Multi-dimensional amplitude and phase analysis method for conformal array antenna based on fusion optimization algorithm

Abstract

The present application relates to the field of conformal array antenna design, in particular to a multi-dimensional amplitude and phase analysis method for conformal array antenna based on fusion optimization algorithm, which improves the optimization effect. The scheme comprises: through brainstorming algorithm, the excitation factors of one-dimensional linear array and one-dimensional circular arc array are iteratively calculated and optimized, when the iterative calculation reaches the set number of rounds, the best idea currently searched is obtained, through particle swarm algorithm, the excitation factors of one-dimensional linear array and one-dimensional circular arc array are iteratively calculated and optimized according to the position information, when the iteration reaches the maximum number of iterations, the current obtained particle position information is decomposed to obtain the excitation factors of all units of the optimized one-dimensional linear array or one-dimensional circular arc array; the excitation factors of the optimized one-dimensional linear array and one-dimensional circular arc array are multiplied to obtain the excitation factors corresponding to the optimized two-dimensional conformal array. The present application is suitable for conformal array antenna design optimization.

Description

Technical Field

[0001] This invention relates to the field of conformal array antenna design, and specifically to a multi-dimensional amplitude and phase analysis method for conformal array antennas based on a fusion optimization algorithm. Background Technology

[0002] Common array structures are linear geometries, which can be directly synthesized using traditional methods such as Taylor, Chebyshev, and Hamming. Compared to planar arrays, conformal array synthesis first needs to overcome the problem of inconsistent maximum radiation directions of the elements. Since the energy radiated by each element is not the same under the same incoming wave direction, the influence of the element radiation pattern must be considered when performing conformal array synthesis. Therefore, some analytical methods used in planar array synthesis are no longer applicable in conformal array synthesis.

[0003] The element excitation synthesis of conformal array antennas is a nonlinear problem. To achieve beam control of large conformal antenna arrays, it is necessary to synthesize the excitation amplitude and phase of each radiating element according to the required beam characteristics and pointing. Regarding methods for pattern synthesis analysis and optimization of conformal array antennas, early conformal array synthesis relied on analytical mathematical methods to achieve synthesis for low-sidelobe pencil beams. However, analytical mathematical methods are generally applicable to known mathematical models, and some complex or nonlinear problems are difficult to solve analytically.

[0004] Therefore, current technologies for comprehensive analysis and optimization of conformal array antenna patterns are not flexible enough, involve a large amount of computation, and have limited optimization effects. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-dimensional amplitude and phase analysis method for conformal array antennas based on a fusion optimization algorithm, which greatly reduces the computational load of numerical optimization and improves the optimization effect.

[0006] This invention achieves the above objectives by adopting the following technical solution: a multi-dimensional amplitude and phase analysis method for conformal array antennas based on a fusion optimization algorithm, comprising:

[0007] Obtain the excitation factors of a one-dimensional linear array and a one-dimensional circular arc array;

[0008] The activation factors of a one-dimensional linear array and a one-dimensional circular arc array are optimized and iteratively calculated using a brainstorming algorithm. When the iteration reaches a set number of rounds, the best idea found at the moment is obtained. This best idea contains a vector of activation factors of all units of the one-dimensional linear array or the one-dimensional circular arc array. This best idea will be passed as position information to an initial particle in the particle swarm algorithm during the initialization of the particle swarm algorithm.

[0009] The particle swarm optimization algorithm is used to optimize and iterate the excitation factors of the one-dimensional linear array and the one-dimensional circular arc array based on the position information. When the maximum number of iterations is reached, the currently obtained particle position information is decomposed to obtain the optimized excitation factors of all units of the one-dimensional linear array or the one-dimensional circular arc array.

[0010] Multiply the optimized one-dimensional linear array by the excitation factor of the one-dimensional circular arc array element to obtain the excitation factor corresponding to the optimized two-dimensional conformal array.

[0011] Furthermore, the method also includes:

[0012] Obtain one-dimensional linear array radiation patterns and one-dimensional circular arc array radiation patterns;

[0013] Multiplying the one-dimensional linear array pattern with the one-dimensional circular arc array pattern yields the two-dimensional conformal array antenna pattern.

