Antenna and radome electrical performance interval analysis method based on support function summation

Abstract

The application discloses an antenna and antenna cover electric performance interval analysis method based on support function summation, relates to the technical field of radar antennas, and comprises the following steps: acquiring the nominal complex excitation of each array element of the antenna and the amplitude and phase interval of the excitation of each array element; obtaining the amplitude and phase interval of the equivalent transmission coefficient of each grid; constructing a general far-field interval model about the far-field complex value of each observation direction of the antenna and the antenna cover, and obtaining the uncertain far-field contribution of each unit in each observation direction; obtaining the first far-field amplitude upper and lower bounds in each observation direction; determining the second far-field amplitude upper and lower bounds in each observation direction; constructing an error index based on the first far-field amplitude upper and lower bounds and the second far-field amplitude upper and lower bounds in each observation direction, and judging whether the second far-field amplitude upper and lower bounds meet the accuracy requirement based on the error index and a preset accuracy threshold; and if yes, outputting a directional diagram interval and an electric performance index interval. The scheme improves the analysis efficiency.

Description

Technical Field

[0001] This invention belongs to the field of radar antenna technology, specifically relating to a method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions. Background Technology

[0002] Unavoidable errors exist in the manufacturing, assembly, and service of antennas and radome systems. For array antennas, common errors include element excitation amplitude errors, phase errors, and element position errors. Among these, amplitude and phase errors directly cause the complex excitation of each element to no longer be a definite value, but rather form a bounded region in the complex plane, which can be described by a sector-shaped ring. For radomes, errors in parameters such as radome wall thickness, dielectric constant, and loss tangent will change the amplitude and phase of electromagnetic waves passing through the radome wall. The influence of the radome on the local electromagnetic field can usually be described by the complex transmission coefficient. When there are bounded errors in thickness and dielectric constant, the transmission coefficient at each grid is no longer a single complex number, but forms a region with both amplitude and phase bounded in the complex plane, which can also be described by a sector-shaped ring. The element excitation errors in array antennas and the transmission coefficient errors in radomes can both be represented as uncertain sector-shaped ring regions in the complex plane. The final far field is composed of a superposition of a large number of uncertain complex contributions, therefore, it is necessary to efficiently perform the summation of a large number of complex intervals.

[0003] Existing techniques for evaluating the electrical performance of antennas and radomes typically begin by obtaining the corresponding complex contribution range based on the sector rings of the antenna or radome. Then, each sector ring is approximated as a convex polygon, and the convex polygons are summed one by one to obtain the upper and lower bounds of the far-field amplitude. Finally, the radiation pattern and electrical performance index ranges are determined.

[0004] In existing technologies, each sector ring needs to be approximated as a convex polygon, and multiple convex polygons need to be accumulated step by step. As the number of array elements or radome meshes increases, the number of vertices of the intermediate summing polygons tends to increase, leading to a significant increase in computation time. When the number of array elements is large, or the radome is divided into a large number of meshes, the traditional convex polygon summation method is difficult to support repeated calculations with multiple observation angles, multiple scanning angles, and multiple error levels, and is not suitable for the analysis of large-scale electromagnetic structures. In addition, the evaluation of the electrical performance of antennas and radomes usually requires not only calculations in a single direction, but also obtaining a radiation pattern interval within a angular domain, and further extracting indicators such as maximum gain, beamwidth, and sidelobe level. If traditional polygon summation is used for each angle, the overall time consumption is high. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a method for analyzing the electrical performance range of antennas and radomes based on the summation of support functions. The method includes: Obtain the nominal complex excitation of each element of the antenna and the amplitude and phase interval of the excitation of each element; The radome is divided into grids to obtain the horizontal polarization transmission coefficient and the vertical polarization transmission coefficient of each grid. Based on the horizontal polarization transmission coefficient, the vertical polarization transmission coefficient and the polarization angle of each grid, the amplitude and phase interval of the equivalent transmission coefficient of each grid is obtained. A general far-field interval model for the far-field complex values ​​of the antenna and radome in each observation direction is constructed. The uncertain far-field contribution of each element in each observation direction is obtained by combining the amplitude and phase interval of the excitation of each array element, the nominal complex excitation of each array element, the amplitude and phase interval of the equivalent transmission coefficient of each grid, and the observation polar angle and azimuth angle in each observation direction. The element is an array element or a grid. Based on the uncertain far-field contribution of each unit in each observation direction, the fan-shaped annular contribution interval of each unit in each observation direction is obtained, and the fan-shaped annular contribution interval is approximated as a convex polygon to obtain the upper and lower bounds of the first far-field amplitude in each observation direction. Multiple uniformly distributed support directions are set in the complex plane, and the upper and lower bounds of the second far-field amplitude in each observation direction are determined based on the first support function sampled values ​​of all first direction vectors and the second support function sampled values ​​of all second direction vectors in the total far-field interval of each observation direction; the first direction vector is the unit direction vector of each support direction; the second direction vector is the opposite vector of the first direction vector. An error index is constructed based on the first far-field amplitude upper and lower bounds and the second far-field amplitude upper and lower bounds in each observation direction, and the second far-field amplitude upper and lower bounds are judged to meet the accuracy requirements based on the error index and the preset accuracy threshold. If satisfied, the output pattern interval and electrical performance index interval are based on the second far-field amplitude upper and lower bounds.

