Laser array antenna pattern optimization method and system based on improved fox optimization algorithm

Abstract

The present invention discloses a method and system for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm. The method includes: obtaining the radiation pattern function of the array antenna according to the principle of electromagnetic field superposition, and obtaining the optimization model of the sparse linear array antenna from the definition of the peak sidelobe level; using the improved fox optimization algorithm to solve the optimization model of the sparse linear array antenna to obtain the optimal array antenna distribution scheme. Applying the improved fox optimization algorithm to the solution of the radiation pattern optimization model of the sparse linear array antenna can quickly achieve the purpose of suppressing the maximum sidelobe level and controlling the null.

Description

Technical Field

[0001] The present invention belongs to the technical field of array antenna optimization, and particularly relates to a method and system for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm. Background Art

[0002] An array antenna is a radiation device composed of multiple antenna elements arranged in a specific manner, and has wide applications in fields such as satellite communication, lidar, and the Internet of Things. At present, swarm intelligence optimization and evolutionary computing algorithms are prone to problems of low solution accuracy and slow convergence speed when solving the sidelobe level suppression and null control of the radiation pattern of a linear laser array antenna. Summary of the Invention

[0003] The present invention provides a method and system for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm, which is used to solve the technical problems of low solution accuracy and slow convergence speed.

[0004] In a first aspect, the present invention provides a method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm, including:

[0005] According to the principle of electromagnetic field superposition, obtain the array antenna radiation pattern function, and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls;

[0006] Adopt an improved fox optimization algorithm to solve the sparse linear array antenna optimization model, and obtain the optimal array antenna distribution scheme. Among them, the process of solving the sparse linear array antenna optimization model specifically includes:

[0007] Use the Pwlcm cosine piecewise chaotic mapping strategy to generate model parameters, and add the element spacing constraint matrix to generate the initial element distribution;

[0008] Calculate the peak sidelobe level and null depth in a specified direction of each element distribution, and obtain the current best fitness and optimal individual;

[0009] Judge whether the local mutation strategy is satisfied. If it is satisfied, use the nonlinear weight golden sine strategy to update the position of the element distribution; otherwise, update the element position according to the fox snowfield predation behavior in the improved fox optimization algorithm;

[0010] Calculate the fitness of each individual to obtain the best fitness and optimal individual;

[0011] According to the hyperbolic cosine and sine optimization strategy, mutate the position of the fox individual, and calculate the fitness of the mutated individual. If it is better, replace the mutated individual before mutation with the mutated individual to obtain a better element distribution;

[0012] Determine whether the termination condition is satisfied. If not, update the iteration count and continue the iteration. Otherwise, proceed to the next step;

[0013] Output the global optimal individual and the best fitness value. The optimal individual is the optimal array antenna distribution, and the best fitness value is the objective function value corresponding to the optimal array antenna distribution.

[0014] In a second aspect, the present invention provides a laser array antenna pattern optimization system based on an improved fox optimization algorithm, including:

[0015] A definition module configured to obtain the array antenna pattern function according to the principle of electromagnetic field superposition and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls;

[0016] A solution module configured to use the improved fox optimization algorithm to solve the sparse linear array antenna optimization model and obtain the optimal array antenna distribution scheme. Specifically, the process of solving the sparse linear array antenna optimization model includes:

[0017] Generate model parameters using the Pwlcm cosine piecewise chaotic mapping strategy, and add the element spacing constraint matrix to generate the initial element distribution;

[0018] Calculate the peak sidelobe level and the null depth in the specified direction of each element distribution to obtain the current best fitness value and the optimal individual;

[0019] Determine whether the local mutation strategy is satisfied. If satisfied, use the non-linear weight golden sine strategy to update the positions of the element distributions. Otherwise, update the element positions according to the fox snow hunting behavior in the improved fox optimization algorithm;

[0020] Calculate the fitness of each individual to obtain the best fitness value and the optimal individual;

[0021] Mutate the positions of the fox individuals according to the hyperbolic sine-cosine optimization strategy, and calculate the fitness of the mutated individuals. If it is better, replace the mutated individuals before mutation with the mutated individuals to obtain a better element distribution;

[0022] Determine whether the termination condition is satisfied. If not, update the iteration count and continue the iteration. Otherwise, proceed to the next step;

[0023] Output the global optimal individual and the best fitness value. The optimal individual is the optimal array antenna distribution, and the best fitness value is the objective function value corresponding to the optimal array antenna distribution.

