CN116306258A - Vulnerability assessment method and system of electrical equipment under strong electromagnetic pulse effect - Google Patents

Vulnerability assessment method and system of electrical equipment under strong electromagnetic pulse effect Download PDF

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CN116306258A
CN116306258A CN202310158868.3A CN202310158868A CN116306258A CN 116306258 A CN116306258 A CN 116306258A CN 202310158868 A CN202310158868 A CN 202310158868A CN 116306258 A CN116306258 A CN 116306258A
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陈宇浩
王宗扬
谢彦召
田爽
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Xian Jiaotong University
Xian Thermal Power Research Institute Co Ltd
Huaneng Group Technology Innovation Center Co Ltd
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Xian Thermal Power Research Institute Co Ltd
Huaneng Group Technology Innovation Center Co Ltd
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Abstract

The invention belongs to the field of electromagnetic vulnerability research of power equipment, and particularly provides a vulnerability assessment method and system of electric equipment under the action of strong electromagnetic pulse, wherein the vulnerability assessment method comprises the following steps: obtaining a Co-Kriging-based coupling electromagnetic parameter response proxy model at a key position of the tested electrical equipment; constructing an electromagnetic coupling parameter and effect relation model at a key position of the tested electrical equipment based on a support vector machine; combining the obtained coupling electromagnetic parameter response proxy model at the key position of the tested electrical equipment based on Co-Kriging with the electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on a support vector machine to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment; the invention can give out the vulnerability probability under the action of different coupling currents or induced electric fields under the condition of a small sample, and improves the accuracy of vulnerability assessment results.

Description

Vulnerability assessment method and system of electrical equipment under strong electromagnetic pulse effect
Technical Field
The invention belongs to the field of electromagnetic vulnerability research of power equipment, and particularly relates to a vulnerability assessment method and system of electrical equipment under the action of strong electromagnetic pulse.
Background
The high-altitude electromagnetic pulse is an electromagnetic pulse generated by nuclear explosion with the explosion center height of more than 40km, is a powerful electromagnetic interference source and has the characteristics of high field intensity peak value, wide frequency spectrum range and wide distribution range. The strong electromagnetic pulse can directly act on equipment through electromagnetic radiation coupling on one hand, and on the other hand, high induced voltage and high induced current can be formed at an equipment port through a power transmission cable and the like, so that the strong electromagnetic pulse has serious threat to electric equipment in a large area range near the ground. Therefore, the vulnerability of the electrical equipment under the action of strong electromagnetic pulse is studied by methods such as simulation calculation, simulation experiment and the like.
The simulation calculation method, such as a time domain finite difference method and a finite element method, can be conveniently used for analyzing and calculating antenna gain, coupling efficiency of apertures on a cavity, field distribution inside and outside the cavity, shielding effectiveness of a metal cavity and the like in a system, and a large amount of data can be generated, but the calculation precision and accuracy depend on modeling accuracy and mesh subdivision size. The experimental method has higher result authenticity, can accurately reflect the response of a system or a device in an electromagnetic pulse environment, plays an important role in research, is inconvenient to operate and high in cost, and can only acquire a few observation samples in consideration of cost limitation.
The accuracy of experimental observation data which better accords with actual conditions in the existing vulnerability assessment is high, but the cost is high and the sample size is smaller; the accuracy of the simulation data is often low due to the complexity and the reality of the model, but a large number of samples can be obtained.
Disclosure of Invention
The invention aims to provide a vulnerability assessment method of electrical equipment under the action of strong electromagnetic pulse, which solves the defects in the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention provides a vulnerability assessment method of electrical equipment under the action of strong electromagnetic pulse, which comprises the following steps:
step 1, respectively obtaining experimental data and simulation data of a key position of tested electrical equipment, wherein the experimental data comprise electromagnetic pulse amplitude values, electromagnetic coupling parameter measurement results of the key position and effect states; the simulation data comprise electromagnetic pulse amplitude values and electromagnetic coupling parameter simulation results at key positions;
step 2, obtaining a coupling electromagnetic parameter response proxy model at a key position of the tested electrical equipment based on Co-Kriging according to the obtained experimental data and simulation data;
step 3, constructing an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine according to the obtained experimental data;
and step 4, combining the obtained coupling electromagnetic parameter response proxy model with the electromagnetic coupling parameter and effect relation model to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.
