Interpolation-based analysis method for electrical performance interval of radome

Abstract

This invention discloses a method for analyzing the electrical performance range of an antenna radome based on interpolation. The method includes randomly generating multiple sets of thickness error and relative permittivity error distribution values ​​within the radome's thickness error range and relative permittivity error range; plotting the far-field radiation pattern of the antenna after adding the radome; extracting the variation range of electrical performance indicators from the pattern; discretizing the incident angle, polarization angle, thickness, and relative permittivity at various points on the radome; and calculating the transmission coefficient T of the main polarization component based on the discrete points. M Extract T M The amplitude and phase variation ranges are used to obtain T by interpolation. M In the sector-shaped interval formed in the complex domain, the sector-shaped interval is divided into polygonal intervals. The polygonal intervals are added together to calculate the range of changes in the far-field radiation pattern of the radome. The range of changes in the electrical performance index is extracted. It is determined whether the electrical performance index of the radome meets the preset requirements. If it does, the process ends. Otherwise, the number of segments in the sector arc is modified until the range of changes in the electrical performance index that meets the preset requirements is obtained.

Description

Technical Field

[0001] This invention belongs to the field of radar antenna technology and relates to a method for analyzing the range of electrical performance of radomes based on interpolation. Background Technology

[0002] A radome is a wave-transparent shell that protects an antenna from the influence of the natural environment. It is a covering made of natural or artificial dielectric materials, or a specially shaped electromagnetic window constructed from a dielectric shell supported by a truss. A well-designed radome, in addition to its protective, conductive, reliable, concealing, and decorative functions, can extend the lifespan of all components of the system, reduce lifespan and operating costs, simplify design, reduce maintenance costs, ensure the accuracy of the antenna surface and position, and create a good working environment for antenna operators. However, radomes can also affect the electromagnetic radiation of an ideal antenna, thus reducing its electrical performance.

[0003] Furthermore, due to manufacturing errors during processing and the influence of external environmental factors during service, the design parameters of the radome will always deviate to some extent, causing the electrical performance of the radome to deviate from the design value and introducing a certain degree of uncertainty. To ensure the normal and reliable operation of the radome, it is necessary to effectively and accurately predict the uncertainty of the radome's electrical performance under the influence of error factors.

[0004] From the perspective of geometric optics, the amplitude and phase of electromagnetic waves are affected as they pass through a radome. The transmission coefficient is used to characterize the influence of the radome. Since the transmission coefficient of a radome is related to multiple parameters such as its shape, thickness, and dielectric constant, and the relationship is complex, accurately assessing the range of the radome's transmission coefficient and electrical performance under the influence of errors is an extremely difficult problem.

[0005] Existing technologies all start from deriving the analytical expression of the radome transmission coefficient, giving a strict range of some parameters of the radome transmission coefficient. Since the expression of the transmission coefficient is extremely complex, the range of the analytical expression of the transmission coefficient is often very coarse, and can only obtain the range of a certain term in the expression. The overall problem of expansion still exists, resulting in insufficient range accuracy. Summary of the Invention

[0006] The purpose of this invention is to provide a method for analyzing the electrical performance range of radomes based on interpolation. By combining traversal and interpolation, the accurate range of the radome's transmission coefficient is obtained, thereby improving the accuracy of the analysis of the electrical performance range of radomes.

[0007] The technical solution adopted in this invention is an interpolation-based method for analyzing the electrical performance range of an antenna radome, comprising the following steps:

[0008] Step 1: Randomly generate multiple sets of thickness error and relative permittivity error distribution values ​​within the range of radome thickness error and relative permittivity error;

[0009] Step 2: Combine the structural and material parameters of the radome to calculate the far field generated by the aperture field through the radome, draw the far field radiation pattern of the antenna after the radome is added, and extract the variation range of the electrical performance index from the figure.

[0010] Step 3: Discretize the incident angle, polarization angle, thickness, and relative permittivity at various points on the radome;

[0011] Step 4: Calculate the transmission coefficient of the main polarization component based on the incident angle, polarization angle, thickness, and discrete points of the relative permittivity obtained in Step 3. ,extract The range of amplitude and phase variation;

[0012] Step 5, according to The amplitude and phase variation ranges are obtained using interpolation. The sector-shaped interval formed in the complex field;

[0013] Step 6, The resulting sector is divided into polygonal regions. The order of the endpoints of the polygonal regions is adjusted so that the starting point has the smallest imaginary part in the complex field, and all points are arranged in a counterclockwise order around the original sector.

