A sparse fabric planar array synthesis method

Abstract

This invention relates to the field of array antenna synthesis, and more particularly to a method for synthesizing sparsely distributed planar arrays. To balance the development and exploration processes, this invention employs nonlinear function reconstruction for the arithmetic optimization accelerator in the arithmetic optimization algorithm; it uses the top three best individuals to replace the current best individual for exploration and development and introduces an elite mutation strategy to enhance the algorithm's ability to escape local optima and improve its convergence accuracy; it proposes an adaptive matrix mapping rule to judge the current array element distribution, and if it does not meet the minimum element spacing constraint, it adjusts it through an adjustment strategy, avoiding infeasible solutions while ensuring the degrees of freedom of the array elements.

Description

Technical Field

[0001] This invention relates to the field of array antenna synthesis, and more particularly to a method for synthesizing sparsely distributed planar arrays. Background Technology

[0002] Array synthesis is a key research area in the field of array antennas. Its core is determining the number of array elements and the excitation phase, amplitude, and position of each element according to the required array radiation characteristics. When each element in the array antenna is an isotropic radiating element, the synthesis of a uniformly weighted array can be simplified to optimizing the position of each element in the array. Currently, the optimization of element positions mainly falls into two categories: sparse array optimization, which only allows element positions to appear at given grid points, and sparse array optimization, which allows each element to be freely placed under given array aperture and element spacing constraints. Because sparse arrays have higher element freedom, the desired radiation characteristics can usually be achieved with fewer elements, giving them a significant advantage over sparse arrays.

[0003] Synthesis of sparse planar arrays has always been a challenging problem due to the minimum element spacing constraint. Existing methods for synthesizing sparse planar arrays adjust the element positions to satisfy the minimum element spacing constraint. While this avoids infeasible solutions, it also forces adjustments to many array distributions that originally met the minimum element spacing constraint, limiting the degrees of freedom of the elements and causing some feasible solutions to be unsearchable. Furthermore, existing intelligent optimization algorithms suffer from low search efficiency and insufficient convergence accuracy during array antenna optimization.

[0004] To address the above problems, this invention proposes a synthesis method for sparse planar arrays based on an improved arithmetic optimization algorithm, which can ensure the degree of freedom of array elements and improve optimization accuracy while avoiding infeasible solutions. Summary of the Invention

[0005] To overcome the problems in the prior art, this invention proposes a sparsely distributed planar array synthesis method.

[0006] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a synthesis method for sparsely distributed planar arrays, specifically including the following steps:

[0008] Step 1. Assume there is a rectangular sparsely distributed planar array with an array aperture of 2L×2H on the xoy plane, the number of array elements is 4N, and the array is symmetric about the x-axis and y-axis. Construct the initialization population matrix of the rectangular sparsely distributed planar array.

[0009] Step 2. Use the adaptive matrix mapping rule to map individuals in the initial population matrix to the actual positions of array elements, and calculate the fitness of each individual;

[0010] Step 3. Calculate the values ​​of the arithmetic optimization accelerator coefficients based on the current iteration number;

[0011] Step 4. Select either exploration update or development update based on the value of the arithmetic optimization accelerator coefficient;

[0012] Step 5. Perform elite mutation on the globally optimal individual;

[0013] Step 6. If the maximum number of iterations is reached, output the optimization result and exit; otherwise, proceed to step 2.

[0014] Furthermore, step 1 includes: selecting an appropriate optimized array matrix dimension based on the array aperture, wherein the optimized array matrix dimensions P and Q need to satisfy:

[0015]

[0016] Where, d c This represents the minimum array element spacing.

[0017] Furthermore, step 2 specifically includes the following steps:

[0018] Step 21. Initialize the population matrix. There are m individuals, each with n dimensions, where n is 3P×Q. The first P×Q variables of each individual are the x-direction mapping matrix A∈R. P×Q The mapping matrix B∈R from P×Q+1 to 2P×Q is in the y-direction. P×Q Finally, the P×Q variables form a weight matrix W∈R P×Q ;

[0019] Step 22. Based on the minimum element spacing d of the optimized array c The array dimensions P and Q generate a fixed partial matrix DX ∈ R in the x-direction. P×Q The fixed part matrix DY∈R in the y-direction P×Q ;

[0020] Step 23. Determine the actual position matrix X of the array elements in the x direction based on the mapping matrix A in the x direction, and determine the actual position matrix Y of the array elements in the y direction based on the mapping matrix B in the y direction;

[0021] Step 24. Calculate the distance between array elements in different rows and columns based on the actual position of each array element; if the minimum array element spacing constraint is not met, then adaptively adjust the array element positions.

