Flexible conformal array structure scattering characteristic analysis method and device

Abstract

The invention discloses a flexible conformal array structure scattering characteristic analysis method and device, and the method comprises the steps: carrying out the fitting of a whole flexible array surface arc length through employing a plurality of osculating circles through the evaluation of a flexible array surface structure, and determining the number of osculating circles divided by a whole arc length curve through iteration; constructing feature units to realize reconstruction of the whole flexible array plane, and calculating an initial excitation coefficient, a feature weight coefficient and a mutual coupling coefficient between the units of each flexible unit; and constructing and solving a balance equation to obtain an actual excitation coefficient of each flexible unit considering the mutual coupling effect, and calculating a total scattering field of the flexible array structure to obtain a radar cross section of the flexible array. According to the method, the scattering characteristic analysis of the flexible conformal array structure is realized, the problem of inconsistent deformation degree of each unit caused by the flexible structure is considered, a small number of characteristic units are used for replacing the units in the actual flexible array structure through an iteration mode, and the analysis efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic scattering, and particularly relates to a method and device for analyzing the scattering characteristics of a flexible conformal array structure. Background Art

[0002] Since the conformal array structure can be consistent with the shape of the carrier platform, without damaging the aerodynamic performance of the carrier itself and having a high space occupancy rate, it is widely used in military, communication, and navigation fields such as airborne radars, base station antennas, and wireless sensors. Among them, the flexible conformal array structure is easier to attach to the carrier platform than a general conformal array. However, due to the different bending degrees and pointing directions of each unit, it is difficult to analyze the flexible array structure by conventional electromagnetic analysis methods, and often only full-wave software or measurement can be relied on. With the increase in the scale of the array, how to quickly and accurately realize the scattering characteristics of the flexible conformal array has important research value.

[0003] Generally, the existing methods for analyzing the scattering characteristics of arrays can be divided into the following two categories. The first analysis strategy regards the entire array structure as a whole and usually uses numerical methods such as the finite element method and the multilevel fast multipole method for solution. Such methods can achieve accurate analysis, but the calculation cost is too high when the array scale is large or the unit structure is complex. The second is to establish the connection between the unit structure and the entire array to achieve rapid analysis. For example, in the scattering pattern method, the array scattering is also expressed as the product of the element factor and the array factor. However, due to the mutual coupling effect between elements not being considered, the analysis result is not accurate. The active pattern method evaluates the scattering characteristics of the entire array structure by calculating or measuring the patterns in the array one by one. Although it can meet the needs of engineering applications, the pre-analysis time is long and the actual operation is relatively cumbersome. The subarray extrapolation method developed on this basis improves the calculation speed by reasonably considering the edge effect of the array, but it is only applicable to planar arrays and cannot analyze flexible arrays. Thus, there is an urgent need for an analysis method with low cost and guaranteed accuracy requirements.

[0004] The infinitesimal dipole model is a method that uses a group of infinitesimal dipoles to equivalent the electromagnetic characteristics of the target. Its application scenarios are flexible and changeable, and it can not only handle radiation and scattering problems, but also avoid the multi-scale problems of complex models. However, most of the previous studies only focused on the case where the unit structures in the array environment are consistent. For flexible arrays, due to problems such as inconsistent deformation degrees of each unit and inconsistent pointing directions caused by structural characteristics, it is impossible to extract units with consistent structures like planar arrays to achieve rapid analysis. Therefore, exploring the scattering performance of flexible arrays based on the infinitesimal dipole model has important research significance for guiding the scattering performance analysis and design of actual engineering. Summary of the Invention

[0005] To solve the above-mentioned defects existing in the prior art, the object of the present invention is to provide a method for analyzing the scattering characteristics of a flexible conformal array structure. This method adopts the idea of approximate substitution. By closely fitting the entire flexible surface with circles, and then constructing characteristic units to approximately substitute each unit on the entire flexible array, it can solve the problem of inconsistent deformation degrees of each unit in the flexible array, and at the same time improve the analysis efficiency.

[0006] The present invention is realized through the following technical solutions.