[0024] In a third aspect, an electronic device is provided, which includes: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the steps of the method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to any embodiment of the present invention.

[0025] In a fourth aspect, the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the program instructions are executed by a processor, the processor is caused to execute the steps of the method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to any embodiment of the present invention.

[0026] The method and system for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm of the present application adopt a Pwlcm cosine segmented chaotic mapping strategy to generate the initial solution of the population, so as to form an initialization population with high quality and diversity. The nonlinear weight golden sine strategy is used to optimize the algorithm. Among them, the nonlinear weight factor makes the golden sine strategy more effectively expand the solution space, improves the global search ability of the algorithm and the diversity of the fox population. The hyperbolic cosine and sine optimization strategy is introduced to help the algorithm jump out of the local optimum. Here, the development is divided into two stages to achieve extensive search and in-depth development, thereby accelerating the convergence speed and improving the accuracy of the solution. The organic combination of the two balances the global search ability and the local development ability, enabling the algorithm to improve the convergence accuracy while accelerating the convergence speed during the optimization process. Description of the Drawings

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0028] Figure 1 It is a flowchart of a method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm provided by an embodiment of the present invention;

[0029] Figure 2 It is the radiation pattern of the array after sparse by different algorithms in a specific embodiment provided by an embodiment of the present invention;

[0030] Figure 3 It is a comparison diagram of the maximum sidelobe levels of different element numbers in a specific embodiment provided by an embodiment of the present invention;

[0031] Figure 4A comparison chart of the maximum sidelobe levels of different experiments in a specific embodiment provided by an embodiment of the present invention;

[0032] Figure 5 A radiation pattern of an array antenna with nulls and different numbers of array elements in a specific embodiment provided by an embodiment of the present invention;

[0033] Figure 6 A structural block diagram of a laser array antenna pattern optimization system based on an improved fox optimization algorithm provided by an embodiment of the present invention;

[0034] Figure 7 It is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. Specific implementation manners

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0036] Please refer to Figure 1 which shows a flowchart of a method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to the present application.

[0037] As Figure 1 shown, the method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm specifically includes the following steps:

[0038] Step S101, obtain the array antenna pattern function according to the principle of electromagnetic field superposition, and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls.

[0039] In this step, the objective function of the sparse linear array antenna optimization model is:

[0040] ,

[0041] ,

[0042] ,

[0043] ,

[0044] In the formula, is the established objective function, is the maximum sidelobe level calculation formula, is the weight coefficient of the maximum sidelobe level, is the weight coefficient of the null, is the main lobe gain, is the null depth at a specified angle, is the target null depth, and are the initial weight coefficients, which are set to 0.16 and 0.12 respectively, is the maximum sidelobe gain, is the maximum number of iterations.

[0045] Step S102, using the improved fox optimization algorithm, solve the sparse linear array antenna optimization model to obtain the optimal array antenna distribution scheme.

[0046] In this step, the process of solving the sparse linear array antenna optimization model specifically includes:

[0047] Initializing the population: The mathematical model of the fox optimization algorithm is described as follows. Let the size of the fox population be P, and the initial fox population , and the dimension of the feasible solution space be d. Then the i-th fox in the solution space is represented as . The initial fox population of the fox optimization algorithm is randomly generated within a certain search range and evenly distributed in the solution space.

[0048] Randomly forming the initial population means that: in the process of optimizing the laser array antenna, the present invention aims at optimizing the peak sidelobe level and null control of the pattern of the sparse linear laser array antenna. The optimization problem is the distribution of the laser array antenna elements, and each distribution method is represented by a fox , and each element is represented by a fox , that is, the fox is used to represent a solution to the distribution of the elements of a sparse linear array antenna. Within a certain search parameter range, each fox in the fox population is determined by using the random rand method to form the initial population.

