.e., the actual sample distribution is included at a probability of 95%, and the calculation is performed by equation (6)
M1≥1/(1-p)×104＝2.0×105
Is selected to include the interval length reserved to 2 significant digits, which can be calculated from equation (7)
The Monte Carlo sampling times M are at least M1And M2The larger value of M is set to 1.0 × 10 for convenience of description and certain redundancy of sampling results6。
The fourth step: performing Monte Carlo sampling
According to the transformation ratio N of the voltage transformer, the voltage representation value V and the parallel polar plate distance DTLinear expansion coefficient alpha of parallel polar plate material, laboratory temperature T and temperature T in tracing0And a background DC electric field E0And measuring the probability density function of the repetitive rep, and respectively carrying out M-1.0 multiplied by 106After the sub-discrete sampling, the histogram of the probability distribution of each input quantity is shown in fig. 4, and M is obtained as 1.0 × 106An input matrix and an output matrix of vectors.
Further calculated estimated value of the measurement model Y
And standard uncertainty u (y);
u(y)＝0.48kV/m
the fifth step: non-decreasing ordering of output quantities
Mixing y in the fourth steprSorting according to a non-decreasing order to obtain a sorted output quantity y(r)Probability distribution, further obtaining distribution function G of output quantityY(η) discrete expression G, as shown in FIG. 5.
A sixth step: determining an inclusion interval
The inclusion interval of output Y at 95% inclusion probability is calculated using the discrete expression G [9.53,10.48], as shown in FIG. 6.
The present invention also provides a system 200 for assessing measurement uncertainty of a calibration system, as shown in FIG. 7, comprising:
the model building module 201 is used for building a measurement model of the direct current synthetic electric field calibration system aiming at the state that the ion current density of the direct current synthetic electric field reaches saturation;
a sampling frequency determining module 202, configured to set a probability density distribution function for the input quantity of the measurement model, and determine the monte carlo sampling frequency through the probability density distribution function;
the sampling module 203 is used for simplifying the measurement model, carrying out Monte Carlo sampling according to the determined Monte Carlo sampling times, determining that the estimation value and the standard of the measurement model are uncertain, and acquiring an output matrix of the measurement model;
the calculation module 204 performs non-decreasing ordering on the output quantity according to the simplified model and the output matrix, determines the discrete expression of the distribution function of the output quantity after the ordering is completed, and calculates the inclusion interval of the output quantity under the appointed inclusion probability through the discrete expression;
and the output module 205 evaluates the measurement uncertainty of the direct current synthesis electric field calibration system according to the estimated value, the standard uncertainty and the containing interval of the measurement model.
The measurement model specifically comprises:
wherein E is the nominal value of the DC synthesized electric field generated by the calibration system, UTIs a voltage representation value of a high-voltage polar plate, N is a transformation ratio of a voltage transformer, E0For background DC field, T is laboratory temperature, T0The temperature during tracing, alpha is the linear expansion coefficient of the material of the parallel polar plate in the calibration zone, and dTThe distance between parallel polar plates in a calibration area at a tracing temperature is adopted, and rep is measurement repeatability;
the input quantity comprises a plurality of input quantities, and each input quantity is provided with a probability density function;
the input quantity includes: the device comprises a voltage representation value, a voltage transformer transformation ratio, a parallel polar plate distance of a calibration area, a linear expansion coefficient of a parallel polar plate material, laboratory temperature, temperature during tracing, a background direct current electric field and measurement repeatability.
Wherein the number of sampling M is at least M1And M2The larger of (a), the formula is as follows:
M≥MAX(M1,M2)
M1should be greater than or equal to 10 of 1/(1-p)4The formula is as follows:
M1≥1/(1-p)×104
wherein M is1P is the expected inclusion probability for the minimum number of samples when providing the expected inclusion interval with guaranteed uncertainty;
M2should be equal to or greater than the degree of freedom required to retain sufficient significant figures for uncertainty, the formula is as follows:
wherein M is2Minimum number of samples to retain sufficient number of significant digits to ensure uncertainty, v is the degree of freedom required, u (y) is the standard uncertainty, σ [ u (y)]Is the standard deviation of the standard uncertainty u (y).
