Sparse array optimization method based on improved differential evolution algorithm

Abstract

The present invention discloses a sparse wire array optimization method based on an improved differential evolution algorithm (Teaching Quality Evaluation based Differential Evolution, TQEDE). Compared with the traditional differential evolution algorithm, the innovation of the improved algorithm lies in its unique population generation method. The new population generation method can not only utilize the differences between individuals within a subpopulation, but also utilize the differences between subpopulations to guide the evolution direction. Numerical experiments on standard test functions verify the effectiveness of TQEDE, accelerate the convergence speed, and improve the accuracy of the solution; the application results of TQEDE in sparse wire array optimization show that TQEDE can improve antenna performance and further reduce the peak sidelobe level of sparse wire arrays.

Description

Technical Field

[0001] The invention relates to the technical field of array antennas, and in particular to a sparse wire array optimization method based on an improved differential evolution algorithm. Background Art

[0002] An antenna is a device that radiates electromagnetic waves into space or receives electromagnetic waves from space. It is widely used in many aspects of life, such as radar, broadcasting, wireless communications, and deep space exploration. With the increasing requirements for antenna performance, such as the need for antennas to have high gain and strong directivity, or to be able to achieve electronic scanning, it is now difficult for a single antenna to achieve the desired goal. In order to enable antennas to achieve functions such as high gain, low side lobes, strong directivity, and electronic scanning, array antennas came into being. An array antenna refers to an antenna in the form of an array, which consists of multiple antenna units (array elements) arranged in accordance with certain rules, and can produce special radiation characteristics based on the interference principle and superposition principle of electromagnetic waves.

[0003] Array antenna synthesis is one of the important research contents in the field of array antennas, which has aroused great interest and attention of researchers. Antenna synthesis is the inverse problem of antenna analysis. Antenna analysis refers to the process of obtaining performance parameters based on known antenna structures. In contrast, antenna synthesis refers to determining the structure of the antenna based on the performance requirements of the antenna. Linear array antennas, due to their simple structure, have become the basis for studying other forms of array antennas. And compared with sparse array antennas, sparse array antennas have higher degrees of freedom.

[0004] Antenna array synthesis can be viewed as an optimization problem. The antenna pattern is a complex exponential function of the array element position, so this optimization problem is a non-convex nonlinear optimization problem, and the commonly used numerical analysis optimization method is no longer applicable to antenna array synthesis. In recent years, swarm intelligence evolutionary algorithms have been widely used in antenna array optimization, such as genetic algorithm (GA), particle swarm optimization (PSO), differential evolution algorithm (DE), invasive weed optimization (IWO), cuckoo search algorithm (CSA), and moth-to-fire algorithm (MFO). In addition to these population-based random methods, compressed sensing methods (CS) and matrix beam method (MPM) have also been applied to antenna array synthesis.

[0005] Differential evolution (DE) has the advantages of simple operation, rich population diversity, and strong global optimization ability. In order to improve the performance of DE, many variants have emerged, which mainly focus on parameter settings, evolution strategies (especially mutation strategies), and combinations with heuristic or other classical algorithms.

[0006] One prior art proposes a differential evolution algorithm based on a global and local neighborhood algorithm (DEGL). DEGL defines a neighborhood range centered on the i-th individual, and then generates a local donor vector and a global donor vector based on the neighborhood range and the entire population, respectively, instead of generating only a global donor vector like the traditional DE. The local and global donor vectors are then merged by a proportional weight w to generate an actual donor vector, thereby controlling the balance between exploration and exploitation capabilities. In addition, another prior art develops a hybrid mutation strategy to prevent the algorithm from converging too quickly while exploring the entire search space to produce high-quality results. In the above process, a local search technique, the SolisWet algorithm, is also introduced, and the improved method is applied to the synthesis of circular arrays. The hybrid DE algorithm and the ABC (artificial bee colony) algorithm to the ABC-DE algorithm explore the balance between global optimization and local optimization, and are used for the synthesis of time-modulated antenna arrays. In traditional DE and most of its variant algorithms, the evolutionary population is generated as a whole. Although these methods can use individual differences to guide the direction of evolution to a certain extent, this use of information on differences between individuals is not sufficient, resulting in slow convergence and low accuracy. Summary of the invention