[0007] The present invention provides a method for analyzing the scattering characteristics of a flexible conformal array structure, including the following steps:

[0008] According to the curve equation of the flexible conformal surface, calculate the total arc length of the surface of the flexible array structure; divide the total arc length of the surface equally according to the number of array elements to obtain the set of discrete coordinate points of the arc length of each unit on the flexible surface;

[0009] Perform a close circle fitting according to the set of discrete coordinate points of the arc length of each unit, and calculate the fitting error; set a fitting error threshold, and determine the number of close circles for dividing the entire arc length curve through iteration;

[0010] Construct characteristic units according to the number of close circles and the radius of the close circles, equivalently obtain the parameters of infinitesimal dipoles, and calculate the current distribution of each characteristic unit;

[0011] According to the current distribution of each characteristic unit, calculate the initial excitation coefficient, characteristic weight coefficient of each characteristic unit, and the mutual coupling coefficient between each characteristic unit of the flexible array;

[0012] Construct and solve the balance equation, calculate the actual excitation coefficient of each characteristic unit considering the mutual coupling effect in the flexible array environment, obtain the array factor of the entire flexible array, calculate the total scattered field of the flexible array, and obtain the radar cross section of the entire flexible array structure.

[0013] Preferably, dividing the total arc length of the flexible surface equally according to the number of array elements to obtain the set of discrete coordinate points of the arc length of each unit on the flexible surface includes:

[0014] When the curve equation is known, perform numerical integration on the curve equation to obtain the arc length of the entire curve. When the curve equation is unknown, perform linear fitting on the known measured point coordinates to obtain the expression of the curve equation, and perform numerical integration on the curve equation to obtain the total arc length of the entire array surface curve;

[0015] According to the total arc length of the flexible array surface curve and the number of array elements, divide the total arc length equally to obtain the set of discrete coordinate points of the arc length of each unit.

[0016] Perform a close circle fitting according to the discrete coordinate points of the arc length of each unit, and calculate the fitting error.

[0017] Preferably, determining the number of osculating circles for the entire arc length curve division includes:

[0018] Setting a threshold for the fitting error, calculating the fitting error of each osculating circle using the root mean square error, and determining the number of osculating circles for the entire arc length curve division when the average value of the root mean square error of the osculating circles is less than the fitting error threshold.

[0019] Preferably, constructing characteristic units according to the number and radius of each osculating circle, equivalently obtaining the infinitesimal dipole parameters, and calculating the current distribution of each characteristic unit includes:

[0020] Constructing a flexible unit with the same radius as the osculating circle as the characteristic unit of the osculating circle according to the number and radius of each osculating circle;

[0021] Obtaining the scattering field of each characteristic unit through the quantum particle swarm optimization algorithm, equivalently characterizing the unit, obtaining multiple groups of infinitesimal dipole parameters, and calculating the current distribution of each characteristic unit.

[0022] Preferably, calculating the radar cross section of the entire flexible array structure includes:

[0023] Constructing a balance equation considering the entire flexible array;

[0024] Solving the balance equation to obtain the actual excitation coefficients of each unit considering the mutual coupling effect in the flexible array environment;

[0025] Based on the pattern multiplication theorem, calculating the total scattering field of the flexible array and calculating the radar cross section.

[0026] Another aspect of the present invention provides an analysis device for the scattering characteristics of a flexible conformal array structure of the method, including:

[0027] A division module for equally dividing the total arc length of the curved surface according to the number of array elements to obtain a set of discrete coordinate points of the arc length of each unit;

[0028] A fitting module for performing osculating circle fitting according to the set of discrete coordinate points of the arc length of each unit to obtain the fitting error; determining the number of osculating circles for the entire arc length curve division according to the fitting error threshold;

[0029] A construction module for constructing characteristic units according to the number and radius of the osculating circles to obtain the current distribution of each characteristic unit;

[0030] A calculation module for calculating the initial excitation coefficient, characteristic weight coefficient, mutual coupling coefficient between each characteristic unit of the flexible array, actual excitation coefficient, and total scattering field of the flexible array to obtain the radar cross section of the entire flexible array structure.

[0031] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0032] The present invention evaluates the characteristics of the entire flexible conformal array surface, and then fits the entire flexible array surface into a combination of multiple osculating circles. By constructing characteristic units, the reconstruction of the entire flexible array surface is realized.