[0049] For the optimization of the array antenna, the fox optimization algorithm better balances the global and local search performances of the algorithm, which is beneficial to the effective search for the global optimal solution and the improvement of the overall execution efficiency. However, the initial population distribution of the fox optimization algorithm is not uniform enough and the quality is not high, which affects the convergence speed of the algorithm. In view of the above defects of the basic fox optimization algorithm, a Pwlcm cosine piecewise chaotic mapping initialization strategy is proposed.

[0050] As is well known, the chaotic distribution is a relatively uniform distribution function. Due to its characteristics of randomness, ergodicity, and regularity, it can well maintain population diversity and has been widely applied in swarm intelligence algorithms. Traditional chaotic mappings are easily affected by parameter sensitivity, resulting in population distribution aggregation or periodic repetition. Compared with other mappings, the Pwlcm piecewise chaotic mapping has a uniform density function in its defined interval, and the distribution of x is very flat at a specific p value. In addition, introducing the perturbation mechanism of the Cosine cosine function into the Pwlcm piecewise chaotic mapping further enhances the diversity, flexibility, and global exploration ability of the chaotic system. This ergodic and random characteristic is conducive to the distribution of fox individuals throughout the solution space and enhances population diversity.

[0051] Through the proposed Pwlcm cosine piecewise chaotic mapping initialization strategy, a large number of numerical values are generated within a certain range of model parameter search. These numerical values, together with the spacing constraint matrix, form the initial population. The expression of the Pwlcm cosine piecewise chaotic mapping strategy is:

[0052] ,

[0053] where, is the position of the (j + 1)-th element of the i-th fox, is the position of the j-th element of the i-th fox, is the control parameter of the mapping, ∈[0, 1];

[0054] The expression of the element spacing constraint matrix is:

[0055] ,

[0056] where, is the position of the first element, is the position of the N-th element, is the initial position of the array after Pwlcm cosine piecewise chaotic mapping, is the shortest spacing between each element, is the number of elements, is the position of the second element in X, is the position of the third element in X, is the position of the N-th element in X.

[0057] Calculate the peak sidelobe level and null depth in the specified direction of each element distribution to obtain the current best fitness and optimal individual.

[0058] Judge whether the local mutation strategy is satisfied. If it is satisfied, use the non-linear weight golden sine strategy to update the positions of the array elements; otherwise, update the positions of the array elements according to the fox's snowfield predation behavior in the improved fox optimization algorithm. Among them, the expression of the non-linear weight golden sine strategy is:

[0059]

[0060] ,

[0061] ,

[0062] ,

[0063] In the formula, is the position of the i-th fox in the (it + 1)-th generation, is the first non-linear weight factor, is a random number in the interval [0, 2π], is the position of the i-th fox in the it-th generation, is a random number in the interval [0, π], is the position of the optimal fox individual, is the maximum value of the first non-linear weight factor, is the minimum value of the first non-linear weight factor, is the maximum number of iterations, is the current number of iterations, 、 are both coefficients containing the golden ratio, is the golden ratio.

[0064] Calculate the fitness of each individual to obtain the best fitness and the optimal individual.

[0065] According to the hyperbolic sine-cosine optimization strategy, mutate the positions of the fox individuals and calculate the fitness of the mutated individuals. If it is better, that is, the fitness of the mutated individual is smaller than the fitness of the individual before mutation, then replace the individual before mutation with the mutated individual to obtain a better array element distribution. Among them, the hyperbolic sine-cosine optimization strategy includes:

[0066] In the first exploitation stage, exploit the space near the fox, and the expression is:

[0067] ,

[0068] ,

[0069] In the formula, is the position of the i-th fox in the (it + 1)-th generation, is the position of the optimal fox individual, is the second non - linear weight factor, is the position of the i - th fox in the it - th generation, , , , are all random numbers in the interval (0, 1), is the maximum number of iterations, is the current number of iterations, , are both sensitivity coefficients with different values;

[0070] In the second exploration stage, the optimal solution of the foxes obtained is further explored, and the exploration intensity around the optimal solution will increase with the increase of the number of iterations. The expression is:

[0071] ,

[0072] ,

[0073] In the formula, , , are all random numbers in the interval (0, 1), is the third non - linear weight factor, is the sensitivity coefficient, different from the values of , , where cosh is the hyperbolic cosine function and sinh is the hyperbolic sine function.