[0006] Optionally, the step of setting multiple uniformly distributed support directions in the complex plane, and determining the upper and lower bounds of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function in all first direction vectors and the sampled values ​​of the second support function in all second direction vectors of the total far-field interval in each observation direction, includes: Multiple uniformly distributed support directions are set in the complex plane to obtain multiple first direction vectors; Obtain the first support function sample value of the total far-field interval in each observation direction for each first direction vector; Obtain the second support function sample value of the total far-field interval in each observation direction for each second direction vector; Based on the sampled values ​​of the second support function of the total far-field interval in each observation direction, the lower bound of the second far-field amplitude in each observation direction is determined; Based on the sampled values ​​of the first support function of the total far-field interval in each observation direction and the number of support directions in all first direction vectors, the upper bound of the second far-field amplitude in each observation direction is obtained.

[0007] Optionally, obtaining the first support function sample value of the total far-field interval in each observation direction for each first direction vector includes: Obtain the support value of each unit convex polygon in each observation direction on each first direction vector; The support values ​​of all unit convex polygons in each observation direction are summed on each first direction vector to obtain the first support function sample value of the total far-field interval in each observation direction on each first direction vector.

[0008] Optionally, determining the lower bound of the second far-field amplitude in each observation direction based on the sampled values ​​of the second support function of the total far-field interval in each observation direction across all second-direction vectors includes: Obtain the maximum value of the total far-field interval in each observation direction among the second support function samples of all second direction vectors; Determine the magnitude of the maximum value among the sampled values ​​of the second support function in each observation direction and 0, and use the larger value in the determination result as the lower bound of the second far-field amplitude in each observation direction.

[0009] Optionally, obtaining the sampled value of the second support function of the total far-field interval in each observation direction for each second direction vector includes: Obtain the support value of each unit convex polygon in each observation direction on each second direction vector; The support values ​​of all unit convex polygons in each observation direction are summed on each second direction vector to obtain the second support function sample value of the total far-field interval in each observation direction on each second direction vector.

[0010] Optionally, obtaining the upper bound of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function and the number of support directions of the total far-field interval in each observation direction includes: Obtain the maximum value of the total far-field interval in each observation direction among the first support function samples of all first direction vectors; The angular interval between adjacent support directions is determined based on the number of support directions. The upper bound of the second far-field amplitude in each observation direction is obtained based on the maximum value of the first support function sampled values ​​in each observation direction and the angular interval.

[0011] Optionally, determining whether the upper and lower bounds of the second far-field amplitude meet the accuracy requirements based on the error index and the preset accuracy threshold includes: If the requirements are not met, the number of support directions is iteratively increased, and the corresponding upper and lower bounds of the second far-field amplitude are determined based on the increased number of support directions, until the new upper and lower bounds of the second far-field amplitude determined based on the increased number of support directions meet the accuracy requirements. Based on the new second far-field amplitude upper and lower bounds, output a new radiation pattern range and a new electrical performance index range.

[0012] Optionally, approximating the sector-shaped annular contribution range as a convex polygon to obtain the first far-field amplitude upper and lower bounds in each observation direction includes: The contribution range of the sector-shaped ring is approximated as a convex polygon. Minkowski summation is performed on the convex polygon corresponding to all units in each observation direction to obtain the upper and lower bounds of the first far-field amplitude in each observation direction.

[0013] Optionally, obtaining the nominal complex excitation of each element of the antenna and the amplitude and phase interval of the excitation of each element includes: The nominal complex excitation of each element is determined based on the nominal excitation amplitude and nominal excitation phase of each element of the antenna. The amplitude and phase range of each element's excitation is determined based on the amplitude and phase errors of each element in the antenna array.

[0014] Optionally, obtaining the horizontal polarization transmission coefficient and vertical polarization transmission coefficient of each grid of the radome includes: The horizontal polarization transmission coefficient and the vertical polarization transmission coefficient of each grid of the radome are obtained based on the radome wall thickness, the relative permittivity of the material, and the incident angle between the outer normal and the propagation direction at each grid.

[0015] The present invention has the following beneficial effects: 1. This application does not construct intermediate summation polygons step by step. Instead, it directly calculates the upper and lower bounds of the far-field amplitude from the total support values ​​in each direction, transforming complex geometric summation into scalar summation. The main computational load is determined by the number of elements and the number of support directions, reducing the construction and updating of intermediate polygons, effectively shortening the interval summation time, and improving the computational efficiency of the interval summation stage. This application adopts a unified far-field interval expression, allowing the array antenna and radome to be processed under the same summation framework. The array element error of the array antenna and the transmission coefficient error of the radome are both entered into the far-field calculation using complex coefficient intervals, facilitating the completion of interval summation and electrical performance extraction within the same program structure. 2. This application uses the Minkowski summation result as a benchmark to determine whether the support function summation result meets the requirements; when the error is too large, the accuracy can be improved by increasing the number of support directions, thus precisely controlling the accuracy.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions, provided by an embodiment of the present invention. Figure 2 The normalized power pattern of the planar array antenna obtained by using existing methods and the method of the present invention in this embodiment of the invention; Figure 3 The normalized power radiation patterns obtained by using existing methods and the method of the present invention for a tangential oval radome are shown in the embodiments of the present invention. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0019] This invention provides a method for analyzing the electrical performance range of antennas and radomes based on the summation of support functions, such as... Figure 1 As shown, it includes the following steps: Step 101: Obtain the nominal complex excitation of each element of the antenna and the amplitude and phase interval of the excitation of each element.

