A fast and universal method for analyzing the electrical performance of rotating radome

Abstract

The invention discloses a fast and universal method for analyzing the electrical performance of a radome, which belongs to the field of radar antenna technology, and includes: interpolating the inner surface of the radome using a cubic spline formula under non-kinked boundary conditions, and meshing it; establishing an antenna radiation cylinder to determine the cylindrical equivalent source, and screening the mesh units inside it; calculating the antenna radiation near field incident on the cylindrical equivalent source area, and equating it to a quasi-plane wave; decomposing the antenna radiation near field into parallel and vertical polarized waves, and obtaining the transmission field at the outer surface of the radome based on the local plate approximation theory; using the surface integral technique to numerically integrate the tangential component of the transmission field, and obtaining the far-field radiation pattern under the conditions of loaded and unloaded radomes, and accelerating the overall calculation task using multi-threaded parallel technology, and finally realizing the rapid solution of the electrical performance parameters of the radome ...

Description

Technical Field

[0001] The invention belongs to the technical field of radar antennas and relates to a rapid and universal method for analyzing the electrical performance of a radome of a rotating body, which is applied to the rapid analysis and design of the electrical performance of an aircraft radome. Background Art

[0002] Aircraft radome is a shell component that protects the antenna system from the harsh external environment. Its existence inevitably deteriorates the radiation characteristics of the antenna. Obtaining electrical performance parameters through numerical analysis methods can effectively evaluate the impact of the radome on antenna performance, which is also an important means to guide the design of the radome.

[0003] At present, the electrical performance analysis methods of radomes can be divided into three categories: high-frequency method, low-frequency method and high-low frequency mixed method. For conventional streamlined rotating radomes, the physical optics method in the high-frequency method has an efficient computing capability that is unmatched by the other two methods, and its computing accuracy can meet the analysis and design of this type of radome. Due to the complex and diverse contours of radomes, the mathematical models corresponding to different radomes are very different, which leads to cumbersome changes in the overall calculation model of the traditional physical optics method and poor versatility; on the other hand, the influence of the electrically large size properties of such components on the calculation efficiency is not obvious in a single electrical performance analysis, but it is extremely prominent in the iterative optimization process of the radome design. Therefore, improving the versatility and computational efficiency of the traditional physical optics method is an urgent problem to be solved in order to achieve rapid analysis and design of the electrical performance of rotating radomes.

[0004] In recent years, domestic and foreign scholars have conducted theoretical and experimental research on the modeling of the mechanism of physical optics, mesh refinement, transmission coefficient, etc., and have achieved a series of research results. Gu Hao and others from the Shanghai Radio Equipment Research Institute first used the improved transmission coefficient calculation formula to obtain the initial electromagnetic flow on the surface of the antenna cover, and then applied the iterative physical optics method to the electromagnetic flow update on the surface of the dielectric material antenna cover by introducing the equivalent magnetic flow. Finally, under the preset mesh size, the electromagnetic flow on the surface of the cover was iterated by GPU acceleration to a steady state to obtain the electrical performance parameters of the antenna cover. As far as the rotating body antenna cover is concerned, the calculation accuracy of the modified iterative physical optics method proposed by this method is excessive, resulting in a loss of calculation efficiency; on the other hand, GPU acceleration and mesh subdivision planning are both in the category of solution strategies. For the improvement of calculation efficiency, this method still lacks effective research in the model mechanism. Zhang Chunbo and others from Dalian University of Technology used cubic spline functions to establish a unified mathematical expression for various streamlined rotating body antenna covers, established the antenna radiation cone with the center of the antenna aperture as the vertex, and then numerically solved the intersection of the cover surface and the antenna radiation cone, that is, the limit boundary of the effective equivalent source. The cubic spline function used in this method is established under fixed boundary conditions. When the first-order derivative of the endpoint of the radome busbar is zero (such as the tangent oval radome), the interpolation accuracy of the mathematical model will be severely reduced, resulting in the failure of the universality of the method. For a specific antenna-radome system, the article obtained a cone apex angle of 140° after a large number of calculations and adjustments, but did not give a method or empirical formula for determining the cone apex angle, resulting in a long preliminary preparation time for the electrical performance analysis or design of the radome. Summary of the invention