[0074] Judge whether the termination condition is satisfied. If not, update the number of iterations and continue the iteration; otherwise, proceed to the next step.

[0075] Output the global optimal individual and the best fitness value. The optimal individual is the optimal array antenna distribution, and the best fitness value is the objective function value corresponding to the optimal array antenna distribution.

[0076] In summary, the method of this application uses the Pwlcm cosine - segmented chaotic mapping strategy to generate the initial solution of the population to form a high - quality and diverse initial population, and uses the non - linear weight golden sine strategy to optimize the algorithm. Among them, the non - linear weight factor makes the golden sine strategy more effectively expand the solution space, enhances the global search ability of the algorithm and the diversity of the fox population, introduces the hyperbolic cosine - sine optimization strategy to help the algorithm jump out of the local optimum. Here, the exploration is divided into two stages to achieve extensive search and in - depth exploration, thereby accelerating the convergence speed and improving the accuracy of the solution. The organic combination of the two balances the global search ability and the local exploration ability, enabling the algorithm to accelerate the convergence speed and improve the convergence accuracy during the optimization process.

[0077] In a specific embodiment, an example of optimizing the radiation pattern of a sparse linear array antenna using an improved fox optimization algorithm is presented. To ensure the fairness of the experiment, unified experimental parameters are set: the population size and the maximum number of iterations for all algorithms are 60 and 200 respectively, the number of array elements is 32, and the interval between array elements is .

[0078] This simulation applies the improved fox optimization algorithm (IFXO), genetic algorithm (GA), grey wolf algorithm (GWO), whale optimization algorithm (WOA), particle swarm optimization algorithm (PSO), and fox optimization algorithm (FOX) to suppress the maximum sidelobe level of different linear array antenna radiation patterns and compares their optimization effects. The fitness iteration curves of these six optimization algorithms are as Figure 2 shown. Compared with the other five algorithms, the IFXO algorithm exhibits better performance. It widely explores the solution space through a global search strategy in the initial stage; in the later stage, it avoids local optima through an individual mutation strategy, effectively accelerating the convergence to the global optimal solution.

[0079] Among them, the maximum sidelobe level value of the radiation pattern optimized by the improved fox algorithm is -22.7138 dB. Compared with the uniformly excited current, the maximum sidelobe level value is reduced by 9.4778 dB. The maximum sidelobe level values obtained after optimization by the fox optimization algorithm, genetic algorithm (GA), grey wolf algorithm (GWO), whale optimization algorithm (WOA), and particle swarm optimization algorithm (PSO) are reduced by 7.5702, 5.7645, 7.3504, 6.061, and 5.9534 respectively compared with the maximum sidelobe level value obtained by the uniformly excited current.

[0080] Figure 3 The maximum sidelobe level values of the radiation patterns obtained by different optimization algorithms are given when the number of array elements is 8, 16, 24, 32, 40, and 48 respectively. It can be seen from the figure that the fox optimization algorithm is superior to other algorithms in solving the optimization problems of linear array antennas with different dimensions (number of array elements).

[0081] In addition, 20 independent repeated experiments are designed to verify the performance of the fox optimization algorithm. In this experiment, each optimization algorithm is applied to solve the radiation pattern optimization problem of a 32-element linear array antenna, and each algorithm runs independently 20 times. Figure 4 The distribution of the maximum sidelobe level values obtained by different algorithms in the experiment is given, and Table 1 gives the statistical results. It can be seen that the fox optimization algorithm has obvious advantages in terms of the mean compared with other algorithms.