[0020] Specifically, complex excitation refers to the excitation signal expressed in complex number form, while nominal complex excitation refers to error-free complex excitation, i.e., ideal excitation, represented by nominal excitation amplitude and nominal excitation phase. When the antenna excitation is error-free, the excitation is a point in the complex plane.

[0021] Due to the existence of amplitude and phase errors of the array elements, the complex excitation of each array element is no longer a fixed value, but forms a bounded region in the complex plane. The amplitude and phase interval of the array element excitation can be determined based on the error, that is, the amplitude and phase interval of the array element excitation is determined based on the amplitude and phase errors of the array elements.

[0022] Step 102: Divide the radome into grids to obtain the horizontal polarization transmission coefficient and vertical polarization transmission coefficient of each grid. Based on the horizontal polarization transmission coefficient, the vertical polarization transmission coefficient and the polarization angle of each grid, obtain the amplitude and phase interval of the equivalent transmission coefficient of each grid.

[0023] Specifically, a radome is a structure that protects an antenna system from the influence of the external environment. It has good electromagnetic wave penetration characteristics and can withstand the effects of harsh external environments.

[0024] The transmission coefficient describes the effect of the radome on the local electromagnetic field. When there are bounded errors in the radome thickness and dielectric constant, the transmission coefficient at each grid point is no longer a single complex number, but forms a region with both amplitude and phase bounded in the complex plane. The transmission coefficient includes the horizontally polarized transmission coefficient and the vertically polarized transmission coefficient. The amplitude and phase intervals of the equivalent transmission coefficient include the amplitude interval and the phase interval.

[0025] When the object of analysis is a radome, the operating frequency, radome geometric model, mesh generation results, local incident angle and polarization angle of each mesh, radome wall thickness and its error range, and material relative permittivity and its error range are determined. The radome wall thickness and material relative permittivity of the nth mesh satisfy the following:

[0026] In the formula, This represents the thickness of the cover at the nth grid. This represents the relative permittivity of the material at the nth grid point. This indicates the error range of the wall thickness at the nth grid. This represents the error range of the relative permittivity of the material at the nth grid.

[0027] The horizontal and vertical polarization transmission coefficients are calculated based on transmission line theory.

[0028] The horizontal and vertical polarization transmission coefficients of each grid are synthesized, and the equivalent transmission coefficients corresponding to the principal polarization components are:

[0029] In the formula, This represents the equivalent transmission coefficient used for far-field calculations. This represents the polarization angle at the nth grid point. This represents the horizontal polarization transmission coefficient at the nth grid. This represents the vertical polarization transmission coefficient at the nth grid.

[0030] In this embodiment of the invention, a definite equivalent transmission coefficient can be obtained based on a defined wall thickness and a defined relative permittivity of the material. However, in reality, the thickness and permittivity are not fixed values, but rather a range with many possible values. Therefore, by iterating through the range, for example, the thickness range is discretized into 100 values, and the permittivity range is discretized into 100 values. Substituting these 100 × 100 combinations into the above formula yields 100 × 100 equivalent transmission coefficients. This represents a region on the complex plane. By finding the corresponding upper and lower bounds of the amplitude and phase, the equivalent transmission coefficient can be obtained. The amplitude and phase intervals are as follows:

[0031] in, This represents the magnitude of the equivalent transmission coefficient. The phase represents the equivalent transmission coefficient. This represents the amplitude range of the equivalent transmission coefficient. This represents the phase interval of the equivalent transmission coefficient.

[0032] Step 103: Construct a general far-field interval model for the far-field complex values ​​of the antenna and radome in each observation direction, and combine the amplitude and phase interval of the excitation of each array element, the nominal complex excitation of each array element, the amplitude and phase interval of the equivalent transmission coefficient of each grid, and the observation polar angle and azimuth angle in each observation direction to obtain the uncertain far-field contribution of each element in each observation direction; the element is an array element or a grid.

[0033] Specifically, although array antennas and radomes have different sources of error, they share a unified form in interval analysis modeling. The element excitation error in the array antenna and the transmission coefficient error in the radome can both ultimately be represented as a sector-shaped circular uncertainty region in the complex plane. Far-field calculations then manifest as the superposition of multiple complex uncertainty regions under deterministic weights.

[0034] The following explanation illustrates that, for a given observation direction, the far field can be expressed as the sum of contributions from multiple cells, as shown below:

[0035] In the formula, This represents the complex contribution of the nth element or the nth radome grid to the far field. n represents the nth element; for an antenna, n is the nth element; for a radome, n is the nth grid. N represents the number of elements or grids, and F represents the far field. When errors exist, It is no longer a definite complex number, but a range of complex numbers. Therefore, the possible range of values ​​for the far field is the Minkowski sum of all complex ranges for all elements. The purpose of electrical performance range analysis is to further determine the upper and lower bounds of electrical performance indicators such as amplitude pattern, power pattern, maximum gain, beamwidth, and sidelobe level based on the far field complex range.