[0007] In view of the above-mentioned problems, the present invention aims to provide an improved differential evolution algorithm and apply it to sparse array optimization. This method can improve antenna performance and further reduce the peak sidelobe level of the antenna.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] A sparse array optimization method based on an improved differential evolution algorithm, characterized in that it comprises the following steps:

[0010] S1: Building a sparse array optimization model

[0011] S101: Taking the reduction of the peak sidelobe level of the antenna as the optimization goal, the sparse array is optimized in combination with the constraints of the array antenna, and an optimization model is established;

[0012] S2: Improved differential evolution algorithm

[0013] S201: Parameter initialization, determine the population size NP, the number of subpopulations N, the weight vector w, the scaling factor F, the crossover probability Cr, and the number of iterations NI;

[0014] S202: Generate subpopulations and calculate the fitness values ​​of individuals in the subpopulations;

[0015] S203: Determine the standards of high score, excellent and passing according to the population size NP and the rated ratio of high score individuals, excellent individuals and passing individuals;

[0016] S204: Calculate the evaluation index of each subpopulation;

[0017] S205: Calculate the evaluation score of each subpopulation according to the weight vector w and the calculated evaluation index;

[0018] S206: Determine the number of new individuals generated by each subpopulation according to the evaluation score, and generate new individuals;

[0019] S207: Compare the fitness values ​​of the parent individual and the newly generated individual, and select the better one to be passed to the next generation population;

[0020] S208: Determine whether the termination condition is met. If so, the algorithm terminates; otherwise, execute S209;

[0021] S209: merge the new individuals in all subpopulations together and re-divide them into N new subpopulations; return to step S203 and start the next iteration;

[0022] S3: using an improved differential evolution algorithm to solve the sparse array optimization model, and verifying the improved differential evolution algorithm through comparison.

[0023] Furthermore, the peak sidelobe level calculation method in step S101 is as follows:

[0024] For a linear array with 2N+1 array elements, the array factor AF can be calculated using equation (1):

[0025]

[0026] For a linear array with 2N array elements, the array factor AF is calculated by equation (2):

[0027]

[0028] Where k represents the wave number, and k = 2π / λ, λ is the wavelength; u = sinθ, x n is the position coordinate of the nth array element;

[0029] In an array antenna, the smaller the peak sidelobe level, the more concentrated the energy will be in the main beam direction, and the better the antenna performance will be. The calculation formula is:

[0030]

[0031] Among them, AF max Indicates the maximum level value of the main lobe area, AF(u s ) represents the level value of other areas except the main lobe area.

[0032] Furthermore, the optimization model established for the sparse array in step S101 is:

[0033]

[0034] Among them, d c is the minimum array element spacing, usually d c =0.5λ, N is half of the total number of array elements, and L is half of the array aperture.

[0035] Furthermore, the evaluation index of each subpopulation in step S204 includes the high score r h , excellent rate g , pass rate p The calculation formulas of the three evaluation indicators are as follows:

[0036]

[0037] Among them, r h 、r g 、r p Respectively represent high score rate, excellent rate, and pass rate; n h 、n g 、n p Respectively represent the number of high scores, excellent students and passing students in the class; N h 、N g 、N p They respectively represent the rated number of high scores, excellent scores and passing scores in the grade, which are determined by the total number of students in the grade and the rated ratios of high scores, excellent scores and passing scores.

[0038] Furthermore, in step S205, the calculation formula of the evaluation score is:

[0039] score = 100 × r h × h +100×r g × g +100×r p × p (8)

[0040] Among them, w h ,w g ,w p are the weights assigned to the three indicators.

[0041] Furthermore, the formula for determining the number of new individuals in step S206 is:

[0042]

[0043] Among them, C i represents the number of new individuals that the ith subpopulation can produce, Si represents the evaluation score of the ith subpopulation, round() is the integer function, and the calculation formula when j=N ensures that the total number of new individuals generated by all subpopulations does not exceed NP.

[0044] Further, the method of determining the new individual in step 206 is: using O i represents the number of new individuals determined by the evaluation score of the ith subpopulation, P i represents the number of individuals in the ith subpopulation;

[0045] When O i <P i When the parent population is reduced, the subpopulation P i Randomly select O from i Different individuals serve as the parent population for generating new individuals;

[0046] When O i >P i When the parent population is expanded, if nP i <O i <=(n+1)P i , then the parent population P i Each individual is replicated into n pieces, and then from P i Randomly select (O i -nP i ) different individuals, thus forming a network that can produce O i The beneficial effects of the present invention are:

[0047] In order to further improve the solution quality and accelerate the convergence speed, this paper proposes an improved differential evolution algorithm (TQEDE) and applies it to sparse array optimization. The unique innovation of TQEDE lies in the improvement of the DE population generation method. In traditional DE and most of its variants, the evolutionary population is generated as a whole. Although this method can use the differences of individuals to guide the evolutionary direction to a certain extent, this utilization is insufficient, resulting in slow convergence and low accuracy.