[0014] Step 7: Use Minkowski summation to add up the polygonal intervals, calculate the range of changes in the far-field radiation pattern of the radome, and extract the range of changes in the electrical performance indicators.

[0015] Step 8: Compare the range of changes in the radome's electrical performance indicators extracted in Step 2 and Step 7 to determine whether the radome's electrical performance indicators meet the preset requirements. If they do, the analysis process of the radome's electrical performance range ends. Otherwise, modify the number of segments in the sector arc and repeat Steps 6 to 8 until the range of changes in electrical performance indicators that meet the preset requirements is obtained.

[0016] Step 1 specifically includes the following steps:

[0017] Step 1.1: Establish the geometric model of the radome based on its structural features, and mesh the model, setting the mesh edge length to [value missing]. ,in Let be the wavelength of the antenna, and let the number of grids be . N；

[0018] Step 1.2, assuming the thickness error range of the radome is... Randomly generated within this range according to a uniform distribution N A random number;

[0019] Step 1.3, assuming the relative permittivity error range of the radome is... Randomly generated within this range according to a uniform distribution N A random number;

[0020] Step 1.4, repeat steps 1.2 and 1.3 multiple times to obtain multiple sets of random thickness error and relative permittivity error distribution values ​​corresponding to the number of radome grids.

[0021] Step 2 specifically includes the following steps:

[0022] Step 2.1, along the height of the radome, with the center of the bottom surface of the radome as the origin and the bottom surface as... Establish a coordinate system on a plane The height of the cover is along the z-direction, where For the antenna aperture surface, The aperture surface is visible through the radome;

[0023] Step 2.2: Calculate the transmission coefficient of the radome based on its structural and material parameters. And based on the known antenna aperture field Calculate the aperture field through the radome. ;

[0024] Step 2.3, according to Calculate the far field of the radome antenna Plot the far-field radiation pattern and extract the gain from the far-field radiation pattern. G 1. Main beam position B 1 and the level of the first sidelobe S 1. Range of variation of electrical performance indicators.

[0025] Step 2.2 specifically includes the following steps:

[0026] Step 2.2.1, for the coordinate system established in Step 2.1, ... x , y , z The directional components are represented by i, j, and k, respectively;

[0027] Step 2.2.2: Based on the geometry of the radome and the incident aperture field, calculate the incident angle at each point on the radome. and polarization angle The angle between the incident ray of the electromagnetic wave and the normal at the point of incidence is denoted as the angle of incidence. The angle between the polarization direction of the electromagnetic wave and the incident plane is denoted as the polarization angle. The incident plane is formed by the electromagnetic wave incident ray and the normal at the incident point;

[0028] Step 2.2.3: Set the loss tangent of the radome material to be positive. The value is 0, depending on the thickness of the radome at various points. Relative permittivity Calculate the transmission coefficient of the horizontal polarization component at each point on the radome. and vertical polarization component transmission coefficient :

[0029]

[0030]

[0031] in, , , , , , , , , , , These parameters are all intermediate variables. , They are respectively , The modulus, , They are respectively , The phase;

[0032] Step 2.2.4, based on the transmission coefficient of the horizontal polarization component and vertical polarization component transmission coefficient The transmission coefficient of the principal polarization component is obtained:

[0033]

[0034] in, As an intermediate variable;

[0035] Step 2.2.5, calculate the aperture field through the radome: .

[0036] Step 2.3 specifically includes the following steps:

[0037] Step 2.3.1, based on the aperture field through the radome Calculate the far field generated by the aperture field through the radome. :

[0038]

[0039] in, , It is an observation point P In a rectangular coordinate system spherical coordinate angles in Let be the free space propagation constant. , It is the wavelength of the antenna. , Indicates the antenna's operating frequency. Represents the speed of light;

[0040] Step 2.3.2, based on the far field generated by the aperture field through the radome. Plot the far-field radiation pattern of the antenna with the radome, and extract the gain from the radiation pattern. G 1. Main beam position B 1 and the level of the first sidelobe S 1. Range of variation of electrical performance indicators.