[0022] Step 25. Calculate the fitness of the current individual based on the actual position of the current array element.

[0023] Step 23 specifically includes the following steps:

[0024] Sort each row of the mapping matrix A in the x-direction from smallest to largest to form the sorted mapping matrix A′ in the x-direction, and combine it with the fixed part matrix DX in the x-direction to obtain the actual position matrix X of the array elements in the x-direction.

[0025] Arrange the elements of each column of the mapping matrix B in the y-direction from smallest to largest to form the sorted mapping matrix B' in the y-direction, and combine it with the fixed part matrix DY in the y-direction to obtain the actual position matrix Y of the array elements in the y-direction.

[0026] Furthermore, step 24 specifically includes the following steps:

[0027] Generate the offset matrix B based on the mapping matrix B' in the y-direction. offset :

[0028]

[0029] Where, β i,max β is the maximum value of each row in the mapping matrix B' in the y-direction. i,max Monotonically increasing; This represents the maximum value in the z-row of the sorted y-direction mapping matrix B';

[0030] like The mapping matrix B' in the y-direction is further adjusted, and the offset matrix B is updated. offset ;

[0031]

[0032] In the formula, d c Indicates the minimum array element spacing;

[0033] After adjustment, the actual coordinate matrix Y in the y-direction of each array element is:

[0034] Y = B′ + DY + B offset .

[0035] Furthermore, step 3 specifically includes the following steps:

[0036] The mathematical model for reconstructing the arithmetic optimization accelerator coefficients using nonlinear functions yields the following values:

[0037]

[0038] Where G is the current iteration number, G M It represents the maximum number of iterations, and Max and Min represent the maximum and minimum values ​​of the arithmetic optimization accelerator coefficients, respectively.

[0039] Furthermore, step 4 specifically includes the following steps:

[0040] Before each individual updates, a random number r is generated uniformly distributed between [0,1]. When r>MOA(G), the development stage is selected; otherwise, the exploration stage is selected, where G is the current iteration number.

[0041] The following formula is used for updating during the exploration phase:

[0042]

[0043] During the development phase, the following update method is used:

[0044]

[0045] leader=(gbest+best2+best3) / 3

[0046] Where, p i,j LB represents the element of the j-th dimension of the i-th individual. j and UB j ε represents the lower and upper bounds of the search space for the j-th dimension solution; μ is a constant used to control optimization; r2 and r3 are random numbers uniformly distributed between [0,1]; ε is a very small constant used to prevent division by zero; gbest represents the current best individual, best2 represents the current second-best individual, and best3 represents the current third-best individual; MOP (Multi-Objective Programming) is a mathematical optimization probabilistic generator used to control the accuracy of exploration and development; the mathematical model of MOP is:

[0047]

[0048] Where σ is the sensitivity coefficient, G 1 / σ It is the current iteration number, G M 1 / σ It represents the maximum number of iterations.

[0049] Furthermore, step 5 specifically includes the following steps:

[0050] Two individuals p are randomly selected from the population. rd1 p rd2 Elite mutation is performed on the globally optimal individual, and the elite mutated individual is gbest. * for:

[0051]

[0052] Where, p rd1 p rd2These are two individuals randomly selected from the current population, where F is the perturbation coefficient, r4 is a uniformly distributed random number between [0,1], and gbest represents the current best individual; the elite mutant individual gbest is calculated. * If the fitness of the current gbest is better than that of the current gbest, then the current gbest is updated.