Preferably, in step 1, electromagnetic topology analysis is performed on the electrical equipment to be tested, and a sensitive key position of the electrical equipment to be tested is determined.
Preferably, in the step 2, the specific method for establishing the coupling electromagnetic parameter response proxy model at the sensitive key position of the tested electrical equipment based on Co-Kriging is as follows:
setting experimental calculation data D according to the obtained vulnerability experimental data e ＝[X e ，Y e ]Wherein X is e ＝[x 1 e ，x 2 e ，...，x ne e ]，Y e ＝[y 1 e ，y 2 e ，...，x ne e ]；
Setting simulation calculation data D according to the obtained vulnerability simulation data s ＝[X s ，Y s ]Wherein X is s ＝[x 1 s ，x 2 s ，...，x ns s ],Y s ＝[y 1 s ，y 2 s ，...，y ns s ]；
Wherein D is e Calculating data for the set experiment; d (D) s Calculating data for the set simulation; x is X e Is the electromagnetic pulse amplitude; y is Y e The electromagnetic coupling parameter measurement result is the electromagnetic coupling parameter measurement result at the sensitive key position; ne is the sample size of experimental data; x is X s Is the electromagnetic pulse amplitude; y is Y s The simulation result of electromagnetic coupling parameters at sensitive key positions is obtained; ns is the simulated data sample size;
and obtaining a coupling electromagnetic parameter response proxy model at the sensitive key position of the tested electrical equipment based on Co-Kriging according to the set experimental calculation data and simulation calculation data.
Preferably, in step 2, the coupled electromagnetic parameters respond to the mathematical expression of the proxy model:
f e (x)＝ρ s f s (x)+δ e (x)
wherein f e (x) Responding to the proxy model for the coupled electromagnetic parameters; ρ s Is a regression parameter; delta e (x) Is a smooth gaussian process.
Preferably, in step 3, an electromagnetic coupling parameter and effect relation model of the key position of the tested electrical equipment based on the support vector machine is constructed according to the obtained experimental data, and the specific method is as follows:
set effect experimental data D e l ＝[Y e ，Z e ]Wherein D is e l Is effect experimental data; y is Y e The electromagnetic coupling parameter measurement result is the electromagnetic coupling parameter measurement result at the sensitive key position; z is Z e Is an effect state;
and obtaining an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine and the Sigmoid function.
Preferably, in step 3, the mathematical expression of the electromagnetic coupling parameter and effect relation model:
Figure BDA0004093462840000031
wherein A is a slope parameter; b is an intercept parameter; p(s) is an electromagnetic coupling parameter and effect relation model; s is the classification.
Preferably, in step 4, the obtained coupled electromagnetic parameter response proxy model and the electromagnetic coupling parameter and effect relation model are combined to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment, and the specific method is as follows:
taking the high-altitude electromagnetic pulse with a given amplitude as the input of a coupling electromagnetic parameter response proxy model to obtain coupling electromagnetic parameter response and uncertainty distribution thereof at a key position;
and taking the obtained coupling electromagnetic parameter response and uncertainty distribution thereof at the key position as input of an electromagnetic coupling parameter and effect relation model to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.
A vulnerability assessment system for an electrical device under the action of a strong electromagnetic pulse, comprising:
the data acquisition unit is used for respectively acquiring experimental data and simulation data of the key position of the tested electrical equipment, wherein the experimental data comprise electromagnetic pulse amplitude values, electromagnetic coupling parameter measurement results of the key position and effect states; the simulation data comprise electromagnetic pulse amplitude values and electromagnetic coupling parameter simulation results at key positions;
the agent model construction unit is used for acquiring a coupling electromagnetic parameter response agent model at a key position of the tested electrical equipment based on Co-Kriging according to the acquired experimental data and simulation data;
the effect relation model construction unit is used for constructing an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine according to the obtained experimental data;
and the vulnerability assessment unit is used for combining the obtained coupling electromagnetic parameter response proxy model, the electromagnetic coupling parameter and the effect relation model to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.