[0048] In TQEDE, the entire population is replaced by several subpopulations. These subpopulations are then evaluated based on several evaluation metrics. The subpopulations generate a corresponding number of new individuals based on the evaluation scores. Subpopulations with high evaluation scores generate more individuals, while subpopulations with low evaluation scores generate fewer individuals.

[0049] In addition, after the generation of new individuals, an information exchange mechanism is introduced, including the integration and re-division of subpopulations. In this way, the differences between subpopulations are reflected in the number of new individuals. Through information exchange, good individuals in the better subpopulation can spread to other subpopulations, thereby improving the convergence speed of the entire population and the accuracy of the solution.

[0050] Compared with the traditional population generation method, the new population generation method can not only use the differences between individuals within the subpopulation, but also use the differences between subpopulations in the entire population to guide the evolution direction. Numerical experiments on standard test functions verify the effectiveness of TQEDE. The application results of TQEDE in sparse array optimization show that TQEDE can improve antenna performance and further reduce the peak sidelobe level of array antennas. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of a linear sparse array with symmetrical structure and uneven element spacing.

[0052] Figure 2 Schematic diagram of the information exchange process among subpopulations.

[0053] Figure 3 This is the flow chart of the TQEDE algorithm proposed in the present invention.

[0054] Figure 4a This is the distribution diagram of the experimental results of running Example I 50 times; Figure 4b is the normalized direction map of the optimal result of Example 1; Figure 4c This is the optimal array element arrangement for Example I.

[0055] Figure 5a This is the distribution diagram of the experimental results of running Example II 50 times; Figure 5b It is the normalized direction map of the optimal result of Example II; Figure 5c This is the optimal array element arrangement for Example II.

[0056] Figure 6a The distribution diagram of the experimental results of Example III after running 50 times; Figure 6b is the normalized direction map of the optimal result of Example III; Figure 6c This is the optimal array element arrangement for Example III. DETAILED DESCRIPTION

[0057] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0058] The present invention uses sparse array optimization as the problem background of the algorithm.

[0059] Introduction to Traditional Differential Evolution Algorithm

[0060] Similar to the genetic algorithm, the differential evolution algorithm is also an intelligent optimization algorithm based on population evolution. It guides the direction of population evolution through information exchange and sharing between individuals in the population, so that individuals in the population are closer to the optimal solution. The basic principle of the differential evolution algorithm is that, first, the target vector is perturbed by the differential vector of two different individuals in the parent population to generate a mutation vector. Second, the mutation vector and the target vector generate an experimental vector according to a certain crossover probability. Finally, selection is made based on the fitness values ​​of the target vector and the experimental vector, and the vector with a better fitness value is retained for the next generation. In the process of generational evolution, the quality of the population can be improved, and individuals are constantly approaching the optimal solution.

[0061] The main operations of the differential evolution algorithm include population initialization, mutation, crossover and selection.

[0062] Population initialization. In the variable value range [l 0 ,u 0 ](l 0 0 ) generates NP individuals, each of which is D-dimensional.

[0063] X 0 = l 0 +rand(NP,D)×(u 0 -l 0 )

[0064] Among them, X 0 represents the initial population, l 0 and u 0 They represent the lower and upper limits of the variable value range respectively; rand(NP, D) represents an NP×D matrix, and the elements in the matrix are random numbers generated in [0,1].

[0065] The mutation operation generates a mutation vector based on the difference vector and the target vector. The mutation strategy is usually represented by DE / x / y, where x can be rand, best, or current, indicating whether the target vector is a random individual in the population, the best individual, or the current individual; y represents the number of difference vectors, usually 1 or 2. Common mutation strategies include:

[0066]

[0067]

[0068]

[0069]

[0070] ​

[0071] The i-th individual of the t-th iteration, r1 to r5, is a random number in [1, NP] except i and is different from each other. represents the best individual in the current population, and F is the scaling factor used to control the scale of the difference vector.