[0005] The invention discloses a rapid and universal method for analyzing the electrical performance of a rotating body radome, the method comprising the following steps:

[0006] S1: Establish the radome coordinate system, use the cubic spline formula to interpolate the mathematical model of the inner surface of the radome, and mesh it in three-dimensional space;

[0007] S2: establishing an antenna radiation cylinder, determining the inner surface of the radome contained in the antenna radiation cylinder as an equivalent source of the antenna radiation cylinder, and determining the grid cells inside the equivalent source of the antenna radiation cylinder;

[0008] S3: Establish a radiation model based on the amplitude and phase characteristics of the excitation antenna, calculate the antenna radiation near field incident on the cylindrical equivalent source area, and equate it to a quasi-plane wave propagating in the direction of the Poynting vector;

[0009] S4: Decompose the antenna radiation near field at each field point in the cylindrical equivalent source area into parallel polarized waves and vertical polarized waves, and obtain the transmission field at the outer surface of the radome based on the local plate approximation theory;

[0010] S5: Extract the tangential component of the transmitted field relative to the outer surface of the radome, perform three-dimensional numerical integration on it using the surface integration technique, obtain the far-field radiation pattern under loaded and unloaded radome conditions, and calculate the electrical performance parameters of the radome.

[0011] Furthermore, the cubic spline formula in step S1 is established under non-kinked boundary conditions; the grid division size in three-dimensional space is λ / 2 to λ / 3, and λ represents the working wavelength of the electromagnetic wave.

[0012] Furthermore, the antenna radiation cylinder in step S2 is established in the antenna coordinate system, and the antenna aperture boundary is vertically extended to the inner surface of the antenna cover with the antenna surface as a reference.

[0013] Furthermore, the excitation antenna radiation model in step S3 is established by using the plane angle spectrum method. In the antenna coordinate system, the radiation model of the y-polarized uniformly distributed circular aperture antenna is:

[0014]

[0015] In the formula, is the near field of the antenna radiation incident on the inner surface of the radome, (k x ,k y ,k z ) is the free space wave vector, j is the imaginary unit, and are the unit direction vectors of the y-axis and z-axis of the antenna coordinate system, respectively. x ,k y ) is the plane angular spectral density function, which is obtained by Fourier transform of the tangential component of the electric field at the antenna aperture, and the expression is:

[0016]

[0017] Where S is the antenna aperture area, E y (x′, y′) is the tangential component of the electric field at the antenna aperture.

[0018] Furthermore, the decomposition formula of the antenna radiation near field in step S4 is:

[0019]

[0020] In the formula, is the transmission field at the outer surface of the radome, φ M and θ M are the polarization angle and the incident angle at the field point M, T / / (θ M ) and T ⊥ (θ M ) are the dielectric plate corresponding to the radome at the incident angle θ MThe transmission coefficients of parallel and perpendicular polarized waves under and are the unit direction vectors of parallel and vertical polarized waves at the field point M respectively.

[0021] Further, the tangential component of the transmission field extracted in step S5 is and The expression of far-field radiation intensity is:

[0022]

[0023] In the formula, E far is the radiation field strength of the excitation antenna in the far field, k0 is the amplitude of the free space wave vector, S C is the cylindrical equivalent source area, μ0 and ε0 are the magnetic permeability and dielectric constant of free space, respectively. is the unit external normal vector at the outer surface of the radome, can be And Maxwell's equations are derived to obtain: is the unit direction vector from the origin to the far field point, and r is the distance from the origin to the far field point.

[0024] Furthermore, the acquisition of far-field radiation patterns under loaded and unloaded radome conditions, the determination of electrical performance parameters of the radome, and the calculation of loops at various levels within the method are accelerated through multi-threaded parallel technology.

