A method for processing equivalent electromagnetic parameters of reinforced concrete for time-domain coupling characteristics analysis in electromagnetic pulse environment

Abstract

The present invention discloses a method for processing equivalent electromagnetic parameters of reinforced concrete for analyzing the time-domain coupling characteristics of electromagnetic pulse environments. The method first obtains the S parameters of a reinforced concrete wall structure; then, the relationship between the S parameters and the reflection coefficient and transmission coefficient is calculated; then, the relationship between the relative permittivity and relative magnetic permeability and the reflection coefficient and transmission coefficient is calculated; then, the intermediate variables, the reflection coefficient and transmission coefficient, are eliminated to obtain a relationship expressing the relative permittivity and relative magnetic permeability using the S parameters; finally, the obtained equivalent electromagnetic parameters are fitted into a specific, frequency-continuous mathematical polynomial form. The present invention overcomes the multi-valued nature of the equivalent electromagnetic parameter calculation results through imaginary part compensation, and achieves frequency-domain continuous parameter calculation in the frequency band of interest through polynomial fitting. This method can effectively reduce the computational resource consumption of complex reinforced concrete building models, and provides a method for calculating the time-domain electromagnetic coupling response of large-scale buildings to external electromagnetic pulse environments.

Description

Technical Field

[0001] The present 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, belonging to the technical field of electromagnetic compatibility. Background Art

[0002] With the development and weaponization of pulse technology, the electromagnetic environment in which various devices and systems operate is becoming increasingly complex. In particular, high-power electromagnetic pulses (EMPs), generated by EMP weapons and broadband electromagnetic radiation sources, with their extremely high field strength and spectrum, pose a serious threat to electronic information systems on various platforms and ground structures.

[0003] Buildings, while not ideal shields, still play a role in shielding against external high-power pulses and protecting indoor electronic equipment. Reinforced concrete structures have become the predominant form of ground-based construction. Reinforced concrete walls separate the interior of a building from the outside. When external electromagnetic pulses strike these walls, they are attenuated, reflected, and scattered. When these pulses become part of the indoor electromagnetic environment through backdoor coupling, they directly impact various electronic and electrical equipment. Furthermore, they interact with the equipment's antennas, generating interference signals that enter the connected circuits or equipment. This can cause brief bursts of high voltage or current in electronic and electrical equipment, power supply systems, and communications systems. This can degrade the functionality of the equipment or system at best, or even damage components within the equipment or system. Therefore, to ensure the safety of various components within buildings, it is essential to study the time-domain coupling characteristics of reinforced concrete structures, such as their attenuation of electromagnetic pulses.

[0004] Rebar diameters in reinforced concrete walls are on the order of millimeters, while building scales range from several meters to hundreds of meters. When calculating such multi-scale objects, small meshes are often required to ensure computational accuracy, resulting in a significant number of meshes and extremely long computational times. Therefore, achieving equivalent modeling of reinforced concrete structures, using large meshes to segment the wall and building, and subsequently reducing computational resource consumption after equivalent modeling, is crucial for calculating the time-domain electromagnetic coupling characteristics of large-scale buildings with external electromagnetic pulses. Research on equivalent electromagnetic parameter extraction has historically focused on extracting and optimizing the equivalent electromagnetic parameters of honeycomb-structured absorbers and metamaterials. However, common electromagnetic parameter extraction methods still offer valuable insights. Electromagnetic parameter extraction methods are primarily classified into two categories: the resonant cavity method and the network parameter method. The resonant cavity method involves placing the material under test in a resonant cavity. After sample placement, the cavity's electromagnetic field structure changes. By measuring the changes in the cavity's quality factor (Q) and resonant frequency before and after material placement, the complex dielectric constant of the material can be further inferred. However, the resonant cavity method is often difficult to apply to existing reinforced concrete walls due to their limited area and thickness. Network parameter methods are primarily categorized into the rectangular waveguide method and the free-space method. Due to the limitations of the test platform, the rectangular waveguide method is primarily used for measuring sheet-like material samples and, therefore, is unsuitable for measuring the equivalent electromagnetic parameters of reinforced concrete walls. The free-space method, on the other hand, primarily uses antennas to measure the material's scattering parameters to infer its electromagnetic parameters. It offers the advantages of a wide range of applicability, non-destructive measurement capabilities under high-temperature conditions, for inhomogeneous or composite materials, and non-contact measurement. Many researchers have used free-space test systems to test dielectric properties such as the dielectric constant of materials like concrete and glass. Some universities have also conducted simulations or field tests of the equivalent dielectric constant and conductivity of reinforced concrete walls using the free-space method. Due to experimental constraints, most tests are performed only at widely spaced discrete frequency points. Furthermore, the results of free-space method calculations suffer from multi-valued results, requiring special processing during 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 characteristic analysis of 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 as follows:

[0007] A method for processing equivalent electromagnetic parameters of reinforced concrete 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, the relative dielectric constant ε r and relative magnetic permeability μ r They are fitted into continuous polynomials in the frequency domain;

[0011] S4. Convert 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, eliminating the common intermediate variables reflection coefficient Γ and transmission coefficient T in the relationship, 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 ; 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.

[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) is simplified to formula (2),

[0018]

[0019] Rewriting formula (2) yields 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] Where the propagation constant The free space wave number k0 = 2π / λ0 = 2πf / c, where c is the speed of light in vacuum;

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

[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 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] Furthermore, in step S22, according to the second term of formula (4), T=e -γd Reverse deduction can be obtained 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] Furthermore, 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] Where, 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 can be expressed as 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 extremes Multiply σ(s) and f(s), assuming that during the iteration of the extremes, σ(s)f(s) and σ(s) have the same extremes.

[0040]

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

[0042] Divide equation (9) and equation (10) to get 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 perform subtraction operation with equation (10), and we can get the value of the parameter r.n 、 The linear equations of m and e are 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 formula (12) we can get a set of linear equations, whose matrix form is

[0049] Ax=b (13)

[0050] By solving 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. Based on 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 parameters ε of the building wall r and μ r , which makes it possible to use large grids to segment wall buildings, 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 the 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 in 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 of the S parameters of the wall before and after the equivalent embodiment 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) equivalent ε r Phase; (c) Equivalent μ r Amplitude; (d) Equivalent μ r phase.

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

[0066] Figure 9 -Verification diagram of the time domain coupling characteristics of the wall before and after equivalent; among them, (a) time domain waveform at point P1; (b) time domain waveform at point P2. DETAILED DESCRIPTION

[0067] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0068] This invention proposes a method for processing the equivalent electromagnetic parameters of reinforced concrete for time-domain coupling characteristic analysis of electromagnetic pulse environments. The inventive concept is as follows: first, the S parameters of the reinforced concrete wall structure are obtained through simulation calculation or actual measurement; then, the Fresnel theorem is used to determine the relationship between the S parameters and the reflection coefficient Γ and the transmission coefficient T; and finally, the relative permittivity ε is calculated 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, to process the equivalent electromagnetic parameters of reinforced concrete walls in FDTD, the obtained equivalent electromagnetic parameters need to be fitted 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 to 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 parameters (S) of reinforced concrete walls through simulation calculation or actual measurement 11 , S 21 ). S 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 and Γ and T can be obtained as shown in formula (1).

[0072]

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

[0078] If the equivalent relative permittivity and relative permeability of reinforced concrete walls 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 equation (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 formula (3) into formula (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 characteristics, which is because the propagation constant (According to the second term of formula (4) T=e -γd Inversely, there is uncertainty in the imaginary part of . In fact, if the thickness of the wall to be measured and the wavelength of the electromagnetic wave satisfy d<λ, then the equivalent electromagnetic parameters of the wall to be measured 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 measured 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 Equation (6) (with ε r for example).

[0088]

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

[0090] In order to calculate the equivalent electromagnetic parameters in the 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 amplitude and phase data of the relative dielectric constant corresponding to each known 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 can be expressed as a rational function as shown in formula (8):

[0095]

[0096] 1) Pole positioning

[0097] Introduce the auxiliary function σ(s) and randomly set its initial extremes Multiply σ(s) and f(s), assuming that during the iteration of the extremes, σ(s)f(s) and σ(s) have the same extremes.