[0072] The crossover operation generates the experimental vector u using the target vector x and the mutation vector v according to the following formula.

[0073]

[0074] Where Cr is the crossover probability, rand j is a random number generated in [0,1].

[0075] The selection operation determines whether to pass the experimental vector or the target vector to the next generation. For the minimization optimization problem, if the fitness value of the experimental vector u is less than the fitness value of the target vector x, the experimental vector will be passed to the next generation. Otherwise, the target vector will be passed to the next generation. This process can be achieved by the following formula.

[0076]

[0077] The selection operation selects the better one between the target vector and the experimental vector to form the offspring, so that the fitness value of the offspring is better than that of the parent, thus making the population closer to the optimal solution.

[0078] Example 1: Sparse Array Optimization Model

[0079] Generally, a sparse array has a symmetrical geometric structure, with array elements symmetrically distributed on both sides of the origin. Figure 1 As shown, the array elements are arranged on a straight line at non-uniform intervals. In the figure, Δx represents the array element interval, L represents the half aperture length of the array, and θ represents the pitch angle.

[0080] For the convenience of analysis, it is assumed that the array elements are omnidirectional elements with the same excitation amplitude and phase, and the excitation is recorded as 1, and the main beam of the array points to the normal direction of the array. For a linear array with 2N+1 elements, the array factor AF can be calculated by formula (1):

[0081]

[0082] For a linear array with 2N array elements, the array factor AF is calculated by equation (2):

[0083]

[0084] Where k represents the wave number, and k = 2π / λ, λ is the wavelength; u = sinθ, x nis the position coordinate of the nth array element.

[0085] In an array antenna, the smaller the peak side lobe level (PSLL), the more energy will be concentrated in the main beam direction, and the better the antenna performance. Therefore, the optimization goal of the present invention is set to reduce the PSLL of the antenna. PSLL is defined by the following formula (3):

[0086]

[0087] Among them, AF max Indicates the maximum level value of the main lobe area, AF(u s ) represents the level value of other areas except the main lobe area.

[0088] When optimizing a sparse array, it is necessary to consider constraints such as the number of array elements, array aperture, and minimum array element spacing. Therefore, the following mathematical model can be established for optimizing a sparse array based on these constraints:

[0089]

[0090] Among them, d c is the minimum array element spacing, usually d c =0.5λ, N is half of the total number of elements, and L is half of the array aperture.

[0091] Example 2: Improved differential evolution algorithm

[0092] Population generation is not only the first step of the DE algorithm, but also an extremely important step. The appropriate population can lay a solid foundation for the subsequent steps. In the classic DE algorithm, the initial population is usually randomly generated as a whole within the independent variable definition interval, which will lead to problems such as slow convergence speed and low solution quality. In order to effectively solve this problem, the present invention proposes a differential evolution algorithm (TQEDE) using a new population generation method, which is inspired by teaching quality evaluation. The teaching quality evaluation method is first introduced below.

[0093] A. Teaching Quality Evaluation

[0094] As an indispensable part of the entire teaching process, the evaluation of teaching quality based on student scores can not only evaluate the teaching effect to a certain extent, but also play a guiding role in the evaluation mechanism, providing reference guidance for the next teaching focus, such as whether to focus on cultivating high-scoring students or improving the average level of the class. Common indicators used in teaching quality evaluation include: high score rate, excellent rate, pass rate, and average score coefficient. The definition of each indicator is shown below.

[0095]

[0096] Among them, r h 、r g 、r p 、r a Respectively represent the high score rate, excellent rate, passing rate and average score coefficient; n h 、n g 、n p Respectively represent the number of high scores, excellent students and passing students in the class; N h 、N g 、N p They represent the number of high-scoring students, excellent students and passing students in the grade, respectively. They are determined by the total number of students in the grade and the rated ratios of high-scoring students, excellent students and passing students. For example, if the total number of students in the grade is 100 and the rated ratios of high-scoring students, excellent students and passing students are 20%, 20% and 30%, then 20 students in the whole grade will be rated as high-scoring students, 20 students will be rated as excellent students (excluding the 20 students with high scores), and 30 students will be rated as passing students (excluding the 40 students with high scores and excellent students). a and g a Represent the class average score and grade average score respectively. According to the above evaluation indicators and the following formula (6), the class evaluation score is calculated.

