An irregular polygon patch antenna design method and device based on improved NSGA-II

Abstract

The application provides an irregular polygon patch antenna design method and device based on improved NSGA-Ⅱ, adopts an optimization strategy of irregular polygons, and gives the antenna higher flexibility and diversity in the premise of maintaining the continuity of the antenna shape. Specifically, a multi-objective quantum particle swarm optimization algorithm is combined with a non-dominated sorting genetic algorithm NSGA-Ⅱ, a quantum search mechanism is introduced, the global search capability of the solution space is significantly enhanced, the deficiency that the traditional particle swarm optimization algorithm is prone to local optimal solution is overcome, and the optimization process is accelerated; meanwhile, in combination with the NSGA-Ⅱ algorithm, the relationship between optimization objectives in the multi-objective optimization process can be effectively balanced, and the diversity of the solution set is ensured.

Description

Technical Field

[0001] This application belongs to the field of antenna design technology, and in particular relates to a design method and apparatus for an irregular polygonal patch antenna based on the improved NSGA-Ⅱ. Background Technology

[0002] Traditional antenna design methods mostly rely on experience and manual optimization. Although these methods can improve antenna performance to some extent, they often have obvious limitations when faced with complex geometries and multi-objective optimization. In particular, traditional methods are difficult to achieve efficient optimization when dealing with irregular antenna shapes and multiple design objectives.

[0003] Irregular polygonal antennas offer greater design flexibility and versatility, allowing for the adjustment of geometric parameters to meet diverse design requirements. This necessitates exploring optimal solutions within a broader design space, simultaneously satisfying multiple performance requirements such as bandwidth, size, and gain. Consequently, the significant design freedom and numerous optimizable parameters of irregular polygonal antennas result in an extremely large computational load. Especially during complex multi-objective optimization, traditional parameter scanning methods prove inefficient and unable to find the optimal solution within a reasonable timeframe.

[0004] Therefore, a new technical solution is needed to overcome the above-mentioned technical problems and achieve the optimized design of irregular polygonal patch antennas. Summary of the Invention

[0005] A design method and apparatus for irregular polygon patch antennas based on an improved NSGA-II algorithm are presented to address the aforementioned technical problems. The improved NSGA-II algorithm is used to design multiple irregular polygon patch antennas, combining a multi-objective quantum particle swarm optimization algorithm with the non-dominated sorting genetic algorithm NSGA-II, significantly improving design efficiency and computational performance.

[0006] In a first aspect, this application provides a design method for an irregular polygonal patch antenna based on the improved NSGA-II, characterized by comprising the following steps:

[0007] S1. Set the optimization objectives and constraints for the irregular polygon patch antenna;

[0008] S2. Set the population size M and the number of sides N of the irregular polygon patch antenna, and randomly generate an initial population that satisfies the constraints.

[0009] S3. Initialize the relevant parameters of the NSGA II algorithm, including the maximum number of iterations, external file size, crossover rate, and mutation rate;

[0010] S4. Calculate the population fitness, perform non-dominated sorting on the initial population, update the individual extreme value of each particle, calculate the crowding distance, select the global optimal solution based on the crowding distance, calculate the average value of the individual optimal solutions of the population, and establish an external profile.

[0011] S5. Update particle positions based on quantum behavior to obtain the offspring population;

[0012] S6. Calculate the individual fitness of the offspring population, merge the parent and offspring populations, perform non-dominated sorting and calculate crowding distance, and update the external archives.

[0013] S7. Perform selection, crossover, and mutation operations on individuals in the new population to obtain offspring individuals;

[0014] S8. Merge the parent and offspring populations, calculate the fitness of all individuals in the population, perform non-dominated sorting and calculate crowding distance, and select individuals to enter the next generation based on fitness.

[0015] S9. Repeat steps S4-S8 until the maximum number of iterations is met.

[0016] Furthermore, the optimization objective in step S1 is:

[0017] min{V,X-db,F gf};

[0018] Where V represents the antenna volume, db represents the antenna bandwidth, and F gf X represents the antenna gain flatness, and X represents the maximum frequency within the antenna's operating frequency band.