[0014] Set an objective function, which serves as the fitness function for the brainstorming and particle swarm optimization algorithms in the iterative calculation. The calculated activation factor makes the one-dimensional linear array pattern and the one-dimensional circular arc array pattern as close as possible to the corresponding target pattern.

[0015] The objective function is: Where f d (θ, φ) is the desired synthesized ideal target pattern, M s F(θ, φ) is the number of sample points in the spatial angle, and F(θ, φ) is the radiation pattern of the two-dimensional conformal array antenna.

[0016] Furthermore, the method for obtaining the one-dimensional linear array pattern is as follows: k represents the free space wavenumber, F Linear (θ, φ) represents the radiation pattern of a one-dimensional linear array, where θ and φ represent the elevation and azimuth angles of the cylindrical conformal array antenna, respectively. n Let n be the coordinate position of the nth array element on the z-axis.

[0017] Furthermore, the method for obtaining the one-dimensional circular arc array pattern is as follows:

[0018]

[0019] F Quarter-ccircular (θ, φ) represents the one-dimensional circular arc array pattern, z m Let be the coordinate position of the m-th array element on the z-axis.

[0020] Furthermore, the method for obtaining the radiation pattern of the two-dimensional cylindrical conformal array antenna is as follows:

[0021] FQuarter-cylinder (θ, φ) = F Linear (θ,φ)×F Quarter-circular (θ, φ).

[0022] Furthermore, the method for obtaining the excitation factor of the one-dimensional linear array is as follows: I n =a n +jb n a n Incentive factor I n The real part, b n Incentive Factor I n The imaginary part of , where j is the imaginary unit.

[0023] The method for obtaining the excitation factor of the one-dimensional circular arc array is as follows: I m =a m +jb m a m Incentive factor I m The real part, b m Incentive factor I m The imaginary part.

[0024] The excitation factor corresponding to the two-dimensional conformal array is:

[0025] I mn =I m I n =(a m +jb m )×(a n +jb n ) = a mn +jb mn I mn a represents the excitation factor corresponding to the radiation pattern of a two-dimensional cylindrical conformal array antenna. mn For I mn The real part, b mn For I mn The imaginary part.

[0026] Furthermore, the optimization and iterative calculation of the activation factors for one-dimensional linear arrays and one-dimensional circular arc arrays using a brainstorming algorithm specifically includes:

[0027] The brainstorming algorithm first generates N ideas and then divides them into M clusters based on similarity, where N = 4d + 1, M = N / 5, and d is the dimension of the algorithm's optimization variables. In a one-dimensional linear array, N = 65, M = 13; in a one-dimensional circular array, N = 129, M = 26. Each algorithm is represented by a d-dimensional vector, where d is determined by the number of optimization variables. Then, the cluster center of each cluster is selected, and N new ideas are generated based on the current best idea. The way new ideas are generated is determined by several random parameters, and a new idea is randomly generated from one or more clusters.

[0028] Ideas are updated using the following formula:

[0029]

[0030]

[0031] Where K is the maximum number of iterations, and k is the current number of iterations. It is a Gaussian random vector with a mean of 0 and a variance of 1. yes A weighted coefficient, which also includes a random variable. And it changes with the number of iterations, new ideas Born from the ideas of the previous generation according to Formula generation;

[0032] When a new idea is created by a cluster It is either the best idea for selecting a cluster or a randomly generated idea, when generated jointly by two clusters. At that time, according to A new idea for generating random proportions using formulas. Related to the size of the search space, R is a random number between 0 and 1.

[0033] Furthermore, the optimization and iterative calculation of the excitation factors of the one-dimensional linear array and the one-dimensional circular arc array based on the position information using the particle swarm optimization algorithm specifically includes:

[0034] The particle swarm optimization algorithm first randomly generates the positions of n particles. One of the initial particles receives the best idea obtained through brainstorming and iterative optimization. This best idea is then assigned as the position information to that initial particle.