[0033] Construct characteristic units to realize the reconstruction of the entire flexible array surface, calculate the initial excitation coefficients, characteristic weight coefficients and mutual coupling coefficients between units of each flexible unit; construct and solve the balance equation to obtain the actual excitation coefficients of each flexible unit considering the mutual coupling effect, calculate the total scattered field of the flexible array structure, and obtain the radar cross section of the flexible array, so as to realize the analysis of the scattering characteristics of the flexible array surface structure.

[0034] The method of the present invention evaluates the characteristics of the entire flexible conformal array surface, uses the method of segmentally fitting the entire arc length curve with osculating circles, and then constructs characteristic units to replace different curvature units of the entire array surface. Translate and rotate the equivalent infinitesimal dipoles to realize the reconstruction of the entire flexible array surface, calculate the actual excitation coefficients of each unit, and establish a characterization of the coupling relationship between units. Finally, based on the pattern multiplication theorem, the radar cross section of the entire flexible conformal array structure is obtained, which has important significance in practical engineering.

[0035] Compared with the traditional method for analyzing the scattering characteristics of flexible arrays, the method of the present invention takes into account the influence brought by the deformation of the unit structure. At the same time, by setting the threshold of the fitting error, the number of equivalent units is reduced, and the analysis efficiency is improved. At the same time, this method can also be used to analyze other arrays with similar unit characteristics. Description of the Drawings

[0036] The drawings described herein are used to provide a further understanding of the present invention, form a part of this application, and do not constitute an improper limitation to the present invention. In the drawings:

[0037] Figure 1 is the flow chart of the method for analyzing the scattering characteristics of the flexible conformal array of the present invention;

[0038] Figure 2 is the iterative flow chart of the osculating circle fitting the arc length of each unit of the present invention;

[0039] Figure 3 is the schematic diagram of the osculating circle arc fitting the flexible surface;

[0040] Figure 4 is the schematic diagram of constructing characteristic units from osculating circle arcs;

[0041] Figure 5 is the schematic diagram of using the cylindrical coordinate system to equivalent the characteristic unit as an infinitesimal dipole;

[0042] Figure 6 It is a schematic diagram of the mutual coupling of the flexible conformal array environment;

[0043] Figure 7 It is a schematic diagram of the cylindrical frequency selective surface array structure;

[0044] Figure 8 It is a schematic diagram of the unit structure of the cylindrical frequency selective surface;

[0045] Figure 9 It is the comparison between the single - station radar cross - section (MoRCS) of the yoz plane of the cylindrical frequency selective surface using the present invention and the method of moments;

[0046] Figure 10 They are the geometric parameters of the third - order Bessel curve;

[0047] Figure 11 It is a schematic diagram of the third - order Bessel flexible frequency selective surface array structure;

[0048] Figure 12 It is the comparison between the single - station radar cross - section (MoRCS) of the xoz plane of the third - order Bessel flexible frequency selective surface array using the present invention and the method of moments;

[0049] Figure 13 It is a schematic diagram of the flexible conformal array structure analysis device shown in the embodiment of the present invention. Detailed implementation manners

[0050] The present invention will be described in detail below in conjunction with the drawings and specific embodiments. Here, the schematic embodiments of the present invention and the descriptions are used to explain the present invention, but not to limit the present invention.

[0051] The present invention provides a method for analyzing the scattering characteristics of a flexible conformal array structure. The analysis process is as Figure 1 shown, and the specific steps are as follows:

[0052] Step 1: According to the flexible array surface curve equation, calculate the total arc length of the flexible conformal array structure surface. Divide the total arc length of the flexible surface equally according to the number of array elements to obtain the discrete coordinate point set of the arc length of each unit of the flexible surface.

[0053] (1a) Numerically integrate the flexible array surface curve equation to obtain the total arc length of the entire array surface curve.

[0054] Flexible arrays are usually composed of multiple identical array elements. These array elements are formally the same, but due to the characteristics of the flexible structure, the deformations of the individual array elements are inconsistent. When the curve equation is known, numerical integration is performed on the curve equation to obtain the arc length of the entire curve. When the curve equation is unknown, the coordinates of the known measurement points are linearly fitted to obtain the expression of the curve equation, and numerical integration is performed on the curve equation to obtain the total arc length of the entire flexible array surface curve:

[0055]

[0056] Among them, f(x) is the curve equation of the flexible array surface, a and b are the upper and lower limits of numerical integration, and l is the total arc length of the curve of the flexible array surface.