[0019] Furthermore, the antenna volume, antenna bandwidth, and antenna gain flatness are obtained in the following manner:

[0020] S11. Use HFSS three-dimensional electromagnetic simulation software to construct an irregular polygon patch antenna model for electromagnetic simulation, and obtain the return loss and gain of the irregular polygon patch antenna.

[0021] S12. Calculate the antenna volume V: V = L 2 h;

[0022] Where L is the side length of the antenna dielectric substrate, and h is the thickness of the antenna dielectric substrate;

[0023] S13. Calculate antenna bandwidth bd: bd = max{fre(S 11 <-10)}-min{fre(S 11 <-10)};

[0024] Where fre(S11<-10) represents the frequency band in which the input return loss is less than -10dB within the operating frequency band, max{fre(S11<-10)} represents the maximum frequency within the frequency band, and min{fre(S11<-10)} represents the minimum frequency within the frequency band.

[0025] S14. Calculate antenna gain flatness F gf :F gf =max{Gain(θ)}-min{Gain(θ)};

[0026] Where Gain(θ) represents the antenna gain in a fixed direction within a frequency band where the input return loss is less than -10dB, max{Gain(θ)} represents the maximum gain within that frequency, and min{Gain(θ)} represents the minimum gain within that frequency.

[0027] Furthermore, the constraints in step S1 include:

[0028] (1) The origin coincides with the centroid of the polygon:

[0029]

[0030] Where (0,0) are the coordinates of the origin, (x... i ,y i ) represents the coordinates of the i-th vertex of the polygon, and n is the number of vertices of the polygon;

[0031] (2) The distance f between the center of the feed point and the origin is less than or equal to the average distance f from the vertices of the polygon to the origin:

[0032]

[0033] (3) The edges of a polygon are connected only from the vertex with the smaller argument to the vertex with the larger argument:

[0034]

[0035] θ i θ represents the argument of the i-th vertex. i Calculated using the following formula:

[0036]

[0037] (4) The side length of the polygonal antenna substrate shall not be less than twice the average distance from the vertex of the polygon to the origin:

[0038]

[0039] Furthermore, in step S2, each individual in the initial population represents the geometric parameters of the irregular polygon patch antenna, including: the side length of the dielectric substrate, the distance between the centroid of the feed point and the origin, and the coordinates of each vertex.

[0040] Furthermore, in step S2, randomly generating an initial population that satisfies the constraints specifically includes:

[0041] S21. For each individual in the population, randomly generate the side length L of the dielectric substrate that satisfies the following constraints:

[0042] L min< L < L max ;

[0043] Among them, L min and L max These represent the minimum and maximum allowable values ​​for the side length of the dielectric substrate;

[0044] S22. Initialize the feeder point position;

[0045] S23. Based on the number of sides N of the polygon, generate the angle of each vertex according to a uniform angular distribution;

[0046] S24. Apply a random perturbation to the angle of each vertex to obtain the initialized argument θ of each vertex. i And randomly generate a radius r according to the size L of the substrate. i :

[0047]

[0048] r i =random(0.7,0.9)×L×0.45;

[0049] S25. Based on the generated angle and radius, obtain the coordinates of each vertex through polar coordinate transformation, and calculate the geometric center (x, y) of all vertices based on the obtained coordinates of each vertex. c ,y c ):

[0050]

[0051] S26. Translate each vertex based on its geometric center:

[0052] x′ i =x i -x c ,(y′ i =y i -y c ;

[0053] Among them, (xi ,y i ) and (x' i ,y' i () represent the coordinates of the i-th vertex before and after translation, respectively;

[0054] S27. Calculate the distance from each vertex to the origin after translation, and determine whether the distance exceeds the maximum allowable radius r. maxallowed If it exceeds the limit, the entire polygon will be uniformly scaled.

[0055]

[0056] Where, r i and r' i Let r represent the distance from the i-th vertex to the origin before and after scaling, respectively. maxallowed =L×0.45,

[0057] S28. Check each vertex P i Its adjacent vertex P i-1 P i+1 internal angle formed If the size of the interior angle is less than the preset minimum interior angle value, then adjust vertex P. i Location;

[0058] S29. Calculate the argument θ of each vertex. i The vertices are sorted according to their arguments to ensure that the vertex order satisfies either clockwise or counterclockwise direction.

