Method for sum and difference beam optimization of a covered array antenna

Abstract

The application discloses a sum and difference beam optimization method of a cover array antenna, and comprises the following steps: creating an array antenna model and a cover array antenna model; performing quadrilateral mesh division on the models respectively; based on the corresponding quadrilateral mesh division of the models, performing simulation calculation by using a high-order moment method, and extracting corresponding active unit directional diagrams; applying excitation to the antenna units in the models, combining the active unit directional diagrams, calculating the sum and difference beams of the models under different scanning angles, and comparing corresponding performance indexes; and using an improved hybrid differential evolution algorithm to optimize the sum and difference beams of the cover array antenna model which does not meet the index requirements; wherein the improved hybrid differential evolution algorithm performs global and local iterative searches, and adaptively calculates a mutation factor and a crossover factor in the global and local iterative search processes. The application realizes the optimization design of the sum and difference beams of the cover array antenna, and is more in line with engineering application requirements.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a method for optimizing the sum and difference beams of a radome array antenna. Background Technology

[0002] With continuous innovation in aerospace technology, radome antennas, as a crucial component of major information-based weapons such as hypersonic vehicles, benefit from radomes that protect the array antenna's performance from external environmental or electromagnetic interference. However, radomes can also influence the original radiation characteristics of the array antenna to some extent. Therefore, it is necessary to assess the impact of the radome during the design phase. Integrated simulation of radome array antennas can accurately predict the electromagnetic performance of both the array antenna and the radome, avoiding unnecessary experiments and improving design efficiency. Furthermore, integrated simulation of radome array antennas can identify problems early in the design phase, reducing costs and risks. Therefore, integrated simulation of array antennas and radomes is of significant research importance.

[0003] In practical applications, designing an ideal radome is often difficult to achieve, thus the radome inevitably affects the performance of the array antenna within it to some extent. To reduce or eliminate this effect, optimization algorithms can be used to optimize the amplitude and phase of the excitation of each element in the array antenna, thereby ensuring that the relevant performance indicators of the radome array antenna meet the requirements. However, the optimization design problem of radome array antennas is typically a complex, nonlinear, multi-objective optimization problem. As the complexity of the problem increases, the optimization difficulty also increases, undoubtedly posing a greater challenge to the performance of the optimization algorithm itself. Therefore, how to efficiently simulate and optimize the design of radome array antennas has become a research challenge. For example, Liu Lu et al. disclosed a phase compensation and amplitude optimization scheme in their paper "Performance Improvement of Antenna Array-Radome System Based on Efficient Compensation and Optimization Scheme" (IEEE Antennas and Wireless Propagation Letters, 2020) to improve the adverse effects of the radome on the radiation characteristics of the array antenna. The steps of the scheme are as follows: using an ideal point source model to replace the actual antenna structure, and the shape of the radome is described by the hyperellipsoid equation; using the method of moments combined with the multilayer fast multipole algorithm to calculate the far-field characteristics before and after adding the radome, and extracting the amplitude and phase distortion caused by the radome at different angles; performing phase compensation to correct the pointing error for each antenna element; and using a quasi-Newton algorithm to optimize the amplitude of the excitation of each element so that the beamwidth and sidelobe level of the radome array antenna and the beam meet the set index requirements.

[0004] However, the existing scheme proposed by Liu Lu et al. has the following problems: it uses an ideal point source instead of the actual antenna element, without considering the real model, which will produce large errors in practical engineering applications; it does not consider the correlation between excitation amplitude control and phase compensation, and for beams with different scanning angles, this scheme needs to compensate and correct the beam direction by itself; the quasi-Newton algorithm used has high requirements for the initial point and the objective function, and has poor versatility; it does not perform optimization analysis on the difference beam after the radome is added, and in practical engineering applications, the sum and difference beams of the radome antenna are often used for target tracking; it only deals with the radome linear array antenna model and does not perform optimization analysis on large radome planar array antennas. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a method for optimizing the sum and difference beams of a radome array antenna. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a method for optimizing the sum and difference beams of a radome array antenna, comprising:

[0007] Create array antenna models and radome array antenna models;

[0008] The array antenna model and the radome array antenna model are respectively subjected to quadrilateral meshing;

[0009] Based on the array antenna model and the quadrilateral mesh corresponding to the radome array antenna model, simulation calculations are performed using the higher-order method of moments to extract the corresponding active element radiation patterns.

[0010] Excitation is applied to the antenna elements in the array antenna model and the radome array antenna model. Combined with the radiation pattern of the active element, the sum and difference beams corresponding to the array antenna model and the radome array antenna model at different scanning angles are calculated, and the corresponding performance indicators are compared.

[0011] An improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of the radome array antenna model that does not meet the performance requirements. The improved hybrid differential evolution algorithm performs global iterative search and local iterative search respectively, and adaptively calculates the mutation factor and crossover factor during the global iterative search and local iterative search processes.

[0012] In one embodiment of the present invention, the array antenna model is composed of a plurality of antenna elements, each antenna element including a dielectric substrate disposed on a floor, and two intersecting dielectric plates disposed perpendicularly to the dielectric substrate; each dielectric plate is provided with a feed and radiating patch, and each feed and radiating patch is provided with a coaxial port.

[0013] In one embodiment of the present invention, based on the array antenna model and the quadrilateral mesh corresponding to the radome array antenna model, simulation calculations are performed using the higher-order method of moments to extract the corresponding active element radiation patterns, including:

[0014] Initialization excitation amplitude and phase are applied to each antenna element in the array antenna model and the radome array antenna model, respectively.

[0015] Based on the applied initial excitation amplitude and phase, simulation calculations are performed using the higher-order method of moments on the quadrilateral mesh corresponding to the array antenna model and the radome array antenna model, respectively, to extract the corresponding active element radiation patterns.

[0016] In one embodiment of the present invention, an improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of the radome array antenna model that does not meet the performance requirements, including:

[0017] The population parameters involved in the optimization design process are determined based on the sum and difference beams of the radome array antenna model, and the population is initialized based on the population parameters.