[0082] Table 1 Statistical results of the maximum sidelobe level obtained from 20 independent repeated experiments

[0083] ,

[0084] Optimization objective: Suppress the maximum sidelobe level of a linear array antenna and obtain a null at the 70° direction. = 15, = 1, the target null depth a = -100. Figure 5 The radiation patterns of 16 - element and 32 - element linear array antennas obtained after being optimized by different algorithms are respectively given. Tables 2 and 3 respectively give the numerical results of the maximum sidelobe level and null in the radiation patterns obtained by different algorithms. It can be seen from Table 2 that when the number of array elements is 16, the maximum sidelobe level obtained by the fox optimization algorithm is -15.6747, and the null value at the 70° direction is -99.5188, both of which are better than other algorithms. When the number of array elements increases to 32, the maximum sidelobe level obtained by the fox optimization algorithm is -17.0989. Although this value is higher than -17.3664 obtained by the genetic algorithm, the former's null value at the 70° direction is -99.9967, far lower than -46.1909 of the latter. Therefore, the fox algorithm still has advantages in solving the joint optimization problem of maximum sidelobe suppression and null control.

[0085] Table 2 Maximum sidelobe level and null values obtained by a 16 - element linear array antenna with a null

[0086] ,

[0087] Table 3 Maximum sidelobe level and null values obtained by a 32 - element linear array antenna with a null

[0088] ,

[0089] Based on the existing fox optimization algorithm, a chaotic mapping strategy and a local mutation search strategy are introduced to enhance the performance of the algorithm. The chaotic mapping strategy is used to generate a more uniform and higher - quality initial solution set, while the local mutation search strategy includes a spiral flight strategy and a Gaussian random walk strategy, which improve the efficiency of the algorithm in global search and local exploitation. The organic combination of these strategies significantly enhances the global exploration ability and the ability to escape from local optima of the algorithm, and effectively accelerates the convergence process of the algorithm. Applying this improved fox optimization algorithm to solve the radiation pattern optimization model of a sparse linear array antenna can quickly achieve the purpose of suppressing the maximum sidelobe level and controlling the null.

[0090] In the present invention, the chaotic mapping strategy generates an initial population, enabling the algorithm to obtain a larger search range with a uniform distribution and a better initial solution set in the early stage, which is conducive to maintaining the diversity of the population in the early stage and obtaining better global search ability. In addition, the local mutation search strategy balances global search and local exploitation, ensuring the convergence speed and stability in the later stage of the algorithm, and improving the optimization effect of the peak sidelobe level and the null control effect. In summary, the simulation experiment results prove that the method has a good optimization result, can improve the optimization efficiency of the sparse linear laser array antenna, and thus provides a new method and technology for the pattern optimization of the actual sparse linear laser array antenna.

[0091] Please refer to Figure 6 , which shows a structural block diagram of a pattern optimization system for a laser array antenna based on an improved fox optimization algorithm of the present application.

[0092] As Figure 6 shown, the pattern optimization system 200 for a laser array antenna includes a definition module 210 and a solution module 220.

[0093] Among them, the definition module 210 is configured to obtain the array antenna pattern function according to the electromagnetic field superposition principle, and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls.

[0094] The solution module 220 is configured to use an improved fox optimization algorithm to solve the sparse linear array antenna optimization model and obtain the optimal array antenna distribution scheme. Among them, the process of solving the sparse linear array antenna optimization model specifically includes:

[0095] Generate model parameters using the Pwlcm cosine piecewise chaotic mapping strategy, and add the element spacing constraint matrix to generate the initial element distribution.

[0096] Calculate the peak sidelobe level and the null depth in the specified direction of each element distribution to obtain the current best fitness and the optimal individual.

[0097] Judge whether the local mutation strategy is satisfied. If it is satisfied, use the non-linear weight golden sine strategy to update the position of the element distribution; otherwise, update the element position according to the fox snow hunting behavior in the improved fox optimization algorithm.