[0025] In summary, the present invention provides a fast and universal method for analyzing the electrical performance of a gyroscopic radome. The method establishes an antenna radiation cylinder perpendicular to the antenna surface and extending from the antenna aperture boundary; uses the cubic spline interpolation theory under non-kinked boundary conditions to establish a universal mathematical model for gyroscopic radomes of different shapes, and determines the inner surface of the radome contained in the antenna radiation cylinder as the antenna radiation cylinder equivalent source; uses multi-threaded parallel technology to accelerate the calculation process of the traditional physical optics method in the cylindrical equivalent source area, and finally realizes the rapid solution of the electrical performance parameters of the radome. This method improves the traditional physical optics method by introducing the antenna radiation cylinder equivalent source, the cubic spline interpolation model under non-kinked boundary conditions, and the multi-threaded parallel technology, and provides a fast and universal numerical method for the analysis and design of the electrical performance of the gyroscopic radome. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A flowchart of a fast and universal method for analyzing the electrical performance of a rotating radome provided by the present invention;

[0027] Figure 2 This is a schematic diagram of establishing the coordinate system and meshing the radome;

[0028] Figure 3Establishment of antenna coordinate system and schematic diagram of antenna radiation cylindrical equivalent source;

[0029] Figure 4 This is a comparison chart between the simulated and measured values ​​of the aiming error of the antenna-cover system;

[0030] Figure 5 This is a comparison chart between the simulated and measured values ​​of the aiming error rate of the antenna-cover system. DETAILED DESCRIPTION

[0031] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0032] The process of the rapid and universal method for analyzing the electrical performance of a rotating radome provided by the present invention is as follows: Figure 1 As shown, this method can be used for the rapid analysis and design of the electrical performance of rotating radomes with different shapes;

[0033] The analytical method comprises the following steps:

[0034] S1: The center of the bottom of the radome is the origin and the height direction of the radome is z R Axis direction, establish the radome coordinate system, such as Figure 2 As shown in the figure; the cubic spline interpolation theory under non-kink boundary conditions is used to establish similar mathematical models for the inner surfaces of rotating radomes of different shapes, unifying the establishment mechanism of the overall calculation model to improve the versatility of the overall calculation model; compared with the traditional fixed boundary conditions, the non-kink boundary conditions do not need to specify the first-order derivative at the endpoint of the radome busbar, thus avoiding the phenomenon that the interpolation accuracy is seriously reduced when the first-order derivative is zero; a tangent oval radome with a slenderness ratio of 2:1 is used as the interpolation object, and the base circle diameter of the radome is 18λ (λ represents the working wavelength of the electromagnetic wave), and its expression is:

[0035]

[0036]

[0037] In the formula, (x R ,y R ,z R ) is any point on the inner surface of the radome, a i , b i 、c i and d i is the cubic spline interpolation coefficient under non-kinked boundary conditions, (z Ri ,x Ri ) is the interpolation node on the radome busbar, m i is the second-order derivative value at the i-th interpolation node, z Ri ≤z R ≤z Ri+1; In three-dimensional space, the unit side length is constrained to be in the range of λ / 2 to λ / 3 according to expression (1), and the inner surface of the radome is meshed;

[0038] S2: With the center of the antenna aperture as the origin and the antenna axis as the z-axis, establish the antenna coordinate system, such as Figure 3 As shown in the figure, a y-polarized uniformly distributed circular aperture antenna with a diameter of 14λ is used as the excitation source, and an antenna radiation cylinder extending from the antenna aperture boundary is established perpendicular to the antenna surface. The expression is:

[0039]

[0040] Where (ρ, θ, z) is the cylindrical coordinate value of any point (x, y, z) on the cylinder; by solving the intersection line between the antenna radiation cylinder and the inner surface of the radome, the inner surface of the radome contained in the intersection line is determined as the antenna radiation cylinder equivalent source to reduce the surface integration area and improve the calculation efficiency; by analyzing the positional relationship between the center of the grid unit and the intersection line, the grid unit inside the antenna radiation cylinder equivalent source is determined;

[0041] In order to facilitate the calculation of the antenna radiation field strength in the subsequent steps, the grid cells inside the cylindrical equivalent source are transformed into the antenna coordinate system using the following expression:

[0042]

[0043] Where Ω is the elevation scanning angle of the antenna, ω is the azimuth scanning angle of the antenna, and Δ Ω It is the elevation scan offset of the antenna.