[0041] Step 4 specifically includes the following steps:

[0042] Step 4.1: Based on the incident angle, thickness and discrete values ​​of relative permittivity obtained in Step 3, calculate the horizontal polarization component transmission coefficient and the vertical polarization component transmission coefficient at each point on the radome.

[0043] Step 4.2: Using the discrete points of polarization angle obtained in Step 3, and the transmission coefficients of the horizontal and vertical polarization components at various points on the radome obtained in Step 4.1, calculate the transmission coefficient of the main polarization component of the radome, and extract its amplitude variation range. and the range of phase changes .

[0044] Step 5 specifically includes the following steps:

[0045] Step 5.1: Using the interp2 function, with the incident angle and polarization angle as interpolation parameters, respectively... Lower bound of amplitude range Upper bound of amplitude range Lower bound of phase interval Upper bound of phase interval Perform interpolation;

[0046] Step 5.2, convert the transmission coefficient of the main polarization component in the far field. The amplitude of the sector interval formed in the formula The range of change is denoted as Phase The range of change is denoted as The details are as follows:

[0047]

[0048]

[0049]

[0050]

[0051] in , , The area of ​​the divided grid cells;

[0052] Step 5.3, at various points on the radome The range of amplitude variation formed and phase change range It constitutes in complex space The sector-shaped interval.

[0053] Step 6 specifically includes the following steps:

[0054] Step 6.1, the four endpoints of the sector formed by the transmission coefficient of the main polarization component. , , and coordinates and , and , and , and as follows:

[0055] ,

[0056] ,

[0057] ,

[0058] ,

[0059] in and , and The corresponding part is the arc of a fan shape;

[0060] Step 6.2, Endpoint and between, and between, and Connect them with straight lines, endpoints and The phase range of the sector is divided into 10 equal parts by connecting the segments of the arc with tangents that surround the arc. Each part corresponds to a segment, thus representing the sector as a polygonal region. This polygonal region is the polygonal region formed by the transmission coefficient of the main polarization component.

[0061] Step 6.3: Adjust the order of the endpoints of the polygonal interval in Step 6.2 so that the starting point has the smallest imaginary part in the complex domain, and all points are arranged in a counterclockwise order around the original sector.

[0062] Step 7 specifically includes the following steps:

[0063] Step 7.1: Perform polygon summation on each polygon interval of the transmission coefficient of the main polarization component at each point of the radome obtained in Step 6 to obtain the polygon interval of the field value at each discrete point in the far-field radiation pattern.

[0064] Step 7.2: Based on the polygonal intervals of field values ​​at each discrete point in the far-field radiation pattern, calculate the amplitude at each endpoint of the polygonal interval, extract the maximum value to form the supremum of the far-field radiation pattern, and extract the minimum value to form the infimum of the far-field radiation pattern, thereby obtaining the variation range of the far-field radiation pattern. Finally, extract the gain from this range. G 2. Main beamwidth B 2 and the level of the first sidelobe S The range of variation for 2.

[0065] Step 7.1 specifically includes the following steps:

[0066] Step 7.1.1, for any two sets of polygon endpoints, denoted as... and The endpoints of the synthesized polygon are denoted as Take temporary variable ;

[0067] Step 7.1.2, , ,in and The endpoints of the synthesized polygon are respectively of x and y coordinate, and They are respectively of x and y coordinate, and They are respectively of x and y coordinate;

[0068] Step 7.1.3, calculate from point Point of view The angle between the vector and the positive direction of the x-axis And calculate from point point to The angle between the vector and the positive direction of the x-axis ,like Then let Otherwise ;

[0069] Step 7.1.4, if and If the summation process ends, then the summation process ends; otherwise, let Proceed to step 7.1.2.

[0070] The beneficial effect of this invention is that it uses interpolation to analyze the range of transmission coefficient variation under the error of radome thickness and relative permittivity, and uses Minkowski summation of polygonal intervals to analyze the far field, thereby improving the accuracy of interval analysis. Attached Figure Description

[0071] Figure 1 This is a flowchart illustrating the interpolation-based range analysis method for antenna radome electrical performance of the present invention.