Compared with the prior art, the invention has the beneficial effects that:
according to the vulnerability assessment method of the electrical equipment under the action of the strong electromagnetic pulse, the electromagnetic pulse vulnerability assessment process of the electrical equipment is divided into two parts, namely the electromagnetic coupling process and the vulnerability statistics process of the key position, different data information is fused by adopting a machine learning method, and calculation deviation caused by adopting a single data type is reduced; by adopting the Co-Kriging model, simulation calculation information can be fused on the basis of electromagnetic pulse vulnerability experimental data of electrical equipment, so that the accuracy of relation description between electromagnetic pulse amplitude and electromagnetic coupling parameters at key positions is effectively improved, and errors caused by small sample size of the experimental data are reduced; the support vector machine method is adopted to establish the functional relation between the electromagnetic coupling parameters at the key positions of the electrical equipment and the final vulnerability result, so that the vulnerability probability under the action of different coupling currents or induced electric fields can be given under the condition of small samples, and the accuracy of the vulnerability assessment result is improved.
In conclusion, the simulation data information with a large amount of low accuracy is fused on the basis of the small sample high accuracy effect experimental data, so that the electromagnetic pulse vulnerability assessment precision of the electrical equipment is improved, and the simulation data information has important application value.
Drawings
Fig. 1 is a flow chart of the technical scheme of the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the method for evaluating vulnerability of electrical equipment under the action of strong electromagnetic pulse provided by the invention comprises the following specific implementation steps:
step 1, carrying out electromagnetic topology analysis on electrical equipment to be tested, and determining to obtain a sensitive key position of the electrical equipment to be tested;
simplifying a tested electrical equipment model, and extracting a key structure and a cable corresponding to the tested electrical equipment; and combining the obtained key structure and the cable with three-dimensional electromagnetic field simulation software to build a three-dimensional structure model.
And 2, vulnerability data acquisition.
Experimental data for the electrical equipment under test is obtained by performing an effect experiment under an electromagnetic pulse boundary wave simulator. In the experiment, the electric equipment to be tested is placed in the working area of the bounded wave simulator, the electromagnetic pulse field intensity is gradually increased from low amplitude, the radiation field intensity at the sensitive key position and the induction current in the system are measured, and the effect phenomenon of the electric equipment to be tested is observed and recorded, so that vulnerability experimental data [ X ] is obtained e ，Y e ，Z e ]Wherein X is e ,Y e And Z e Electromagnetic pulse amplitude, electromagnetic coupling parameter measurement results at sensitive key positions and effect states are respectively obtained; the effect state is classified as invalid or normal, wherein the invalid state is recorded as 1, and the normal state is recorded as 0; x is X e ＝[x 1 e ，x 2 e ，...，x ne e ]；Y e ＝[y 1 e ，y 2 e ，...，y ne e ]；Z e ＝[z 1 e ，z 2 e ，...，z ne e ]，z i e E {0,1}, i=1,., ne; ne is the experimental data sample size.
Simulation calculation of different electromagnetic pulse amplitude values X by adopting three-dimensional electromagnetic field simulation software s Electromagnetic coupling parameter simulation result Y at sensitive key position of tested electrical equipment under action s And needs to meet
Figure BDA0004093462840000061
Thereby obtaining vulnerability simulation data [ X ] s ，Y s ]The effect process of the electric equipment is strongerNonlinear characteristics cannot obtain simulation results of the effect states.
Simulation calculation of electromagnetic coupling parameters at sensitive key positions is obtained by adopting methods such as time domain finite difference, finite element and the like through field line coupling calculation and shielding effectiveness calculation, and simulation data are [ X ] s ，Y s ]，X s And Y s Electromagnetic pulse amplitude of simulation data and electromagnetic coupling parameter simulation results at sensitive key positions are respectively obtained; x is X s ＝[x 1 s ，x 2 s ，...，x ns s ]，Y s ＝[y 1 s ，y 2 s ，...，y ns s ]Ns is the simulated data sample size.
Thus, the vulnerability data collected includes vulnerability experimental data [ X e ，Y e ，Z e ]And vulnerability simulation data [ X s ，Y s ]。
And step 3, acquiring a coupling electromagnetic parameter response proxy model at the key position of the tested electrical equipment.