[0018] Calculate the fitness function value for each individual in the initial population;

[0019] Design and calculate the mutation factor, select several intermediate optimal individuals from the initial population according to the fitness function value corresponding to each individual in the initial population, and perform mutation operation on all individuals in the initial population according to the mutation factor and the several intermediate optimal individuals;

[0020] Design and calculate the crossover factor, and perform crossover operations on individuals in the initial population and mutated individuals based on the crossover factor;

[0021] Calculate the fitness function value of each individual after crossover, and determine whether the fitness function value of each individual in the initial population is greater than the fitness function value of each individual after crossover. If so, retain the individual corresponding to the crossover and update the initial population; otherwise, retain the individual corresponding to the initial population and update the initial population.

[0022] From the updated initial population, select the final best individual and determine whether the fitness function values ​​of the final best individuals from the preset threshold generations are the same:

[0023] If they are not the same, then determine whether the maximum number of iterations or the preset precision threshold has been reached:

[0024] If so, output the final optimal individual;

[0025] If not, calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean, and recalculate the mutation factor using the mean used for adaptively calculating the mutation factor. At the same time, calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean, and recalculate the crossover factor using the mean used for adaptively calculating the crossover factor. Repeat the above mutation operation, crossover operation, and selection operation until the maximum number of iterations or the preset precision threshold is reached.

[0026] If they are the same, then an initial simplex is constructed based on the final optimal individuals. The Nelder-Mead simplex method is used to perform a local search on the initial simplex, outputting the optimal individual after the local search. The fitness function value corresponding to the optimal individual after the local search is calculated, and it is determined whether the fitness function value corresponding to the optimal individual after the local search meets the preset accuracy threshold.

[0027] If so, output the best individual after this local search as the final best individual;

[0028] If not, calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population. Update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean, and recalculate the mutation factor using the mean used for adaptively calculating the mutation factor. At the same time, calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population. Update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean, and recalculate the crossover factor using the mean used for adaptively calculating the crossover factor. Repeat the above mutation, crossover, and selection operations until the maximum number of iterations or the preset precision threshold is reached.

[0029] In one embodiment of the present invention, the designed variation factor is expressed by the formula:

[0030] ;

[0031] in, Indicates the first t The first generation of the initial population i The variation factors corresponding to each individual , Indicates the first t The mean value used to initialize the population adaptive calculation of the variation factor. The generated mean is The variance is 0.1 Cauchy Random numbers from a distribution, and ;

[0032] Correspondingly, the mutation operation formula is expressed as:

[0033] ;

[0034] in, Indicates the first t The corresponding mutated number in the initial population i Individual, Indicates the first t The first corresponding mutated digit in the initial population i Individual, Indicates from the first In the initialization population, select several intermediate-optimal individuals and then randomly select one individual from these intermediate-optimal individuals. Indicates the first Randomly select an individual from the initial population. Indicates from the first A single individual is randomly selected from the initial population, and and , , They are not equal.

[0035] In one embodiment of the present invention, the designed cross factor is expressed by the formula:

[0036] ;

[0037] in, Indicates the first t The first generation of the initial population i The cross factor corresponding to each individual Indicates the first t The mean value used to adaptively calculate the crossover factor for the initial population is used. The generated mean is Random numbers that are normally distributed with a variance of 0.1, and ;

[0038] Correspondingly, the crossover operation formula is expressed as:

[0039] ;

[0040] in, Indicates the first t The first generation corresponding to crossover in the initialization population i The first individual j dimensional variables, Indicates the first t The corresponding mutated number in the initial population i The first individualj dimensional variables, Indicates from Randomly select a number from the list. Indicates from Randomly select a positive integer. Indicates the first t The first corresponding mutated digit in the initial population i The first individual j Dimensional variables.

[0041] In one embodiment of the present invention, the Lehmer mean is calculated using the following formula:

[0042] ;

[0043] in, , Indicates population size;

[0044] Correspondingly, the mean used to adaptively calculate the variation factor is updated based on the Lehmer mean, as expressed by the formula:

[0045] ;

[0046] in, Indicates the first t The mean value used for adaptive calculation of the mutation factor corresponding to the +1 generation initialization population. Indicates the first t The mean value used for adaptive calculation of the mutation factor corresponding to the initialization population. This represents the adaptive parameter.

[0047] In one embodiment of the present invention, the arithmetic mean is calculated using the following formula:

[0048] ;

[0049] in, , Indicates population size;

[0050] Correspondingly, the mean used to adaptively calculate the crossover factor is updated based on the arithmetic mean, as expressed by the formula:

[0051] ;

[0052] in, Indicates the first t +1 generation initialization population corresponding to the mean value used for adaptive calculation of crossover factor Indicates the first t The mean value used for adaptive crossover factor calculation corresponding to the initialization population is replaced. This represents the adaptive parameter.

[0053] The beneficial effects of this invention are:

[0054] The proposed method for optimizing the sum and difference beams of a radome array antenna comprehensively considers the characteristics of both the array antenna model and the radome array antenna model. It utilizes an improved hybrid differential evolution algorithm to optimize the array model of the radome planar array antenna. Specifically: an array antenna model and a radome array antenna model are created; quadrilateral meshes are performed on both models; based on the corresponding quadrilateral meshes, simulation calculations are conducted using the higher-order method of moments to extract the corresponding active element radiation patterns; excitation is applied to the antenna elements in both models, and the sum and difference beams are calculated at different scanning angles using the active element radiation patterns, and the corresponding performance indicators are compared; the improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of radome array antenna models that do not meet the performance requirements. Specifically, the improved hybrid differential evolution algorithm performs both global and local searches, adaptively calculating the mutation factor and crossover factor during both searches. As can be seen, this invention uses a higher-order method of moments (MoM) with fewer unknowns to perform integrated simulation calculations on the array antenna model and the radome array antenna model. However, the optimization problem of the radome array antenna model is usually a high-dimensional, nonlinear, and multi-objective complex optimization problem, which places high demands on the performance of the optimization algorithm. To accelerate the convergence speed, this invention proposes an improved hybrid differential evolution algorithm, which combines the higher-order method of moments with the improved hybrid differential evolution algorithm. This can be achieved with the help of a high-performance computing platform to efficiently optimize the design of large radome array antennas, overcoming the problem that existing technologies can only optimize simple radome linear arrays, making this invention more universal. To efficiently achieve integrated optimization of the radome array antenna model and accurately consider the coupling between the radome array antenna models, this invention uses a higher-order method of moments (MoM) to optimize the large radome array antenna model. The step-moment method extracts the active element radiation pattern of each antenna element and superimposes it with the excitation amplitude and phase of each antenna element obtained during the optimization process. That is, based on the excitation amplitude and phase modulation of each antenna element in the array antenna model and the radome array antenna model, the far-field radiation pattern of the array antenna model and the radome array antenna model can be quickly calculated, realizing the optimization design of both the sum and difference beams of the radome array antenna, which is more in line with the needs of engineering applications. The improved hybrid differential evolution algorithm proposed in this invention performs iterative search from global and local perspectives, which can guarantee that the optimal solution is obtained after iterative search. At the same time, the mutation factor and cross factor are adaptively calculated during the search iteration. Compared with the fixed mutation factor and cross factor design in the standard differential evolution algorithm, it further guarantees that the optimal solution is obtained after iterative search, and the algorithm converges faster.