[0072] Figure 2 This is a schematic diagram illustrating the relationship between the antenna and the radome in this invention;

[0073] Figure 3 This is a comparison chart of the far-field radiation patterns obtained by the method of this invention and the traditional method. Detailed Implementation

[0074] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0075] This invention provides a range analysis method for the electrical performance of an antenna radome based on interpolation, referring to... Figure 1 This includes the following steps:

[0076] Step 1: Randomly generate 1000 sets of thickness error and relative permittivity error distribution values ​​within the range of radome thickness error and relative permittivity error;

[0077] Step 1 specifically includes the following steps:

[0078] Step 1.1: Establish the geometric model of the radome based on its structural features, and mesh the model, setting the mesh edge length to [value missing]. ,in Let be the wavelength of the antenna, and let the number of grids be . N；

[0079] Step 1.2, assuming the thickness error range of the radome is... Randomly generated within this range according to a uniform distribution N A random number;

[0080] Step 1.3, assuming the relative permittivity error range of the radome is... Randomly generated within this range according to a uniform distribution N A random number;

[0081] Step 1.4: Repeat steps 1.2 and 1.3 1000 times to obtain 1000 sets of random thickness error and relative permittivity error distribution values ​​corresponding to the number of radome grids.

[0082] Step 2: Combine the structural and material parameters of the radome to calculate the far field generated by the aperture field through the radome, draw the far field radiation pattern of the antenna after the radome is added, and extract the variation range of the electrical performance index from the figure.

[0083] Step 2 specifically includes the following steps:

[0084] Step 2.1, along the height of the radome, with the center of the bottom surface of the radome as the origin and the bottom surface as... Establish a coordinate system on a plane The height of the cover is along the z-direction, where For the antenna aperture surface, For the aperture surface behind the radome (see Figure 2 );

[0085] Step 2.2: Based on the structural and material parameters of the radome, calculate the transmission coefficient of the radome using transmission line theory. And based on the known antenna aperture field Calculate the aperture field through the radome. ;

[0086] Step 2.2 specifically includes the following steps:

[0087] Step 2.2.1, for the coordinate system established in Step 2.1, ... x , y , z The directional components are represented by i, j, and k, respectively;

[0088] Step 2.2.2: Based on the geometry of the radome and the incident aperture field, calculate the incident angle at each point on the radome. and polarization angle The angle between the incident ray of the electromagnetic wave and the normal at the point of incidence is denoted as the angle of incidence. The angle between the polarization direction of the electromagnetic wave and the incident plane is denoted as the polarization angle. The incident plane is formed by the electromagnetic wave incident ray and the normal at the incident point;

[0089] Step 2.2.3: Set the loss tangent of the radome material to be positive. The value is 0, depending on the thickness of the radome at various points. Relative permittivity Calculate the transmission coefficient of the horizontal polarization component at each point on the radome. and vertical polarization component transmission coefficient :

[0090]

[0091]

[0092] in, , , , , , , , , , , These parameters are all intermediate variables. , They are respectively , The modulus, , They are respectively , The phase;

[0093] Step 2.2.4, based on the transmission coefficient of the horizontal polarization component and vertical polarization component transmission coefficient The transmission coefficient of the principal polarization component is obtained:

[0094]

[0095] in, As an intermediate variable;

[0096] Step 2.2.5, calculate the aperture field through the radome: .

[0097] Step 2.3, according to Calculate the far field of the radome antenna Plot the far-field radiation pattern and extract the gain from the far-field radiation pattern. G 1. Main beam position B 1 and the level of the first sidelobe S 1. Range of variation of electrical performance indicators.

[0098] Step 2.3 specifically includes the following steps:

[0099] Step 2.3.1, based on the aperture field through the radome Calculate the far field generated by the aperture field through the radome. :

[0100]

[0101] in, , It is an observation point P In a rectangular coordinate system spherical coordinate angles in Let be the free space propagation constant. , It is the wavelength of the antenna. , Indicates the antenna's operating frequency. Represents the speed of light;

[0102] Step 2.3.2, based on the far field generated by the aperture field through the radome. Plot the far-field radiation pattern of the antenna with the radome, and extract the gain from the radiation pattern. G 1. Main beam position B 1 and the level of the first sidelobe S 1. Range of variation of electrical performance indicators.

