Reinforced concrete equivalent electromagnetic parameter processing method for electromagnetic pulse environment time domain coupling characteristic analysis

Abstract

The invention discloses a reinforced concrete equivalent electromagnetic parameter processing method for electromagnetic pulse environment time domain coupling characteristic analysis. The method comprises the following steps: firstly, obtaining an S parameter of a reinforced concrete wall structure; then solving a relational expression among the S parameter, the reflection coefficient and the transmission coefficient; then solving a relational expression among the relative dielectric coefficient, the relative permeability, the reflection coefficient and the transmission coefficient; eliminating an intermediate variable reflection coefficient and a transmission coefficient to obtain a relational expression of the relative dielectric coefficient and the relative permeability expressed by an S parameter; and finally, fitting the obtained equivalent electromagnetic parameters into a specific mathematical polynomial form with continuous frequency. According to the method, the multi-valued problem of an equivalent electromagnetic parameter calculation result is solved through imaginary part compensation, frequency domain continuous parameter calculation on a concerned frequency band is achieved through polynomial fitting, and calculation resource consumption of a reinforced concrete complex building model can be effectively reduced; and a method is provided for carrying out time-domain electromagnetic coupling response calculation of the large-size building and the external electromagnetic pulse environment.

Description

Technical Field

[0001] The invention relates to determination of electromagnetic parameters of reinforced concrete, and in particular to a method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristic analysis of an electromagnetic pulse environment, and belongs to the technical field of electromagnetic compatibility. Background Art

[0002] With the development of pulse technology and its weaponized application, the electromagnetic environment of various equipment and systems is becoming more and more complex. In particular, the high-power electromagnetic pulse environment with extremely high field strength and spectrum generated by electromagnetic pulse weapons and broadband electromagnetic radiation sources will pose a serious threat to electronic information systems on various platforms and ground buildings.

[0003] As a non-ideal shield, buildings still play the role of shielding external high-power pulses and protecting indoor electronic equipment, and reinforced concrete structures have become the main form of ground buildings. Reinforced concrete walls separate the interior of the building from the outside. When external electromagnetic pulses hit the walls, they will be attenuated, reflected, and scattered. When external electromagnetic pulses become part of the indoor electromagnetic environment through backdoor coupling, on the one hand, they directly irradiate various electronic and electrical equipment in the room, and on the other hand, they generate interference signals with the antenna of the equipment and enter the terminal circuit or equipment, thereby generating short-term strong voltages or large currents in electronic and electrical equipment, power supply, and communication systems, which may reduce the functionality of the equipment or system at the least, or burn out the components in the equipment or system at the worst. Therefore, in order to ensure the safety of various components inside the building, it is necessary to carry out research on the time domain coupling characteristics such as the attenuation effect of reinforced concrete structures on electromagnetic pulses.