Setting experimental calculation data D e [X e ，Y e ]Wherein X is e ＝[x 1 e ，x 2 e ，...，x ne e ]，Y e ＝[y 1 e ，y 2 e ，...，y ne e ]；
Setting simulation calculation data D s ＝[X s ，Y s ]Wherein X is s ＝[x 1 s ，x 2 s ，...，x ns s ]，Y s ＝[y 1 s ，y 2 s ，...，y ns s ]；
And according to the set experimental calculation data and simulation calculation data, obtaining a Co-Kriging-based coupling electromagnetic parameter response proxy model at the key position of the tested electrical equipment, wherein the model is subjected to Gaussian process distribution.
Specifically:
based on the Co-Kriging model, the simulation calculation data is obtainedTo the simulation data response model f s (x) The simulation data response model f is shown in the formula (1) s (x) Is set to obey a gaussian process distribution:
f s (x)～GP(h(x) T β s ，σ s 2 exp{-b s (x-x′) T (x-x′)}) (1)
wherein: GP (·) represents a Gaussian process function; h (x) is a multidimensional regression function; beta s Coefficients of a multidimensional regression function corresponding to the simulation calculation data; sigma (sigma) s 2 And b s Are all hyper-parameters in the covariance function of the Gaussian process function corresponding to the simulation calculation data.
By considering the internal relation rule between the experimental calculation data and the simulation calculation data, the simulation calculation data are fused on the basis of the experimental calculation data, and the vulnerability experimental response model f with higher accuracy is obtained e (x) I.e. using experimental calculation data and simulation data response model f s (x) The method comprises the following steps:
[f e (x)|D s ，D e ] (2)
in fact, under the Co-Kriging model, the simulation data response model f s (x) And vulnerability experimental response model f e (x) The relation between the two is:
cov{f e (x)，f s (x′)|f s (x)}＝0 (3)
wherein: x is not equal to x'; cov () represents the covariance between two variables.
This is a markov property: the observation result of the high-accuracy vulnerability experimental response model at the input variable x is only related to the observation result of the low-accuracy simulation data response model at the input variable x, and is not related to other observation results of the low-accuracy simulation data response model.
Then based on this property f s (x) And f e (x) The expression of the coupling electromagnetic parameter response proxy model at the key position of the tested electrical equipment based on Co-Kriging is obtained at the stationarity of the input variable x:
f e (x)＝ρ s f s (x)+δ e (x) (4)
wherein: ρ s Is a regression parameter, delta e (x) Is a smooth gaussian process.
δ e (x) The expression is:
δ e (x)～GP(h(x) T β e ，σ e 2 exp{-b e (x-x′) T (x-x') (5) in the formula: GP (·) represents a Gaussian process function; h (x) is a multidimensional regression function; beta e Calculating coefficients of a multidimensional regression function corresponding to the data for the experiment; sigma (sigma) e 2 And b e Are all hyper-parameters in the covariance function of the Gaussian process function corresponding to the experimental calculation data.
At the same time observe data set D s And D e Satisfy the following requirements
Figure BDA0004093462840000081
And the covariance of any two observation points is as follows:
Figure BDA0004093462840000091
then, the parameters in the coupled electromagnetic parameter response proxy model (4) are β= (β) s ，β e ) And phi = [ sigma ] s 2 ，σ e 2 ，b s ，b e ，ρ s ]。
Based on Gaussian process basic property and coupling electromagnetic parameter response proxy model (4), obtaining [ f ] s (x)，f s (x′)，x|β，φ]Is a multidimensional gaussian process by applying a method of transformation to beta= (beta) s ，β e ) Is integrated to obtain [ f ] e (x)|x，φ]Is a gaussian process:
[f e (x)|x e ，x s ，β，φ]～GP(m′(x)，c′(x)) (7)
1) The mean function m' (x) is:
Figure BDA0004093462840000092
wherein: (1) h' (x) T ＝(ρ s h(x) T ，h(x) T )；ρ s Is a regression parameter; h (x) is a multidimensional regression function in formula (1); h' (x) is a multidimensional regression function in equation (8).