[0044] S3: Based on the amplitude and phase characteristics of the excited antenna, the radiation model is established using the plane angle spectrum method to calculate the antenna radiation near field incident on the cylindrical equivalent source area and equate it to a quasi-plane wave propagating in the direction of the Poynting vector. The expression is:

[0045]

[0046] In the formula, is the near field of the antenna radiation incident on the inner surface of the radome, (k x ,k y ,k z ) is the free space wave vector, j is the imaginary unit, and are the unit direction vectors of the y-axis and z-axis of the antenna coordinate system, respectively. x ,k y ) is the plane angular spectral density function, which is obtained by Fourier transform of the tangential component of the electric field at the antenna aperture, and the expression is:

[0047]

[0048] Where S is the antenna aperture area, E y (x′, y′) is the tangential component of the electric field at the antenna aperture;

[0049] S4: Decompose the antenna radiation near field at each field point in the cylindrical equivalent source area into parallel polarized waves and vertical polarized waves, and then obtain the transmission field at the outer surface of the antenna cover based on the local plate approximation theory. The expression is:

[0050]

[0051] In the formula, is the transmission field at the outer surface of the radome, φ M and θ M are the polarization angle and the incident angle at the field point M, T / / (θ M ) and T ⊥ (θ M ) are the dielectric plate corresponding to the radome at the incident angle θ M The transmission coefficients of parallel and perpendicular polarized waves under and are the unit direction vectors of the parallel and vertical polarized waves at the field point M respectively;

[0052] S5: Extract the tangential component of the transmission field relative to the outer surface of the radome, perform three-dimensional numerical integration on it using surface integration technology, combine computer hardware resources such as cores and threads, and use multi-threaded parallel technology to accelerate the acquisition of far-field radiation patterns under loaded and unloaded radome conditions, the determination of radome electrical performance parameters, and the calculation of each level of internal loops of the method, and obtain the far-field radiation field strength E of the excitation antenna under the two conditions. far and E′ far , the expression is:

[0053]

[0054] In the formula, E far is the far-field radiation intensity of the excitation antenna under the condition of loading the radome, j is an imaginary unit, k0 is the amplitude of the free space wave vector, S C is the cylindrical equivalent source area, μ0 and ε0 are the magnetic permeability and dielectric constant of free space, respectively. is the unit external normal vector at the outer surface of the radome, can be And Maxwell's equations are derived to obtain: and is the tangential component of the transmitted field, is the unit direction vector from the origin to the far field point, and r is the distance from the origin to the far field point. By setting the material properties of the radome to free space, the far-field radiation intensity E′ of the excited antenna under the condition of no radome loading can be obtained. far .

[0055] After obtaining the far-field radiation patterns under loaded and unloaded radome conditions, the electrical performance parameters of the radome can be obtained.

[0056] Figure 4 and Figure 5 They are comparison diagrams of the simulation values ​​and the measured values ​​of the aiming error BSE and the aiming error rate BSES of the antenna-cover system. It can be seen that the electrical performance parameters simulated by the method of the present invention are in good consistency with the measured values, which verifies the effectiveness and accuracy of the method of the present invention in analyzing the electrical performance of the rotating antenna cover. The rapid and universal characteristics of the method can be derived from simple theoretical analysis, which will not be repeated here.