[0004] The diameter of the steel bars in the reinforced concrete wall structure is in the order of millimeters, and the scale of the building is in the order of several meters to hundreds of meters. When calculating such multi-scale research objects, in order to ensure the calculation accuracy, it is often necessary to set a smaller grid, which will result in a large number of grids and a very long calculation time. Therefore, it is of great significance to realize the equivalent modeling of reinforced concrete structures, use large grids to divide the wall buildings, and then reduce the consumption of computing resources after equivalent, which is of great significance for the calculation of the time-domain electromagnetic coupling characteristics between large-sized buildings and external electromagnetic pulses. For a long time, the research hotspots of equivalent electromagnetic parameter extraction have mainly focused on the extraction and optimization of equivalent electromagnetic parameters of honeycomb structure absorbing materials and metamaterials, but it is still of reference significance for common electromagnetic parameter extraction methods. Electromagnetic parameter extraction methods are mainly divided into two categories: resonant cavity method and network parameter method. The resonant cavity method requires the material to be tested to be placed in the resonant cavity. After the sample is placed, the electromagnetic field structure of the cavity changes. Then, by measuring the changes in the quality factor (Q value) and resonant frequency of the resonant cavity before and after the material is placed, the complex dielectric constant of the material is further calculated. It is often difficult to use the resonant cavity method for built reinforced concrete walls due to their area and thickness limitations. The network parameter method is mainly divided into the rectangular waveguide method and the free space method. The rectangular waveguide method is limited by the test platform and is mainly used for the measurement of sheet material samples. Therefore, it is not suitable for the equivalent electromagnetic parameter measurement of reinforced concrete walls. The free space method mostly uses antennas to measure the scattering parameters of materials to infer their electromagnetic parameters. It has the advantages of a wide range of applicable objects and can perform non-destructive measurements under high temperature conditions, non-uniform or composite materials, and non-contact measurement conditions. Many scholars have used the free space method test system to test the dielectric properties of materials such as concrete and glass, and some universities have also carried out simulation or field tests of the equivalent dielectric constant and conductivity of reinforced concrete walls based on the free space method. Due to the experimental conditions, most tests are completed only at discrete frequency points with large intervals. In addition, the results calculated by the free space method have multi-value problems, and special processing must be performed during the calculation. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to propose a method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis in an electromagnetic pulse environment. The present invention overcomes the multi-value problem of equivalent electromagnetic parameter calculation results through imaginary part compensation, and realizes frequency domain continuous parameter calculation in the frequency band of interest through polynomial fitting.

[0006] The technical solution of the present invention is achieved in this way:

[0007] A reinforced concrete equivalent electromagnetic parameter processing method for time domain coupling characteristic analysis of an electromagnetic pulse environment comprises the following steps:

[0008] S1, first obtain the S parameters of the reinforced concrete wall structure;

[0009] S2. Calculate the equivalent relative dielectric constant ε of the reinforced concrete wall structure using the S parameter obtained in step S1 r and relative magnetic permeability μ r ;

[0010] S3, relative dielectric constant ε r and relative magnetic permeability μ r They are fitted into continuous polynomials in the frequency domain respectively;

[0011] S4, converting the frequency domain continuous polynomial obtained in step S3 into a time domain continuous polynomial, which can be used to calculate the equivalent electromagnetic parameters in the FDTD method.

[0012] In step S1, the S parameters are obtained by simulation calculation or actual measurement; the S parameters include S 11 and S 21 ; Among them, S 11 represents the total reflection coefficient of reinforced concrete wall in free space, S 21 represents the total transmission coefficient of the wall.

[0013] Furthermore, the specific implementation process of step S2 is as follows: first, the Fresnel theorem is used to establish the relationship between the S parameter and the reflection coefficient Γ and the transmission coefficient T; then, the relative dielectric constant ε is calculated by the equivalent two-port theory. r , relative magnetic permeability μ r The relationship between the reflection coefficient Γ and the transmission coefficient T; finally, the common intermediate variables reflection coefficient Γ and transmission coefficient T in the relationship are eliminated, and the equivalent relative dielectric constant ε of the reinforced concrete wall structure expressed and calculated by the S parameter is obtained. r and relative magnetic permeability μ r ; Wherein, Γ represents the reflection coefficient of the plane wave propagating from the air to the wall boundary surface, and T represents the transmission coefficient of the plane wave between the two surfaces of the wall with a thickness of d.

[0014] The specific steps of step S2 are as follows:

[0015] S21, establish the relationship between the S parameter and the reflection coefficient Γ and the transmission coefficient T as shown in formula (1);

[0016]

[0017] Using the knowledge of geometric series summation, formula (1) can be simplified to formula (2):

[0018]

[0019] Rewriting formula (2), we can obtain the reflection coefficient Γ and transmission coefficient T represented by S parameters, as shown in formula (3),

[0020]

[0021] Where K is the intermediate variable;

[0022] S22. Establish the equivalent relative dielectric constant ε as shown in formula (4) r , relative magnetic permeability μ r The relationship between the reflection coefficient Γ and the transmission coefficient T is:

[0023]