The simplified measurement model is denoted as Y ═ f (X)1,…XN)，X1～XNIs N input quantities.
Wherein, according to the determined Monte Carlo sampling times, carrying out Monte Carlo sampling, specifically:
from X of N input quantitiesiProbability density function gxi(ξi) Extract M vectors xr＝(x1,r,…xN,r) Determining M output quantities yr＝f(xr) R 1, …, M, according to the output quantityConstructing an input matrix xrAnd an output matrix yr；
Input matrix xrComprises the following steps:
output matrix yrComprises the following steps:
the method effectively solves the problems that the measurement model is poor in regularity and remarkable in nonlinearity due to more influence factors of the measurement result of the direct current synthetic electric field calibration system, and the result is unreliable when the GUM method is used for evaluating the measurement uncertainty.
The method effectively solves the problem that the derivation calculation is difficult when the existing method faces the nonlinear model of the direct current synthetic electric field calibration system, and meanwhile, the approximate conversion of the model function does not exist, so that more accurate measurement uncertainty evaluation is realized.
The calculation processing process of the invention is clear, avoids the introduction of subjective hypothesis conditions in the prior method, is convenient to be executed by using computer language, and provides a new method and certain beneficial reference for the DC synthetic electric field calibration system to realize high-precision, high-efficiency and high-reliability measurement uncertainty evaluation work.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The scheme in the embodiment of the application can be implemented by adopting various computer languages, such as object-oriented programming language Java and transliterated scripting language JavaScript.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all alterations and modifications as fall within the scope of the application.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Claims (12)
1. A method for assessing calibration system measurement uncertainty, the method comprising:
aiming at the state that the ion current density of the direct current synthetic electric field reaches saturation, a measurement model of the direct current synthetic electric field calibration system is established;
setting a probability density distribution function for the input quantity of the measurement model, and determining the Monte Carlo sampling times through the probability density distribution function;
simplifying the measurement model, carrying out Monte Carlo sampling according to the determined Monte Carlo sampling times, determining that the estimation value and the standard of the measurement model are uncertain, and acquiring an output matrix of the measurement model;
according to the simplified model and the output matrix, non-descending sorting is carried out on the output quantity, after sorting is completed, discrete expression of a distribution function of the output quantity is determined, and an inclusion interval of the output quantity under the condition of an appointed inclusion probability is calculated through the discrete expression;
and evaluating the measurement uncertainty of the direct current synthesis electric field calibration system according to the estimated value, the standard uncertainty and the contained interval of the measurement model.
2. The method according to claim 1, wherein the measurement model is in particular:
wherein E is the nominal value of the DC synthesized electric field generated by the calibration system, UTIs a voltage representation value of a high-voltage polar plate, N is a transformation ratio of a voltage transformer, E0For background DC field, T is laboratory temperature, T0The temperature during tracing, alpha is the linear expansion coefficient of the material of the parallel polar plate in the calibration zone, and dTThe parallel plate spacing of the calibration zone at the traceable temperature is used, and rep is the measurement repeatability.
3. The method of claim 1, wherein the input quantity comprises a plurality of input quantities, each input quantity setting a probability density function;
the input quantity includes: the device comprises a voltage representation value, a voltage transformer transformation ratio, a parallel polar plate distance of a calibration area, a linear expansion coefficient of a parallel polar plate material, laboratory temperature, temperature during tracing, a background direct current electric field and measurement repeatability.
4. The method of claim 1 wherein said number of samples M is at least M1And M2The larger of (a), the formula is as follows:
M≥MAX(M1,M2)
M1should be greater than or equal to 10 of 1/(1-p)4The formula is as follows:
M1≥1/(1-p)×104
wherein M is1P is the expected inclusion probability for the minimum number of samples when providing the expected inclusion interval with guaranteed uncertainty;
M2should be equal to or greater than the degree of freedom required to retain sufficient significant figures for uncertainty, the formula is as follows:
wherein M is2Minimum number of samples to retain sufficient number of significant digits to ensure uncertainty, v is the degree of freedom required, u (y) is the standard uncertainty, σ [ u (y)]Is the standard deviation of the standard uncertainty u (y).