②
Figure BDA0004093462840000101
Wherein H is a defined matrix; x is x 1 s ，...x ns s The input quantity of simulation data; x is x 1 e ，...X ne e Is the input of the effect experimental data.
(3) V is the data covariance matrix:
Figure BDA0004093462840000102
wherein A is s And A e Respectively, observation data set X s And X e Is a covariance matrix of (a).
④
Figure BDA0004093462840000103
Is the posterior mean of beta:
Figure BDA0004093462840000104
where y is a matrix of simulated calculated response data and experimental response data.
⑤
Figure BDA0004093462840000105
Wherein y is e Is f e () The output is responded to on x.
2) In addition, [ f e (x)|x，φ]The covariance function is:
c′(x，x′)＝c(x，x′)-t(x) T V -1 t(x)+(h′(x)-t(x) T V -1 H) T (H T V -1 H) -1 (h′(x)-t(x) T V - 1 H) (9)
wherein:
Figure BDA0004093462840000111
c e is the covariance function in equation (5); c s Is the covariance function in equation (1).
The estimation of the parameter β can be determined by finding the posterior mean value of (4) of equation (8).
Based on the independence of the distribution, the final result is an independent estimation of the parameters (b s ，σ s 2 ) Sum (. Rho) s ，b s ，σ e 2 )。
Therefore, the coupling electromagnetic parameter response proxy model of the tested electrical equipment key position based on Co-Kriging containing richer prior information is established by fusing simulation calculation data on the basis of the electromagnetic pulse vulnerability experimental data of the electrical equipment, and errors caused by small sample size of the experimental data can be effectively reduced.
And 4, establishing an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine.
Set effect experimental data D e l =[Y e ，Z e ]；
Based on effect experimental data D e l =[Y e ，Z e ]Establishing a vulnerability assessment classification model between electromagnetic coupling parameters and effect results at key positions of the tested electrical equipment;
combining the vulnerability assessment classification model with the Sigmoid function to obtain an electromagnetic coupling parameter and effect relation model based on the key position of the tested electrical equipment of the support vector machine.
Specifically, the vulnerability assessment classification model is established by adopting a support vector machine method, so that the problems of less sample data, nonlinear effect process, high dimension and the like are effectively solved, and the accuracy of the vulnerability assessment result is improved.
In the vulnerability assessment, failure state data is regarded as positive class, which is indicated by '1', normal state data is regarded as negative class, which is indicated by '1', and then effect experimental data can be transformed into:
Figure BDA0004093462840000121
wherein: z i e E {0,1}, i=1,., ne; ne is the experimental data sample size.
If the training data is linearly separable, its separation hyperplane can be expressed as:
Figure BDA0004093462840000123
wherein omega l As normal vector, b l And y is an electromagnetic coupling parameter at a key position of the tested electrical equipment for intercept.
And the corresponding classification decision function may be expressed as:
Figure BDA0004093462840000124
wherein sign is a sign function.
That is to say
Figure BDA0004093462840000125
The size of (2) determines the classification result, let M be a certain sample point y i If (3)
Figure BDA0004093462840000126
The classification result of the sample M is a positive class; if (I)>
Figure BDA0004093462840000127
The sample M classification result is negative; if->
Figure BDA0004093462840000128
The sample M is at the interface.
Generally, the distance of a point from the classification hyperplane may indicate the accuracy of the classification prediction, i.e., the classification hyperplane (w l ，b l ) With respect to sample point y i Is provided for the geometric spacing of (a).
Let M be the class label z l i W is the normal vector of the classification hyperplane, the geometric interval is defined by the length of line segment L
Figure BDA0004093462840000131
The expression is that:
Figure BDA0004093462840000132
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0004093462840000133
marked as effect results.
It can be seen that the classification hyperplane (w l ，b l ) With respect to the sample point M (y i ，z l i ) The geometric spacing of (2) is typically the signed distance of the sample point to the classification hyperplane, which is the distance of the sample point to the classification hyperplane in the case of a sample point that is correctly classified, also referred to herein as the "classification index".