[0024] The propagation constant The free space wave number k0 = 2π / λ0 = 2πf / c, where c is the speed of light in a vacuum;

[0025] Rewriting equation (4) yields the relative dielectric constant ε expressed in terms of reflection coefficient Γ and transmission coefficient T as shown in equation (5): r , relative magnetic permeability μ r Relational formula:

[0026]

[0027] Where Q is the intermediate variable;

[0028] S23, Substitute equation (3) into equation (5), that is, eliminate the common intermediate variables reflection coefficient Γ and transmission coefficient T in the relationship equations of steps S21 and S22, and obtain the equivalent relative dielectric constant ε represented by the S parameter r and relative magnetic permeability μ r .

[0029] Further, in step S22, according to the second term of formula (4), T = e -γd Reverse inference The imaginary part n is determined by the following steps: (a) at the initial frequency, set n = 0; (b) when the imaginary part of log(1 / T) is at a certain frequency f m (c) Repeat step b until the highest frequency is reached, and obtain the n corresponding to the highest frequency. The n corresponding to the highest frequency is used as the value of n in the imaginary part, thus achieving the unique determination of the propagation constant γ.

[0030] Further, in step S3, the relative dielectric constant ε r The process of fitting into a continuous mathematical polynomial in the frequency domain is as follows:

[0031] Assume the relative dielectric constant ε r Fitting into a frequency domain continuous polynomial is shown in formula (6):

[0032]

[0033] In the formula, ε ∞ is the relative permittivity at infinite frequency, χ(ω) is the polarizability function;

[0034] Based on the known amplitude and phase data of the relative dielectric constant corresponding to each frequency point, ε is fitted as follows: ∞ , each group a p and c p , and a p 、c p Both can be plural;

[0035] The relative dielectric constant of the electro-dispersive medium is expressed in the form of a rational function as shown in formula (8):

[0036]

[0037] In the formula, the residue r n and the extreme point p n is a real number or a conjugate complex number pair, m and e are real numbers, and N is the order of formula (8);

[0038] 1) Pole positioning

[0039] Introduce the auxiliary function σ(s) as shown in formula (9), and randomly set its initial poles Multiply σ(s) and f(s), assuming that during the iteration of the poles, σ(s)f(s) has the same pole as σ(s)

[0040]

[0041] In the formula, is the residue of the auxiliary function σ(s), r n is the residue of the function σf(s); is the pole of function σf(s), the m+se term of function σ(s) is forced to 1; z n is the zero of the auxiliary function σ(s), is the zero point of the function σf(s);

[0042] Dividing equation (9) and equation (10) yields equation (11);

[0043]

[0044] The poles of the function f(s) are the zeros of the auxiliary function σ(s);

[0045] 2) Determine relevant parameters

[0046] Multiply both ends of equation (9) by f(s) and subtract them from equation (10), and we can get the value of the parameter r.n , The linear equation of m and e is shown in formula (12):

[0047]

[0048] A set of test data f(s k )(k=1、2、…、P) and its corresponding frequency point s k Substituting into equation (12) we can get a set of linear equations, whose matrix form is:

[0049] Ax=b (13)

[0050] Through the linear least squares problem of formula (13), the residue, constant term and linear term of function f(s) are solved;

[0051] When e=0 is set, the obtained data m corresponds to ε ∞ , each group (p n ,r n ) corresponds to (a p ,c p ).

[0052] In step S4, the frequency domain continuous polynomial obtained in step S3 is converted into a time domain continuous polynomial, as shown in formula (7);

[0053]

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. On the basis of obtaining the S parameters of the building wall, the present invention adopts the free space method and overcomes the multi-value problem of the traditional method through imaginary part compensation, and finally obtains the equivalent electromagnetic parameter ε of the building wall r and μ r , so that the wall buildings can be divided by large grids, thereby reducing the consumption of computing resources after equivalence.

[0056] 2. The present invention is applicable to the equivalent modeling of reinforced concrete structures with different steel bar sizes, different numbers of steel mesh layers, and different concrete thicknesses, and has universal applicability.