[0036] For the One observation direction ,in, The observation polar angle is relative to the antenna axis. Let be the azimuth angle within the aperture plane. The far field of an antenna or radome can be written as the sum of the complex contributions of multiple elements. Let the ... The first observation direction Each element or the first The sector-shaped annular contribution range formed by the radome grid is denoted as . If n ranges from 1 to N, then the total far-field complex interval can be expressed as:

[0037] In the formula, Indicates the first The total far-field complex interval in each observation direction This indicates the number of array elements or the number of radome grids. This represents the Minkowski summation. If each sector-shaped annular interval... Approximately a convex polygon Then the far-field complex interval calculated by the traditional Minkowski summation method is:

[0038] In the formula, The far-field complex interval obtained by traditional Minkowski summation, For the first An approximate convex polygon for each unit contribution interval, where n ranges from 1 to N.

[0039] This invention employs a support function to describe the boundary of the convex polygon in a given direction. The complex plane is equated to a two-dimensional real plane, with complex points... The corresponding two-dimensional vector is denoted as:

[0040] Given a unit direction vector , convex set The support function in this direction is defined as:

[0041] In the formula, Represents a set Along direction Maximum projection value, This represents the two-dimensional inner product.

[0042] For any convex set The support functions of Minkowski sums satisfy:

[0043] in,

[0044] Therefore, given a set of support directions, the support values ​​of the total far-field complex interval in each direction can be obtained by directly adding the support values ​​of all element polygons. This property allows the original polygon successive summation process to be replaced by the summation of support functions, thereby reducing the computational complexity of the interval summation step.

[0045] In this embodiment of the invention, for the first One observation direction Discretize the radome into Unit 1. The position of each unit is denoted as The corresponding array element nominal excitation is denoted as Area weight is denoted as The complex coefficients of the error influence are denoted as The far-field expression is written as:

[0046] In the formula, Indicates the first The far-field complex value in each observation direction, Indicates the observed polar angle. Indicates azimuth; Indicates the number of array elements or the number of radome grids; Indicates the first The error of each element affects the complex coefficients, which, for an array antenna, represent the amplitude and phase error coefficients of the array element excitation. The transmission coefficient is represented by the radome. ; Indicates the first The nominal excitation of each array element; Indicates the first The area weight of each radome grid, for array antennas, can be taken as... ; Represents the free space wavenumber; Indicates the first The coordinates of each element in the aperture plane or array plane.

[0047] The effect of error on complex coefficients Rewritten in a uniform polar coordinate form, as shown below:

[0048] In the formula, and These respectively represent the amplitude and phase ranges of the complex coefficients affected by the error. In this embodiment of the invention, the subscripts... This indicates that the variable is a range number.

[0049] When the object of analysis is an antenna:

[0050] In the formula, For the first The amplitude error of each array element For the first Phase error of each array element For the first The amplitude error range of each array element For the first The phase error range of each array element.

[0051] When the object of analysis is a radome:

[0052] Will Substituting into the far-field expression, we obtain a unified far-field interval form:

[0053] in,

[0054]

[0055] In the formula, Indicates the first The amplitude range of the far-field contribution of each unit Indicates the first The unit in the first Phase intervals in each observation direction, index This indicates that the corresponding variable is a range number. and The first The nominal excitation amplitude and nominal excitation phase of each array element.

[0056] In the The first observation direction Uncertain far-field contribution of each unit for:

[0057] This region is a sector-shaped annular interval in the complex plane, which can be written as:

[0058] In the formula, and These are the lower and upper bounds of the radius amplitude, respectively. and These are the lower and upper bounds of the angular phase, respectively. For radius, For angle.

[0059] Step 104: Based on the uncertain far-field contribution of each unit in each observation direction, obtain the fan-shaped annular contribution interval of each unit in each observation direction, and approximate the fan-shaped annular contribution interval as a convex polygon to obtain the upper and lower bounds of the first far-field amplitude in each observation direction.

[0060] Specifically, the convex polygons of each unit in each observation direction are summed to obtain the corresponding far-field complex interval, and then the upper and lower bounds of the far-field amplitude in each observation direction are extracted.

[0061] Step 105: Set multiple uniformly distributed support directions in the complex plane, and determine the upper and lower bounds of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function of all first direction vectors and the sampled values ​​of the second support function of all second direction vectors in the total far-field interval of each observation direction; the first direction vector is the unit direction vector of each support direction; the second direction vector is the opposite vector of the first direction vector.

[0062] Specifically, multiple uniformly distributed support directions are set in the complex plane, as follows:

[0063] In the formula, This represents the number of sampling directions of the support function. Indicates the first One support direction. The corresponding unit direction vector is the first direction vector. for:

[0064] Number of support directions These are parameters used in embodiments of the present invention to control the discretization accuracy of the support function. The larger the value, the denser the sampling direction, and the closer the summation result of the support function is to the traditional Minkowski summation result.

[0065] Obtain the first support function sample value of the total far-field interval in each observation direction across all first direction vectors, obtain the second support function sample value of the total far-field interval in each observation direction across all second direction vectors, and then obtain the upper and lower bounds of the far-field amplitude based on the first and second support function sample values.