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating a sum and difference beam optimization method for a radome array antenna provided in an embodiment of the present invention.

[0057] Figure 2 (a)~ Figure 2 (b) is a schematic diagram of the array antenna model and the radome array antenna model provided in the embodiments of the present invention;

[0058] Figure 3 (a)~ Figure 3 (b) is a schematic diagram of the structure of each antenna element in the array antenna model provided in the embodiment of the present invention;

[0059] Figure 4 (a)~ Figure 4 (b) is a schematic diagram of the comparison of the sum and difference beams along the xoz and yoz planes before and after beam scanning provided in an embodiment of the present invention;

[0060] Figure 5 (a)~ Figure 5 (b) is a schematic diagram of the comparison of sum and difference beams before and after adding a cover during beam scanning at elevation scan of -10° and azimuth scan of 10°, provided in an embodiment of the present invention.

[0061] Figure 6 (a)~ Figure 6 (b) is a schematic diagram comparing the sum and difference beams of the radome array antenna model before and after optimization under an elevation scan of -10°, provided in an embodiment of the present invention.

[0062] Figure 7 (a)~ Figure 7 (b) is a schematic diagram comparing the sum and difference beams of the radome array antenna model before and after optimization under 10° azimuth sweep provided in the embodiment of the present invention;

[0063] Figure 8 (a)~ Figure 8 (b) is a schematic diagram of the optimization results of different optimization algorithms for the differential beam under a pitch scan of -10° provided in the embodiments of the present invention;

[0064] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0065] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0066] To overcome the limitation of existing technologies that only optimize simple radome linear arrays, and to achieve efficient optimization of large radome array antennas, thereby making radome array antennas more versatile, please refer to [link to relevant documentation]. Figure 1 This invention provides a method for optimizing the sum and difference beams of a radome array antenna, specifically including the following steps:

[0067] S10. Create an array antenna model and a radome array antenna model.

[0068] Antenna elements are created based on actual application requirements; these can be symmetrical dipoles, microstrip antennas, waveguide slot antennas, etc. For example... Figure 3 As shown in (a), the created antenna unit includes a dielectric substrate disposed on the floor and two intersecting dielectric plates disposed perpendicularly to the dielectric substrate; each dielectric plate is provided with a feed and a radiating patch, and each feed and radiating patch is provided with a coaxial port (coaxial port 1, coaxial port 2). Figure 3 (b) is Figure 3 (a) shows a partial enlarged view. The embodiment of the present invention provides exemplary dimensional parameters for the antenna element, specifically: the length and width of the ground plane are both 13.5 mm, the length and width of the dielectric substrate are both 13.5 mm, the thickness is 0.18 mm, and both the dielectric substrate and the dielectric plate are made of FR4.

[0069] An array antenna model consists of several antenna elements. These elements can be arranged into one-dimensional linear arrays or two-dimensional planar arrays. The spacing between the antenna elements can be equal or non-equal. Figure 2 As shown in (a). Figure 2 The numbers marked in (a) indicate the order of excitation for each antenna element. Placing this array antenna model inside a radome creates a radome-equipped array antenna model, as shown below. Figure 2 As shown in (b), the dimensional parameters of the radome array antenna are provided by example in this embodiment of the invention. Specifically, the radome height is 0.66m, the aperture size is: major axis 0.569m, minor axis 0.376m, relative permittivity is 2.2, loss tangent is 0.05, and the array antenna is placed 0.084m from the bottom of the radome. The calculated frequency is 11GHz.

[0070] S20. Perform quadrilateral meshing on the array antenna model and the radome array antenna model respectively.

[0071] Using existing methods, quadrilateral meshes are performed on the array antenna model and the radome array antenna model respectively, and subsequent calculations are based on the meshed quadrilateral meshes.

[0072] S30. Based on the quadrilateral meshes corresponding to the array antenna model and the radome array antenna model, simulation calculations are performed using the higher-order method of moments to extract the corresponding active element radiation patterns.

[0073] This invention proposes an optional scheme: based on the quadrilateral meshes corresponding to the array antenna model and the radome array antenna model, simulation calculations are performed using the higher-order method of moments to extract the corresponding active element radiation patterns, including:

[0074] Initialization excitation amplitude and phase are applied to each antenna element in the array antenna model and the radome array antenna model, respectively. Based on the applied initialization excitation amplitude and phase, simulation calculations are performed using the higher-order method of moments based on the quadrilateral meshes corresponding to the array antenna model and the radome array antenna model, and the corresponding active element radiation patterns are extracted.

[0075] For example, using the higher-order method of moments (MMT), simulations are performed on both the array antenna model and the radome array antenna model. The initial excitation amplitude of only one antenna element in each model is set to 1V and the phase to 0°, while the initial excitation amplitudes and phases of the other antenna elements are set to 0V and 0°. The calculated radiation pattern is the active element radiation pattern of that antenna element. The active element radiation patterns corresponding to all antenna elements are extracted sequentially and denoted as follows: , , Indicates the first n The active element radiation pattern corresponding to each antenna element is as follows: The calculation can be performed using existing methods.