[0057] 3. The present invention realizes an integrated calculation process of calculating equivalent electromagnetic parameters of reinforced concrete walls and performing FDTD equivalent modeling using the obtained electromagnetic parameters in any form. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 - Schematic diagram of the effect of plane wave vertically incident on the wall of the present invention.

[0059] Figure 2 -Schematic diagram of the single-layer reinforced concrete wall model of the present invention.

[0060] Figure 3 -Electromagnetic parameter curve of concrete according to the present invention.

[0061] Figure 4 - Schematic diagram of the imaginary part compensation method of the present invention.

[0062] Figure 5 -Equivalent electromagnetic parameter curve diagram of the present invention; wherein, (a) relative dielectric constant; (b) relative magnetic permeability.

[0063] Figure 6 - Comparison diagram of the S parameters of the wall before and after the equivalent of the present invention; wherein, (a) S11 amplitude; (b) S11 phase; (c) S21 amplitude; (d) S21 phase.

[0064] Figure 7 - The fitting result diagram of the equivalent electromagnetic parameters of the present invention; wherein, (a) equivalent ε r The amplitude of (b) the equivalent ε r phase; (c) equivalent μ r The amplitude of (d) the equivalent μ r phase.

[0065] Figure 8 - Schematic diagram of the calculation of the time domain coupling characteristics of the present invention.

[0066] Fig. 9 -The verification diagram of the time domain coupling characteristics of the wall before and after the equivalent of the present invention; wherein, (a) the time domain waveform at point P1; (b) the time domain waveform at point P2. DETAILED DESCRIPTION

[0067] The specific implementation modes of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0068] The present invention proposes a method for processing equivalent electromagnetic parameters of reinforced concrete for time-domain coupling characteristic analysis of electromagnetic pulse environment. The invention concept is as follows: firstly, the S parameters of reinforced concrete wall structure are obtained by simulation calculation or actual measurement; then, the relationship between S parameters and reflection coefficient Γ and transmission coefficient T is obtained by using Fresnel's theorem; then, the relative dielectric constant ε is obtained by using the equivalent two-port theory. r , relative magnetic permeability μ r The relationship between the reflection coefficient Γ and the transmission coefficient T; then eliminate the intermediate variables reflection coefficient Γ and transmission coefficient T, and further obtain the relative dielectric constant ε calculated by S parameters r , relative magnetic permeability μ rFinally, in order to process the equivalent electromagnetic parameters of reinforced concrete walls in FDTD, it is necessary to fit the obtained equivalent electromagnetic parameters into a specific, frequency-continuous mathematical polynomial form. This method can effectively reduce the computational resource consumption of complex reinforced concrete building models, provide a method for calculating the time-domain electromagnetic coupling response of large-scale buildings and external electromagnetic pulse environments, and provide data support for electromagnetic interference suppression of indoor electronic equipment or systems.

[0069] The specific implementation method of the present invention is as follows:

[0070] (1) Calculate equivalent electromagnetic parameters based on reinforced concrete wall S parameters;

[0071] 1) Obtain the S parameter (S) of the reinforced concrete wall through simulation calculation or actual measurement 11 , S 21 ). 11 represents the total reflection coefficient of reinforced concrete wall in free space, S 21 represents the total transmission coefficient of the wall. The effect of reinforced concrete wall on vertically incident plane waves is as follows: Figure 1 As shown. Figure 1 The relationship between S parameters, Γ and T can be obtained as shown in formula (1).

[0072]

[0073] Where Γ represents the reflection coefficient of the plane wave propagating from the air to the wall boundary surface, and T represents the transmission coefficient of the plane wave between the two surfaces of the wall with a thickness of d. Using the knowledge of geometric series summation, formula (1) is simplified to formula (2).

[0074]

[0075] Rewriting formula (2) yields the relationship between the reflection coefficient Γ, the transmission coefficient T and the S parameter, as shown in formula (3).