[0103] Step 3: Discretize the incident angle, polarization angle, thickness, and relative permittivity at various points on the radome. Based on the range of incident angle and polarization angle values ​​at each point on the radome, obtain discrete values ​​of the incident angle and polarization angle at each point using a step size of 1°. Then, based on the range of the radome's thickness and relative permittivity, discretize the thickness using a step size of 0.01 mm, and discretize the relative permittivity using a step size of 0.01 mm, obtaining a set of discrete thickness values ​​and relative permittivity values.

[0104] Step 4: Calculate the transmission coefficient of the main polarization component based on the incident angle, polarization angle, thickness, and discrete points of the relative permittivity obtained in Step 3. ,extract The range of amplitude and phase variation;

[0105] Step 4 specifically includes the following steps:

[0106] Step 4.1: Based on the incident angle, thickness and discrete values ​​of relative permittivity obtained in Step 3, use transmission line theory and the formula in Step 2.2.3 to calculate the horizontal polarization component transmission coefficient and the vertical polarization component transmission coefficient at each point on the radome.

[0107] Step 4.2: Using the discrete points of polarization angle obtained in Step 3, and the transmission coefficients of the horizontal and vertical polarization components at various points on the radome obtained in Step 4.1, calculate the transmission coefficient of the main polarization component of the radome, and extract its amplitude variation range. and the range of phase changes .

[0108] Step 5, according to The amplitude and phase variation ranges are obtained using interpolation. The sector-shaped interval formed in the complex field;

[0109] Step 5 specifically includes the following steps:

[0110] Step 5.1, in step 4, yielded discrete points of the incident angle and polarization angle. The amplitude and phase vary within a certain range, but the incident angle at each point on the radome is continuously distributed. Therefore, two-dimensional interpolation is required to calculate the incident angle from discrete points. Interpolation yields the values ​​at various points on the radome. The interp2 function is used, with the incident angle and polarization angle as interpolation parameters, to perform interpolation on... Lower bound of amplitude range Upper bound of amplitude range Lower bound of phase interval Upper bound of phase interval Perform interpolation;

[0111] Step 5.2, convert the transmission coefficient of the main polarization component in the far field. The amplitude of the sector interval formed in the formula The range of change is denoted as Phase The range of change is denoted as The details are as follows:

[0112]

[0113]

[0114]

[0115]

[0116] in , , The area of ​​the divided grid cells;

[0117] Step 5.3, at various points on the radome The range of amplitude variation formed and phase change range It constitutes in complex space The sector-shaped interval.

[0118] Step 6, The resulting sector is divided into polygonal regions. The order of the endpoints of the polygonal regions is adjusted so that the starting point has the smallest imaginary part in the complex domain, and all points are arranged in a counterclockwise order around the original sector.

[0119] Step 6 specifically includes the following steps:

[0120] Step 6.1, the four endpoints of the sector formed by the transmission coefficient of the main polarization component. , , and coordinates and , and , and , and as follows:

[0121] ,

[0122] ,

[0123] ,

[0124] ,

[0125] in and , and The corresponding part is the arc of a fan shape;

[0126] Step 6.2, Endpoint and between, and between, and Connect them with straight lines, endpoints and The phase range of the sector is divided into 10 equal parts by connecting the segments of the arc with tangents that surround the arc. Each part corresponds to a segment, thus representing the sector as a polygonal region. The polygonal region is the polygonal region formed by the transmission coefficient of the main polarization component.

[0127] Step 6.3: Adjust the order of the endpoints of the polygonal interval in Step 6.2 so that the starting point has the smallest imaginary part in the complex domain, and all points are arranged in a counterclockwise order around the original sector.

[0128] Step 7: Use Minkowski summation to add up the polygonal intervals, calculate the range of changes in the far-field radiation pattern of the radome, and extract the range of changes in the electrical performance indicators.

[0129] Step 7 specifically includes the following steps:

[0130] Step 7.1: Perform polygon summation on each polygon interval of the transmission coefficient of the main polarization component at each point of the radome obtained in Step 6 to obtain the polygon interval of the field value at each discrete point in the far-field radiation pattern.