Further defining a classification hyperplane (w l ，b l ) Experimental data on effects D e l Is a hyperplane (w) l ，b l ) Regarding D e l The minimum geometric spacing of all sample points, namely:
Figure BDA0004093462840000134
correspondingly, the classification hyperplane (w l ，b l ) With respect to the sample point (y i ，z l i ) Sum effect experimental data D e l The functional intervals of (2) can be expressed as:
Figure BDA0004093462840000141
Figure BDA0004093462840000142
and their relationship to the geometric spacing can be expressed as:
Figure BDA0004093462840000143
Figure BDA0004093462840000144
the basic idea of the support vector machine is to solve a classification hyperplane which can correctly divide a training data set and has the largest geometric interval, and for a linearly separable training data set, the linearly separable hyperplanes have infinite numbers, but the largest geometric interval is unique; the visual interpretation of interval maximization is to classify training data with a sufficiently large degree of certainty, that is, not only separating positive and negative samples, but also separating them with a sufficiently large degree of certainty for the most difficult to separate sample points, so that it has a good classification predictive ability for unknown points, and in particular, the problem can be represented by a constraint optimization problem:
Figure BDA0004093462840000145
Figure BDA0004093462840000146
wherein: gamma ray l To classify hyperplane (w l ，b l ) Experimental data on effects D e l ＝[Y e ，Z e ]All sample points in (1)Geometric spacing minimum FF1B y of (2) i Electromagnetic coupling parameters at key positions in effect experimental data; z e i Marked as effect results.
The constraint optimization problem is that the classification hyperplane (w l ，b l ) With respect to training dataset D e l ＝[Y e ，Z e ]Is a geometric spacing gamma of (2) l Maximization, while constraints represent a classification hyperplane (w l ，b l ) The geometric spacing for each sample point is at least gamma l 。
The model has been built up by analysis of the problem, and then the normal vector w of the classification hyperplane is calculated according to equation (19) only l And intercept b l 。
Since equation (19) is not a convex function, it is inconvenient to optimize the solution, and it can be rewritten as follows based on the relation between the geometric interval and the function interval, that is, equation (18):
Figure BDA0004093462840000151
Figure BDA0004093462840000152
to ensure that the solution is unique, it is necessary to
Figure BDA0004093462840000153
Some restrictions are made, for convenience of taking +.>
Figure BDA0004093462840000154
The meaning of this is that the global function interval is defined as 1, i.e. the distance from the nearest point to the hyperplane is defined as 1/||w l I; due to the 1/||w l The maximum value of i corresponds to finding w l || 2 The minimum value of/2, therefore, the result after overwriting is:
Figure BDA0004093462840000161
Figure BDA0004093462840000162
therefore, the objective function is converted into a quadratic function, and the constraint function is an affine function, so that the interval maximization problem to be solved is converted into a convex quadratic programming problem, and the calculation is convenient to solve.
In practice, classification problems tend to be nonlinear and require processing with nonlinear models; one advantage of the support vector machine is that a kernel function can be introduced and the problem of nonlinearity solved, the basic idea of which is to correspond the input space (euclidean space or discrete set) to one feature space (hilbert space) such that the hyperplane model of the input space corresponds to the hyperplane model in the feature space. Therefore, the problem can be solved in a feature space by using a linear support vector machine, and the corresponding classification indexes are as follows:
Figure BDA0004093462840000163
where K (x, z) is a kernel function, and K (x, z) =f (x) ×f (z), Φ (x) is a mapping function.
Common kernel functions include polynomial kernel functions, gaussian kernel functions, etc., which are respectively expressed as follows:
(1) polynomial core
Figure BDA0004093462840000164
Wherein p is the order of the polynomial; x and
Figure BDA0004093462840000165
two different variables.
(2) Gaussian kernel function
Figure BDA0004093462840000171
Wherein sigma is the standard deviation; x and
Figure BDA0004093462840000172
two different variables; exp is expressed as an exponential function.
After the classification hyperplane in the support vector machine model is obtained, the distance from the predicted point to the classification hyperplane is recorded as classification score s, and the classification score is converted into a vulnerability probability result through a Sigmoid function, so that an electromagnetic coupling parameter and effect relation model is obtained:
Figure BDA0004093462840000173
wherein: a is a slope parameter; b is an intercept parameter; setting the probability of 0.1 and the size of s when the probability is 0.9 according to the prior information to obtain the values of A and B; p(s) is a model of the relationship between electromagnetic coupling parameters and effects.