[0076]

[0077] Where K is an intermediate variable.

[0078] If the equivalent relative permittivity and relative magnetic permeability of reinforced concrete wall are ε r , μ r , the propagation constant The free space wave number k0 = 2π / λ0 = 2πf / c, where c is the speed of light in a vacuum. The reflection coefficient Γ and the transmission coefficient T are expressed as formula (4):

[0079]

[0080] Rewrite equation (4) to obtain the equivalent electromagnetic parameter εr , μ r The relationship between the reflection coefficient Γ and the transmission coefficient T is (5):

[0081]

[0082] Where Q is the intermediate variable.

[0083] Finally, by substituting equation (3) into equation (5), the equivalent relative dielectric constant ε can be expressed and calculated by S parameters. r , relative magnetic permeability μ r .

[0084] 2) The calculated equivalent electromagnetic parameters show multi-valued properties, which is because the propagation constant (According to formula (4), the second term T = e -γd Inversely, we can obtain that there is uncertainty in the imaginary part of log(1 / T). In fact, if the thickness of the wall to be tested and the wavelength of the electromagnetic wave satisfy d<λ, then the equivalent electromagnetic parameters of the wall to be tested have a unique solution. However, as the test frequency increases, the corresponding λ becomes shorter. To ensure that the equation has a unique solution, the thickness of the wall to be tested is required to be less than the corresponding working wavelength, while the actual thickness of the wall is often known and cannot be changed. To this end, based on the theoretical basis that the imaginary part of the propagation constant γ increases linearly with frequency, the imaginary part compensation method can be used to compensate for the imaginary part of log(1 / T) to overcome the multi-value problem. The compensation method is as follows: Figure 4 shown.

[0085] The imaginary part n of the propagation constant of the present invention is determined by the following steps: (a) when the initial frequency is very low, n = 0; (b) when the imaginary part of log (1 / T) is at a certain frequency point f m (c) Repeat step b until the highest frequency is reached, and obtain the n corresponding to the highest frequency. The n corresponding to the highest frequency is used as the value of n in the imaginary part, thus achieving the unique determination of the propagation constant γ.

[0086] (2) Mathematical expression of equivalent electromagnetic parameters based on vector matching method;

[0087] In section (1), the equivalent electromagnetic parameter ε in the frequency domain is obtained as r , μ r In order to apply the equivalent electromagnetic parameters in the finite-difference time-domain (FDTD) algorithm, it is necessary to rewrite the equivalent electromagnetic parameters into a specific, frequency-domain continuous polynomial through fitting, as shown in formula (6) (with ε r for example).

[0088]

[0089] In the formula, ε ∞is the relative permittivity when the frequency is infinite, and χ(ω) is the polarizability function.

[0090] In order to calculate the equivalent electromagnetic parameters in the subsequent FDTD method, it is necessary to further obtain the equivalent ε r The frequency domain expression is converted to the time domain, as shown in equation (7).

[0091]

[0092] Therefore, the key to fitting the dispersion electromagnetic parameters is to fit the ε based on the known amplitude and phase data of the relative dielectric constant corresponding to each frequency point. ∞ , each group a p and c p , and a p 、c p Both can be plural.

[0093] The specific steps of fitting are as follows:

[0094] The relative dielectric constant of the electro-dispersive medium is expressed in the form of a rational function as shown in formula (8):

[0095]

[0096] 1) Pole positioning

[0097] Introduce an auxiliary function σ(s) and randomly set its initial poles Multiply σ(s) and f(s), assuming that during the iteration of the poles, σ(s)f(s) has the same pole as σ(s)

[0098]

[0099] In the formula, is the residue of the auxiliary function σ(s), r n is the residue of the function σf(s); is the pole of function σf(s), the m+se term of function σ(s) is forced to 1; z n is the zero of the auxiliary function σ(s), is the zero of the function σf(s).

[0100] Dividing equation (9) and equation (10) yields equation (11).