[0066] Step 106: Construct an error index based on the first far-field amplitude upper and lower bounds and the second far-field amplitude upper and lower bounds in each observation direction, and determine whether the second far-field amplitude upper and lower bounds meet the accuracy requirements based on the error index and the preset accuracy threshold.

[0067] Specifically, the Minkowski summation result is compared with the support function summation result, assuming there are a total of Based on one observation direction, the following error index is constructed. :

[0068] In the formula, The error index is the maximum relative error between the summation result of the support function and the traditional Minkowski summation result. For the first The upper bound of the second far-field amplitude in the observation direction Indicates the first The second lower bound of the far-field amplitude in the observation direction The first summation obtained for Minkowski The upper bound of the far-field amplitude in the observation direction, i.e. the th The upper bound of the first far-field amplitude in each observation direction The first summation obtained for Minkowski The lower bound of the far-field amplitude in the nth observation direction, i.e., the nth The lower bound of the first far-field amplitude in the observation direction.

[0069] Step 107: If satisfied, output the radiation pattern interval and the electrical performance index interval based on the upper and lower bounds of the second far-field amplitude.

[0070] If the error index Less than or equal to the preset precision threshold The system determines whether the upper and lower bounds of the second far-field amplitude meet the accuracy requirements. Based on these bounds, the final radiation pattern interval is obtained. From this interval, the gain interval, the normalized maximum directivity interval, the -3 dB beamwidth interval, and the first sidelobe level interval can be extracted. For example, the... Set to 0.001.

[0071] In this embodiment of the invention, instead of constructing intermediate summation polygons step by step, the upper and lower bounds of the far-field amplitude are directly calculated from the total support values ​​in each direction. This transforms complex geometric summation into scalar summation. The main computational load is determined by the number of elements (array elements or meshes) and the number of support directions, reducing the construction and updating of intermediate polygons and effectively shortening the interval summation time, thus improving the computational efficiency of the interval summation stage. This application adopts a unified far-field interval expression, allowing the array antenna and radome to be processed within the same summation framework. The array element errors of the array antenna and the transmission coefficient errors of the radome are both entered into the far-field calculation using complex coefficient intervals, facilitating the completion of interval summation and electrical performance extraction within the same program structure.

[0072] In one possible implementation, obtaining the nominal complex excitation of each antenna element and the amplitude and phase interval of the excitation of each element includes: The nominal complex excitation of each element is determined based on the nominal excitation amplitude and nominal excitation phase of each element of the antenna. The amplitude and phase range of each element's excitation is determined based on the amplitude and phase errors of each element in the antenna array.

[0073] Specifically, when the object of analysis is an array antenna, the operating frequency, observation angle sampling points, number of array elements, array element positions, nominal excitation, array element amplitude error, and phase error range are determined.

[0074] No. The nominal complex excitation of each array element is denoted as:

[0075] in, and The first The nominal excitation amplitude and nominal excitation phase of each array element. After considering amplitude and phase errors, the nominal excitation amplitude and phase phase of each array element are... Individual element excitation amplitude and phase error coefficient for

[0076] In the formula, and They represent the first The amplitude and phase errors of each array element are represented by the superscripts L and U, which denote the lower and upper bounds of the errors, respectively. For the first The amplitude error range of each array element For the first The phase error range of each array element.

[0077] For array antennas, the amplitude and phase range of the array element excitation is directly given by the input error, i.e., the first... The amplitude range of the excitation of each element is as follows: , No. The phase interval of the excitation of each element is .

[0078] In one possible implementation, obtaining the horizontal polarization transmission coefficient and vertical polarization transmission coefficient of each grid of the radome includes: The horizontal polarization transmission coefficient and the vertical polarization transmission coefficient of each grid of the radome are obtained based on the radome wall thickness, the relative permittivity of the material, and the incident angle between the outer normal and the propagation direction at each grid.

[0079] Specifically, for the nth grid, the horizontal polarization transmission coefficient and the vertical polarization transmission coefficient at that grid are respectively:

[0080]

[0081]

[0082]

[0083]

[0084] In the formula, This represents the horizontal polarization transmission coefficient at the nth grid. This represents the vertical polarization transmission coefficient at the nth grid. Represents the wavelength in free space. This represents the angle of incidence between the propagation direction and the outer normal of the grid. Indicates public items, This represents the imaginary part of the horizontal polarization term. This represents the imaginary part of vertical polarization. This represents the thickness of the cover at the nth grid. This represents the relative permittivity of the material at the nth grid.

[0085] In one possible implementation, approximating the sector-shaped annular contribution range as a convex polygon to obtain the first far-field amplitude upper and lower bounds in each observation direction includes: The contribution range of the sector-shaped ring is approximated as a convex polygon. Minkowski summation is performed on the convex polygon corresponding to all units in each observation direction to obtain the upper and lower bounds of the first far-field amplitude in each observation direction.