[0059] Furthermore, in step S28, vertex P is adjusted. i The locations specifically include:

[0060] S281, Calculate vertex P i Angle bisector direction

[0061]

[0062] in, and Vertex P i Two adjacent vectors;

[0063] S282. Adjust the vertex coordinates along the angle bisector.

[0064] Furthermore, step S5, which updates the particle position based on quantum behavior, specifically involves employing a dual dynamic search evolution strategy to update the particle position, including:

[0065] S51. Set the evolutionary process control parameter ω:

[0066] ω=e (1-t) / MaxIt *rand;

[0067] Where t represents the current iteration number, Maxlt represents the maximum iteration number, and rand represents a random number between 0 and 1. As the iteration number increases, the overall trend of ω becomes smaller and smaller.

[0068] S52. When ω is less than ωs, the particle position is updated using the local search priority principle. The particle position update formula is:

[0069] X id (t+1)=p i (t)±β·|gbest(t)-X id (t)|·ln(1 / u);

[0070] When ω is greater than ωs, the particle position is updated using the global search priority principle. The particle position update formula is:

[0071] X id (t+1)=p i (t)±β·|mbest(t)-X id (t)|·ln(1 / u);

[0072] Where ωs is a pre-set threshold, gbest(t) is the current global optimal position of the particle, and p i (t) represents the optimal position of the i-th particle at time t, β is the expansion coefficient used to control the convergence speed of the algorithm, μ is a random number between 0 and 1, and X id (t) and X id (t+1) represent the solutions for the i-th particle at time t and time t+1, respectively, and mbest(t) is the average optimal position of the current particle, calculated using the following formula:

[0073]

[0074] Where m is the total number of particles and D is the dimension of the particles.

[0075] Furthermore, in step S7, individuals in the new population undergo a dynamic crossover operation, specifically:

[0076] When ω is less than ωs, the particle is crossed with the average optimal position of the individual; when ω is greater than ωs, the particle is crossed with the global optimal position.

[0077] The crossover rate is dynamically adjusted based on the algorithm's iterative algebraic progression. The formula for calculating the crossover rate is as follows:

[0078]

[0079] Among them, C r0 Let k be the initial crossover rate, and k be the current generation. max This represents the maximum number of iterations.

[0080] Furthermore, in step S7, an adaptive mutation mechanism is used to perform mutation operations on individuals in the new population. Specifically:

[0081] The mutation rate is adjusted according to the iterative algebraic rules of the algorithm, and the formula for calculating the mutation rate is:

[0082]

[0083] Among them, M r0 Let k be the initial mutation rate, and k be the current generation. max This represents the maximum number of iterations.

[0084] Secondly, this application provides a design device for an irregular polygonal patch antenna based on the improved NSGA-II, characterized in that the device comprises:

[0085] The optimization target setting module is used to set the optimization target and constraints for irregular polygon patch antennas;

[0086] The initialization population generation module is used to set the population size M and the number of sides N of the irregular polygon patch antenna, and randomly generate an initial population that satisfies the constraints.

[0087] The initialization parameter setting module is used to initialize the relevant parameters of the NSGA II algorithm, including the maximum number of iterations, the size of the external archive, the crossover rate, and the mutation rate.

[0088] The iterative optimization module is used to calculate the population fitness, perform non-dominated sorting on the initial population, update the individual extreme value of each particle, calculate the crowding distance, select the global optimal solution based on the crowding distance, calculate the average value of the individual optimal solutions of the population, and establish an external profile.

[0089] The offspring population is obtained by updating the particle positions based on quantum behavior.

[0090] Calculate the individual fitness of the offspring population, merge the parent and offspring populations, perform non-dominated sorting and calculate crowding distance, and update the external profile;

[0091] Select, crossover, and mutate individuals in the new population to obtain offspring individuals;

[0092] Merge the parent and offspring populations, calculate the fitness of all individuals in the population, perform non-dominated sorting and calculate crowding distance, and select individuals to enter the next generation based on fitness.