[0097] score = 100 × r h × h +100×r g × g +100×r p × p +100×r a × a (6)

[0098] Formula (6) can be simplified as:

[0099] score=100Iw′ (7)

[0100] Among them, the indicator vector I = [r h r g r p r a ], weight vector w = [w h w g w p w a ],w h w g w p w a represents the weights assigned to the four indicators, and w' is the transposed vector of w.

[0101] To facilitate understanding of the above process, we will use an example of teaching quality evaluation to illustrate. Assume that there are two classes (Class 1 and Class 2) in the grade, with a total number of 100 students and 50 students in each class. The rated proportions of high scores, excellent scores, and pass scores in the grade are 10%, 20%, and 30%, that is, the rated number of high scores, excellent scores, and pass scores in the grade are 10, 20, and 30. The distribution of student scores in the two classes is shown in Table 1.

[0102] Table 1 Distribution of student scores in Class 1 and Class 2

[0103]

[0104] According to the distribution of student scores in Table 1, the values ​​of various evaluation indicators for Class 1 and Class 2 are calculated, as shown in Table 2. The evaluation results of Class 1 and Class 2 under different weights are shown in Table 3.

[0105] Table 2 Evaluation index values ​​for class 1 and class 2

[0106]

[0107] Table 3 Evaluation scores and results of class 1 and class 2 under different weights

[0108]

[0109] As shown in Table 3, if the weight vector w = [0.5 0.3 0.1 0.1], the evaluation score of class 1 is 51.9360, and the evaluation score of class 2 is 58.0640. This weight vector means that in the evaluation process, the number of high-scoring students in the class is more important than the class average score. Therefore, the evaluation result of class 2 with more high-scoring students is better than that of class 1. When the weight vector becomes w = [0.1 0.3 0.1 0.5], that is, the evaluator believes that the class average score is more important, the evaluation score of class 1 is 85.0120, and the evaluation score of class 2 is 64.9880. Since the average score of class 1 is higher than that of class 2, under this weight vector, the evaluation result of class 1 is better than that of class 2.

[0110] In the above example, we can see that the two different weight vectors reflect different teaching objectives. The teaching objective corresponding to the first weight vector is to cultivate more high-scoring students. According to the evaluation scores, it can be inferred that Class 1, which performs slightly worse, will pay more attention to cultivating high-scoring students in the next stage of teaching in order to improve the next evaluation score. The teaching objective corresponding to the second weight vector is to improve the class average score. According to the evaluation scores, Class 2 will focus on the performance of the entire class in the next stage of teaching.

[0111] The above analysis process reflects the guiding role of teaching quality evaluation on teaching work, and provides important inspiration for the new population generation method in the DE algorithm proposed in this paper.

[0112] B. Differential evolution algorithm based on teaching quality evaluation

[0113] The conventional method of population generation in standard DE is to treat a population containing a certain number of individuals as a whole. The population generated in this way has strong randomness, resulting in slow convergence and poor solution quality. Inspired by the above teaching quality evaluation, the present invention proposes an improved differential evolution algorithm (TQEDE).

[0114] In the TQEDE algorithm, when generating a population, a population is no longer generated as a whole, but several subpopulations are generated. Assuming that the size of the population as a whole is NP, and N subpopulations are generated in TQEDE, the size of each subpopulation is NP / N. After the subpopulations are generated, the subpopulations are evaluated according to the evaluation indicators, and the score of each subpopulation is calculated according to the weight vector. In TQEDE, the high score r is used. h , excellent rate g , pass rate p Three evaluation indicators are used instead of the four indicators mentioned above for teaching quality evaluation. Correspondingly, the weight vector w becomes [w h w g w p ], no longer [w h w g w p w a ]. The reason for simplifying the evaluation index is that the information contained in the average coefficient can be reflected in the pass rate to a certain extent. On the other hand, the more important reason is that in order to improve the convergence speed of the algorithm and the quality of the solution, when evaluating subpopulations, the algorithm should be more inclined to solutions with higher quality (similar to high-scoring students) than the average level of the subpopulation (similar to the average grade of the class). Therefore, formula (6) can be rewritten as formula (8):

[0115] score = 100 × r h × h +100×r g × g +100×r p × p (8)

[0116] According to the evaluation score, the number of new individuals that each subpopulation can produce can be determined. The higher the evaluation score, the more new individuals are produced; the lower the evaluation score, the fewer new individuals are produced. The specific number is calculated according to the following formula (9):

[0117]

[0118] Among them, C i represents the number of new individuals that the ith subpopulation can produce, S i represents the evaluation score of the ith subpopulation, round() is the integer function, and the calculation formula when j=N ensures that the total number of new individuals generated by all subpopulations does not exceed NP.