[0086] Specifically, no. The first observation direction The sector-shaped annular contribution range of each unit The traditional method of segmenting a sector-shaped circular arc approximates it as a convex polygon. Let the outer arc of the sector-shaped annulus be approximately... Line segment, the first The unit in the first The approximate polygons along each observation direction are:

[0087] In the formula, The approximate number of polygonal segments representing the sector arc. Indicates the first The unit in the first The first observation direction A polygonal vertex, This indicates the number of vertices of the polygon. This represents the convex hull formed by the vertices. The vertices obtained in this step also serve as input to the support function summation step.

[0088] For the For each observation direction, the far-field complex interval is calculated using the Minkowski summation method for convex polygons:

[0089] In the formula, This represents the far-field complex interval obtained by the Minkowski summation. This indicates that Minkowski requested a summation.

[0090] Depend on Extracting the upper and lower bounds of the far-field amplitude:

[0091] In the formula, and These represent the upper and lower bounds of the far-field amplitude obtained by the Minkowski summation, respectively. Specifically, For the first The upper bound of the first far-field amplitude in each observation direction For the first The first far-field amplitude lower bound in each observation direction is used to determine whether the summation result of the support function meets the preset accuracy requirements.

[0092] In one possible implementation, the step of setting multiple uniformly distributed support directions in the complex plane, and determining the upper and lower bounds of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function in all first direction vectors and the sampled values ​​of the second support function in all second direction vectors of the total far-field interval in each observation direction, includes: Multiple uniformly distributed support directions are set in the complex plane to obtain multiple first direction vectors; Obtain the first support function sample value of the total far-field interval in each observation direction for each first direction vector; Obtain the second support function sample value of the total far-field interval in each observation direction for each second direction vector; Based on the sampled values ​​of the second support function of the total far-field interval in each observation direction, the lower bound of the second far-field amplitude in each observation direction is determined; Based on the sampled values ​​of the first support function of the total far-field interval in each observation direction and the number of support directions in all first direction vectors, the upper bound of the second far-field amplitude in each observation direction is obtained.

[0093] In one possible implementation, obtaining the first support function sample value of the total far-field interval in each observation direction for each first direction vector includes: Obtain the support value of each unit convex polygon in each observation direction on each first direction vector; The support values ​​of all unit convex polygons in each observation direction are summed on each first direction vector to obtain the first support function sample value of the total far-field interval in each observation direction on each first direction vector.

[0094] In one possible implementation, obtaining the second support function sample value of the total far-field interval in each observation direction for each second direction vector includes: Obtain the support value of each unit convex polygon in each observation direction on each second direction vector; The support values ​​of all unit convex polygons in each observation direction are summed on each second direction vector to obtain the second support function sample value of the total far-field interval in each observation direction on each second direction vector.

[0095] In one possible implementation, determining the lower bound of the second far-field amplitude in each observation direction based on the sampled values ​​of the second support function across all second-direction vectors of the total far-field interval in each observation direction includes: Obtain the maximum value of the total far-field interval in each observation direction among the second support function samples of all second direction vectors; Determine the magnitude of the maximum value among the sampled values ​​of the second support function in each observation direction and 0, and use the larger value in the determination result as the lower bound of the second far-field amplitude in each observation direction.

[0096] In one possible implementation, obtaining the upper bound of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function and the number of support directions of the total far-field interval in each observation direction includes: Obtain the maximum value of the total far-field interval in each observation direction among the first support function samples of all first direction vectors; The angular interval between adjacent support directions is determined based on the number of support directions. The upper bound of the second far-field amplitude in each observation direction is obtained based on the maximum value of the first support function sampled values ​​in each observation direction and the angular interval.

[0097] Specifically, the support values ​​of the polygon vertex calculation units are obtained using the aforementioned method. Indicates the first The unit in the first The first observation direction A polygon with vertices, if a complex number of vertices Its two-dimensional vector form is:

[0098] Then the first The first observation direction Unit polygon In direction Support value above for:

[0099] For the The support values ​​of all element polygons in the nth observation direction are added together in each direction to obtain the nth... The total far-field interval in each observation direction is in the direction Support function sample values :

[0100] At the same time, for the opposite direction vector, i.e., the second direction vector Obtain the corresponding support function sample value, i.e., the first... The total far-field interval in each observation direction is in the direction Support function sample values :

[0101] In the formula, This represents the corresponding far-field complex interval obtained by summing the support functions. In actual calculations, this interval does not need to be explicitly constructed through successive polygon Minkowski summations; the required boundary information is given by the sampled values ​​of the support functions mentioned above.

[0102] The upper and lower bounds of the far-field amplitude are determined based on the sampled values ​​of the support function obtained above. Here, the upper and lower bounds of the far-field amplitude are the second upper and lower bounds of the far-field amplitude.

[0103]

[0104] In the formula, Indicates the first The second lower bound of the far-field amplitude in the observation direction. This formula is consistent with the calculation of the lower bound of the support function: when the origin is located within the complex interval of the far field, the lower bound is 0; when the origin is located outside the interval, the lower bound is determined by the support value in the opposite direction.

[0105] The expression for calculating the upper bound of the second far-field amplitude is as follows:

[0106] in,

[0107] In the formula, Indicates the first The upper bound of the second far-field amplitude in the observation direction This represents the angular interval between adjacent support directions. The upper bound of the second far-field amplitude is calculated by multiplying the maximum total support value across all sampling directions by the direction sampling factor. get.