[0093] Repeat the above steps until the maximum number of iterations is met.

[0094] The beneficial effects of the embodiments of this application compared with the prior art are:

[0095] This invention provides a design method and apparatus for irregular polygonal patch antennas based on an improved NSGA-II. Employing an optimization strategy for irregular polygons, it grants greater flexibility and diversity to the antenna geometry while maintaining shape continuity. This not only broadens the design freedom but also enables the antenna to better adapt to complex and changing working environments and application requirements. Through an automated design process, this invention achieves automated design of irregular antennas, significantly improving design efficiency and reducing manual intervention and trial-and-error costs.

[0096] Furthermore, by combining the multi-objective quantum particle swarm optimization algorithm with the non-dominated sorting genetic algorithm NSGA-II, the global search capability of the solution space is significantly enhanced by introducing a quantum search mechanism. This overcomes the shortcomings of traditional particle swarm optimization algorithms, which are prone to getting trapped in local optima, and accelerates the optimization process. At the same time, by combining the NSGA-II algorithm, the relationship between various optimization objectives can be effectively balanced in the multi-objective optimization process, ensuring the diversity of the solution set. Attached Figure Description

[0097] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0098] Figure 1 This is a flowchart of an irregular polygon patch antenna design method based on the improved NSGA-II, provided in an embodiment of this application.

[0099] Figure 2 This is a planar view of the basic geometric structure of the irregular polygon patch antenna provided in the embodiments of this application in the XOY plane;

[0100] Figure 3 This is a planar view of the basic geometric structure of the irregular polygon patch antenna provided in the embodiments of this application in the XOZ plane;

[0101] Figure 4 This is a schematic diagram of the irregular polygonal patch antenna provided in an embodiment of this application;

[0102] Figure 5 This is a schematic diagram of the S-parameter curves of the irregular polygonal antenna provided in the embodiments of this application;

[0103] Figure 6 This is a schematic diagram of the gain curve of the irregular polygonal antenna provided in the embodiments of this application;

[0104] Figure 7 This is a schematic diagram of an irregular polygon patch antenna design device based on the improved NSGA-Ⅱ provided in an embodiment of this application. Detailed Implementation

[0105] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0106] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0107] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0108] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0109] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," "fourth," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0110] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0111] First Embodiment

[0112] In the first embodiment, an irregular polygonal patch antenna operating in the X-band (8-12GHz) was designed, and its design process is as follows: Figure 1 As shown, it aims to achieve performance requirements such as small size, wide bandwidth, and low gain flatness.

[0113] The basic geometric structure of the irregular polygonal patch antenna constructed in this embodiment is as follows: Figure 2 and Figure 3 As shown, O is the origin, P1……P n Let there be n vertices, L be the side length of the dielectric substrate, h be the thickness of the dielectric substrate, f be the distance between the center of the feed point and the origin, and D0 and D... i These are the outer and inner diameters of the coaxial line, respectively.

[0114] The antenna substrate is made of FR4, with a dielectric constant of 4.4, a loss tangent of 0.02, and a thickness of 1.6 mm.

[0115] The parameters to be optimized for the irregular polygon patch antenna include: the side length L of the antenna's dielectric substrate, the distance f between the center of the feed point and the origin, and the coordinates of the N vertices.

[0116] The irregular polygon patch antenna design method based on the improved NSGA-II specifically includes:

[0117] S1. Set the optimization objectives and constraints for the irregular polygon patch antenna;

[0118] The optimization objective in step S1 is:

[0119] min{V,X-db,F gf};

[0120] Where V represents the antenna volume, db represents the antenna bandwidth, and F g x represents the antenna gain flatness, and X represents the maximum frequency within the antenna's operating frequency band.

[0121] Specifically, in this embodiment, X = 12.

[0122] The antenna volume, antenna bandwidth, and antenna gain flatness are obtained in the following way:

[0123] S11. Use HFSS three-dimensional electromagnetic simulation software to construct an irregular polygon patch antenna model for electromagnetic simulation, and obtain the return loss and gain of the irregular polygon patch antenna.