[0035] Each particle records its personal best position and the global best position of the entire swarm. Based on the recorded best position, the velocity and position for the next iteration are updated according to the following formula:

[0036] The subscript n and superscript k represent the nth particle in the kth iteration, where n = 5d + 1, meaning the number of particles in the particle swarm optimization algorithm is the same as the number of ideas in the brainstorming algorithm.

[0037] It is the position of each particle. It's speed, w k It is an inertia factor that changes with the number of iterations. and These represent the individual's optimal position and the global optimal position. c1 and c2 are weighting coefficients. and It is a random variable in the range {0, 1}.

[0038] The beneficial effects of this invention are as follows:

[0039] This invention decomposes the radiation pattern of a two-dimensional conformal array antenna into a two-dimensional one-dimensional array radiation pattern, namely a one-dimensional linear array radiation pattern and a one-dimensional circular arc array radiation pattern. At the same time, it decomposes the excitation factor of the two-dimensional conformal array into the excitation factor of the one-dimensional linear array and the excitation factor of the one-dimensional circular arc array, which greatly reduces the computational workload of numerical optimization and improves the computational efficiency.

[0040] This invention is based on a fusion optimization algorithm that combines brainstorming and particle swarm optimization. By using brainstorming and particle swarm optimization to perform iterative optimization calculations on the decomposed array radiation pattern and excitation factors, better array antenna analysis results are obtained, avoiding locality of optimization and improving the overall optimization effect. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of a cylindrical conformal array antenna provided in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of the brainstorming algorithm flow provided in an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the particle swarm algorithm provided in an embodiment of the present invention;

[0044] Figure 4 This is a schematic diagram of the brainstorming-particle swarm optimization algorithm provided in an embodiment of the present invention;

[0045] Figure 5 This is a schematic diagram illustrating the optimized effect of the array antenna provided in an embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0047] This invention comprises two core components: conformal array antenna pattern decomposition and optimization based on a fusion optimization algorithm.

[0048] I. Decomposition of Conformal Array Antenna Radiation Pattern

[0049] like Figure 1 The figure shows a schematic diagram of a cylindrical conformal array antenna provided in an embodiment of the present invention. As shown, a quarter-cylindrical coordinate system is established, with the center of the top surface of the cylinder as the origin O. The x-axis and y-axis are located on the top surface and are perpendicular to each other, and the z-axis is the center line of the cylinder. According to the relevant theory of coordinate system transformation, the above rectangular coordinate system can be converted into a spherical coordinate system.

[0050] The antenna radiation pattern of a cylindrical conformal array can be calculated by superimposing the radiation fields of each radiating element, and can be expressed as:

[0051] Where f mn (θ, φ) are the radiation directivity factors of the unit oscillator, where θ and φ are the pitch and azimuth angles of the cylinder, respectively. mn and Z mn Let be the angular and axial positions of the m-th and n-th elements, respectively, where k is the free-space wavenumber and R is the radius of the conformal cylindrical structure. The excitation of the m-th and n-th elements can be expressed as:

[0052] When synthesizing the array factor of a conformal antenna, unlike a planar array where each factor faces a different direction, it is necessary to rotate the main lobe direction of each element according to its position in the array before superposition. The calculation uses the cosine wave angle commonly used in directional antenna elements. q The (θ) model models the radiation pattern of a microstrip antenna element, and taking q = 1, the antenna element radiation pattern is approximated as follows:

[0053]

[0054] To reduce the dimensionality of the solution space in the optimization algorithm, and since the radiation direction characteristics in the θ and φ directions can be separated, this invention synthesizes the one-dimensional array radiation pattern from the two dimensions respectively. The final two-dimensional cylindrical array radiation pattern will be the product of the two one-dimensional array direction factors. The two decomposed one-dimensional arrays are as follows:

[0055] (1) A linear array arranged along the Z-axis has a radiation pattern F. Linear(θ, φ). The ideal array orientation factor as the target when optimizing a linear array can be expressed as:

[0056]

[0057] This array factor provides a beam pointing at θ = 90° with a width of 14°. Since the linear array is uniformly arranged along the Z-axis, the array factor remains unchanged in the φ direction, eliminating the need for element pattern rotation. Therefore, the linear array factor along the Z-axis can be directly expressed as a weighted excitation factor through the superposition of elements:

[0058] z n Let n be the coordinate position of the nth array element on the z-axis.