[0057] (1b) According to the total arc length of the flexible array surface curve and the number of array elements, the total arc length is divided into equal arc lengths:

[0058] l = Ql Q (2)

[0059] Among them, Q is the number of array elements, and l Q is the segmented arc length.

[0060] At the same time, according to the segmented arc length, the set of discrete coordinate points of each unit arc length can be obtained:

[0061]

[0062] Among them, is the discrete point coordinate on the segmented arc length l Q , and i is the number of discrete points of the arc length.

[0063] Step 2: Perform osculating circle fitting according to the set of discrete coordinate points of each unit arc length, and calculate the fitting error; set the fitting error threshold, and determine the number of osculating circles for dividing the entire arc length curve through iteration.

[0064] As Figure 2 shown in the flowchart of the iteration of the number of osculating circles, first set the fitting error threshold [δ], initialize the number of osculating circles P and the array element index number Q. By fitting the set of coordinate points l Q of the array element arc length, the root mean square error δ of the fitting is obtained; when the root mean square error δ of the unit fitting is less than or equal to the set fitting error threshold [δ], it indicates that the flexible unit can be fitted using the same osculating circle. At this time, increase the number of flexible units and recalculate the root mean square error δ of the fitting. Otherwise, update the number of osculating circles required for fitting and update the flexible array element number; when the flexible array element number is greater than the total number of flexible array elements, output information such as the number and radius of the obtained osculating circles, and the iteration is completed.

[0065] By using the osculating circle to fit the arc length l of the flexible array surfaceQ , while calculating the root mean square error δ of the osculating circle fitting, the calculation formula of the root mean square error is

[0066]

[0067] where is the fitting coordinate value of the osculating circle, is the actual arc length coordinate value of the array surface.

[0068] When the root mean square error of each unit fitting is less than the initially set fitting error threshold, it indicates that this arc length containing multiple units can be fitted by the osculating circle

[0069]

[0070] where δ is the root mean square error of multiple flexible units fitting the osculating circle, and [δ] is the preset root mean square error threshold. When the loop is completed, the number of osculating circles is obtained, indicating that the entire flexible array surface can be approximated by the obtained osculating circles within the allowable range of the error threshold.

[0071] Step 3, construct characteristic units according to the number and radius of the osculating circles, equivalently obtain the infinitesimal dipole parameters, and calculate the current distribution of each characteristic unit.

[0072] (3a) According to the number and radius of each osculating circle, construct flexible units with the same radius as the osculating circle as the characteristic units of the osculating circle.

[0073] As Figure 3 shows the schematic diagram of the osculating circle fitting the flexible surface. After determining the number and radius of the osculating circles in Step 2, the entire flexible array surface can be reconstructed by multiple osculating circles. At the same time, as Figure 4 shows, a single osculating circle contains multiple flexible units. At this time, construct flexible units with the same radius as the osculating circle as the characteristic units of the osculating circle, and the other units on the entire osculating circle can be obtained by rotating the characteristic unit.

[0074] (3b) Obtain the scattering fields of each characteristic unit through the quantum particle swarm optimization algorithm, equivalent characteristic units, obtain multiple groups of infinitesimal dipole parameters, and calculate the current distribution of each characteristic unit.

[0075] As Figure 5 shows, in order to make the obtained infinitesimal dipole parameters fit the surface of the characteristic unit, modify the constraint space of the quantum particle swarm optimization algorithm to cylindrical coordinate system parameters, fix the infinitesimal dipole parameters in groups of three on the grid nodes. Among them, ρ1 is the inner radius of the cylinder, ρ2 is the outer radius of the cylinder, C is the central angle of the flexible characteristic unit, and z is the height of the unit. Through the above four parameters, the position parameters of each dipole can be accurately obtained.

[0076] Furthermore, calculate the current distribution based on the optimized dipole parameters obtained:

[0077]

[0078] Among them, is the dipole current distribution, N d is the number of dipoles, is the dipole moment of the dipole, χ is the delta function, is the position vector of the characteristic unit, is the dipole position vector.