[0124] Specifically, the antenna model is constructed using Python-HFSS co-simulation. A corresponding program is written in Python to call HFSS for parametric modeling, resulting in a model of an irregular polygonal antenna.

[0125] Electromagnetic simulation was performed using the solver of HFSS 3D electromagnetic simulation software to obtain the return loss and gain of the irregular polygonal antenna.

[0126] S12. Calculate the antenna volume V: V = L 2 h;

[0127] Where L is the side length of the antenna dielectric substrate, and h is the thickness of the antenna dielectric substrate;

[0128] S13. Calculate antenna bandwidth bd: bd = max{fre(S 11 <-10)}-min{fre(S 11 <-10)};

[0129] Where fre(S11<-10) represents the frequency band in which the input return loss is less than -10dB within the operating frequency band, max{fre(S11<-10)} represents the maximum frequency within the frequency band, and min{fre(S11<-10)} represents the minimum frequency within the frequency band.

[0130] S14. Calculate antenna gain flatness F gf :F gf =max{Gain(θ)}-min{Gain(θ)};

[0131] Where Gain(θ) represents the antenna gain in a fixed direction within a frequency band where the input return loss is less than -10dB, max{Gain(θ)} represents the maximum gain within that frequency, and min{Gain(θ)} represents the minimum gain within that frequency.

[0132] The constraints in step S1 include:

[0133] (1) The origin coincides with the centroid of the polygon:

[0134]

[0135] Where (0,0) are the coordinates of the origin, (x... i ,y i ) represents the coordinates of the i-th vertex of the polygon, and n is the number of vertices of the polygon;

[0136] Specifically, XOY plane coordinates will be established, and the entire polygon patch will be placed within the XOY plane to obtain the coordinates of each vertex of the polygon patch.

[0137] (2) The distance f between the center of the feed point and the origin is less than or equal to the average distance f from the vertices of the polygon to the origin:

[0138]

[0139] (3) The edges of a polygon are connected only from the vertex with the smaller argument to the vertex with the larger argument:

[0140]

[0141] θ i θ represents the argument of the i-th vertex. i Calculated using the following formula:

[0142]

[0143] (4) The side length of the polygonal antenna substrate shall not be less than twice the average distance from the vertex of the polygon to the origin:

[0144]

[0145] S2. Set the population size M and the number of sides N of the irregular polygon patch antenna, and randomly generate an initial population that satisfies the constraints.

[0146] Specifically, the population size M can be set to 80, and the number of sides N of the irregular polygon patch antenna can be set to 40. Then, the geometric parameters of the irregular polygon patch antenna and the coordinates of the 40 vertices need to be initialized.

[0147] The geometric parameters include: the side length L of the dielectric substrate, the distance f between the centroid of the feed point and the origin, and the coordinates (x, y) of each vertex. i ,y i );

[0148] Furthermore, in step S2, randomly generating an initial population that satisfies the constraints specifically includes:

[0149] S21. For each individual in the population, randomly generate the side length L of the dielectric substrate that satisfies the following constraints:

[0150] L min< L < L max；

[0151] Among them, L min and L max These represent the minimum and maximum allowable values ​​for the side length of the dielectric substrate;

[0152] S22. Initialize the feeder point position;

[0153] Specifically, the radius f of the feed point is randomly sampled from the uniform distribution U(0,r), ensuring that the distance between the feed point and the origin does not exceed the average distance r of the vertex, and the angle of the feed point is randomly sampled from the uniform distribution U(0,2π).

[0154] S23. Based on the number of sides N of the polygon, generate the angle of each vertex according to a uniform angle distribution;

[0155] S24. Apply a random perturbation to the angle of each vertex to obtain the initialized argument θ of each vertex. i And randomly generate a radius r according to the size L of the substrate. i :

[0156]

[0157] r i =random(0.7,0.9)×L×0.45;

[0158] S25. Based on the generated angle and radius, obtain the coordinates of each vertex through polar coordinate transformation, and calculate the geometric center (x, y) of all vertices based on the obtained coordinates of each vertex. c ,y c ):

[0159]

[0160] The polar coordinate transformation formula is as follows:

[0161] x i =r i ×cos(θ i ), y i =r i ×sin(θ i );

[0162] S26. Translate each vertex based on its geometric center:

[0163] x′ i =x i -x c ,(y′ i =yi -y c ;

[0164] Among them, (x i ,y i ) and (x' i ,y' i () represent the coordinates of the i-th vertex before and after translation, respectively;

[0165] Translation ensures that the generated polygons meet the requirements, avoiding unnecessary deformation or overlap.