[0076] S40. Apply excitation to the antenna elements in the array antenna model and the radome array antenna model, and calculate the sum and difference beams corresponding to the array antenna model and the radome array antenna model at different scanning angles, and compare the corresponding performance indicators, in conjunction with the active element radiation pattern.

[0077] In the array antenna model and the radome array antenna model, each antenna element is excited with an amplitude of 1V, and the phase is set according to the relevant theoretical calculation results. For example, only the [number] antenna element is excited. The calculated active element radiation pattern of the antenna element is as follows: The formula for calculating the total far field is then expressed as:

[0078] (1)

[0079] in, , and Represented as the first The excitation amplitude and phase of each antenna element,N This represents the number of antenna elements in the antenna array model, for example... N =256.

[0080] As can be seen, in this embodiment of the invention, the total far field is calculated using formula (1) based on the extracted active element radiation pattern and the excitation amplitude and phase applied to the set antenna element. Then, the corresponding directional coefficient is calculated through the total far field. Finally, the sum and difference beams corresponding to the array antenna model and the radome array antenna model are calculated through the directional coefficients. The performance indicators such as the pointing and sidelobe level of the sum beam and the zero depth position, zero depth level and sidelobe level of the difference beam are compared under different scanning conditions before and after the radome is added.

[0081] S50. An improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of a radome array antenna model that does not meet the performance requirements. The improved hybrid differential evolution algorithm performs global iterative search and local iterative search respectively, and adaptively calculates the mutation factor and crossover factor during the global iterative search and local iterative search processes.

[0082] Standard differential evolution algorithms typically use fixed crossover and mutation factors throughout the iteration process. However, this design may fail to yield optimal solutions if the fixed values ​​are not properly configured. Therefore, this invention proposes a hybrid differential evolution algorithm based on the standard differential evolution algorithm. This algorithm improves convergence speed when dealing with sum and difference beam optimization problems for radome array antennas. Specifically, this invention employs an improved hybrid differential evolution algorithm to optimize the sum and difference beams of radome array antenna models that do not meet performance requirements, including:

[0083] The population parameters involved in the optimization design process are determined based on the sum and difference beams of the radome array antenna model, and the population is initialized based on the population parameters.

[0084] Calculate the fitness function value for each individual in the initial population;

[0085] Design and calculate the mutation factor, select several intermediate optimal individuals from the initial population based on the fitness function value corresponding to each individual in the initial population, and perform mutation operation on all individuals in the initial population based on the mutation factor and several intermediate optimal individuals;

[0086] Design and calculate the crossover factor, and perform crossover operations on individuals in the initial population and mutated individuals based on the crossover factor;

[0087] Calculate the fitness function value of each individual after crossover, and determine whether the fitness function value of each individual in the initial population is greater than the fitness function value of each individual after crossover. If so, retain the individual corresponding to the crossover and update the initial population; otherwise, retain the individual corresponding to the initial population and update the initial population.

[0088] From the updated initial population, select the final best individual and determine whether the fitness function values ​​of the final best individuals from the preset threshold generations are the same:

[0089] If they are not the same, then determine whether the maximum number of iterations or the preset precision threshold has been reached:

[0090] If so, output the final optimal individual;

[0091] If not, calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean, and recalculate the mutation factor based on the mean used for adaptively calculating the mutation factor. At the same time, calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean, and recalculate the crossover factor based on the mean used for adaptively calculating the crossover factor. Repeat the above mutation, crossover, and selection operations until the maximum number of iterations or the preset precision threshold is reached.

[0092] If they are the same, then the initial simplex is constructed based on the final optimal individual. The Nelder-Mead simplex method is used to perform a local search on the initial simplex, outputting the optimal individual after the local search. The fitness function value corresponding to the optimal individual after the local search is calculated, and it is determined whether the fitness function value corresponding to the optimal individual after the local search meets the preset accuracy threshold.

[0093] If so, output the best individual after this local search as the final best individual;

[0094] If not, calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population. Update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean, and recalculate the mutation factor using the mean used for adaptively calculating the mutation factor. At the same time, calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population. Update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean, and recalculate the crossover factor using the mean used for adaptively calculating the crossover factor. Repeat the above mutation, crossover, and selection operations until the maximum number of iterations or the preset precision threshold is reached.

[0095] In this embodiment of the invention, optimizing each individual in the population refers to the excitation amplitude and phase of 256 antenna elements. The population is composed of... Composed of individual entities, NPThe population size is set, and fitness functions are set according to the desired optimization objectives. Here, the optimization objectives are the sum beam and the difference beam, and the corresponding fitness functions are the fitness functions for the sum beam and the difference beam, respectively. The sum beam achieves maximum pointing accuracy and reduces sidelobe level, while the difference beam achieves accurate zero-depth position and reduces both sidelobe and zero-depth levels. The population size is then initialized. The mean used for adaptive calculation of the variation factor initial value The mean used for adaptive calculation of the cross factor initial value The proportion of outstanding individuals Reflectance coefficient elongation coefficient Shrinkage coefficient Preset threshold Maximum number of iterations =10000, adaptive parameter =0.5. Here, because the mutation factor and crossover factor undergo an adaptive calculation process, the selection of initial values ​​has little impact on the algorithm's solution accuracy, and there are no requirements on the characteristics of the objective function, making it highly versatile.

[0096] Correspondingly, the initial population formula is expressed as:

[0097] (2)

[0098] In the formula, Indicates the first t The first corresponding mutated digit in the initial population i Individual, , This represents the lower bound of the optimization variable. This represents the upper bound of the optimization variable. Indicates generation A random number between [a certain number of points].

[0099] In this embodiment of the invention, existing methods are used to calculate the fitness function value corresponding to each individual in the initial population based on the fitness function of the difference beam and the fitness function of the beam.