5. The method of claim 1, the simplified measurement model denoted as Y ═ f (X)1,…XN)，X1～XNIs N input quantities.
6. The method according to claim 1, wherein the monte carlo sampling is performed according to the determined monte carlo sampling times, and specifically comprises:
from X of N input quantitiesiProbability density function gxi(ξi) Extract M vectors xr＝(x1,r,…xN,r) Determining M output quantities yr＝f(xr) R 1, …, M, constructing an input matrix x from the output quantitiesrAnd an output matrix yr；
Input matrix xrComprises the following steps:
output matrix yrComprises the following steps:
7. a system for assessing calibration system measurement uncertainty, the system comprising:
the model building module is used for building a measurement model of the direct current synthetic electric field calibration system aiming at the state that the ion current density of the direct current synthetic electric field reaches saturation;
the sampling frequency determining module is used for setting a probability density distribution function for the input quantity of the measurement model and determining the Monte Carlo sampling frequency through the probability density distribution function;
the sampling module is used for simplifying the measurement model, carrying out Monte Carlo sampling according to the determined Monte Carlo sampling times, determining that the estimation value and the standard of the measurement model are uncertain, and acquiring an output matrix of the measurement model;
the calculation module performs non-descending sequencing on the output quantity according to the simplified model and the output matrix, determines the discrete expression of the distribution function of the output quantity after the sequencing is completed, and calculates the inclusion interval of the output quantity under the appointed inclusion probability through the discrete expression;
and the output module is used for evaluating the measurement uncertainty of the direct current synthesis electric field calibration system according to the estimated value, the standard uncertainty and the contained interval of the measurement model.
8. The system according to claim 7, wherein the measurement model is in particular:
wherein E is the nominal value of the DC synthesized electric field generated by the calibration system, UTIs a voltage representation value of a high-voltage polar plate, N is a transformation ratio of a voltage transformer, E0For background DC field, T is laboratory temperature, T0The temperature during tracing, alpha is the linear expansion coefficient of the material of the parallel polar plate in the calibration zone, and dTThe parallel plate spacing of the calibration zone at the traceable temperature is used, and rep is the measurement repeatability.
9. The system of claim 7, wherein the input quantity comprises a plurality of input quantities, each input quantity setting a probability density function;
the input quantity includes: the device comprises a voltage representation value, a voltage transformer transformation ratio, a parallel polar plate distance of a calibration area, a linear expansion coefficient of a parallel polar plate material, laboratory temperature, temperature during tracing, a background direct current electric field and measurement repeatability.
10. The system of claim 7, wherein the number of samples M is at least M1And M2The larger of (a), the formula is as follows:
M≥MAX(M1,M2)
M1should be greater than or equal to 10 of 1/(1-p)4The formula is as follows:
M1≥1/(1-p)×104
wherein M is1P is the expected inclusion probability for the minimum number of samples when providing the expected inclusion interval with guaranteed uncertainty;
M2should be equal to or greater than the degree of freedom required to retain sufficient significant figures for uncertainty, the formula is as follows:
wherein M is2Minimum number of samples to retain sufficient number of significant digits to ensure uncertainty, v is the degree of freedom required, u (y) is the standard uncertainty, σ [ u (y)]Is the standard deviation of the standard uncertainty u (y).
11. The system of claim 7, the simplified measurement model denoted as Y ═ f (X)1,…XN)，X1～XNIs N input quantities.
12. The system of claim 7, wherein the Monte Carlo sampling is performed according to the determined Monte Carlo sampling times, and specifically comprises:
from X of N input quantitiesiProbability density function gxi(ξi) Extract M vectors xr＝(x1,r,…xN,r) Determining M output quantities yr＝f(xr) R 1, …, M, constructing an input matrix x from the output quantitiesrAnd an output matrix yr；
Input matrix xrComprises the following steps:
output matrix yrComprises the following steps:
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