[0079] At the same time, the current of other rotated characteristic units on the osculating circle is

[0080]

[0081] Among them, is the current of the rotated characteristic unit, T x , T y , T z are the rotation matrices along the x, y, and z directions, and A, B, and C are the rotation angles along the three coordinate axes of x, y, and z.

[0082] Step 4: Calculate the initial excitation coefficient, characteristic weight coefficient of each characteristic unit, and the mutual coupling coefficient between each characteristic unit of the flexible array.

[0083] The specific steps are as follows:

[0084] (4a) Calculate the initial excitation coefficient and characteristic weight coefficient of each characteristic unit according to the current distribution of each characteristic unit.

[0085] Since the deformation degrees of each unit of the flexible array are different and the excitations at different angles are different, after obtaining the current distribution of each characteristic unit according to Step 3, calculate the initial excitation coefficient of each characteristic unit:

[0086]

[0087]

[0088] Among them, V is the initial excitation coefficient of each characteristic unit, is the excitation electric field of the plane wave, E is the excitation intensity of the plane wave, is the unit vector of the polarization direction, k is the free space wave number, is the incident direction of the plane wave, is the position vector of the characteristic array element.

[0089] Furthermore, obtain the characteristic weight coefficient of each characteristic unit

[0090]

[0091] Among them, \(W\) is the characteristic weight coefficient of each characteristic unit, is the scattered field of the rotated characteristic unit calculated from the equivalent dipole, is the unit field obtained by software calculation.

[0092] (4b) Calculate the mutual coupling coefficient between each characteristic unit of the flexible array.

[0093] The different directions of each characteristic unit lead to the rotation of the dipole moment direction, making the mutual coupling effect in the flexible conformal array environment different from that of the planar array. After obtaining the characteristic weight coefficients of each characteristic unit under different angle excitations, the mutual coupling effect between each characteristic element is further characterized. The mutual coupling effect between any two characteristic units can be characterized based on the reciprocity theorem:

[0094]

[0095] Among them, \(C\) mn is the mutual coupling coefficient characterizing the mutual coupling effect between two characteristic units \(m\) and \(n\), is the current distribution of characteristic unit \(m\), is the electric field of characteristic unit \(n\).

[0096] At the same time, the scattered field of the characteristic unit can also be characterized as

[0097]

[0098] Among them, \(\omega\) is the free space angular frequency, \(\mu\) is the magnetic permeability, is the free space dyadic Green's function. Combining formulas (5), (14) and (15) gives

[0099]

[0100] Among them, is the position vector of the \(i\)-th dipole of characteristic unit \(m\), is the position vector of the \(j\)-th dipole of characteristic unit \(n\), is the complex dipole moment of the \(i\)-th dipole of characteristic unit \(m\).

[0101] Step 5, construct and solve the equilibrium equation, calculate the actual excitation coefficient of each characteristic unit considering the mutual coupling effect in the flexible array environment, obtain the array factor of the entire flexible array, calculate the total scattered field of the entire flexible array, and calculate the radar cross section of the entire flexible array.

[0102] Based on obtaining the mutual coupling coefficient between any two characteristic units in the flexible array environment, construct a mutual coupling matrix characterizing the mutual coupling effect between the entire flexible arrays. Such as Figure 6As shown, in addition to the initial excitation received by each unit itself, it is also affected by the scattered fields of other surrounding units.

[0103] The specific steps are as follows:

[0104] (5a) According to the mutual coupling coefficients obtained in step 4, construct the balance equation among the entire flexible arrays.

[0105] Assume that the total number of elements in the flexible array is M, and the total scattered electric field on element m is

[0106]

[0107] where is the total scattered electric field of element m, is the initial incident electric field of element m, is the scattered electric field of other elements in the entire flexible array on element m.

[0108] The actual excitation coefficient of element m in the flexible array environment is

[0109]

[0110] where V m is the actual excitation coefficient of element m in the flexible array environment, is the current distribution of element m.

[0111] Meanwhile, the scattered electric field can be characterized as

[0112]

[0113] where V n is the initial excitation coefficient of element n, W n is the characteristic weight coefficient of element n, is the electric field of element n.