And 4, evaluating the electromagnetic pulse vulnerability of the tested electrical equipment.
After a coupling electromagnetic parameter response proxy model and an electromagnetic coupling parameter and effect relation model are established, the coupling electromagnetic parameter response proxy model and the electromagnetic coupling parameter and effect relation model are combined, the coupling electromagnetic parameter response y and the uncertainty distribution thereof at a key position are obtained by taking high-altitude electromagnetic pulses with given amplitude as input, and then an electromagnetic pulse vulnerability threshold evaluation result and a confidence interval thereof corresponding to the tested electrical equipment are obtained by taking y and the uncertainty distribution thereof as input of the electromagnetic coupling parameter and the effect relation model.
The invention provides a vulnerability assessment system of electrical equipment under the action of strong electromagnetic pulse, comprising:
the data acquisition unit is used for respectively acquiring experimental data and simulation data of the key position of the tested electrical equipment, wherein the experimental data comprise electromagnetic pulse amplitude values, electromagnetic coupling parameter measurement results of the key position and effect states; the simulation data comprise electromagnetic pulse amplitude values and electromagnetic coupling parameter simulation results at key positions;
the agent model construction unit is used for acquiring a coupling electromagnetic parameter response agent model at a key position of the tested electrical equipment based on Co-Kriging according to the acquired experimental data and simulation data;
the effect relation model construction unit is used for constructing an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine according to the obtained experimental data;
and the vulnerability assessment unit is used for combining the obtained coupling electromagnetic parameter response proxy model at the key position of the tested electrical equipment based on Co-Kriging with the electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.

Claims (8)

1. A method for evaluating vulnerability of an electrical device under the action of strong electromagnetic pulses, comprising the steps of:
step 1, vulnerability experimental data and vulnerability simulation data of a sensitive key position of detected electrical equipment are respectively obtained, wherein the vulnerability experimental data comprises electromagnetic pulse amplitude values, electromagnetic coupling parameter measurement results of the sensitive key position and effect states; the vulnerability simulation data comprise electromagnetic pulse amplitude values and electromagnetic coupling parameter simulation results at key positions;
step 2, fusing vulnerability simulation data based on Co-Kriging and on the basis of vulnerability experimental data, and establishing a coupling electromagnetic parameter response proxy model at a sensitive key position of the tested electrical equipment based on Co-Kriging;
step 3, constructing an electromagnetic coupling parameter and effect relation model at a sensitive key position of the tested electrical equipment based on the support vector machine according to the obtained vulnerability experimental data;
and step 4, combining the obtained coupling electromagnetic parameter response proxy model with the electromagnetic coupling parameter and effect relation model to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.
2. The method for evaluating vulnerability of electrical equipment under the action of strong electromagnetic pulse according to claim 1, wherein in step 1, electromagnetic topology analysis is performed on the electrical equipment to be tested, and sensitive key positions of the electrical equipment to be tested are determined.
3. The method for evaluating vulnerability of electrical equipment under the action of strong electromagnetic pulse according to claim 1, wherein in step 2, the specific method for establishing the coupled electromagnetic parameter response proxy model at the sensitive key position of the tested electrical equipment based on Co-Kriging is as follows:
setting experimental calculation data D according to the obtained vulnerability experimental data e ＝[X e ，Y e ]Wherein X is e ＝[x 1 e ，x 2 e ，...，x ne e ]，Y e ＝[y 1 e ，y 2 e ，...，y ne e ]；
Setting simulation calculation data D according to the obtained vulnerability simulation data s ＝[X s ，Y s ]Wherein X is s ＝[x 1 s ，x 2 s ，...，x ns s ]，Y s ＝[y 1 s ，y 2 s ，...，y ns s ]；
Wherein D is e Calculating data for the set experiment; d (D) s Calculating data for the set simulation; x is X e Is the electromagnetic pulse amplitude; y is Y e The electromagnetic coupling parameter measurement result is the electromagnetic coupling parameter measurement result at the sensitive key position; ne is the sample size of experimental data; x is X s Is the electromagnetic pulse amplitude; y is Y s The simulation result of electromagnetic coupling parameters at sensitive key positions is obtained; ns is the simulated data sample size;
and obtaining a coupling electromagnetic parameter response proxy model at the sensitive key position of the tested electrical equipment based on Co-Kriging according to the set experimental calculation data and simulation calculation data.