[0100] The variation factor designed in this embodiment of the invention is expressed by the following formula:

[0101] (3)

[0102] in, Indicates the first t The first generation of the initial population i The variation factors corresponding to each individual Indicates the first tThe mean value used to initialize the population adaptive calculation of the variation factor. The generated mean is The variance is 0.1 Cauchy Random numbers from a distribution, and ;

[0103] Correspondingly, the mutation operation formula is expressed as:

[0104] (4)

[0105] in, Indicates the first t The corresponding mutated number in the initial population i Individual, Indicates the first t The first corresponding mutated digit in the initial population i Individual, Indicates from the first In the initialization population, select several intermediate best individuals, for example, select... The optimal individual in the middle and from Randomly select one individual from the best intermediate individuals. Indicates the first Randomly select an individual from the initial population. Indicates from the first A single individual is randomly selected from the initial population, and and , , They are not equal.

[0106] The cross factor designed in this embodiment of the invention is expressed by the following formula:

[0107] (5)

[0108] in, Indicates the first t The first generation of the initial population i The cross factor corresponding to each individual Indicates the first t The mean value used to adaptively calculate the crossover factor for the initial population is used. The generated mean is Random numbers that are normally distributed with a variance of 0.1, and ;

[0109] Correspondingly, the crossover operation formula is expressed as:

[0110] (6)

[0111] in, Indicates the firstt The first generation corresponding to crossover in the initialization population i The first individual j dimensional variables, Indicates the first t The corresponding mutated number in the initial population i The first individual j dimensional variables, Indicates from Randomly select a number from the list. Indicates from Randomly select a positive integer. Indicates the first t The first corresponding mutated digit in the initial population i The first individual j Dimensional variables.

[0112] Here, it is determined whether the fitness function value of each individual in the initial population is greater than the fitness function value of each individual after crossover. If so, then Store in the set of individuals with poor fitness function values; otherwise, store in the set of individuals with poor fitness function values. Store them in the set of individuals with poor fitness function values.

[0113] The Lehmer mean is calculated in this embodiment of the invention, and the formula is expressed as follows:

[0114] (7)

[0115] in, , Indicates population size, Represents a vector Calculate the Lehmer mean of all elements in the set;

[0116] Correspondingly, the mean used for adaptively calculating the factor of variation is updated based on the Lehmer mean, as expressed by the formula:

[0117] (8)

[0118] in, Indicates the first t The mean value used for adaptive calculation of the mutation factor corresponding to the +1 generation initialization population. Indicates the first t The mean value used for adaptive calculation of the mutation factor corresponding to the initialization population. This represents the adaptive parameter, which takes a positive constant between 0 and 1.

[0119] The arithmetic mean is calculated in this embodiment of the invention, and the formula is expressed as follows:

[0120] (9)

[0121] in, , Indicates population size;

[0122] Correspondingly, the mean used to adaptively calculate the cross-factor is updated based on the arithmetic mean, as expressed by the formula:

[0123] (10)

[0124] in, Indicates the first t +1 generation initialization population corresponding to the mean value used for adaptive calculation of crossover factor Indicates the first t The mean value used for adaptive crossover factor calculation corresponding to the initialization population is replaced. Indicates adaptive parameters, Represents a vector Calculate the arithmetic mean of all elements in the expression.

[0125] The embodiments of the present invention did not reach the preset threshold. n The fitness function value of the final optimal individual with a value of 20 is obtained. Then, the Lehmer mean is calculated using formula (7) based on the mutation factors corresponding to all individuals in the updated initial population. Formula (8) is used to update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean. Formula (3) is used to recalculate the mutation factor based on the mean used for adaptively calculating the mutation factor. At the same time, the arithmetic mean is calculated using formula (9) based on the crossover factors corresponding to all individuals in the updated initial population. Formula (10) is used to update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean. Formula (5) is used to recalculate the crossover factor based on the mean used for adaptively calculating the crossover factor. The mutation operation of formula (4), the crossover operation of formula (6), and the selection operation are repeated until the maximum number of iterations or the preset precision threshold is reached. Here, the improved hybrid differential evolution algorithm performs a global iterative search, and adaptively calculates the mutation factor and crossover factor during the global iterative search process.

[0126] The embodiments of the present invention reach a preset threshold. n If the fitness function values ​​of the final optimal individuals with a value of 20 are the same, then the final optimal individual in the currently initialized population will be used. Using this as the initial point, Substitution ( , Indicates the first One element is 1, and the rest are 0. In a 3D row vector, This indicates generating random numbers that follow a normal distribution with a mean of 0 and a variance of 1, and generating other random numbers. The initial simplex is formed by 3 points, and the Nelder-Mea method is used to update the initial simplex population by performing a local search on the initial simplex. Output the best individual after the local search, calculate the fitness function value corresponding to the best individual after the local search, and determine whether the fitness function value corresponding to the best individual after the local search meets the preset precision threshold: if yes, output the best individual after the local search as the final best individual; if not, use formula (7) to calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population, use formula (8) to update the mean used for adaptive calculation of mutation factors in the next iteration based on the Lehmer mean, and use formula (3) to recalculate the mutation factor based on the mean used for adaptive calculation of mutation factors. At the same time, use formula (9) to calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population, use formula (10) to update the mean used for adaptive calculation of crossover factors in the next iteration based on the arithmetic mean, and use formula (5) to recalculate the crossover factor based on the mean used for adaptive calculation of crossover factors. Repeat the mutation operation of formula (4), the crossover operation of formula (6), and the selection operation until the maximum number of iterations or the preset precision threshold is reached. Here, the improved hybrid differential evolution algorithm performs local iterative search, adaptively calculating the mutation factor and crossover factor during the local iterative search process.

[0127] To verify the effectiveness of the sum and difference beam optimization method for the radome array antenna provided in this embodiment of the invention, the following experiments were conducted.

[0128] 1. Simulation experimental conditions:

[0129] The hardware platform for the simulation experiment of this invention is an Inspur computing cluster, model NF5468M5. Each node is configured with two Intel Xeon 6248R Gold processors; each processor has 24 cores and a clock speed of 3.0GHz; and 1TB of ECC Registered DDR4 2933 memory.