[0098] Calculate the fitness of each individual to obtain the best fitness and the optimal individual.

[0099] Mutate the fox individual positions according to the hyperbolic cosine and sine optimization strategy, and calculate the fitness of the mutated individuals. If it is better, replace the mutated individuals before mutation with the mutated individuals to obtain a better element distribution.

[0100] Determine whether the termination condition is satisfied. If not, update the iteration count and continue the iteration. Otherwise, proceed to the next step;

[0101] Output the global optimal individual and the best fitness value. The optimal individual is the optimal array antenna distribution, and the best fitness value is the objective function value corresponding to the optimal array antenna distribution.

[0102] It should be understood that Figure 6 the various modules described in Figure 1 correspond to the respective steps in the method described in the reference Figure 6 Therefore, the operations, features, and corresponding technical effects described above for the method also apply to

[0103] In some other embodiments, the embodiments of the present invention further provide a computer-readable storage medium, on which a computer program is stored. When the program instructions are executed by a processor, the processor executes the method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm in any of the above method embodiments;

[0104] As an implementation manner, the computer-readable storage medium of the present invention stores computer-executable instructions, and the computer-executable instructions are set as:

[0105] Obtain the array antenna radiation pattern function according to the electromagnetic field superposition principle, and construct an optimization model for a sparse linear array antenna with the goal of optimizing the maximum sidelobe level with nulls;

[0106] Adopt an improved fox optimization algorithm to solve the optimization model of the sparse linear array antenna, and obtain the optimal array antenna distribution scheme. Among them, the process of solving the optimization model of the sparse linear array antenna specifically includes:

[0107] Generate model parameters using the Pwlcm cosine piecewise chaotic mapping strategy, and add the element spacing constraint matrix to generate the initial element distribution;

[0108] Calculate the peak sidelobe level and the null depth in the specified direction of each element distribution to obtain the current best fitness value and the optimal individual;

[0109] Determine whether the local mutation strategy is satisfied. If satisfied, use the non-linear weight golden sine strategy to update the positions of the element distributions; otherwise, update the element positions according to the fox's snowfield predation behavior in the improved fox optimization algorithm;

[0110] Calculate the fitness of each individual to obtain the best fitness value and the optimal individual;

[0111] According to the hyperbolic sine and cosine optimization strategy, the positions of the fox individuals are mutated, and the fitness of the mutated individuals is calculated. If it is better, the mutated individuals replace the corresponding individuals before mutation to obtain a better element distribution;

[0112] Determine whether the termination condition is satisfied. If not, update the iteration count and continue the iteration; otherwise, proceed to the next step;

[0113] Output the globally optimal individual and the best fitness. The optimal individual is the optimal array antenna distribution, and the best fitness is the objective function value corresponding to the optimal array antenna distribution.

[0114] A computer-readable storage medium may include a storage program area and a storage data area. Among them, the storage program area can store an operating system and application programs required for at least one function; the storage data area can store data created according to the use of the laser array antenna pattern optimization system based on the improved fox optimization algorithm, etc. In addition, the computer-readable storage medium may include high-speed random access memory, and may also include memory, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some embodiments, the computer-readable storage medium may optionally include a memory remotely provided with respect to the processor, and these remote memories can be connected to the laser array antenna pattern optimization system based on the improved fox optimization algorithm through a network. Examples of the above networks include, but are not limited to, the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof.

[0115] Figure 7 is a schematic structural diagram of the electronic device provided by the embodiment of the present invention, as Figure 7 shown. The device includes: a processor 310 and a memory 320. The electronic device may further include: an input device 330 and an output device 340. The processor 310, the memory 320, the input device 330, and the output device 340 can be connected through a bus or other means, Figure 7 taking connection through the bus as an example. The memory 320 is the above-mentioned computer-readable storage medium. The processor 310 executes various functional applications and data processing of the server by running non-volatile software programs, instructions, and modules stored in the memory 320, that is, implements the laser array antenna pattern optimization method based on the improved fox optimization algorithm in the above method embodiment. The input device 330 can receive input digital or character information, and generate key signal inputs related to the user settings and function controls of the laser array antenna pattern optimization system. The output device 340 may include a display device such as a display screen.