4. A method of vulnerability assessment of electrical apparatus under strong electromagnetic pulse according to claim 1 or 3, characterized in that in step 2, the coupled electromagnetic parameters respond to the mathematical expression of the proxy model:
f e (x)＝ρ s f s (x)+δ e (x)
wherein f e (x) Responding to the proxy model for the coupled electromagnetic parameters; ρ s Is a regression parameter; delta e (x) Is a smooth gaussian process.
5. The method for evaluating vulnerability of electrical equipment under the action of strong electromagnetic pulse according to claim 1, wherein in step 3, an electromagnetic coupling parameter and effect relation model based on a support vector machine at a key position of the tested electrical equipment is constructed according to the obtained experimental data, and the specific method is as follows:
set effect experimental data D e l ＝[Y e ，Z e ]Wherein D is e l Is effect experimental data; y is Y e The electromagnetic coupling parameter measurement result is the electromagnetic coupling parameter measurement result at the sensitive key position; z is Z e Is an effect state;
and obtaining an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine and the Sigmoid function.
6. The method for evaluating vulnerability of electrical equipment under strong electromagnetic pulse according to claim 1 or 5, wherein in step 3, the mathematical expression of the electromagnetic coupling parameter and effect relation model is as follows:
Figure FDA0004093462820000031
wherein A is a slope parameter; b is an intercept parameter; p(s) is an electromagnetic coupling parameter and effect relation model; s is a classification; exp is expressed as an exponential function.
7. The method for evaluating vulnerability of electrical equipment under the action of strong electromagnetic pulse according to claim 1, wherein in step 4, the obtained coupling electromagnetic parameter response proxy model and the electromagnetic coupling parameter and effect relation model are combined to obtain an electromagnetic pulse vulnerability evaluation result corresponding to the electrical equipment to be tested, and the specific method comprises the following steps:
taking the high-altitude electromagnetic pulse with a given amplitude as the input of a coupling electromagnetic parameter response proxy model to obtain coupling electromagnetic parameter response and uncertainty distribution thereof at a key position;
and taking the obtained coupling electromagnetic parameter response and uncertainty distribution thereof at the key position as input of an electromagnetic coupling parameter and effect relation model to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.
8. A vulnerability assessment system for an electrical device under strong electromagnetic pulses, comprising:
the data acquisition unit is used for respectively acquiring experimental data and simulation data of the key position of the tested electrical equipment, wherein the experimental data comprise electromagnetic pulse amplitude values, electromagnetic coupling parameter measurement results of the key position and effect states; the simulation data comprise electromagnetic pulse amplitude values and electromagnetic coupling parameter simulation results at key positions;
the agent model construction unit is used for acquiring a coupling electromagnetic parameter response agent model at a key position of the tested electrical equipment based on Co-Kriging according to the acquired experimental data and simulation data;
the effect relation model construction unit is used for constructing an electromagnetic coupling parameter and effect relation model at the key position of the tested electrical equipment based on the support vector machine according to the obtained experimental data;
and the vulnerability assessment unit is used for combining the obtained coupling electromagnetic parameter response proxy model, the electromagnetic coupling parameter and the effect relation model to obtain an electromagnetic pulse vulnerability assessment result corresponding to the tested electrical equipment.
CN202310158868.3A 2023-02-23 2023-02-23 Vulnerability assessment method and system of electrical equipment under strong electromagnetic pulse effect Pending CN116306258A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117556750A (en) * 2023-10-24 2024-02-13 广东工业大学 Method and device for quickly calculating electromagnetic coupling between wires, electronic equipment and medium

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117556750A (en) * 2023-10-24 2024-02-13 广东工业大学 Method and device for quickly calculating electromagnetic coupling between wires, electronic equipment and medium

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