[0114] Combining formulas (18) - (20), the actual excitation coefficient considering the mutual coupling effect of the entire array is obtained

[0115]

[0116] where V m is the actual excitation coefficient of element m, is the initial excitation coefficient of element m.

[0117]

[0118] where is the current distribution of element m.

[0119] Construct the actual excitation array composed of the actual excitation coefficients of the entire flexible array according to the actual excitation coefficients characterized by formula (21). That is, the balance equation considering the mutual coupling effect between flexible arrays is:

[0120]

[0121] Among them, is the actual excitation array of each unit of the entire flexible array composed of actual excitation coefficients, is the initial excitation array of each unit of the entire flexible array composed of initial excitation coefficients. C is the mutual coupling matrix, and its elements are composed of the mutual coupling coefficients between any two flexible units. K is the matrix composed of the characteristic weight coefficients of each unit.

[0122]

[0123] Among them, V1 is the actual excitation coefficient of the first array element, and so on. The superscript T represents the transpose operation.

[0124]

[0125] Among them, is the initial excitation coefficient of the first array element, and so on.

[0126]

[0127] Among them, the elements in the matrix respectively represent the mutual coupling coefficients between any two flexible units in the entire flexible array.

[0128]

[0129] Among them, W1 is the characteristic weight coefficient of the first array element, and so on.

[0130] (5b) Solve the balance equation to obtain the actual excitation coefficients of each unit considering the mutual coupling effect in the flexible array environment, obtain the array factor of the entire array, calculate the total scattered field of the flexible array, and calculate the radar cross section of the flexible array.

[0131] Solve the balance equation of formula (23) to obtain the actual excitation coefficients of each unit in the flexible array environment

[0132]

[0133] Among them, U is the unit matrix, and the superscript -1 represents the matrix inversion operation, is the initial excitation coefficient of each flexible unit.

[0134] After obtaining the actual excitation of each flexible unit, the array factor of the entire flexible array can be characterized as

[0135]

[0136] Among them, P is the array factor of the flexible array.

[0137] Thus, the total scattered field of the entire flexible array can be calculated using the pattern multiplication theorem

[0138]

[0139] Among them, is the total scattered field of the entire flexible array, is the column array composed of the scattered fields of each flexible array, where is the scattered field of the flexible unit, is the spatial unit vector.

[0140] According to the obtained total scattered field of the entire flexible array, the radar cross-section of the flexible array is

[0141]

[0142] Among them, σ is the radar cross-section, R is the far-field distance, E s is the scattered field of the entire flexible array, E inc is the initial incident electric field of the entire flexible array.

[0143] Next, taking the cylindrical frequency selective surface array and the third-order Bessel flexible frequency selective surface array as examples, the present invention will be further described through the following simulation cases.

[0144] 1. Simulation parameters

[0145] As Figure 7 shown is the structure of the cylindrical frequency selective surface array, and the array scale is 31×31. As Figure 8 shown is the structure of the cylindrical frequency selective surface unit. The inner layer is a metal layer, and the outer layer is a dielectric layer. The central angle A of the unit is 2°, the radius R is 300 mm, the thickness H1 is 3 mm, the width W1 is 10 mm, the inner diameter r1 of the metal slit ring is 3 mm, and the outer diameter r2 is 4 mm. The dielectric constant δ1 is 4.0, and the loss tangent X1 is 0.004. The plane wave excitation amplitude is 1 V / m, the polarization direction is [0, -1, 0], and the excitation azimuth is θ = -90° to 90°, The calculation frequency is 8 GHz.

[0146] 2. Simulation parameters

[0147] As Figure 10The structural parameters of a third-order Bezier curve are shown. The coordinates of the four control points of the third-order Bezier curve are: [0,0,0], [80,0,100], [200,0,-100], [300,0,0]. As Figure 11 The schematic diagram of the third-order Bezier frequency selective surface array structure is shown. The array scale is 30×30. The inner layer is a dielectric layer, and the outer layer is a metal layer. For the dielectric layer, the inner diameter r3 of the metal slot ring is 2 mm, the outer diameter r4 is 4 mm, the thickness H2 is 2 mm, and the width W1 is 10 mm. The dielectric constant ε2 is 2.85, and the loss tangent χ2 is 0.023. The excitation amplitude of the plane wave is 1 V / m, the polarization direction is [-1,0,0], and the excitation azimuth is θ = -90° to 90°. The calculated frequency is 10 GHz.