[0053] Compared with the prior art, the present invention has the following technical effects:

[0054] To balance the development and exploration processes, this invention reconstructs the arithmetic optimization accelerator in the arithmetic optimization algorithm using a nonlinear function. It replaces the current best individual with the top three individuals for exploration and development and introduces an elite mutation strategy to enhance the algorithm's ability to escape local optima and improve its convergence accuracy. Furthermore, it proposes an adaptive matrix mapping rule to assess the current element distribution. If the distribution does not meet the minimum element spacing constraint, it adjusts the distribution through a strategy, avoiding infeasible solutions while ensuring the degree of freedom of the elements. Attached Figure Description

[0055] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of the improved arithmetic optimization algorithm of the present invention;

[0057] Figure 2 This is a convergence curve diagram of the present invention;

[0058] Figure 3 This is the optimal array element distribution diagram for Experiment 1 of this invention;

[0059] Figure 4 Experiment 1 of this invention Directional cross-section;

[0060] Figure 5 Experiment 1 of this invention Directional cross-section;

[0061] Figure 6 This is the three-dimensional orientation pattern corresponding to the optimal array element distribution in Experiment 1 of this invention;

[0062] Figure 7 Experiment 2 of this invention Directional cross-section;

[0063] Figure 8 This is the optimal array element distribution diagram for Experiment 2 of this invention;

[0064] Figure 9 This is a three-dimensional orientation pattern corresponding to the optimal array element distribution in Experiment 2 of this invention. Detailed Implementation

[0065] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the technical solutions proposed according to the present invention are described in detail below with reference to the accompanying drawings and preferred embodiments. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0066] This invention addresses the problems existing in the prior art by proposing an array antenna synthesis method based on an improved arithmetic optimization algorithm. First, to balance the development and exploration processes, a nonlinear function reconstruction is applied to the arithmetic optimization accelerator in the arithmetic optimization algorithm. Second, the top three best individuals are used instead of the current best individual for exploration and development, and an elite mutation strategy is introduced to enhance the algorithm's ability to escape local optima and improve its convergence accuracy. Finally, an adaptive matrix mapping rule is proposed to judge the current array element distribution. If it does not meet the minimum element spacing constraint, an adjustment strategy is used to adjust it, avoiding infeasible solutions while ensuring the degrees of freedom of the array elements.

[0067] Reference Figure 1 This invention proposes a synthesis method for sparsely distributed planar arrays, specifically including the following steps:

[0068] Step 1. Assume there is a rectangular sparsely distributed planar array with an array aperture of 2L×2H on the xoy plane, and the number of array elements is 4N. The array is symmetric about the x-axis and y-axis. Optimize the N array elements in the first quadrant to obtain the array elements in other quadrants by mirroring them, and construct the initial population matrix of the rectangular sparsely distributed planar array.

[0069] Choose an appropriate optimized array matrix dimension based on the array aperture. The optimized array matrix dimensions P and Q must satisfy the following:

[0070]

[0071] Where, d c This represents the minimum array element spacing.

[0072] To determine the elements to be sparsified, a weight matrix W is established with dimensions P×Q. W contains N 1s representing retained elements and P×QN 0s representing sparsed elements. The upper bound UB and lower bound LB of the optimization variables are set according to the specific rectangular sparse planar array.

[0073] Based on the upper bound UB and lower bound LB of the optimization variables, the population matrix P is randomly initialized, and its mathematical expression is as follows:

[0074]

[0075] Where P is the initial population matrix, and the population has m individuals, p m,n Let m represent the m-th individual. The dimension of an individual is n-dimensional, and the size of n is 3P×Q.

[0076] Step 2. Use the adaptive matrix mapping rule to map individuals in the initial population matrix to the actual positions of array elements, and calculate the fitness of each individual.

[0077] This step specifically includes:

[0078] Step 21. Initialize the population matrix. There are m individuals, each with n dimensions, where n is 3P×Q. The variable to be optimized is one individual in the population, and the first P×Q variables of each individual are... x The mapping matrix of direction A∈R P×Q The mapping matrix B∈R from P×Q+1 to 2P×Q is in the y-direction. P×Q Finally, the P×Q variables form a weight matrix W∈R P×Q P is the number of elements in each column of the mapping matrix, and Q is the number of elements in each row of the mapping matrix.

[0079]

[0080] Where, α P,Q The elements in row P and column Q of the mapping matrix A representing the x-direction, β P,Q Let α be the element in row P, column Q of the mapping matrix B in the y-direction, and let α be the element in the mapping matrix A in the x-direction [0, S]. x Random numbers within the interval, the element β in the mapping matrix B in the y-direction is [0, S]. y Random numbers within the interval; S x It is the margin S of the array element in the x-direction. x =L-(Q-0.5)d c S y It is the margin S of the array element in the y direction. y =H-(P-0.5)d c d c This represents the minimum array element spacing.