[0119] After the subpopulations produce offspring individuals, TQEDE introduces an information exchange mechanism between subpopulations, namely fusion and redistribution. It first merges the new individuals produced by all subpopulations together, and then randomly divides them into N subpopulations. Since the evaluation scores of each subpopulation are different, the number of new individuals they can produce is also different, some are more than the parent population, and some are less than the parent population. Without an information exchange mechanism, each subpopulation will remain relatively closed, and individuals in subpopulations with higher evaluation scores cannot be spread to other subpopulations, which will not play a role in guiding the direction of evolution, and will not be able to increase the convergence speed. Taking NP=50 and N=2 as an example, the schematic diagram of the information exchange mechanism is shown below: Figure 2 shown.

[0120] To facilitate understanding, Table 4 is used to make an analogy summary between TQEDE and the concepts in teaching quality assessment.

[0121] Table 4 Conceptual analogy between TQEDE and teaching quality evaluation

[0122]

[0123]

[0124] In summary, based on the DE algorithm flow and the teaching quality evaluation process, the algorithm steps of TQEDE of the present invention are as follows:

[0125] Step 1: Parameter initialization. Determine the population size NP, the number of subpopulations N, the weight vector w, the scaling factor F, the crossover probability Cr, and the number of iterations NI.

[0126] Step 2: Generate subpopulations and calculate the fitness values ​​of individuals in the subpopulations.

[0127] Step 3: Determine the standards for high scores, excellent scores, and passing scores based on the population size NP and the rated proportions of high-scoring individuals, excellent individuals, and passing individuals.

[0128] It is important to note here that for the minimum optimization problem, a high score corresponds to a small fitness value; for the maximum optimization problem, a high score corresponds to a large fitness value.

[0129] Step 4: Calculate the evaluation metrics for each subpopulation.

[0130] Step 5: Calculate the evaluation score of each subpopulation according to the weight vector w and the evaluation index calculated in step 4.

[0131] Step 6: According to the evaluation score, determine the number of new individuals generated by each subpopulation and generate new individuals. Here, this paper selects DE / rand / 1 as the mutation operator to generate new individuals.

[0132] Step 7: Compare the fitness values ​​of the parent individuals and the newly generated individuals, and select the better one to pass on to the next generation population.

[0133] Step 8: Determine whether the termination condition is met. If so, the algorithm terminates; otherwise, proceed to step 9.

[0134] Step 9: Merge the new individuals in all subpopulations together and redivide them into N new subpopulations; return to step 3 to start the next iteration.

[0135] It should be noted that when determining the number of new individuals generated by each subpopulation, some subpopulations have more individuals than the parent population, and some subpopulations have less individuals than the parent population. In this case, it is necessary to determine which parent individuals are used to generate new individuals. There are many ways to determine this, and the present invention uses the following method to determine:

[0136] Use O i represents the number of new individuals determined by the evaluation score of the ith subpopulation, P i represents the number of individuals in the ith subpopulation. i <P i When the parent population is reduced, the subpopulation P i Randomly select O from i Different individuals serve as the parent population for generating new individuals; i >P i When the parent population is expanded, if nP i <O i <=(n+1)P i , then the parent population P i Each individual is replicated into n pieces, and then from P i Randomly select (O i -nP i ) different individuals, thus forming a network that can produce O i The parent population of the new individuals.

[0137] For example, suppose P i =5, and use 1 / 2 / 3 / 4 / 5 / to represent the individuals in the parent population, that is, the parent population is [1 2 34 5]. If O i=3, then three different individuals are randomly selected from the five individuals, and the reduced parent population may be [1 2 5], [23 4], etc.; if O i =12, then each individual in the parent population is replicated into 2, that is, [1 2 3 4 5 1 2 3 4 5], and then 2 different individuals are randomly selected from the 5 individuals. The parent population after expansion may be [1 2 3 4 5 1 2 3 4 5 2 5], [12 3 4 5 1 2 3 4 5 1 3], etc.