[0116] The above-mentioned electronic device can execute the method provided by the embodiments of the present invention, and has the corresponding functional modules and beneficial effects for executing the method. For the technical details not described in detail in this embodiment, reference may be made to the method provided by the embodiments of the present invention.

[0117] As an implementation manner, the above-mentioned electronic device is applied to a laser array antenna pattern optimization system based on an improved fox optimization algorithm and is used for a client, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein, the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to:

[0118] Obtain the array antenna pattern function according to the principle of electromagnetic field superposition, and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls;

[0119] Adopt an improved fox optimization algorithm to solve the sparse linear array antenna optimization model and obtain the optimal array antenna distribution scheme. Among them, the process of solving the sparse linear array antenna optimization model specifically includes:

[0120] Use the Pwlcm cosine piecewise chaotic mapping strategy to generate model parameters, and add the element spacing constraint matrix to generate the initial element distribution;

[0121] Calculate the peak sidelobe level and the null depth in the specified direction of each element distribution to obtain the current best fitness and the optimal individual;

[0122] Judge whether the local mutation strategy is satisfied. If it is satisfied, use the non-linear weight golden sine strategy to update the position of the element distribution; otherwise, update the element position according to the fox snowfield predation behavior in the improved fox optimization algorithm;

[0123] Calculate the fitness of each individual to obtain the best fitness and the optimal individual;

[0124] According to the hyperbolic cosine optimization strategy, mutate the positions of the fox individuals, and calculate the fitness of the mutated individuals. If it is better, replace the mutated individuals before mutation with the mutated individuals to obtain a better element distribution;

[0125] Judge whether the termination condition is satisfied. If not, update the iteration times and continue the iteration; otherwise, proceed to the next step;

[0126] Output the global optimal individual and the best fitness. The optimal individual is the optimal array antenna distribution, and the best fitness is the objective function value corresponding to the optimal array antenna distribution.

[0127] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiments.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An optimization method for the radiation pattern of a laser array antenna based on an improved fox optimization algorithm, characterized in that, Including: Obtain the array antenna pattern function according to the electromagnetic field superposition principle, and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls; Adopt an improved fox optimization algorithm to solve the sparse linear array antenna optimization model and obtain the optimal array antenna distribution scheme. Among them, the process of solving the sparse linear array antenna optimization model specifically includes: Generate model parameters using the Pwlcm cosine piecewise chaotic mapping strategy, and add the element spacing constraint matrix to generate the initial element distribution; Calculate the peak sidelobe level and the null depth in the specified direction of each element distribution to obtain the current best fitness and the optimal individual; Judge whether the local mutation strategy is satisfied. If it is satisfied, use the non-linear weight golden sine strategy to update the position of the element distribution; otherwise, update the element position according to the fox snowfield predation behavior in the improved fox optimization algorithm; Calculate the fitness of each individual to obtain the best fitness and the optimal individual; Mutate the position of the fox individuals according to the hyperbolic sine-cosine optimization strategy, and calculate the fitness of the mutated individuals. If it is better, replace the mutated individuals before mutation with the mutated individuals to obtain a better element distribution; Judge whether the termination condition is satisfied. If not, update the iteration times and continue the iteration; otherwise, proceed to the next step; Output the global optimal individual and the best fitness. The optimal individual is the optimal array antenna distribution, and the best fitness is the objective function value corresponding to the optimal array antenna distribution.

2. The method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to claim 1, wherein The expression of the Pwlcm cosine piecewise chaotic mapping strategy is: ， In the formula, is the position of the (j + 1)-th element of the i-th fox, is the position of the j-th element of the i-th fox, is the control parameter of the mapping, ∈ [0, 1]; The expression of the element spacing constraint matrix is: ， In the formula, is the position of the first array element, is the position of the Nth array element, is the initial position of the array after the Pwlcm cosine piecewise chaotic mapping, is the shortest distance between each array element, is the number of array elements, is the position of the second array element in X, is the position of the third array element in X, is the position of the Nth array element in X.