[0081] Step 22. Based on the minimum element spacing d of the array to be optimized c The array dimensions P and Q generate a fixed partial matrix DX ∈ R in the x-direction. P×Q The fixed part matrix DY∈R in the y-direction P×QThe purpose of the fixed part matrix is ​​to ensure that the spacing between two adjacent array elements in the same row and column satisfies the constraints in both the x and y directions.

[0082]

[0083] Where, matrix DX∈R P×Q The fixed portion of the matrix representing the x-direction, matrix DY∈R P×Q The fixed portion of the matrix represents the y-direction.

[0084] Step 23. Determine the actual position matrix X of the array elements in the x direction based on the mapping matrix A in the x direction, and determine the actual position matrix Y of the array elements in the y direction based on the mapping matrix B in the y direction.

[0085] Sort each row of the mapping matrix A in the x-direction from smallest to largest to form the sorted mapping matrix A′ in the x-direction, and combine it with the fixed part matrix DX in the x-direction to obtain the actual position matrix X of the array elements in the x-direction.

[0086]

[0087] X = A' + DX

[0088] In the above formula, X represents the actual position matrix of the matrix elements in the x-direction, A′ represents the sorted mapping matrix in the x-direction, and DX represents the fixed part of the matrix in the x-direction; α' P,Q The elements in row P and column Q of the sorted x-direction mapping matrix, α' i,1 ≤α' i,2 ≤…≤α' i,Q , i represents row, α i ' ,1 α' represents the element in row i, column 1 of the sorted x-direction mapping matrix. i,Q This represents the element in row i and column Q of the sorted x-direction mapping matrix.

[0089] Arrange the elements of each column of the mapping matrix B in the y direction from smallest to largest to form the sorted mapping matrix B' in the y direction, and combine it with the fixed part matrix DY in the y direction to obtain the actual position matrix Y of the array elements in the y direction.

[0090]

[0091] Y = B′ + DY

[0092] In the above formula, Y represents the actual position matrix of the matrix elements in the y-direction, B' represents the sorted mapping matrix in the y-direction, DY represents the fixed part of the matrix in the y-direction, and β' P,Q The elements in row P and column Q of the sorted y-direction mapping matrix, where j represents the column, β' 1,jβ' represents the element in row 1, column j of the sorted y-direction mapping matrix. P,j This represents the element in row P and column j of the sorted y-direction mapping matrix.

[0093] Step 24. Calculate the distance between each array element and array elements in different rows and columns based on the actual position of each array element; if the minimum array element spacing constraint is not met, then adaptively adjust the array element position.

[0094] Generate the offset matrix B based on the mapping matrix B' in the y-direction. offset :

[0095]

[0096] Where, β i,max β is the maximum value of each row in the sorted y-direction mapping matrix B'. Since each column of this matrix is ​​increasing, β increases with row i. i,max Monotonically increasing, This represents the sum of the maximum values ​​in each row of the mapping matrix B' in the y-direction from row 1 to row P-1.

[0097] like This indicates that directly adjusting the array elements in the P-th row will not meet the array aperture requirements. Therefore, further adjustments are needed to the sorted y-direction mapping matrix B', and the offset matrix B needs to be updated. offset ;

[0098]

[0099] After adjustment, the actual coordinate matrix Y in the y-direction of each array element is:

[0100] Y = B′ + DY + B offset

[0101] The y-direction distance between any two adjacent array elements is:

[0102]

[0103] Among them, y i+1,m y i,n β' represents the actual positions of the (i+1)th row and mth column element and the ith row and nth column element in the y-direction. i+1,m ,β' i,n The elements in the (i+1)th row and mth column and the ith row and nth column of the mapping matrix B' in the y-direction, respectively, β z,max β i,max These are the maximum values ​​of the z-th and i-th rows of the mapping matrix B' in the y-direction, respectively.