[0108] Through the above steps, the first... The second far-field amplitude range in each observation direction .

[0109] In one possible implementation, determining whether the upper and lower bounds of the second far-field amplitude meet the accuracy requirements based on the error index and a preset accuracy threshold includes: If the requirements are not met, the number of support directions is iteratively increased, and the corresponding upper and lower bounds of the second far-field amplitude are determined based on the increased number of support directions, until the new upper and lower bounds of the second far-field amplitude determined based on the increased number of support directions meet the accuracy requirements. Based on the new second far-field amplitude upper and lower bounds, output a new radiation pattern range and a new electrical performance index range.

[0110] Specifically, if the upper and lower bounds of the second far-field amplitude do not meet the accuracy requirements based on the error index and the preset accuracy threshold, the number of support directions is increased until the new upper and lower bounds of the second far-field amplitude determined by the new number of support directions meet the accuracy requirements in this embodiment of the invention.

[0111] In this embodiment of the invention, the upper and lower bounds of the second far-field amplitude are determined based on the error index and the preset accuracy threshold to determine whether the accuracy requirements are met, and the accuracy control method is clear. When the error is too large, the accuracy can be improved by increasing the number of support directions. This method is suitable for rapid electrical performance range analysis of antennas and radomes under bounded errors.

[0112] For repetitive analyses involving multiple observation angles, multiple scan angles, multiple error levels, or multiple design schemes, this invention converts complex geometric summations into scalar summations, effectively shortening the interval summation time. It is suitable for batch calculations of radiation patterns and electrical performance indicators.

[0113] To verify the applicability of the method in the embodiments of the present invention in the electromagnetic performance range analysis of antenna arrays and radomes, the following was selected. Planar array antennas and tangential oval radomes are two examples. For Planar array antenna, with a total of 64 elements, operating at a frequency of The element spacing is set to 15mm, which is half-wavelength spacing. The array aperture adopts Taylor amplitude distribution, and the sidelobe level is set to... ,parameter Each array element's excitation amplitude and phase have bounded errors, where the amplitude error half-width is taken as... The phase error half-width is taken as For a tangential oval radome, the radome height is 1m, the bottom diameter is 0.5m, and the internal antenna operates at... A circular aperture antenna with an aperture diameter of The distance between the antenna phase center and the bottom of the radome The radome is made of non-destructive fiberglass, with a designed wall thickness of [missing information]. The relative permittivity is The loss tangent is 0. Considering the influence of manufacturing errors, the half-width of the cover wall thickness error is taken as... The relative permittivity error half-width is taken as In the two embodiments described above, the normalized power pattern intervals are calculated using both the conventional method (i.e., the prior art) and the method of the present invention, and the calculation results and calculation times of the two methods are compared.

[0114] Figure 2 and Figure 3 The images show the normalized power radiation patterns obtained by the conventional method and the method of the present invention in two different embodiments. It can be seen that... In both the planar array antenna and the tangential oval radome cases, the radiation pattern curves obtained by the method in this embodiment of the invention basically coincide with those of the traditional method. The trends of change in the main lobe region, side lobe region, and near the null are consistent, indicating that the method of the present invention can maintain consistent interval analysis results with the traditional method while improving computational efficiency. Table 1 below shows a comparison of the computation time of the two methods. For For planar array antennas, the computation time using traditional methods is... The computation time of the method of the present invention is The calculation speed is increased by approximately The calculation time is reduced by approximately [number] times. For a tangential oval radome, the computation time of the traditional method is... The computation time of the method of the present invention is The calculation speed is increased by approximately The calculation time is reduced by approximately [number] times. Therefore, the method in this embodiment of the invention is not only applicable to the excitation error interval analysis of array antennas, but also to the electromagnetic performance interval analysis of radomes containing a large number of integral grids and transmission coefficient uncertainties, and can significantly reduce the calculation time while ensuring the consistency of the calculation results.

[0115] Table 1

[0116] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0117] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing the electrical performance range of antennas and radomes based on the summation of support functions, characterized in that, include: Obtain the nominal complex excitation of each element of the antenna and the amplitude and phase interval of the excitation of each element; The radome is divided into grids to obtain the horizontal polarization transmission coefficient and the vertical polarization transmission coefficient of each grid. Based on the horizontal polarization transmission coefficient, the vertical polarization transmission coefficient and the polarization angle of each grid, the amplitude and phase interval of the equivalent transmission coefficient of each grid is obtained. A general far-field interval model for the far-field complex values ​​of the antenna and radome in each observation direction is constructed. The uncertain far-field contribution of each element in each observation direction is obtained by combining the amplitude and phase interval of the excitation of each element, the nominal complex excitation of each element, the amplitude and phase interval of the equivalent transmission coefficient of each grid, and the observation polar angle and azimuth angle in each observation direction. The unit is an array element or a grid; Based on the uncertain far-field contribution of each unit in each observation direction, the fan-shaped annular contribution interval of each unit in each observation direction is obtained, and the fan-shaped annular contribution interval is approximated as a convex polygon to obtain the upper and lower bounds of the first far-field amplitude in each observation direction. Multiple uniformly distributed support directions are set in the complex plane, and the upper and lower bounds of the second far-field amplitude in each observation direction are determined based on the first support function sampled values ​​of all first direction vectors and the second support function sampled values ​​of all second direction vectors in the total far-field interval of each observation direction; the first direction vector is the unit direction vector of each support direction. The second direction vector is the opposite vector of the first direction vector; An error index is constructed based on the first far-field amplitude upper and lower bounds and the second far-field amplitude upper and lower bounds in each observation direction, and the second far-field amplitude upper and lower bounds are judged to meet the accuracy requirements based on the error index and the preset accuracy threshold. If satisfied, the output pattern interval and electrical performance index interval are based on the second far-field amplitude upper and lower bounds.