[0166] S27. Calculate the distance from each vertex to the origin after translation, and determine whether the distance exceeds the maximum allowable radius r. maxallowed If the radius exceeds the limit, the entire polygon will be uniformly scaled to ensure that all vertices conform to the maximum allowed radius constraint.

[0167]

[0168] Where, r i and r' i Let r represent the distance from the i-th vertex to the origin before and after scaling, respectively. maxallowed =L×0.45,

[0169] S28. Check each vertex P i Its adjacent vertex P i-1 P i+1 internal angle formed If the size of the interior angle is less than the preset minimum interior angle value, then adjust vertex P. i Location;

[0170] Among them, adjust vertex P i The locations specifically include:

[0171] S281, Calculate vertex P i Angle bisector direction

[0172]

[0173] in, and Vertex P i Two adjacent vectors;

[0174] Among them, vertex P i The interior angles are calculated using the following formula:

[0175]

[0176] Among them, (xi-1 ,y i-1 ), (x i ,y i ), (x i+1 ,y i+1 ) are vertices P i-1 P i P i+1 The coordinates of ||P i-1 P i ||、||P i P i+1 || represent vertex P respectively i-1 With P i The distance between them, and vertex P i With P i+1 The distance between them;

[0177] S282. Adjust the vertex coordinates along the angle bisector. Specifically, the adjustment formula is:

[0178] x′ i =x i +Δx,(y′ i =y i +Δy;

[0179] Where Δx represents the position change of vertex Pi in the x-axis direction, and Δy represents the position change of vertex Pi in the y-axis direction;

[0180] S29. Calculate the argument θ of each vertex. i The vertices are sorted according to their arguments to ensure that the vertex order satisfies either clockwise or counterclockwise direction.

[0181] By adjusting the angle by a small amount, antenna performance and manufacturing requirements can be guaranteed, and by moving the vertex along the direction of the angle bisector, the angle can be ensured to meet design requirements.

[0182] S3. Initialize the relevant parameters of the NSGA II algorithm, including the maximum number of iterations, external file size, crossover rate, and mutation rate;

[0183] S4. Calculate the population fitness, perform non-dominated sorting on the initial population, update the individual extreme value of each particle, calculate the crowding distance, select the global optimal solution based on the crowding distance, calculate the average value of the individual optimal solutions of the population, and establish an external profile.

[0184] S5. Update particle positions based on quantum behavior to obtain the offspring population;

[0185] S6. Calculate the individual fitness of the offspring population, merge the parent and offspring populations, perform non-dominated sorting and calculate crowding distance, and update the external archives.

[0186] In steps S4 and S6, fast non-dominated sorting is used to rank the fitness of individuals in the population. The specific process of fast non-dominated sorting is as follows:

[0187] 1) For each individual x, calculate the number of individuals S(x) that are dominated and the set of individuals D(x) that dominate it;

[0188] 2) If S(x) = 0, then place individual x in the first level and decrease the dominance number of individuals in its dominion set by one;

[0189] 3) Continue iterating, adding undominated individuals to the next level layer by layer, until all individuals are sorted.

[0190] Furthermore, by calculating the non-dominated level and crowding distance of each individual, the individuals in the population are first sorted by non-dominated level, and then individuals of the same level are selected preferentially according to the crowding distance, thereby ensuring that the population can maintain high diversity and improve search efficiency during the optimization process.