[0130] 2. Simulation content and result analysis:

[0131] (1) Comparative analysis of the performance indicators of sum and difference beams before and after beam scanning with a cover

[0132] Only port 1 of each antenna element is excited, and the excitation sequence is as follows: Figure 2As shown in (a). Beam scanning along the xoz plane is defined as elevation beam scanning, and beam scanning along the yoz plane is defined as azimuth beam scanning. The amplitude of each antenna element's excitation is set to 1V. With the y-axis as the axis of symmetry, the phase of each antenna element's excitation in the positive half-plane of the x-axis is 0°, and the phase of each antenna element's excitation in the negative half-plane is 180°. The elevation sweep beam, i.e., the sum and difference beams in the xoz plane, is calculated as follows: Figure 4 As shown in (a); the amplitude of the excitation of each antenna element is set to 1V. With the x-axis as the axis of symmetry, the phase of the excitation of each antenna element in the positive half-plane of the y-axis is 0°, and the phase of the excitation of each antenna element in the negative half-plane is 180°. Calculate the azimuth sweep beam, i.e., the sum and difference beams in the yoz plane, as follows: Figure 4 As shown in (b).

[0133] like Figure 5 (a)~ Figure 5 As shown in (b) Figure 5 (a) Comparison of sum and difference beams before and after adding a cover during a -10° elevation sweep. Figure 5 (b) shows the comparison results of sum and difference beams before and after adding a cover when scanning 10° azimuth. Figure 5 (a) and Figure 5 (b) The x-axis represents θ (theta) in polar coordinates, in degrees (deg), and the y-axis represents the direction coefficient, in dB. It can be seen that... Figure 5 As shown in (a), with an elevation sweep of -10°, the maximum pointing direction of the beam shifted by 1.4° after the cover was added compared to before the cover was added, and the null depth position of the differential beam shifted by 0.9°; Figure 5 As shown in (b), with an azimuth scan of 10°, the maximum pointing of the sum beam shifted by 0.9° after the cover was added, and the null depth position of the difference beam shifted by 0.9°. In addition, the sidelobe electrical average of the sum and difference beams exceeded -20dB after the cover was added, and the null depth electrical average of the difference beam exceeded -25dB.

[0134] (2) Optimization design of sum and difference beams of array antenna with radome

[0135] In practical applications, sum and difference beams are commonly used for target tracking. The maximum pointing of the sum beam and the null depth of the difference beam affect the tracking accuracy and range of the radar antenna. Furthermore, to combat interference, it is necessary to reduce the sidelobe level. Therefore, the design of the radome array antenna, the maximum pointing and sidelobe level of the beam, and the null depth position, null depth level, and sidelobe level of the difference beam will be optimized. Generally, reducing the sidelobes widens the main lobe width of the beam, thereby reducing the maximum gain; it is usually undesirable for the sidelobes to decrease too much.

[0136] The optimization variables are set as the excitation amplitude and phase of 256 antenna elements. The optimization objectives are to ensure the maximum pointing accuracy of the sum beam and the accurate null position of the difference beam, and to make the sidelobe levels of the sum and difference beams less than -20dB and the null level of the difference beam less than -25dB, provided that the main lobe is reduced by no more than 3dB.

[0137] Fitness function for beam optimization:

[0138] ;

[0139] in, , , These are the weighting coefficients. To optimize variables, and The first The amplitude and phase of the excitation of each antenna element, . To the maximum directionality of the beam, To maximize the target direction of the sum beam. When optimizing the sum beam for elevation plane scanning, When optimizing the azimuth scan and beam, . The maximum directional coefficient of the beam. The sidelobe level of the beam; The maximum directional coefficient of the target beam is set based on the maximum directional coefficient before optimization. The first term of the fitness function controls the maximum beam pointing, the second term controls the maximum directional coefficient, and the third term controls the sidelobe level. By optimizing the excitation amplitude and phase, the maximum pointing is made accurate, the sidelobe level is less than -20dB, and the maximum directional coefficient is maximized as much as possible. This can be done according to... The magnitudes of the beams are determined by setting appropriate weighting coefficients. The following methods, including beam optimization, all utilize this principle. , , .

[0140] Fitness function for difference beam optimization:

[0141] ;

[0142] in, , , and These are the weighting coefficients. To optimize variables, and The first The amplitude and phase of the excitation of each antenna element, , The zero-depth position of the difference beam. This represents the target zero-depth position for the difference beam. When optimizing the difference beam for elevation plane scanning, When optimizing the difference beam of the azimuth plane scan, . The maximum directional coefficients of the two main lobes of the difference beam. The zero-depth level of the difference beam, For the sidelobe level of the difference beam, and These are the target maximum directional coefficients of the two main lobes of the difference beam, respectively, and their values ​​are specifically set based on the maximum directional coefficients of the two main lobes of the difference beam before optimization. The first term of the fitness function controls the null depth position of the difference beam, the second term controls the maximum directional coefficients of the two main lobes, the third term controls the null depth level of the difference beam, and the fourth term controls the sidelobe level of the difference beam. Accurate null depth position, with minimal decrease in the maximum directional coefficients of the two main lobes, ensures that the null depth level does not exceed -25dB and the sidelobe level is reduced to below -20dB. Therefore, it can be calculated according to... The magnitude relationship is considered, and appropriate weighting coefficients are set. Lower difference beam optimization uses... , , , .

[0143] like Figure 6 (a)~ Figure 6 As shown in (b) Figure 6 (a) Comparison results of beam before and after optimization at an elevation scan of -10°. Figure 6 (b) shows the optimized front and rear difference beam contrast results when the elevation scan is -10°. Figure 7 (a) Figure 7 (b) The horizontal axis represents θ (theta) in polar coordinates, in degrees (deg), and the vertical axis represents the directional coefficient, in dB. It can be seen that at an elevation sweep of -10°: the maximum pointing of the optimized beam is corrected from -8.5° to -10°, the maximum directional coefficient decreases by 1.73 dB, and the sidelobe level decreases from -16.72 dB to -24.50 dB; the null position of the difference beam is corrected from -9.1° to -10°, the maximum directional coefficients of the two main lobes decrease by 1.75 dB and 1.53 dB respectively, the null level decreases from -25.55 dB to -25.83 dB, and the sidelobe level decreases from -6.58 dB to -20.07 dB.