[0059] (2) An arc-shaped array along the φ direction, having a radiation pattern F Quarter-circular (θ, φ). When the array only has non-zero modes when θ is between 83° and 97°, it is only necessary to synthesize an arc-shaped array along the φ direction when θ is between 83° and 97°. The ideal array orientation factor as the target when optimizing the arc array can be expressed as:

[0060]

[0061] This array factor gives a beam pointing at φ = 45°. By rotating the radiation patterns of each element in the circular arc array according to its position along φ, weighting them with excitation factors, and then superimposing them, the radiation pattern of the circular arc array can be represented as:

[0062] z m Let be the coordinate position of the m-th array element on the z-axis.

[0063] Finally, after completing the comprehensive analysis of linear arrays and circular arrays respectively, the obtained F Linear (θ, φ) and F Quarter-circular The product of (θ, φ) is the two-dimensional cylindrical array pattern:

[0064] F Quarter-cylinder (θ, φ) = F Linear (θ,φ)×F Quarter-circular (θ, φ);

[0065] Multiplying the amplitude and phase excitation factors obtained from the two sets of one-dimensional arrays together yields the required excitation factor I for each element in the two-dimensional array. mn That is, under the requirement of synthesizing the above target beam, the excitation factor corresponding to the m-th element in the φ direction and the n-th element in the Z direction can be expressed as:

[0066] I mn =I m In =(a m +jb m )×(a n +jb n ) = a mn +jb mn ;

[0067] Where a mn and b mn Let be the real and imaginary parts of the excitation for this element, which represent the required excitation for each element obtained through final optimization. Since the previous section decomposed the entire conformal array pattern into the product of the linear array and the circular arc array pattern, the element excitations of the two decomposed arrays will be used as optimization variables for the algorithm, respectively.

[0068] That is, the excitation I of each element of the linear array n The real part a n and the imaginary part b n This will be used as an optimization variable in the fusion algorithm for the linear array. The excitation I of each element of the circular arc array... m The real part a m and the imaginary part b m This will be used as the optimization variable in the fusion algorithm for the effect of the circular arc array. After obtaining the optimal solutions for the two decomposed arrays, their product is the optimal solution for the conformal array.

[0069] To find the activation factors required for two one-dimensional arrays, it can be transformed into an optimization problem, namely, finding a set of (a m b m ), (a n b n This ensures that the one-dimensional linear array pattern and the one-dimensional circular arc array pattern are closest to the corresponding target pattern, thus obtaining F. Linear (θ, φ) and F Quarter-circular (θ, φ) and target pattern f d，Linear (θ, φ) and f d，Quarter-cylinder (θ, φ) is closest.

[0070] To achieve this goal, the objective function is set as follows:

[0071]

[0072] Where f d (θ, φ) is the desired synthesized ideal target pattern, M s This refers to the number of sample points in the spatial angle. The objective function FITNESS serves as the fitness function for both the brainstorming and particle swarm optimization algorithms in the iterative calculations. In the array synthesis analysis, this invention selects (a... n b n ), (a m bm (a) is the variable to be optimized, with total dimensions of 16 and 32, representing the real and imaginary parts of the excitation factors for 8 and 16 antenna elements, respectively. After preliminary calculations and optimizations, (a) is obtained. n b n ), (a m b m The approximate optimal value of ) is within 15, so in order to reduce the amount of computation, the solution space is selected as (-20, 20) in this invention.

[0073] II. Optimization based on fusion optimization algorithm

[0074] BSO (Brainstorm Optimization) is a genetic algorithm. Inspired by collective human behavior, it represents group problem-solving. By organizing ideas from diverse backgrounds and using different approaches, it facilitates the collision of ideas among groups, thereby improving the ability to find solutions.