[0101]

[0102] It can be seen that the poles of the function f(s) are the zeros of the auxiliary function σ(s). Therefore, the poles of f(s) can be further obtained by solving the eigenvalue problem of σ(s).

[0103] 2) Determine the residue, etc.

[0104] Multiply both ends of equation (9) by f(s) and subtract them from equation (10), and we can get the value of the parameter r. n , The linear equations of m and e (12):

[0105]

[0106] A set of test data f(s k )(k=1、2、…、P) and its corresponding frequency point s k Substituting into equation (12) we can get a set of linear equations, whose matrix form is:

[0107] Ax=b (13)

[0108] Therefore, the residue, constant term and linear term of the function f(s) can be solved through the linear least squares problem in the form of equation (13).

[0109] When e=0 is set, the obtained data m corresponds to ε ∞ , each group (p n ,r n ) corresponds to (a p ,c p ).

[0110] The present invention is further described below in conjunction with specific embodiments and drawings.

[0111] Taking a single-layer reinforced concrete structure as an example, the specific implementation of the present invention is demonstrated through simulation verification.

[0112] First, a single-layer reinforced concrete wall model is established, such as Figure 2 As shown. The geometric dimensions of the concrete wall are 1m*0.1m*1m, and the electromagnetic parameters of the concrete are as follows: Figure 3 As shown; the steel bar radius is 10mm, the steel bar arrangement period is 200mm, the lossy metal steel bar conductivity σ=1e6 S / m, the relative magnetic permeability μ r = 1. The S parameters of the structure are obtained by simulation, using the free space method and the imaginary part compensation (see Figure 4 ) overcomes the multi-value problem of the method and finally obtains the equivalent complex electromagnetic parameter ε of the structure in the frequency range of 20MHz-1GHz r and μ r like Figure 5 As shown, the S parameter comparison before and after the equivalent Figure 6 shown.

[0113] Subsequently, in order to model the equivalent wall parameters in the finite-difference time-domain algorithm (FDTD), the equivalent electromagnetic parameter data was polynomially fitted by the vector matching method to obtain ε r and μ r The fitting results are as follows Figure 7 The specific values ​​obtained by fitting are shown in Table 1 and Table 2.

[0114] Table 1 Equivalent ε of single-layer reinforced concrete wall r Parameter fitting table

[0115]

[0116]

[0117] Table 2 Equivalent μ of single-layer reinforced concrete wall r Parameter fitting table

[0118]

[0119] Finally, to verify the effectiveness of the algorithm, the FDTD method is used to calculate the single-layer equivalent reinforced concrete wall model of 1m*0.1m*1m when a modulated Gaussian pulse is vertically irradiated (see the schematic diagram) Figure 8 ), observe the electric field time domain waveforms of points P1 (located 0.5m to the right of the center of the wall) and P2 (located 0.8m to the right of the center of the wall), and compare the calculation results of the present invention with those of the CST three-dimensional electromagnetic field simulation software, as shown in FIG. Fig. 9 shown.

[0120] Taking the electric field time domain results calculated by CST software as a reference, the maximum relative error and mean absolute error of the electric field intensity time domain calculated by the method proposed in the present invention are expressed as formula (14) and formula (15) respectively.

[0121]

[0122] In the formula, Indicates the maximum value of the difference between the electric field value calculated by this method and the electric field value calculated by the simulation software at the same time. It indicates the calculation result of the simulation software when the difference between the electric field value calculated by this method and the simulation software is the maximum value.

[0123]

[0124] Where n represents the total number of time domain results.

[0125] The simulation errors of the electric field time domain results at observation points P1 and P2 are shown in Table 3.

[0126] Table 3 Calculation error

[0127] Observation point coordinates (m) Maximum relative error (dB) Mean absolute error (incident wave amplitude is 1.1V / m) P1[00.50] -3.1199 0.0353 P2[00.80] -2.7352 0.0315

[0128] The comparison of computing resources between the method proposed in the present invention and CST software is shown in Table 4.