[0144] like Figure 7 (a)~ Figure 7 As shown in (b) Figure 7 (a) Comparison of beamform before and after optimization when scanning at -10° azimuth. Figure 7(b) shows the optimized front and rear difference beam contrast results when scanning at -10° azimuth. Figure 7 (a) Figure 7 (b) The horizontal axis represents θ (theta) in polar coordinates, in degrees (deg), and the vertical axis represents the directional coefficient, in dB. It can be seen that at an azimuth scan of -10°: after optimization, the maximum pointing direction of the beam is corrected from 9.0° to 10°, the maximum directional coefficient decreases by 1.55 dB, and the sidelobe level decreases from -15.68 dB to -23.74 dB; the null depth position of the difference beam is corrected from 9.0° to 10°, the maximum directional coefficients of the two main lobes decrease by 0.96 dB and 1.14 dB respectively, the null depth level is -26.87 dB, and the sidelobe level decreases from -11.04 dB to -20.01 dB.

[0145] (3) Comparison of optimization results of different algorithms:

[0146] Particle swarm optimization (PSO) is a global optimization algorithm widely used in various fields due to its fast convergence speed. Differential evolution (DE) has excellent global search capabilities and is highly advantageous in complex optimization problems. This paper compares the hybrid differential evolution algorithm presented in this invention with these two algorithms to verify its performance.

[0147] The comparison results are as follows Figure 8 (a)~ Figure 8 As shown in (b) Figure 8 (a) shows the optimization results for each algorithm. The horizontal axis represents θ (theta) in polar coordinates, in degrees (deg), and the vertical axis represents the direction coefficient, in dB. Figure 8 (b) shows the iteration status of each algorithm. The horizontal axis represents the number of evolution iterations, and the vertical axis represents the fitness function value. It can be seen that the standard Particle Swarm Optimization (PSO) algorithm converges quickly in the early stages, but the fitness function value stops decreasing in the later stages, resulting in premature convergence and larger errors in the calculation results, leading to poor accuracy. The standard Differential Evolution (DE) algorithm has the slowest convergence speed, but it can obtain a higher accuracy solution, only requiring more evolution generations. In contrast, the Hybrid Differential Evolution (HDE) algorithm of this invention can obtain a higher accuracy solution using the fewest evolution generations.

[0148] In summary, the sum and difference beam optimization method for radome array antennas proposed in this invention comprehensively considers the characteristics of both the array antenna model and the radome array antenna model. It utilizes an improved hybrid differential evolution algorithm to optimize the radome planar array antenna model. Specifically: an array antenna model and a radome array antenna model are created; quadrilateral meshes are performed on both models; based on the corresponding quadrilateral meshes, the higher-order method of moments is used for simulation calculations to extract the corresponding active element radiation patterns; excitation is applied to the antenna elements in both models, and the sum and difference beams are calculated at different scanning angles using the active element radiation patterns, and the corresponding performance indicators are compared; the improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of radome array antenna models that do not meet the performance requirements; wherein, the improved hybrid differential evolution algorithm performs both global and local searches, adaptively calculating the mutation factor and crossover factor during the global and local search processes. As can be seen, this invention uses a higher-order method of moments (MoM) with fewer unknowns to perform integrated simulation calculations on the array antenna model and the radome array antenna model. However, the optimization problem of the radome array antenna model is usually a high-dimensional, nonlinear, and multi-objective complex optimization problem, which places high demands on the performance of the optimization algorithm. To accelerate the convergence speed, this invention proposes an improved hybrid differential evolution algorithm, which combines the higher-order method of moments with the improved hybrid differential evolution algorithm. This can be achieved with the help of a high-performance computing platform to efficiently optimize the design of large radome array antennas, overcoming the problem that existing technologies can only optimize simple radome linear arrays, making this invention more universal. To efficiently achieve integrated optimization of the radome array antenna model and accurately consider the coupling between the radome array antenna models, this invention adopts... The high-order method of moments extracts the active element radiation pattern of each antenna element and superimposes it with the excitation amplitude and phase of each antenna element obtained during the optimization process. That is, based on the excitation amplitude and phase modulation of each antenna element in the array antenna model and the radome array antenna model, the far-field radiation pattern of the array antenna model and the radome array antenna model can be quickly calculated, realizing the optimization design of both the sum and difference beams of the radome array antenna, which is more in line with the needs of engineering applications. The improved hybrid differential evolution algorithm proposed in this embodiment of the invention performs iterative search from global and local perspectives, which can ensure that the optimal solution is obtained after iterative search. At the same time, the mutation factor and cross factor are adaptively calculated during the search iteration. Compared with the fixed mutation factor and cross factor design in the standard differential evolution algorithm, it further ensures that the optimal solution is obtained after iterative search, and the algorithm converges quickly.

[0149] Please see Figure 9This invention provides an electronic device, including a processor 901, a communication interface 902, a memory 903, and a communication bus 904, wherein the processor 901, the communication interface 902, and the memory 903 communicate with each other through the communication bus 904;

[0150] Memory 903 is used to store computer programs;

[0151] When the processor 901 executes the program stored in the memory 903, it implements the steps of the above-mentioned sum and difference beam optimization method for the radome array antenna.

[0152] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described sum and difference beam optimization method for a radome array antenna.

[0153] For the embodiments of the device / electronic device / storage medium, since they are basically similar to the method embodiments, the description is relatively simple, and relevant parts can be referred to in the description of the method embodiments.