[0104] The x-direction distance between any two adjacent array elements in a row is:

[0105] x i,m+1 -x i,m =α' i,m+1 +(m+1-0.5)d c -α' i,m -(m-0.5)d c =α' i,m+1 -α' i,m +d c ≥d c

[0106] Where, x i,m+1 x i,m These are the actual positions of the array element in the i-th row and m+1-th column, and the array element in the i-th row and m-th column, respectively, in the x-direction, α'. i,m+1 It is the x-direction margin of the element in the i-th row and m+1-th column, α' i,m The x-direction margin of the array element in the i-th row and m-th column.

[0107] Since the distance between any array elements in the y-direction of any two adjacent rows and the distance between any array elements in the x-direction of any row satisfy the minimum array element spacing requirement, the spacing between any two array elements in the array also satisfies the minimum array element spacing requirement.

[0108] The above adjustment strategy applies to the case where the average adjustment margin in the x-direction is less than the average adjustment margin in the y-direction, i.e., S x / Q y / P, and vice versa.

[0109] Step 25. Calculate the fitness of the current individual based on the actual position of the current array element.

[0110] Step 3. Calculate the value of the Arithmetic Optimization Accelerator Coefficient (MOA) based on the current iteration number.

[0111] The mathematical model of the Math Optimizer Accelerated (MOA) coefficients, reconstructed using a nonlinear function, has the following values:

[0112]

[0113] Where G is the current iteration number, G M It represents the maximum number of iterations, and Max and Min represent the maximum and minimum values ​​of MOA, respectively.

[0114] Step 4. Select exploration update or development update based on the value of the Arithmetic Optimization Accelerator (MOA) coefficient.

[0115] Before each individual updates, a random number r is generated uniformly distributed between [0,1]. When r>MOA(G), the development stage is selected; otherwise, the exploration stage is selected, where G is the current iteration number.​

[0116] The following formula is used for updating during the exploration phase:

[0117]

[0118] During the development phase, the following update method is used:

[0119]

[0120] leader=(gbest+best2+best3) / 3

[0121] Where, p i,j p represents the element of the j-th dimension of the i-th individual. j LB represents the element of the j-th dimension. j and UB j These are the lower and upper bounds of the search space for the j-th dimension solution; μ is a constant used to control optimization, typically taking the value 0.499; r2 and r3 are random numbers uniformly distributed between [0,1]; ε is a very small constant used to prevent division by zero; gbest represents the current best individual, best2 represents the current second-best individual, and best3 represents the current third-best individual. MOP (Multi-Objective Programming) is a mathematical optimization probabilistic model. The mathematical model of MOP is:

[0122]

[0123] Where σ is the sensitivity coefficient, typically set to 5; MOP is a monotonically decreasing value that increases with the number of iterations, used to control the accuracy of exploration and development; G 1 / σ G is the power of 1 / σ of the current iteration number. M 1 / σ The current maximum number of iterations G M 1 / σ.

[0124] Step 5. Perform elite mutation on the globally optimal individual.

[0125] To further improve the AOA algorithm's ability to escape local optima and avoid premature convergence, an elite mutation strategy is introduced. During each generation of the population, the current best individual undergoes an elite mutation. In the early stages of the search, elite individuals rely on the mutation of other individuals in the population, making this mutation strategy relatively efficient. However, in the later stages of the search, due to the small differences between individuals, this mutation strategy becomes relatively inefficient.

[0126] To balance mutation efficiency in both the early and late stages of the search, two individuals p are randomly selected from the population. rd1 p rd2 Elite mutation is performed using the following formula:

[0127]

[0128] Where, p rd1 p rd2 These are two individuals randomly selected from the current population, where F is the perturbation coefficient and r4 is a random number uniformly distributed between [0,1]. The elite mutant individual gbest is calculated. * If the fitness of the current gbest is better than that of the current gbest, then the current gbest is updated.

[0129] Step 6. If the maximum number of iterations is reached, output the optimization result and exit; otherwise, proceed to step 2.