[0131] Step 7.1 specifically includes the following steps:

[0132] Step 7.1.1, for any two sets of polygon endpoints, denoted as... and The endpoints of the synthesized polygon are denoted as Take temporary variable ;

[0133] Step 7.1.2, , ,in and The endpoints of the synthesized polygon are respectively of x and y coordinate, and They are respectively of x and y coordinate, and They are respectively of x and y coordinate;

[0134] Step 7.1.3, calculate from point Point of view The angle between the vector and the positive direction of the x-axis And calculate from point point to The angle between the vector and the positive direction of the x-axis ,like Then let Otherwise ;

[0135] Step 7.1.4, if and If the summation process ends, then the summation process ends; otherwise, let Proceed to step 7.1.2.

[0136] Step 7.2: Based on the polygonal intervals of field values ​​at each discrete point in the far-field radiation pattern, calculate the amplitude at each endpoint of the polygonal interval, extract the maximum value to form the supremum of the far-field radiation pattern, and extract the minimum value to form the infimum of the far-field radiation pattern, thereby obtaining the variation range of the far-field radiation pattern. Finally, extract the gain from this range. G 2. Main beamwidth B 2 and the level of the first sidelobe S The range of variation for 2.

[0137] Step 8: Compare the range of changes in the radome's electrical performance indicators extracted in Step 2 and Step 7 to determine whether the radome's electrical performance indicators meet the preset requirements. That is, the range of changes in the radome's electrical performance indicators obtained in Step 7 is included in the range obtained in Step 2. If it meets the requirements, the radome's electrical performance analysis process ends. Otherwise, modify the number of segments in the sector arc and repeat Steps 6 to 8 until the range of changes in electrical performance indicators that meets the preset requirements is obtained.

[0138] The invention is further illustrated by simulation experiments:

[0139] 1. Simulation parameters

[0140] A spherical radome, 1 meter in diameter, is made of fiberglass with a relative permittivity of 4, a loss tangent of 0.015, and a wall thickness of 7 mm. The antenna aperture inside the radome is 0.5 meters, operating at a frequency of 10 GHz. Its aperture field is of equal amplitude and in phase distribution, and the antenna scanning angle is set to 0°, with the antenna pointing upwards towards the top of the radome. The radome thickness error is [-0.1 mm, 0.1 mm], and the relative permittivity error is mainly [-0.1, 0.1].

[0141] 2. Simulation Content and Results

[0142] The electrical performance of the above-mentioned radome under the influence of thickness error and relative permittivity error was analyzed using this invention. The simulation results are as follows: Figure 3 As shown in Table 1, the simulation data is as follows.

[0143] Figure 3 In this context, "not using interpolation" represents the far-field radiation pattern interval obtained by the interval analysis method without interpolation, "using interpolation" represents the far-field radiation pattern interval obtained by the interval analysis method based on interpolation provided by this invention, and "random error" represents multiple sets of far-field radiation patterns obtained by repeated calculations with the introduction of random error distribution.

[0144] Table 1. System electrical performance index range

[0145]

[0146] Combining Table 1 and Figure 3 It can be seen that, compared with the traditional interval analysis method without interpolation, the interval analysis method based on interpolation of this invention significantly reduces the far-field radiation pattern interval of the radome and the electrical performance interval of the radome. Both are closer to the electrical performance interval obtained by the random method. Therefore, when there is an error in the radome thickness and relative permittivity, this method can provide more accurate electrical performance prediction results.

[0147] The simulation data above demonstrates that the present invention can significantly improve the accuracy of the predicted results of the radome's electrical performance when there are errors in thickness and relative permittivity, thus providing an effective basis for radome design.