[0075] like Figure 2 As shown, the BSO algorithm specifically includes: First, generating N ideas and dividing them into M clusters based on similarity. Here, N = 4d + 1, M = N / 5, and d is the dimension of the algorithm's optimization variables. Since there are 16 variables to be optimized in a linear array and 32 variables to be optimized in a circular array, N = 65 and M = 13 in the linear array; and N = 129 and M = 26 (rounded down) in the circular array. Each algorithm is a d-dimensional vector, where d is determined by the number of optimization variables. Then, the cluster center of each cluster is selected, and N new ideas are generated based on the current best idea. The way new ideas are generated is determined by several random parameters. A new idea may be randomly generated from one or more clusters. Ideas are updated using the following formula:

[0076]

[0077]

[0078] Where K is the maximum number of iterations, and k is the current number of iterations. It is a Gaussian random vector with a mean of 0 and a variance of 1. yes A weighted coefficient, which also includes a random variable. And it changes with the number of iterations, new ideas Born from the ideas of the previous generation according to Formula generation;

[0079] When a new idea is created by a cluster It is either the best idea for selecting a cluster or a randomly generated idea, when generated jointly by two clusters. At that time, according to A new idea for generating random proportions using formulas. Related to the size of the search space, so as to cover the entire solution space in the initial iterations that encourage exploration, R is a random number between 0 and 1.

[0080] The new ideas are evaluated by comparing them with the previous generation of ideas, and the idea with the best adaptability is retained as the best idea in this round.

[0081] When the algorithm iterates to a set number of rounds, the brainstorming algorithm will obtain a best-practice idea, which is a vector containing all the excitations of the linear or circular array of cells. This idea will be passed as position information to an initial particle during the initialization of the particle swarm optimization algorithm.

[0082] PSO (Particle Swarm Optimization) is an optimization algorithm that simulates the behavior of flocks of birds or schools of fish. It searches for the optimal solution by simulating the position and velocity of each individual particle in the solution space, as well as the information sharing among the particles. The position of each particle is a d-dimensional coordinate, where d is the dimension of the algorithm's optimization variables. That is, the position information of each particle is a d-dimensional vector, and the d elements of the phasor are the real and imaginary parts of the excitations of all cells in the array.

[0083] like Figure 3 As shown, the particle swarm optimization algorithm includes:

[0084] Particle initialization involves randomly generating the positions of n particles, one of which is assigned the optimal solution obtained from the BS0 algorithm. Then, the fitness function is calculated. Each particle records its personal best position (pbest) and the global best position (gbest) for the entire swarm. Based on the recorded optimal positions, the velocity and position for the next iteration are updated according to the following formula:

[0085] The subscript n and superscript k represent the nth particle in the kth iteration, where n = 5d + 1, meaning the number of particles in the particle swarm optimization algorithm is the same as the number of ideas in the brainstorming algorithm.

[0086] It is the position of each particle. It's speed, w k It is an inertia factor that changes with the number of iterations. and These represent the individual's optimal position and the global optimal position. c1 and c2 are weighting coefficients. and It is a random variable in the range {0, 1}.

[0087] When the maximum number of iterations is reached, the particle swarm optimization algorithm will generate an optimal particle position. The position information of this particle is the real and imaginary parts of the element excitation of the linear or circular array obtained by decomposition, which yields the optimal excitation factor.

[0088] As can be seen from the algorithms described above, BSO increases the number of random variables in its design, which helps to increase the diversity of generated ideas, thus providing better search capabilities when solving high-dimensional problems. On the other hand, the PSO algorithm continuously converges to generate new positions from the optimal particle position. Therefore, when the PSO algorithm has a relatively good initial position, PSO performs better than BSO. To better explore high-dimensional spaces and improve the convergence speed of the algorithms, BSO and PSO algorithms are fused to obtain the Brainstorming-Particle Swarm fusion optimization algorithm.

[0089] like Figure 4 As shown, the fusion algorithm includes: initializing ideas, calculating the fitness function after initialization, dividing ideas into different clusters, selecting the cluster center to generate a new idea, and passing the new idea as position information to the first generation particles. The first generation particles receive the new idea, which contains particle position information, and then calculate the fitness function to calculate the individual best position pbest and the global best position gbest of the entire group. The particle velocity and position are updated according to the best position. Finally, it is determined whether the conditions are met. If they are met, the algorithm ends.