[0130] The experimental conditions for this invention are as follows: the array aperture of the sparsely distributed planar array is 2L×2H=9.5λ×4.5λ, the number of array elements is 4N=108, the minimum element spacing is d0=0.5λ, the array is symmetrical about the x-axis and y-axis, and the element positions in the other quadrants can be obtained by mirroring the positions of the elements in only the first quadrant. P is set to 4, and Q is set to 9. The population size of the optimization algorithm is set to 100, the maximum number of iterations is 1000, and 10 independent experiments are conducted. The parameters Max and Min of the improved arithmetic optimization algorithm are set to 1 and 0.2, respectively, and σ, μ, and F are set to 5, 0.499, and 0.03, respectively. The optimization objective is to make... and The fitness function is as follows: The sum of peak sidelobe levels on both planes is minimized.

[0131]

[0132] in, Here, θ represents the azimuth angle of the array. Indicates pitch angle, FF max X is the peak value of the main lobe, X is the actual position of the array element in the x direction, Y is the actual position of the array element in the y direction, and N 1s in the state matrix W represent the retained array elements.

[0133] Figure 2 This is the convergence curve of the IAOA algorithm. The optimal fitness value is -61.47 dB. The peak sidelobe level in the plane is -34.78 dB. The peak sidelobe level on the plane is -26.69 dB, the worst fitness is -55.63 dB, and the average fitness is -57.31 dB. Figures 3 to 5 The optimal array element distribution diagrams for different algorithms are given respectively. Directional section diagram and Directional cross-section diagram. Figure 6 It is the three-dimensional orientation pattern corresponding to the optimal value of the proposed algorithm.

[0134] The experimental conditions for this invention are as follows: the sparsely distributed planar array has an array size of 2L×2H=9.5λ×4.5λ, the number of array elements is 4N=100, the minimum element spacing is d0=0.5λ, the array is symmetrical about the x-axis and y-axis, P is 5, and Q is 9. The optimization objective is to minimize the peak sidelobe level while satisfying a specific null depth at a specified angle on the specified plane. Two nulls are placed on the plane at θ = 15° and θ = 45° respectively, with a desired null depth of -70dB. The Nth element is not fixed. The optimization algorithm population size is set to 100, the maximum number of iterations is 1000, and 10 independent experiments are conducted. The parameters Max and Min of the improved arithmetic optimization algorithm are set to 1 and 0.2 respectively, and σ, μ, and F are set to 5, 0.499, and 0.03 respectively. The fitness function is as follows:

[0135]

[0136]

[0137] Among them, FF max The peak value of the main lobe is M, where M is the number of nulls placed, and c and c i These are weighting coefficients, all with a value of 1 or null. d It is the expected depth of the null trap. o It is the actual zero-depression depth obtained.

[0138] The proposed improved algorithm yields an optimal peak sidelobe level of -32.68 dB, a null depth of -70.21 dB at θ = 15°, and a null depth of -72.98 dB at θ = 45°. Figure 7 and Figure 8 The above algorithms are given respectively. Cross-sectional view of the direction and optimal array element distribution diagram. Figure 9 It is the three-dimensional orientation pattern corresponding to the optimal value of the proposed algorithm.

[0139] In summary, the method of this embodiment effectively solves the problems of low search efficiency and insufficient convergence accuracy in current algorithms for synthesizing sparse planar arrays, which reduce the degree of freedom of array elements to avoid infeasible solutions. The improved arithmetic optimization algorithm of this invention has the characteristics of strong ability to escape local optima and high convergence accuracy, and the adaptive matrix mapping rule can ensure the degree of freedom of array elements while avoiding infeasible solutions. Compared with existing algorithms, the proposed method can effectively reduce the peak sidelobe level of sparse planar arrays by 0.75dB-3.07dB and improve the null depth by 0.2dB-2.97dB.

[0140] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated in this invention, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the steps or stages of other steps.