Claims

1. A method for analyzing the electrical performance range of an antenna radome based on interpolation, characterized in that, Includes the following steps: Step 1: Randomly generate multiple sets of thickness error and relative permittivity error distribution values ​​within the range of radome thickness error and relative permittivity error; Step 2: Combine the structural and material parameters of the radome to calculate the far field generated by the aperture field through the radome, draw the far field radiation pattern of the antenna after the radome is added, and extract the variation range of the electrical performance index from the figure. Step 3: Discretize the incident angle, polarization angle, thickness, and relative permittivity at various points on the radome; Step 4: Calculate the transmission coefficient of the main polarization component based on the incident angle, polarization angle, thickness, and discrete points of the relative permittivity obtained in Step 3. ,extract The range of amplitude and phase variation; Step 5, according to The amplitude and phase variation ranges are obtained using interpolation. The sector-shaped interval formed in the complex field; Step 6, The resulting sector is divided into polygonal regions. The order of the endpoints of the polygonal regions is adjusted so that the starting point has the smallest imaginary part in the complex domain, and all points are arranged in a counterclockwise order around the original sector. Step 7: Use Minkowski summation to add up the polygonal intervals, calculate the range of changes in the far-field radiation pattern of the radome, and extract the range of changes in the electrical performance indicators. Step 8: Compare the range of changes in the radome's electrical performance indicators extracted in Step 2 and Step 7 to determine whether the radome's electrical performance indicators meet the preset requirements. If they do, the analysis process of the radome's electrical performance range ends. Otherwise, modify the number of segments in the sector arc and repeat Steps 6 to 8 until the range of changes in electrical performance indicators that meet the preset requirements is obtained.

2. The method for analyzing the electrical performance range of an antenna radome based on interpolation according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Establish the geometric model of the radome based on its structural features, and mesh the model, setting the mesh edge length to [value missing]. ,in Let be the wavelength of the antenna, and let the number of grids be . N； Step 1.2, assuming the thickness error range of the radome is... Randomly generated in a uniform distribution within the specified range N A random number; Step 1.3, assuming the relative permittivity error range of the radome is... Randomly generated in a uniform distribution within the specified range N A random number; Step 1.4, repeat steps 1.2 and 1.3 multiple times to obtain multiple sets of random thickness error and relative permittivity error distribution values ​​corresponding to the number of radome grids.

3. The interpolation-based radome electrical performance range analysis method according to claim 2, characterized in that, Step 2 specifically includes the following steps: Step 2.1, along the height of the radome, with the center of the bottom surface of the radome as the origin and the bottom surface as... Establish a coordinate system on a plane The height of the cover is along the z-direction, where For the antenna aperture surface, The aperture surface is visible through the radome; Step 2.2: Calculate the transmission coefficient of the radome based on its structural and material parameters. And based on the known antenna aperture field Calculate the aperture field through the radome. ; Step 2.3, according to Calculate the far field of the radome antenna Plot the far-field radiation pattern and extract the gain from the far-field radiation pattern. G 1. Main beam position B 1 and the level of the first sidelobe S 1. Range of variation of electrical performance indicators.

4. The interpolation-based radome electrical performance range analysis method according to claim 3, characterized in that, Step 2.2 specifically includes the following steps: Step 2.2.1, for the coordinate system established in Step 2.1, ... x , y , z The directional components are represented by i, j, and k, respectively; Step 2.2.2: Based on the geometry of the radome and the incident aperture field, calculate the incident angle at each point on the radome. and polarization angle The angle between the incident ray of the electromagnetic wave and the normal at the point of incidence is denoted as the angle of incidence. The angle between the polarization direction of the electromagnetic wave and the incident plane is denoted as the polarization angle. The incident plane is formed by the electromagnetic wave incident ray and the normal at the incident point; Step 2.2.3: Set the loss tangent of the radome material to be positive. The value is 0, depending on the thickness of the radome at various points. Relative permittivity Calculate the transmission coefficient of the horizontal polarization component at each point on the radome. and vertical polarization component transmission coefficient : in, , , , , , , , , , , These parameters are all intermediate variables. , They are respectively , The modulus, , They are respectively , The phase; Step 2.2.4, based on the transmission coefficient of the horizontal polarization component and vertical polarization component transmission coefficient The transmission coefficient of the principal polarization component is obtained: in, As an intermediate variable; Step 2.2.5, calculate the aperture field through the radome: .