3. A method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to claim 1, characterized in that, The expression of the non-linear weight golden sine strategy is: ， ， ， ， Wherein, is the position of the i-th fox in the (it + 1)-th generation, is the first non-linear weight factor, is a random number within the interval [0, 2π], is the position of the i-th fox in the it-th generation, is a random number within the interval [0, π], is the position of the optimal fox individual, is the maximum value of the first non-linear weight factor, is the minimum value of the first non-linear weight factor, is the maximum number of iterations, is the current number of iterations, and are both coefficients containing the golden ratio, is the golden ratio.

4. An optimization method for the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to claim 1, characterized in that The objective function of the sparse linear array antenna optimization model is: ， ， ， ， In the formula, is the established objective function, is the calculation formula for the maximum sidelobe level, is the weight coefficient of the maximum sidelobe level, is the weight coefficient of the null, is the main lobe gain, is the null depth at the specified angle, is the target null depth, and are the initial weight coefficients, which are set to 0.16 and 0.12 respectively, is the maximum sidelobe gain, is the maximum number of iterations.

5. A method for optimizing the radiation pattern of a laser array antenna based on an improved fox optimization algorithm according to claim 1, characterized in that The hyperbolic sine-cosine optimization strategy includes: In the first exploration stage, explore the nearby space of the fox, and the expression is: ， ， Wherein, is the position of the i-th fox in the (i+1)-th generation, is the position of the optimal fox individual, is the second non-linear weight factor, is the position of the i-th fox in the i-th generation, , , , are all random numbers within the range of (0, 1), is the maximum number of iterations, is the current number of iterations, , are both sensitivity coefficients with different values; In the second exploration stage, deeply explore the obtained optimal solution of the fox, and the exploration intensity around the optimal solution will increase with the increase of the iteration times. The expression is: ， ， wherein, , , are all random numbers within the interval (0, 1), is the third non-linear weight factor, is the sensitivity coefficient, different from the values of , , and cosh is the hyperbolic cosine function, and sinh is the hyperbolic sine function.

6. A laser array antenna pattern optimization system based on an improved fox optimization algorithm, characterized in that, Including: A definition module configured to obtain the array antenna pattern function according to the electromagnetic field superposition principle and construct a sparse linear array antenna optimization model with the goal of optimizing the maximum sidelobe level with nulls; A solution module configured to adopt an improved fox optimization algorithm to solve the sparse linear array antenna optimization model and obtain the optimal array antenna distribution scheme. Among them, the process of solving the sparse linear array antenna optimization model specifically includes: Generate model parameters using the Pwlcm cosine piecewise chaotic mapping strategy, and add the element spacing constraint matrix to generate the initial element distribution; Calculate the peak sidelobe level and the null depth in the specified direction of each element distribution to obtain the current best fitness and the optimal individual; Judge whether the local mutation strategy is satisfied. If it is satisfied, use the non-linear weight golden sine strategy to update the position of the element distribution; otherwise, update the element position according to the fox snowfield predation behavior in the improved fox optimization algorithm; Calculate the fitness of each individual to obtain the best fitness and the optimal individual; According to the hyperbolic sine and cosine optimization strategy, the position of the fox individual is mutated, and the fitness of the mutated individual is calculated. If it is better, the mutated individual replaces the corresponding individual before mutation to obtain a better array element distribution; Judge whether the termination condition is satisfied. If not, update the iteration number and continue the iteration. Otherwise, proceed to the next step; Output the global optimal individual and the best fitness. The optimal individual is the optimal array antenna distribution, and the best fitness is the objective function value corresponding to the optimal array antenna distribution.

7. An electronic device, characterized in that, It includes: At least one processor, and a memory communicatively connected to the at least one processor. The memory stores instructions executable by the at least one processor. When the instructions are executed by the at least one processor, the at least one processor is enabled to execute the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, the method according to any one of claims 1 to 5 is implemented.

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