[0098]

[0099] Where, is the residue of the auxiliary function σ(s), r n is the residue of the function σf(s); is the pole of the function σf(s), and the m+se term of the function σ(s) is forced to be 1; z n is the zero point of the auxiliary function σ(s), is the zero point 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 perform subtraction operation with 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 formula (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 with reference to specific embodiments and accompanying 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 concrete electromagnetic parameters 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 parameters 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 is 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 were fitted with polynomials using 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 vertical irradiation of a modulated Gaussian pulse on a 1m*0.1m*1m single-layer equivalent reinforced concrete wall model (see the schematic diagram). Figure 8 ), observe the electric field time domain waveforms at 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 calculated by CST three-dimensional electromagnetic field simulation software, as shown in FIG. Figure 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 calculated by the method proposed in this invention are expressed as formula (14) and formula (15) respectively.

[0121]

[0122] Where, 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 moments of the 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 this 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 329.34 seconds CST 672014012 8795.01 seconds

[0131] The proposed method for processing equivalent electromagnetic parameters of reinforced concrete for analyzing the time-domain coupling characteristics of electromagnetic pulse environments shows good agreement between the calculated time-domain electromagnetic coupling characteristics and those of CST electromagnetic simulation software. This method demonstrates its effectiveness in analyzing and calculating the time-domain electromagnetic coupling response of reinforced concrete buildings exposed to high-power electromagnetic pulses (HEPs).

[0132] The present invention proposes a method for processing the equivalent electromagnetic parameters of reinforced concrete for time domain coupling characteristic analysis of electromagnetic pulse environment. The method first calculates the equivalent electromagnetic parameters (ε r and μ r ), since these equivalent electromagnetic parameters are discrete in the frequency domain, they are fitted into a specific, frequency-domain continuous polynomial form through a vector matching method, facilitating 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 computational resource consumption of complex building models and is applicable to the 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, as well as data support for electromagnetic interference suppression in indoor electronic equipment or systems.

[0133] Finally, it should be noted that the above examples of the present invention are merely illustrative of 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 preferred embodiments, those skilled in the art will appreciate that other variations and modifications can be made based on the above description. It is not possible to enumerate all embodiments here. Any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for extracting 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, the relative dielectric constant ε r and relative magnetic permeability μ r They are fitted into continuous polynomials in the frequency domain; 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; 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; 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, eliminating the common intermediate variables reflection coefficient Γ and transmission coefficient T in the relationship, 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 ; Where Γ represents the reflection coefficient of a plane wave propagating from air to the boundary surface of a wall, and T represents the transmission coefficient of a plane wave between two surfaces of a wall with a thickness of d; 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), Where, 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 All are plural; The relative dielectric constant of the electro-dispersive medium can be expressed as 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 extremes Multiply σ(s) and f(s), assuming that during the iteration of the extremes, σ(s)f(s) and σ(s) have the same extremes. Where, is the residue of the auxiliary function σ(s), r n is the residue of the function σf(s); is the pole of the function σf(s), and the m+se term of the function σ(s) is forced to be 1; z n is the zero point of the auxiliary function σ(s), is the zero point of the function σf(s); Divide equation (9) and equation (10) to get 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 perform subtraction operation with equation (10), and we can get the value of the parameter r. n 、 The linear equations of m and e are 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 formula (12) we can get a set of linear equations, whose matrix form is Ax=b (13) By solving 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 ).

2. The method for extracting equivalent electromagnetic parameters of reinforced concrete for time-domain coupling characteristic analysis of electromagnetic pulse environment according to claim 1, 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) is simplified to formula (2), Rewriting formula (2) yields 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: Where the propagation constant The free space wave number k0 = 2π / λ0 = 2πf / c, where c is the speed of light in vacuum; Rewriting formula (4) yields the relative dielectric constant ε expressed in terms of reflection coefficient Γ and transmission coefficient T as shown in formula (5): r , relative magnetic permeability μ r Relationship: 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 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 .

3. The method for extracting equivalent electromagnetic parameters of reinforced concrete for time-domain coupling characteristic analysis of electromagnetic pulse environment according to claim 2, characterized in that: In step S22, according to the second term of formula (4), T=e -γd Reverse deduction to obtain 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 , 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 value of n in the imaginary part, thus achieving the unique determination of the propagation constant γ.

4. The method for extracting equivalent electromagnetic parameters of reinforced concrete for time-domain coupling characteristic analysis of electromagnetic pulse environment according to claim 1, 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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