5. The interpolation-based radome electrical performance range analysis method according to claim 4, characterized in that, Step 2.3 specifically includes the following steps: Step 2.3.1, based on the aperture field through the radome Calculate the far field generated by the aperture field through the radome. : in, , It is an observation point P In a rectangular coordinate system spherical coordinate angles in Let be the free space propagation constant. , It is the wavelength of the antenna. , Indicates the antenna's operating frequency. Represents the speed of light; Step 2.3.2, based on the far field generated by the aperture field through the radome. Plot the far-field radiation pattern of the antenna with the radome, and extract the gain from the radiation pattern. G 1. Main beam position B 1 and the level of the first sidelobe S 1. Range of variation of electrical performance indicators.

6. The interpolation-based radome electrical performance range analysis method according to claim 5, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Based on the incident angle, thickness and discrete values ​​of relative permittivity obtained in Step 3, calculate the horizontal polarization component transmission coefficient and the vertical polarization component transmission coefficient at each point on the radome. Step 4.2: Using the discrete points of polarization angle obtained in Step 3, and the transmission coefficients of the horizontal and vertical polarization components at various points on the radome obtained in Step 4.1, calculate the transmission coefficient of the main polarization component of the radome, and extract its amplitude variation range. and the range of phase changes .

7. The method for analyzing the electrical performance range of a radome based on interpolation according to claim 6, characterized in that, Step 5 specifically includes the following steps: Step 5.1: Using the interp2 function, with the incident angle and polarization angle as interpolation parameters, respectively... Lower bound of amplitude range Upper bound of amplitude range Lower bound of phase interval Upper bound of phase interval Perform interpolation; Step 5.2, convert the transmission coefficient of the main polarization component in the far field. The amplitude of the sector interval formed in the formula The range of change is denoted as Phase The range of change is denoted as The details are as follows: in , , The area of ​​the divided grid cells; Step 5.3, at various points on the radome The range of amplitude variation formed and phase change range It constitutes in complex space The sector-shaped interval.

8. The method for analyzing the electrical performance range of a radome based on interpolation according to claim 7, characterized in that, Step 6 specifically includes the following steps: Step 6.1, the four endpoints of the sector formed by the transmission coefficient of the main polarization component. , , and coordinates and , and , and , and as follows: ， ， ， ， in and , and The corresponding part is the arc of a fan shape; Step 6.2, Endpoint and between, and between, and Connect them with straight lines, endpoints and The phase range of the sector is divided into 10 equal parts by connecting the segments of the arc with tangents that surround the arc. Each part corresponds to a line segment, thus representing the sector with a polygonal interval. The polygonal interval is the polygonal interval formed by the transmission coefficient of the main polarization component. Step 6.3: Adjust the order of the endpoints of the polygonal interval in Step 6.2 so that the starting point has the smallest imaginary part in the complex domain, and all points are arranged in a counterclockwise order around the original sector.

9. The method for analyzing the electrical performance range of a radome based on interpolation according to claim 8, characterized in that, Step 7 specifically includes the following steps: Step 7.1: Perform polygon summation on each polygon interval of the transmission coefficient of the main polarization component at each point of the radome obtained in Step 6 to obtain the polygon interval of the field value at each discrete point in the far-field radiation pattern. Step 7.2: Based on the polygonal intervals of field values ​​at each discrete point in the far-field radiation pattern, calculate the amplitude at each endpoint of the polygonal interval, extract the maximum value to form the supremum of the far-field radiation pattern, and extract the minimum value to form the infimum of the far-field radiation pattern, thereby obtaining the variation range of the far-field radiation pattern. Finally, extract the gain from this range. G 2. Main beamwidth B 2 and the level of the first sidelobe S The range of variation for 2.

10. The interpolation-based radome electrical performance range analysis method according to claim 9, characterized in that, Step 7.1 specifically includes the following steps: Step 7.1.1, for any two sets of polygon endpoints, denoted as... and The endpoints of the synthesized polygon are denoted as Take temporary variable ; Step 7.1.2, , ,in and The endpoints of the synthesized polygon are respectively of x and y coordinate, and They are respectively of x and y coordinate, and They are respectively of x and y coordinate; Step 7.1.3, calculate from point Point of view The angle between the vector and the positive direction of the x-axis And calculate from point point to The angle between the vector and the positive direction of the x-axis ,like Then let Otherwise ; Step 7.1.4, if and If the summation process ends, then the summation process ends; otherwise, let Proceed to step 7.1.2.

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