[0138] To make the steps of the TQEDE algorithm concise and clear, steps 1 to 9 can be divided into four parts, namely initialization (step 1 to step 2), subpopulation evaluation (step 3 to step 5), new individual generation (step 6 to step 7), and information exchange (step 8 to step 9). The flowchart of the TQEDE algorithm is shown in the attached figure. Figure 3 shown.

[0139] Compared with standard DE, the innovation of TQEDE lies mainly in the new population generation method inspired by teaching quality evaluation. The single population in standard DE is replaced by multiple subpopulations in TQEDE. Each subpopulation can generate new individuals, and the number is related to the evaluation score of the subpopulation. Subpopulations with high evaluation scores can generate more new individuals, and through information exchange, that is, subpopulation fusion and redistribution, individuals from dominant subpopulations can spread to other subpopulations, thereby improving the convergence speed of the entire population and obtaining higher quality solutions.

[0140] Example 3: Sparse Array Optimization Simulation Example

[0141] In order to further verify the effectiveness of the TQEDE algorithm proposed in the present invention, the following simulation experiment is used to illustrate it.

[0142] For three different array apertures (2L) and numbers of array elements (N e ) and compare TQEDE with DELF, NBDE, and Boolean PSO. The examples are I: 2L = 73λ, N e =78, II:2L=90.5λ,N e =132, III: 2L = 98.5λ, N e =152. The parameters in the experiment are as follows: population size NP = 50, scaling factor F = 0.5, crossover probability Cr = 0.95, number of iterations NI = 50, number of subpopulations in TQEDE N = 2, weight vector w = [0.5 0.3 0.2], mutation operator is consistent with the mutation operator in DELF, and each experiment is repeated 50 times. The following is the simulation process of Example I, Example II and Example III.

[0143] (1) Example 1

[0144] The parameters are: 2L = 73λ, N e =78, the results of 50 experiments are shown in the attached Figure 4a As shown in the figure, the minimum PSLL is -24.03dB and the average is -22.99dB. Compared with DELF, the optimal PSLL and average PSLL are reduced by 3.44dB and 4.31dB respectively. The normalized directivity diagram of the optimal result is shown in the figure Figure 4b The corresponding array element distribution is shown as Figure 4c shown.

[0145] (2) Example II

[0146] The parameters are: 2L = 90.5λ, N e =132, the results of 50 experiments are shown in the attached Figure 5a As shown in the figure, the minimum PSLL is -25.78dB and the average is -25.06dB. Compared with DELF, the optimal PSLL and average PSLL are reduced by 0.91dB and 1.31dB respectively. The normalized directivity diagram of the optimal result is shown in the figure Figure 5b The corresponding array element distribution is shown as Figure 5c shown.

[0147] (3) Example III

[0148] The parameters are: 2L = 98.5λ, N e =152, 50 experiments were performed and the results are shown in the attached Figure 6a As shown in the figure, the minimum PSLL is -24.34dB and the average is -24.21dB. Compared with DELF, the optimal PSLL and average PSLL are reduced by 0.25dB and 0.41dB respectively. The normalized directivity diagram of the optimal result is shown in the figure Figure 6b The corresponding array element distribution is shown as Figure 6c shown.

[0149] The experimental results of TQEDE optimization of sparse arrays are compared with DELF, NBDE, and Boolean PSO as shown in Table 5.

[0150] Table 5 Comparison of experimental results of sparse array optimization (better results are shown in bold)

[0151]

[0152] in conclusion

[0153] In order to improve the performance of DE algorithm in optimizing sparse wire arrays, a differential evolution algorithm based on teaching quality evaluation is proposed, inspired by teaching quality evaluation. Compared with the standard DE algorithm and other improved DE algorithms, the uniqueness of TQEDE lies in its population generation method. TQEDE replaces the population as a whole in DE with subpopulations, and adds subpopulation evaluation and information exchange behaviors. Subpopulation evaluation can determine the number of new individuals generated by each subpopulation according to the evaluation score, and the number of new individuals generated by high scores is large. Under the premise of subpopulation evaluation, information exchange breaks the closed state of each subpopulation, allowing more individuals generated by subpopulations with high scores to have the opportunity to spread to other populations, thereby forming guidance for the evolutionary direction of the entire population, accelerating the convergence speed, and improving the quality of the solution. TQEDE is used to optimize the sparse wire array. The simulation experiment shows that TQEDE can further reduce the peak sidelobe level of the antenna and improve the antenna optimization performance.