[0129] Table 4 Computing resource comparison

[0130] method Number of grids Calculation time Method of the present invention 4148928 329.34seconds CST 672014012 8795.01seconds

[0131] It can be found that the equivalent electromagnetic parameter processing method for reinforced concrete used for time-domain coupling characteristic analysis of electromagnetic pulse environment proposed in the present invention has a good agreement with the calculation results of time-domain electromagnetic coupling characteristics of CST electromagnetic simulation software after equivalent, has high accuracy, and effectively saves computing resources. This shows that the present invention can effectively analyze and calculate the time-domain electromagnetic coupling response of reinforced concrete buildings under high-power electromagnetic pulse irradiation.

[0132] The present invention proposes a method for processing the equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis of electromagnetic pulse environment. The method first obtains the equivalent electromagnetic parameters (ε r and μ r ), since the equivalent electromagnetic parameters are discrete in the frequency domain, they are fitted into a specific, frequency-domain continuous polynomial form through the vector matching method, so as to facilitate the subsequent equivalent modeling of reinforced concrete walls and the analysis and calculation of time-domain electromagnetic coupling characteristics under electromagnetic pulse irradiation. This method can effectively reduce the consumption of computing resources for complex building models, and is suitable for equivalent modeling of various reinforced concrete structures (rebar size, number of steel mesh layers, concrete thickness). It has universal applicability and can provide a method for calculating the time-domain electromagnetic coupling characteristics of large-scale buildings and external electromagnetic pulse environments, and provide data support for electromagnetic interference suppression of indoor electronic equipment or systems.

[0133] Finally, it should be noted that the above examples of the present invention are merely examples for illustrating the present invention, and are not intended to limit the embodiments of the present invention. Although the applicant has described the present invention in detail with reference to the preferred embodiments, for those of ordinary skill in the art, other different forms of changes and modifications can be made based on the above description. It is impossible to list all the embodiments here. Any obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis of electromagnetic pulse environment, characterized in that: The following steps are involved: S1, first obtain the S parameters of the reinforced concrete wall structure; S2. Calculate the equivalent relative dielectric constant ε of the reinforced concrete wall structure using the S parameter obtained in step S1 r and relative magnetic permeability μ r ; S3, relative dielectric constant ε r and relative magnetic permeability μ r They are fitted into continuous polynomials in the frequency domain respectively; S4, converting the frequency domain continuous polynomial obtained in step S3 into a time domain continuous polynomial, which can be used to calculate the equivalent electromagnetic parameters in the FDTD method.

2. According to claim 1, a reinforced concrete equivalent electromagnetic parameter processing method for electromagnetic pulse environment time domain coupling characteristic analysis is characterized in that: In step S1, the S parameters are obtained by simulation calculation or actual measurement; the S parameters include S 11 and S 21 ; Among them, S 11 represents the total reflection coefficient of reinforced concrete wall in free space, S 21 represents the total transmission coefficient of the wall.

3. The method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis of electromagnetic pulse environment according to claim 2 is characterized in that: The specific implementation process of step S2 is as follows: first, the Fresnel theorem is used to establish the relationship between the S parameter and the reflection coefficient Γ and the transmission coefficient T; then, the relative dielectric constant ε and r , relative magnetic permeability μ r The relationship between the reflection coefficient Γ and the transmission coefficient T; finally, the common intermediate variables reflection coefficient Γ and transmission coefficient T in the relationship are eliminated, and the equivalent relative dielectric constant ε of the reinforced concrete wall structure expressed and calculated by the S parameter is obtained. r and relative magnetic permeability μ r ; Wherein, Γ represents the reflection coefficient of the plane wave propagating from the air to the wall boundary surface, and T represents the transmission coefficient of the plane wave between the two surfaces of the wall with a thickness of d.