[0090] Specifically, this includes sequentially merging BSO and PSO to leverage both algorithms and achieve fast convergence. First, each idea in the population is randomly initialized in the entire D-dimensional solution space of BSO, with each idea represented by a vector containing all unit excitation information. BSO is executed iteratively until a predetermined switching round is reached. Then, the optimal idea and best fitness from BSO are passed to PSO. All particles continue to execute the particle swarm optimization algorithm, iterating using unit excitations as particle position information until a termination condition is met.

[0091] After applying the algorithm to the linear array and the circular arc array respectively, the optimal element excitation for the linear array and the optimal element excitation for the circular arc array are obtained. Multiplying the two sets of excitation matrices gives the optimal excitation for the conformal array.

[0092] In the fusion algorithm, key parameters are adjusted accordingly.

[0093] Inert factor w in particle swarm optimization k In particle swarm optimization (PSO), this parameter is used to balance global exploration and local exploitation. It represents the tendency of particles to maintain their original state, such as... As shown in the formula. Previous studies on PSO have shown that in order to obtain the optimal element excitation solution, the inertia factor w k It needs to be reduced linearly within the range of 0.9 to 0.4.

[0094] The optimization method proposed in this invention enhances the global exploration capability of the particle swarm optimization algorithm by introducing a brainstorming algorithm before the particle swarm optimization algorithm. At this point, the global exploration capability of the particle swarm optimization algorithm is no longer emphasized. Therefore, to avoid wasting iterations and enhance the advantages of the particle swarm optimization algorithm in the local development process, the value of the inertia factor is adjusted. Through research on different values, the inertia factor must satisfy the following rule: w k Within the range of 0.8-0.3, the value decreases linearly with the increase of the number of iterations.

[0095] Furthermore, in the optimization method, it is essential to select an appropriate switching frequency to ensure that both the brainstorming algorithm and the particle swarm optimization algorithm can leverage their respective strengths. The number of switching frequencies should meet the following rule: for solution spaces with less than 25 dimensions, select 10% of the maximum number of iterations as the number of switching frequencies.

[0096] The final optimization result is as follows Figure 5 As shown, the brainstorming-particle swarm optimization algorithm (HBPSO) most closely approximates the ideal pattern. Compared to PSO and BSO, the HBPSO fusion algorithm has a faster convergence speed, especially advantageous when applied to large-scale optimization problems such as large array synthesis.

[0097] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A multi-dimensional amplitude and phase analysis method for conformal array antennas based on fusion optimization algorithms, characterized in that, include: The excitation factors of the two-dimensional conformal array are decomposed into the excitation factors of the one-dimensional linear array and the one-dimensional circular arc array, and the excitation factors of the one-dimensional linear array and the one-dimensional circular arc array are obtained. The activation factors of a one-dimensional linear array and a one-dimensional circular arc array are optimized and iterated through a brainstorming algorithm. When the iteration reaches a set number of rounds, the best idea found is obtained. The best idea contains a vector of activation factors of all units of the one-dimensional linear array or the one-dimensional circular arc array. This best idea will be passed to an initial particle in the particle swarm algorithm as position information during the initialization of the particle swarm algorithm. The particle swarm optimization algorithm is used to optimize and iterate the excitation factors of the one-dimensional linear array and the one-dimensional circular arc array based on the position information. When the maximum number of iterations is reached, the currently obtained particle position information is decomposed to obtain the optimized excitation factors of all units of the one-dimensional linear array or the one-dimensional circular arc array. Multiply the optimized one-dimensional linear array by the excitation factor of the one-dimensional circular arc array element to obtain the excitation factor corresponding to the optimized two-dimensional conformal array.

2. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 1, characterized in that, The method also includes: Obtain one-dimensional linear array radiation patterns and one-dimensional circular arc array radiation patterns; Multiplying the one-dimensional linear array pattern with the one-dimensional circular arc array pattern yields the two-dimensional conformal array antenna pattern. Set an objective function, which serves as the fitness function for the brainstorming and particle swarm optimization algorithms in the iterative calculation. The calculated activation factor makes the one-dimensional linear array pattern and the one-dimensional circular arc array pattern as close as possible to the corresponding target pattern. The objective function is: ,in It is the desired synthesized ideal target pattern. It is the number of sample points in the spatial angle. This is the radiation pattern of a two-dimensional conformal array antenna.

3. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 2, characterized in that, The method for obtaining the one-dimensional linear array pattern is as follows: k represents the free space wavenumber. This represents the radiation pattern of a one-dimensional linear array. and These represent the elevation and azimuth angles of the cylindrical conformal array antenna, respectively. Let be the coordinate position of the nth array element on the z-axis. motivating factors The real part, Indicating incentive factors The imaginary part of , j is the imaginary unit, and N is the total number of one-dimensional linear array elements.

4. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 3, characterized in that, The method for obtaining the one-dimensional circular arc array pattern is as follows: ， This represents a one-dimensional circular arc array radiation pattern. Let be the coordinate position of the m-th array element on the z-axis. motivating factors The real part, motivating factors The imaginary part of is R, which is the radius of the conformal cylindrical structure, and M is the total number of one-dimensional circular arc arrays.

5. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 4, characterized in that, The method for obtaining a two-dimensional conformal array antenna pattern by multiplying a one-dimensional linear array pattern by a one-dimensional circular arc array pattern is as follows: 。 6. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 1, characterized in that, The method for obtaining the excitation factor of a one-dimensional linear array is as follows: = , motivating factors The real part, motivating factors The imaginary part of , where j is the imaginary unit.

7. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 6, characterized in that, The method for obtaining the excitation factor of the one-dimensional circular arc array is as follows: = , motivating factors The real part, motivating factors The imaginary part.

8. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 7, characterized in that, The excitation factor corresponding to the two-dimensional conformal array is: , This represents the excitation factor corresponding to the radiation pattern of a two-dimensional cylindrical conformal array antenna. for The real part, for The imaginary part.

9. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 1, characterized in that, The optimization iterative calculation of the activation factors of a one-dimensional linear array and a one-dimensional circular arc array using a brainstorming algorithm specifically includes: The brainstorming algorithm first generates N ideas and then divides them into M clusters based on similarity, where N = 4d + 1, M = N / 5, and d is the dimension of the algorithm's optimization variables. In a one-dimensional linear array, N = 65, M = 13; in a one-dimensional circular array, N = 129, M = 26. Each idea is a d-dimensional vector, and d is determined by the number of optimization variables. Then, the cluster center of each cluster is selected, and N new ideas are generated based on the current best idea. The way new ideas are generated is determined by several random parameters, and a new idea is randomly generated from one or more clusters. Ideas are updated using the following formula: ， ； ， ； Where K is the maximum number of iterations, and k is the current number of iterations. It is a Gaussian random vector with a mean of 0 and a variance of 1. yes A weighted coefficient, which also includes a random variable. And it changes with the number of iterations, new ideas Born from the ideas of the previous generation according to Formula generation; When a new idea is created by a cluster It is either the best idea for selecting a cluster or a randomly generated idea, when generated jointly by two clusters. At that time, according to A new idea for generating random proportions using formulas. Related to the size of the search space, It is a random number between 0 and 1. These are the best ideas for two clusters. Representing variables respectively The upper and lower bounds.

10. The method for multi-dimensional amplitude and phase analysis of conformal array antennas based on fusion optimization algorithm according to claim 1, characterized in that, The optimization iterative calculation of the excitation factors of the one-dimensional linear array and the one-dimensional circular arc array based on the position information using the particle swarm optimization algorithm specifically includes: The particle swarm optimization algorithm first randomly generates the positions of n particles. One of the initial particles receives the best idea obtained through brainstorming and iterative optimization. This best idea is then assigned as the position information to that initial particle. Each particle records its personal best position and the global best position of the entire swarm. Based on the recorded best position, the velocity and position for the next iteration are updated according to the following formula: , The subscript n and superscript k represent the nth particle in the kth iteration, n=5d+1, that is, the number of particles in the particle swarm algorithm is the same as the number of ideas in the brainstorming algorithm; It is the position of each particle. It's speed. It is an inertia factor that changes with the number of iterations. and These represent the individual's optimal position and the global optimal position. c1 and c2 are weighting coefficients. and It is a random variable in the range {0,1}.

Images