[0057] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A fast and universal method for analyzing the electrical performance of a rotating radome, characterized in that: The method comprises the following steps: S1: Establish the radome coordinate system, use the cubic spline formula to interpolate the mathematical model of the inner surface of the radome, and mesh it in three-dimensional space; S2: establishing an antenna radiation cylinder, determining the inner surface of the radome contained in the antenna radiation cylinder as an equivalent source of the antenna radiation cylinder, and determining the grid cells inside the equivalent source of the antenna radiation cylinder; S3: Establish a radiation model based on the amplitude and phase characteristics of the excitation antenna, calculate the antenna radiation near field incident on the cylindrical equivalent source area, and equate it to a quasi-plane wave propagating in the direction of the Poynting vector; S4: Decompose the antenna radiation near field at each field point in the cylindrical equivalent source area into parallel polarized waves and vertical polarized waves, and obtain the transmission field at the outer surface of the radome based on the local plate approximation theory; S5: Extract the tangential component of the transmitted field relative to the outer surface of the radome, perform three-dimensional numerical integration on it using the surface integration technique, obtain the far-field radiation pattern under loaded and unloaded radome conditions, and calculate the electrical performance parameters of the radome.

2. According to the rapid and universal method for analyzing the electrical performance of a rotating radome according to claim 1, it is also characterized by: The cubic spline formula is based on non-kinked boundary conditions.

3. According to claim 1, a rapid and universal method for analyzing the electrical performance of a rotating radome is characterized by: The grid division size in the three-dimensional space is λ / 2-λ / 3, where λ represents the working wavelength of the electromagnetic wave.

4. According to claim 1, a rapid and universal method for analyzing the electrical performance of a rotating radome is characterized by: The establishment of the antenna radiation cylinder is achieved by the following method: Establish the antenna coordinate system and vertically extend the antenna aperture boundary to the inner surface of the radome based on the antenna surface.

5. According to claim 1, a rapid and universal method for analyzing the electrical performance of a rotating radome is characterized by: The excitation antenna radiation model is established by plane angular spectrum method. In the antenna coordinate system, the radiation model of the y-polarized uniformly distributed circular aperture antenna is: In the formula, is the near field of the antenna radiation incident on the inner surface of the radome, (k x ,k y ,k z ) is the free space wave vector, j is the imaginary unit, and are the unit direction vectors of the y-axis and z-axis of the antenna coordinate system, respectively. x ,k y ) is the plane angular spectral density function, which is obtained by Fourier transform of the tangential component of the electric field at the antenna aperture, and the expression is: Where S is the antenna aperture area, E y (x′, y′) is the tangential component of the electric field at the antenna aperture.

6. The rapid and universal method for analyzing the electrical performance of a rotating radome according to claim 1 is further characterized by: The decomposition of the antenna radiation near field is: In the formula, is the transmission field at the outer surface of the radome, φ M and θ M are the polarization angle and the incident angle at the field point M, T / / (θ M ) and T ⊥ (θ M ) are the dielectric plate corresponding to the radome at the incident angle θ M The transmission coefficients of parallel and perpendicular polarized waves under and are the unit direction vectors of parallel and vertical polarized waves at the field point M respectively.

7. The rapid and universal method for analyzing the electrical performance of a rotating radome according to claim 1 is further characterized by: The tangential component of the transmitted field is and The expression of far-field radiation intensity is: In the formula, E far is the radiation field strength of the excitation antenna in the far field, k0 is the amplitude of the free space wave vector, S C is the cylindrical equivalent source area, μ0 and ε0 are the magnetic permeability and dielectric constant of free space, respectively. is the unit external normal vector at the outer surface of the radome, can be And Maxwell's equations are derived to obtain: is the unit direction vector from the origin to the far field point, and r is the distance from the origin to the far field point.

8. The rapid and universal method for analyzing the electrical performance of a rotating radome according to claim 1 is further characterized by: The acquisition of far-field radiation patterns under the working conditions of loaded and unloaded radomes and the determination of electrical performance parameters of the radomes are accelerated by multi-threaded parallel technology.

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