4. The method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristic analysis of electromagnetic pulse environment according to claim 3 is characterized in that: The specific steps of step S2 are as follows: S21, establish the relationship between the S parameter and the reflection coefficient Γ and the transmission coefficient T as shown in formula (1); Using the knowledge of geometric series summation, formula (1) can be simplified to formula (2): Rewriting formula (2), we can obtain the reflection coefficient Γ and transmission coefficient T represented by S parameters, as shown in formula (3), Where K is the intermediate variable; S22. Establish the equivalent relative dielectric constant ε as shown in formula (4) r , relative magnetic permeability μ r The relationship between the reflection coefficient Γ and the transmission coefficient T is: The propagation constant The free space wave number k0 = 2π / λ0 = 2πf / c, where c is the speed of light in a vacuum; Rewriting equation (4) yields the relative dielectric constant ε expressed in terms of reflection coefficient Γ and transmission coefficient T as shown in equation (5): r , relative magnetic permeability μ r Relational formula: Where Q is the intermediate variable; S23, Substitute equation (3) into equation (5), that is, eliminate the common intermediate variables reflection coefficient Γ and transmission coefficient T in the relationship equations of steps S21 and S22, and obtain the equivalent relative dielectric constant ε represented by the S parameter r and relative magnetic permeability μ r .

5. The method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis of electromagnetic pulse environment according to claim 4 is characterized in that: In step S22, according to the second term of formula (4), T = e -γd Reverse deduction The imaginary part n is determined by the following steps: (a) at the initial frequency, set n = 0; (b) when the imaginary part of log(1 / T) is at a certain frequency f m If the frequency jumps at a certain point, n+1 is used to replace the n corresponding to the previous frequency; (c) Repeat step b above until the highest frequency is reached, and obtain the n corresponding to the highest frequency. The n corresponding to the highest frequency is used as the n value in the imaginary part, thereby achieving the unique determination of the propagation constant γ.

6. The method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis of electromagnetic pulse environment according to claim 1 is characterized in that: In step S3, the relative dielectric constant ε r The process of fitting into a continuous mathematical polynomial in the frequency domain is as follows: Assume the relative dielectric constant ε r Fitting into a frequency domain continuous polynomial is shown in formula (6): In the formula, ε ∞ is the relative permittivity at infinite frequency, χ(ω) is the polarizability function; Based on the known amplitude and phase data of the relative dielectric constant corresponding to each frequency point, ε is fitted as follows: ∞ , each group a p and c p , and a p 、c p Both can be plural; The relative dielectric constant of the electro-dispersive medium is expressed in the form of a rational function as shown in formula (8): In the formula, the residue r n and the extreme point p n is a real number or a conjugate complex number pair, m and e are real numbers, and N is the order of formula (8); 1) Pole positioning Introduce the auxiliary function σ(s) as shown in formula (9), and randomly set its initial poles Multiply σ(s) and f(s), assuming that during the iteration of the poles, σ(s)f(s) has the same pole as σ(s) In the formula, is the residue of the auxiliary function σ(s), r n is the residue of the function σf(s); is the pole of function σf(s), the m+se term of function σ(s) is forced to 1; z n is the zero of the auxiliary function σ(s), is the zero point of the function σf(s); Dividing equation (9) and equation (10) yields equation (11); The poles of the function f(s) are the zeros of the auxiliary function σ(s); 2) Determine relevant parameters Multiply both ends of equation (9) by f(s) and subtract them from equation (10), and we can get the value of the parameter r. n , The linear equation of m and e is shown in formula (12): A set of test data f(s k )(k=1、2、…、P) and its corresponding frequency point s k Substituting into equation (12) we can get a set of linear equations, whose matrix form is: Ax=b (13) Through the linear least squares problem of formula (13), the residue, constant term and linear term of function f(s) are solved; When e=0 is set, the obtained data m corresponds to ε ∞ , each group (p n ,r n ) corresponds to (a p ,c p ).

7. The method for processing equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristics analysis of electromagnetic pulse environment according to claim 1 is characterized in that: In step S4, the frequency domain continuous polynomial obtained in step S3 is converted into a time domain continuous polynomial, as shown in formula (7);

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