[0141] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for synthesizing sparsely distributed planar arrays, characterized in that, Specifically, the following steps are included: Step 1. Assume there is a rectangular sparsely distributed planar array with an array aperture of 2L×2H on the xoy plane, and the number of array elements is 4N. The array is about x axis, y Axisymmetric, construct the initial population matrix for a rectangular sparsely distributed planar array; Step 2. Use the adaptive matrix mapping rule to map the individuals in the initial population matrix to the actual positions of the array elements, and calculate the fitness of each individual; Step 3. Calculate the values ​​of the arithmetic optimization accelerator coefficients based on the current iteration number; Step 4. Select either exploration update or development update based on the value of the arithmetic optimization accelerator coefficient; Step 5. Perform elite mutation on the globally optimal individual; Step 6. If the maximum number of iterations is reached, output the optimization result and exit; otherwise, go to step 2. Step 3 specifically includes the following steps: The mathematical model for reconstructing the arithmetic optimization accelerator coefficients using nonlinear functions yields the following values: in, This is the current iteration number. It is the maximum number of iterations. Max and Min These are the maximum and minimum values ​​of the arithmetic optimization accelerator coefficients, respectively. Step 4 specifically includes the following steps: Before updating, each individual generates a random number uniformly distributed between [0,1]. r ,when Choose the development phase if the time is right, otherwise choose the exploration phase, where G is the current iteration number; The following formula is used for updating during the exploration phase: During the development phase, the following update method is used: in, Indicates the first i The first individual j Dimensional elements, Indicates the first j Dimensional elements, and It is the first j The lower and upper bounds of the search space for dimensional solutions. It is a constant used to control optimization; r 2. r 3 is a random number uniformly distributed between [0,1]. It is a very small constant used to prevent division by zero; gbest Represents the current best individual. best2 Representing the current second-best individual, best3 Represents the current third-best individual; MOP is a mathematical optimization probabilistic unit used to control the accuracy of exploration and development; the mathematical model of MOP is: in, It is the sensitivity coefficient. This is the current iteration number. It represents the maximum number of iterations.

2. The sparsely distributed planar array synthesis method according to claim 1, characterized in that, Step 1 includes: selecting an appropriate optimized array matrix dimension based on the array aperture, and optimizing the array matrix dimension. P , Q The following conditions must be met: in, This represents the minimum array element spacing.

3. The sparsely distributed planar array synthesis method according to claim 2, characterized in that, Step 2 specifically includes the following steps: Step 21. Initialize the population matrix. m Each individual, and the dimension of each individual is... n dimension, n The size is ; the front of each individual The variables are x Direction mapping matrix , arrive The variable is the mapping matrix in the y-direction. ,at last The variables are the weight matrix. ; Step 22. Based on the minimum element spacing of the optimized array Array dimensions P and Q are generated x Fixed part matrix of direction and the fixed part matrix in the y direction ; Step 23. Based on the mapping matrix in the x-direction A Sure x Actual position matrix of direction array elements X According to the mapping matrix in the y direction B Sure y Actual position matrix of direction array elements Y ; Step 24. Calculate the distance between array elements in different rows and columns based on the actual position of each array element; if the minimum array element spacing constraint is not met, then adaptively adjust the array element positions. Step 25. Calculate the fitness of the current individual based on the actual position of the current array element.

4. The sparsely distributed planar array synthesis method according to claim 3, characterized in that, Step 23 specifically includes the following steps: Sort the elements of each row of the mapping matrix A in the x-direction from smallest to largest to form the sorted mapping matrix in the x-direction. and it is fixed in the x-direction matrix. DX The combination yields the actual position matrix of the x-direction array elements. X ; Mapping matrix in the y-direction B Each column of elements is arranged in ascending order to form a sorted mapping matrix along the y-axis. and with y Direction-fixed part matrix DY The combination yields the actual position matrix of the y-direction array elements. Y .

5. The sparsely distributed planar array synthesis method according to claim 4, characterized in that, Step 24 specifically includes the following steps: Based on the mapping matrix in the y-direction Generate offset matrix : in, It is the mapping matrix in the y-direction. The maximum value of each row in the table. Monotonically increasing; The mapping matrix representing the sorted y-direction Maximum value in row z; like The mapping matrix in the y-direction Further adjustments and updates to the offset matrix. ; In the formula ，d c Indicates the minimum array element spacing; Each array element after adjustment y Direction actual coordinate matrix Y for: 。 6. The sparsely distributed planar array synthesis method according to claim 1, characterized in that, Step 5 specifically includes the following steps: Two individuals are randomly selected from the population. , Elite mutation is performed on the globally optimal individual, and the mutated individual... for: in, , These are two individuals randomly selected from the current population. F It is the disturbance coefficient. r 4 is a random number uniformly distributed between [0,1]. gbest Represents the current best individual; calculates elite mutated individuals. If its fitness is better than the current Then for renew.

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