[0148] 3. Simulation content and results

[0149] Figure 9 is the comparison of the monostatic radar cross section (RCS) of the cylindrical frequency selective surface array in the yoz plane using the present invention and the method of moments;

[0150] Figure 12 is the comparison of the monostatic RCS of the third-order Bezier frequency selective surface array in the xoz plane using the present invention and the method of moments;

[0151] From Figure 9 , Figure 12 it can be seen that the method for analyzing the scattering characteristics of the flexible conformal array structure using the present invention can accurately analyze the scattering field of the flexible array, and its results are basically consistent with those of the method of moments, verifying the effectiveness of the method of the present invention.

[0152] As Figure 13 shown, the present invention provides an apparatus 100 for analyzing the scattering characteristics of a flexible conformal array structure of the method, including:

[0153] A division module 110, configured to equally divide the total arc length of the curved surface according to the number of array elements to obtain a set of discrete coordinate points of each unit arc length;

[0154] A fitting module 120, configured to perform osculating circle fitting according to the set of discrete coordinate points of each unit arc length to obtain a fitting error; and determine the number of osculating circles for dividing the entire arc length curve according to a fitting error threshold;

[0155] A construction module 130, configured to construct characteristic units according to the number and radius of the osculating circles to obtain the current distribution of each characteristic unit;

[0156] A calculation module 140 is configured to calculate initial excitation coefficients, feature weight coefficients, mutual coupling coefficients between feature units of the flexible array, actual excitation coefficients, and the total scattered field of the flexible array, so as to obtain the radar cross section of the entire flexible array structure.

[0157] The present invention is not limited to the above embodiments. Based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and deformations to some of the technical features without creative labor according to the disclosed technical content, and these substitutions and deformations are within the protection scope of the present invention.

Claims

1. A method for analyzing the scattering characteristics of a flexible conformal array structure, characterized in that It includes the following steps: According to the curve equation of the flexible conformal surface, calculate the total arc length of the flexible conformal array structure surface; perform equal-arc-length division on the total arc length of the flexible surface according to the number of array elements to obtain the set of discrete coordinate points of the arc length of each unit of the flexible surface; Perform osculating circle fitting according to the set of discrete coordinate points of the arc length of each unit, and calculate the fitting error; set the fitting error threshold, and determine the number of osculating circles for dividing the entire arc length curve through iteration; Construct characteristic units according to the number and radius of the osculating circles, equivalently obtain the parameters of infinitesimal dipoles, and calculate the current distribution of each characteristic unit; According to the current distribution of each characteristic unit, calculate the initial excitation coefficient and characteristic weight coefficient of each characteristic unit, and further calculate the mutual coupling coefficient between the characteristic units of the flexible array; Construct and solve the balance equation, calculate the actual excitation coefficient of each characteristic unit considering the mutual coupling effect in the flexible array environment, obtain the array factor of the entire flexible array, calculate the total scattered field of the flexible array, and obtain the radar cross section of the entire flexible array structure.

2. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, characterized in that Perform equal-arc-length division on the total arc length of the flexible surface according to the number of array elements to obtain the set of discrete coordinate points of the arc length of each unit of the flexible surface, including: When the curve equation is known, perform numerical integration on the curve equation to obtain the arc length of the entire curve; when the curve equation is unknown, perform linear fitting on the known measured point coordinates to obtain the expression of the curve equation, and perform numerical integration on the curve equation to obtain the total arc length of the entire array surface curve; According to the total arc length of the flexible array surface curve and the number of array elements, perform equal-arc-length division on the total arc length to obtain the set of discrete coordinate points of the arc length of each unit.

3. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, wherein When the average value of the root mean square error of the fitting of the total arc length including multiple units is less than the set error threshold, the arc length including multiple units is fitted with an osculating circle: δ ≤ [δ] In the formula, δ is the root mean square error of the osculating circle fitting of multiple flexible units, and [δ] is the preset root mean square error threshold.

4. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, characterized in that, Construct characteristic units according to the number and radius of the osculating circles, equivalently obtain the parameters of infinitesimal dipoles, and calculate the current distribution of each characteristic unit, including: Equivalently obtain the scattered field of the characteristic unit through the quantum particle swarm optimization algorithm to obtain multiple sets of infinitesimal dipole parameters, and calculate the current distribution: In the formula, is the dipole current distribution, i is the number of discrete points of the arc length, N d is the number of dipoles, is the dipole moment of the dipole, v is the delta function, is the position vector of the characteristic unit, is the dipole position vector.

5. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, wherein Construct the balance equation considering the entire flexible array; Solve the balance equation to obtain the actual excitation coefficient of each unit considering the mutual coupling effect in the flexible array environment: Where, V is the initial excitation coefficient of each characteristic unit, is the current of the rotated characteristic unit, is the plane-wave excitation electric field, E is the plane-wave excitation intensity, is the unit vector of the polarization direction, k is the free-space wavenumber, is the plane-wave incident direction, is the position vector of the characteristic array element.

6. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, characterized in that Calculate the characteristic weight coefficient of each characteristic unit as follows: Where W is the feature weight coefficient of each feature unit, is the scattered field of the rotated feature unit calculated by the equivalent dipole, is the unit field calculated by the software, T x , T y , T z are the rotation matrices along the x, y, and z directions.

7. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, characterized in that Calculate the mutual coupling coefficient between the characteristic units of the flexible array as follows: where C mn is the mutual coupling coefficient characterizing the mutual coupling effect between two feature units m and n, is the position vector of the i-th dipole of feature unit m, is the position vector of the j-th dipole of feature unit n, is the free-space dyadic Green's function between the i-th dipole and the j-th dipole, is the complex dipole moment of the j-th dipole of the rotated feature unit n, is the complex dipole moment of the i-th dipole of the rotated feature unit m, is the complex dipole moment of the i-th dipole of feature unit m, T x , T y , T z are the rotation matrices along the x, y, and z directions.

8. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 1, characterized in that, Calculate the actual excitation coefficient V of each characteristic unit considering the mutual coupling effect in the flexible array environment m It is as follows: Wherein, V m is the actual excitation coefficient of the feature unit m, is the initial excitation coefficient of the feature unit m, V n is the initial excitation coefficient of the feature unit n, W n is the feature weight coefficient of the feature unit n, C mn is the mutual coupling coefficient characterizing the mutual coupling effect between the two feature units m and n, and M is the total number of flexible units; Construct the actual excitation column matrix composed of the actual excitation coefficients of the entire flexible array, that is, the balance equation considering the mutual coupling effect between the flexible arrays is: Among them, is the actual excitation array of each unit of the entire flexible array composed of actual excitation coefficients, is the initial excitation array of each unit of the entire flexible array composed of initial excitation coefficients, C is the mutual coupling matrix, and K is the matrix composed of the characteristic weight coefficients of each unit.

9. The method for analyzing the scattering characteristics of the flexible conformal array structure according to claim 8, wherein Calculate the total scattered field of the flexible array: wherein, is the total scattered field of the entire flexible array, P is the array factor of the entire flexible array, U is the identity matrix, is the column array composed of the scattered fields of each flexible element; The radar cross section of the entire flexible array structure obtained is: where σ is the radar cross section, R is the far-field distance, and E inc is the initial incident electric field of the entire flexible array.

10. An analysis device for the scattering characteristics of a flexible conformal array structure according to the method described in any one of claims 1-9, including: A division module for performing equal-arc-length division on the total arc length of the flexible conformal array surface according to the number of array elements to obtain the set of discrete coordinate points of the arc length of each unit; A fitting module for performing osculating circle fitting according to the discrete coordinate points of the arc length of each unit to obtain the fitting error; determining the number of osculating circles for dividing the entire arc length curve according to the fitting error threshold; A building module for constructing feature units according to the number and radius of osculating circles to obtain the current distribution of each feature unit; A calculation module for calculating the initial excitation coefficient, feature weight coefficient, mutual coupling coefficient between feature units of the flexible array, actual excitation coefficient and total scattered field of the flexible array to obtain the radar cross section of the entire flexible array structure.

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