[0154] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0155] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the specification and accompanying drawings, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0156] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the sum and difference beams of a radome array antenna, characterized in that, include: Create array antenna models and radome array antenna models; The array antenna model and the radome array antenna model are respectively subjected to quadrilateral meshing; Based on the array antenna model and the quadrilateral mesh corresponding to the radome array antenna model, simulation calculations are performed using the higher-order method of moments to extract the corresponding active element radiation patterns. Excitation is applied to the antenna elements in the array antenna model and the radome array antenna model. Combined with the radiation pattern of the active element, the sum and difference beams corresponding to the array antenna model and the radome array antenna model at different scanning angles are calculated, and the corresponding performance indicators are compared. An improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of the radome array antenna model that does not meet the performance requirements. The improved hybrid differential evolution algorithm performs global iterative search and local iterative search respectively, and adaptively calculates the mutation factor and crossover factor during the global iterative search and local iterative search process. An improved hybrid differential evolution algorithm is used to optimize the sum and difference beams of the radome array antenna model that does not meet the performance requirements, including: The population parameters involved in the optimization design process are determined based on the sum and difference beams of the radome array antenna model, and the population is initialized based on the population parameters. Calculate the fitness function value for each individual in the initial population; Design and calculate the mutation factor, select several intermediate optimal individuals from the initial population according to the fitness function value corresponding to each individual in the initial population, and perform mutation operation on all individuals in the initial population according to the mutation factor and the several intermediate optimal individuals; Design and calculate the crossover factor, and perform crossover operations on individuals in the initial population and mutated individuals based on the crossover factor; Calculate the fitness function value of each individual after crossover, and determine whether the fitness function value of each individual in the initial population is greater than the fitness function value of each individual after crossover. If so, retain the individual corresponding to the crossover and update the initial population; otherwise, retain the individual corresponding to the initial population and update the initial population. From the updated initial population, select the final best individual and determine whether the fitness function values ​​of the final best individuals from the preset threshold generations are the same: If they are not the same, then determine whether the maximum number of iterations or the preset precision threshold has been reached: If so, output the final optimal individual; If not, calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean, and recalculate the mutation factor based on the mean used for adaptively calculating the mutation factor. At the same time, calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean, and recalculate the crossover factor based on the mean used for adaptively calculating the crossover factor. Repeat the above mutation operation, crossover operation, and selection operation until the maximum number of iterations or the preset precision threshold is reached. If they are the same, then the initial simplex is constructed based on the final optimal individuals. The Nelder-Mead simplex method is used to perform a local search on the initial simplex, outputting the optimal individual after the local search. The fitness function value corresponding to the optimal individual after the local search is calculated, and it is determined whether the fitness function value corresponding to the optimal individual after the local search meets the preset accuracy threshold. If so, output the best individual after this local search as the final best individual; If not, calculate the Lehmer mean based on the mutation factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the mutation factor in the next iteration based on the Lehmer mean, and recalculate the mutation factor using the mean used for adaptively calculating the mutation factor. At the same time, calculate the arithmetic mean based on the crossover factors corresponding to all individuals in the updated initial population, update the mean used for adaptively calculating the crossover factor in the next iteration based on the arithmetic mean, and recalculate the crossover factor using the mean used for adaptively calculating the crossover factor. Repeat the above mutation operation, crossover operation, and selection operation until the maximum number of iterations or the preset precision threshold is reached. The design variation factor is expressed by the formula: ； in, Indicates the first t The first generation of the initial population i The variation factors corresponding to each individual , Indicates the first t The mean value used to initialize the population adaptive calculation of the variation factor. Indicates that the generated mean is The variance is 0.1 Cauchy Random numbers from a distribution, and ; Correspondingly, the mutation operation formula is expressed as: ； in, Indicates the first t The corresponding mutated number in the initial population i Individual, Indicates the first t The first generation of the initial population before mutation. i Individual, Indicates from the first In the initialization population, select several intermediate-optimal individuals and then randomly select one individual from these intermediate-optimal individuals. Indicates the first Randomly select an individual from the initial population. Indicates from the first A single individual is randomly selected from the initial population, and and , , They are not equal.

2. The sum and difference beam optimization method for a radome array antenna according to claim 1, characterized in that, The array antenna model consists of several antenna elements. Each antenna element includes a dielectric substrate disposed on the floor and two intersecting dielectric plates disposed perpendicularly to the dielectric substrate. Each dielectric plate is provided with a feed and a radiating patch, and each feed and radiating patch is provided with a coaxial port.

3. The sum and difference beam optimization method for a radome array antenna according to claim 1, characterized in that, Based on the array antenna model and the quadrilateral mesh corresponding to the radome array antenna model, simulation calculations are performed using the higher-order method of moments to extract the corresponding active element radiation patterns, including: Initialization excitation amplitude and phase are applied to each antenna element in the array antenna model and the radome array antenna model, respectively. Based on the applied initial excitation amplitude and phase, simulation calculations are performed using the higher-order method of moments on the quadrilateral mesh corresponding to the array antenna model and the radome array antenna model, respectively, to extract the corresponding active element radiation patterns.

4. The sum and difference beam optimization method for a radome array antenna according to claim 1, characterized in that, The designed cross factor is expressed by the formula: ； in, Indicates the first t The first generation of the initial population i The cross factor corresponding to each individual Indicates the first t The mean value used to adaptively calculate the crossover factor for the initial population is used. Indicates that the generated mean is Random numbers that are normally distributed with a variance of 0.1, and ; Correspondingly, the crossover operation formula is expressed as: ； in, Indicates the first t The first generation corresponding to crossover in the initialization population i The first individual j dimensional variables, Indicates the first t The corresponding mutated number in the initial population i The first individual j dimensional variables, Indicates from Randomly select a number from the list. Indicates from Randomly select a positive integer. Indicates the first t The first generation of the initial population before mutation. i The first individual j Dimensional variables.

5. The sum and difference beam optimization method for a radome array antenna according to claim 1, characterized in that, The Lehmer mean is calculated using the following formula: ； in, , Indicates population size; Correspondingly, the mean used to adaptively calculate the variation factor is updated based on the Lehmer mean, as expressed by the formula: ； in, Indicates the first t The mean value used for adaptive calculation of the mutation factor corresponding to the +1 generation initialization population. Indicates the first t The mean value used for adaptive calculation of the mutation factor corresponding to the initialization population. This represents the adaptive parameter.

6. The sum and difference beam optimization method for a radome array antenna according to claim 4, characterized in that, The formula for calculating the arithmetic mean is as follows: ； in, , Indicates population size; Correspondingly, the mean used to adaptively calculate the crossover factor is updated based on the arithmetic mean, as expressed by the formula: ； in, Indicates the first t +1 generation initialization population corresponding to the mean value used for adaptive calculation of crossover factor Indicates the first t The mean value used for adaptive crossover factor calculation corresponding to the initialization population is replaced. This represents the adaptive parameter.

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