[0154] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A sparse array optimization method based on improved differential evolution algorithm, Features: The following steps are involved: S1: Building a sparse array optimization model S101: Taking the reduction of the peak sidelobe level of the antenna as the optimization goal, the sparse array is optimized in combination with the constraints of the array antenna, and an optimization model is established; S2: Improved differential evolution algorithm S201: Parameter initialization, determine the population size NP, the number of subpopulations N, the weight vector w, the scaling factor F, the crossover probability Cr, and the number of iterations NI; S202: Generate subpopulations and calculate the fitness values ​​of individuals in the subpopulations; S203: Determine the standards of high score, excellent and passing according to the population size NP and the rated ratio of high score individuals, excellent individuals and passing individuals; S204: Calculate the evaluation index of each subpopulation; S205: Calculate the evaluation score of each subpopulation according to the weight vector w and the calculated evaluation index; S206: Determine the number of new individuals generated by each subpopulation according to the evaluation score, and generate new individuals; S207: Compare the fitness values ​​of the parent individual and the newly generated individual, and select the better one to be passed to the next generation population; S208: Determine whether the termination condition is met. If so, the algorithm terminates; otherwise, execute S209; S209: merge the new individuals in all subpopulations together and redivide them into N new subpopulations; Return to step S203 and start the next iteration; S3: using an improved differential evolution algorithm to solve the sparse array optimization model, and verifying the improved differential evolution algorithm through comparison.

2. According to the sparse array optimization method based on the improved differential evolution algorithm according to claim 1, Features: The peak sidelobe level calculation method in step S101 is as follows: For a linear array with 2N+1 array elements, the array factor AF can be calculated using equation (1): For a linear array with 2N array elements, the array factor AF is calculated by equation (2): Where k represents the wave number, and k = 2π / λ, λ is the wavelength; u = sinθ, x n is the position coordinate of the nth array element; In an array antenna, the smaller the peak sidelobe level, the more concentrated the energy will be in the main beam direction, and the better the antenna performance will be. The calculation formula is: Among them, AF max Indicates the maximum level value of the main lobe area, AF(u s ) represents the level value of other areas except the main lobe area.

3. According to the sparse array optimization method based on the improved differential evolution algorithm of claim 1, Features: The optimization model established for the sparse array in step S101 is: Among them, d c is the minimum array element spacing, usually d c =0.5λ, N is half of the total number of array elements, and L is half of the array aperture.

4. According to the sparse array optimization method based on the improved differential evolution algorithm of claim 1, Features: The evaluation index of each subpopulation in step S204 includes the high score r h , excellent rate g , pass rate p The calculation formulas of the three evaluation indicators are as follows: Among them, r h 、r g 、r p Respectively represent high score rate, excellent rate, and pass rate; n h 、n g 、n p Respectively represent the number of high scorers, excellent students and passing students in the class; N h 、N g 、N p They respectively represent the rated number of high scores, excellent scores and passing scores for the grade, which are determined by the total number of students in the grade and the rated ratios of high scores, excellent scores and passing scores.

5. According to the sparse array optimization method based on the improved differential evolution algorithm of claim 4, Features: In step S205, the calculation formula of the evaluation score is: score=100×r h ×w h +100×r g ×w g +100×r p ×w p (8) Among them, w h , w g , w p are the weights assigned to the three indicators.

6. The sparse array optimization method based on the improved differential evolution algorithm according to claim 1, Features: The formula for determining the number of new individuals in step S206 is: Among them, C i represents the number of new individuals that the ith subpopulation can produce, S i represents the evaluation score of the ith subpopulation, round() is the integer function, and the calculation formula when j=N ensures that the total number of new individuals generated by all subpopulations does not exceed NP.

7. The sparse array optimization method based on the improved differential evolution algorithm according to claim 6, Features: Step 206 determines the new individual by: using O i represents the number of new individuals determined by the evaluation score of the ith subpopulation, P i represents the number of individuals in the ith subpopulation; When O i <P i When the parent population is reduced, the subpopulation P i Randomly select O from i Different individuals serve as the parent population for generating new individuals; When O i >P i When the parent population is expanded, if nP i <O i <=(n+1)P i , then the parent population P i Each individual is replicated into n pieces, and then from P i Randomly select (O i -nP i ) different individuals, thus forming a network that can produce O i The parent population of the new individuals.

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