2. The method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions according to claim 1, characterized in that, The step of setting multiple uniformly distributed support directions in the complex plane, and determining the upper and lower bounds of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function in all first direction vectors and the sampled values ​​of the second support function in all second direction vectors of the total far-field interval in each observation direction, includes: Multiple uniformly distributed support directions are set in the complex plane to obtain multiple first direction vectors; Obtain the first support function sample value of the total far-field interval in each observation direction for each first direction vector; Obtain the second support function sample value of the total far-field interval in each observation direction for each second direction vector; Based on the sampled values ​​of the second support function of the total far-field interval in each observation direction, the lower bound of the second far-field amplitude in each observation direction is determined; Based on the sampled values ​​of the first support function of the total far-field interval in each observation direction and the number of support directions in all first direction vectors, the upper bound of the second far-field amplitude in each observation direction is obtained.

3. The method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions according to claim 2, characterized in that, The step of obtaining the first support function sample value of the total far-field interval in each observation direction for each first direction vector includes: Obtain the support value of each unit convex polygon in each observation direction on each first direction vector; The support values ​​of all unit convex polygons in each observation direction are summed on each first direction vector to obtain the first support function sample value of the total far-field interval in each observation direction on each first direction vector.

4. The method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions according to claim 2, characterized in that, The determination of the lower bound of the second far-field amplitude in each observation direction based on the sampled values ​​of the second support function of the total far-field interval in each observation direction across all second-direction vectors includes: Obtain the maximum value of the total far-field interval in each observation direction among the second support function samples of all second direction vectors; Determine the magnitude of the maximum value among the sampled values ​​of the second support function in each observation direction and 0, and use the larger value in the determination result as the lower bound of the second far-field amplitude in each observation direction.

5. The method for analyzing the electrical performance range of antennas and radomes based on the summation of support functions according to claim 2, characterized in that, The step of obtaining the second support function sample value of the total far-field interval in each observation direction for each second direction vector includes: Obtain the support value of each unit convex polygon in each observation direction on each second direction vector; The support values ​​of all unit convex polygons in each observation direction are summed on each second direction vector to obtain the second support function sample value of the total far-field interval in each observation direction on each second direction vector.

6. The method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions according to claim 2, characterized in that, The method of obtaining the upper bound of the second far-field amplitude in each observation direction based on the sampled values ​​of the first support function of the total far-field interval in each observation direction across all first direction vectors and the number of support directions includes: Obtain the maximum value of the total far-field interval in each observation direction among the first support function samples of all first direction vectors; The angular interval between adjacent support directions is determined based on the number of support directions. The upper bound of the second far-field amplitude in each observation direction is obtained based on the maximum value of the first support function sampled values ​​in each observation direction and the angular interval.

7. The method for analyzing the electrical performance range of antennas and radomes based on the summation of support functions according to claim 2, characterized in that, The step of determining whether the upper and lower bounds of the second far-field amplitude meet the accuracy requirements based on the error index and the preset accuracy threshold includes: If the requirements are not met, the number of support directions is iteratively increased, and the corresponding upper and lower bounds of the second far-field amplitude are determined based on the increased number of support directions, until the new upper and lower bounds of the second far-field amplitude determined based on the increased number of support directions meet the accuracy requirements. Based on the new second far-field amplitude upper and lower bounds, output a new radiation pattern range and a new electrical performance index range.

8. The method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions according to claim 1, characterized in that, The step of approximating the sector-shaped annular contribution range as a convex polygon to obtain the upper and lower bounds of the first far-field amplitude in each observation direction includes: The contribution range of the sector-shaped ring is approximated as a convex polygon. Minkowski summation is performed on the convex polygon corresponding to all units in each observation direction to obtain the upper and lower bounds of the first far-field amplitude in each observation direction.

9. The method for analyzing the electrical performance range of antennas and radomes based on the summation of support functions according to claim 1, characterized in that, The acquisition of the nominal complex excitation of each element of the antenna and the amplitude and phase interval of the excitation of each element includes: The nominal complex excitation of each element is determined based on the nominal excitation amplitude and nominal excitation phase of each element of the antenna. The amplitude and phase range of each element's excitation is determined based on the amplitude and phase errors of each element in the antenna array.

10. The method for analyzing the range of electrical performance of antennas and radomes based on the summation of support functions according to claim 1, characterized in that, The process of obtaining the horizontal and vertical polarization transmission coefficients for each grid of the radome includes: The horizontal polarization transmission coefficient and the vertical polarization transmission coefficient of each grid of the radome are obtained based on the radome wall thickness, the relative permittivity of the material, and the incident angle between the outer normal and the propagation direction at each grid.

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