[0191] Furthermore, in the method for calculating the crowding distance, for individuals of the same non-dominance level, the distance between each individual and its neighboring individuals in the target space is calculated, and the crowding degree of that individual is calculated based on these distances. Specifically, for the i-th individual, its distance dij to its neighboring individual j in the target space is calculated using the following formula:

[0192]

[0193] Among them, f i,k and f j,k Let represent the values ​​of the i-th individual and the j-th individual on the k-th target, respectively, and M be the number of targets.

[0194] Crowding distance of each individual C i It can be calculated using the following formula:

[0195]

[0196] Specifically, step S5, which updates the particle position based on quantum behavior, involves using a dual dynamic search evolution strategy to update the particle position, including:

[0197] S51. Set the evolutionary process control parameter ω:

[0198] ω=e (1-t) / MaxIt *rand;

[0199] Where t represents the current iteration number, Maxlt represents the maximum iteration number, and rand represents a random number between 0 and 1. As the iteration number increases, the overall trend of ω becomes smaller and smaller.

[0200] S52. When ω is less than ωs, the particle position is updated using the local search priority principle. The particle position update formula is:

[0201] X id (t+1)=p i (t)±β·|gbest(t)-X id (t)|·ln(1 / u);

[0202] When ω is greater than ωs, the particle position is updated using the global search priority principle. The particle position update formula is:

[0203] X id (t+1)=p i (t)±β·|mbest(t)-X id (t)|·ln(1 / u);

[0204] Where ωs is a pre-set threshold, gbest(t) is the current global optimal position of the particle, and p i (t) represents the optimal position of the i-th particle at time t, β is the expansion coefficient used to control the convergence speed of the algorithm, μ is a random number between 0 and 1, and X id (t) and X id (t+1) represent the solutions for the i-th particle at time t and time t+1, respectively, and mbest(t) is the average optimal position of the current particle, calculated using the following formula:

[0205]

[0206] Where m is the total number of particles and D is the dimension of the particles.

[0207] Furthermore, in step S7, a dynamic crossover operation is performed on the individuals in the new population. Specifically:

[0208] When ω is less than ωs, the particle is crossed with the average optimal position of the individual; when ω is greater than ωs, the particle is crossed with the global optimal position.

[0209] The crossover rate is dynamically adjusted based on the algorithm's iterative algebraic progression. The formula for calculating the crossover rate is as follows:

[0210]

[0211] Among them, C r0 Let k be the initial crossover rate, and k be the current generation. max Maximum iteration algebra

[0212] Furthermore, in step S7, an adaptive mutation mechanism is used to perform mutation operations on individuals in the new population. Specifically:

[0213] The mutation rate is adjusted according to the iterative algebraic rules of the algorithm, and the formula for calculating the mutation rate is:

[0214]

[0215] Among them, M r0 Let k be the initial mutation rate, and k be the current generation. max Maximum iteration algebra

[0216] S7. Perform selection, crossover, and mutation operations on individuals in the new population to obtain offspring individuals;

[0217] S8. Merge the parent and offspring populations, calculate the fitness of all individuals in the population, perform non-dominated sorting and calculate crowding distance, and select individuals to enter the next generation based on fitness.

[0218] S9. Repeat steps S4-S8 until the maximum number of iterations is met.

[0219] After the iteration is complete, the final optimized parameters and the structure of the irregular polygon patch antenna obtained based on the optimized parameters can be output.

[0220] In this embodiment, the parameters and vertex coordinates of the optimized irregular polygonal patch antenna are shown in the table below:

[0221] L 41.89 (x18, y18) (-5.32，13.58) h 2 (x19, y19) (-5.80,13.20) f 3.31 (x20, y20) (-11.98,13.86) N 40 (x21, y21) (-9.26,8.49) (x0, y0) (13.08,0.11) (x22, y22) (-10.14，2.16) (x1,y1) (14.67,2.29) (x23, y23) (-13.48，2.30) (x2, y2) (2.33，0.59) (x24, y24) (-2.87,-0.05) (x3, y3) (3.04，1.98) (x25, y25) (-8.15,-3.25) (x4, y4) (1.08，2.04) (x26, y26) (-7.19,-3.70) (x5, y5) (1.09，2.05) (x27,y27) (-7.15,-4.57) (x6, y6) (1.08,2.05) (x28, y28) (-16.22,-11.06) (x7, y7) (1.09,2.05) (x29, y29) (-2.64,-2.51) (x8, y8) (1.08，2.05) (x30, y30) (-18.05,-17.34) (x9,y9) (1.08，2.07) (x31, y31) (2.60,-17.18) (x10, y10) (1.07，2.07) (x32, y32) (6.23，-8.19) (x11,y11) (1.07，2.06) (x33, y33) (14.41,-11.44) (x12, y12) (1.07，2.06) (x34, y34) (9.03,-6.84) (x13, y13) (1.06,2.06) (x35, y35) (10.41，-5.81) (x14, y14) (1.06,2.05) (x36, y36) (11.91,-4.28) (x15, y15) (1.05，2.07) (x37, y37) (13.56,-1.67) (x16, y16) (-1.19,4.37) (x38, y38) (4.35,-0.38) (x17, y17) (-3.81，10.74) (x39, y39) (4.75,-0.08)

[0222] The final optimized irregular polygonal patch antenna structure diagram is shown below. Figure 4 As shown, the antenna's S-parameter curves and gain curves are respectively as follows: Figure 5 and 6 As shown, the final optimized irregular polygonal antenna has a bandwidth of 2.7 GHz, a gain flatness of 1.82 dB, and a volume of 1370.27 mm². 3 .

[0223] Second Embodiment

[0224] Figure 7 This illustration shows a schematic diagram of an irregular polygonal patch antenna design device based on the improved NSGA-II, as provided in Embodiment 2 of this application. Figure 7 As shown, the irregular polygon patch antenna design device 7 based on the improved NSGA-II specifically includes:

[0225] The optimization target setting module 71 is used to set the optimization target and constraints for the irregular polygon patch antenna;

[0226] The initialization population generation module 72 is used to set the population size M and the number of sides N of the irregular polygon patch antenna, and randomly generate an initial population that satisfies the constraints.

[0227] The initialization parameter setting module 73 is used to initialize the relevant parameters of the NSGA II algorithm, including the maximum number of iterations, the size of the external archive, the crossover rate, and the mutation rate.

[0228] The iterative optimization module 74 is used to calculate the population fitness, perform non-dominated sorting on the initial population, update the individual extreme value of each particle, calculate the crowding distance, select the global optimal solution based on the crowding distance, calculate the average value of the individual optimal solutions of the population, and establish an external archive.

[0229] The offspring population is obtained by updating the particle positions based on quantum behavior.

[0230] Calculate the individual fitness of the offspring population, merge the parent and offspring populations, perform non-dominated sorting and calculate crowding distance, and update the external profile;

[0231] Select, crossover, and mutate individuals in the new population to obtain offspring individuals;

[0232] Merge the parent and offspring populations, calculate the fitness of all individuals in the population, perform non-dominated sorting and calculate crowding distance, and select individuals to enter the next generation based on fitness.

[0233] Repeat the above steps until the maximum number of iterations is met.

[0234] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0235] In the embodiments provided in this application, it should be understood that the disclosed apparatus / network devices and methods can be implemented in other ways. For example, the apparatus / network device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0236] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0237] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A design method for an irregular polygonal patch antenna based on the improved NSGA-II, characterized in that, Includes the following steps: S1. Set the optimization objectives and constraints for the irregular polygon patch antenna; S2. Set the population size M and the number of sides N of the irregular polygon patch antenna, and randomly generate an initial population that satisfies the constraints. S3. Initialize the relevant parameters of the NSGA II algorithm, including the maximum number of iterations, the size of the external archive, the crossover rate, and the mutation rate; S4. Calculate the population fitness, perform non-dominated sorting on the initial population, update the individual extreme value of each particle, calculate the crowding distance, select the global optimal solution based on the crowding distance, calculate the average value of the individual optimal solutions of the population, and establish an external profile. S5. Update particle positions based on quantum behavior to obtain the offspring population; S6. Calculate the individual fitness of the offspring population, merge the parent and offspring populations, perform non-dominated sorting and calculate crowding distance, and update the external archives. S7. Perform selection, crossover, and mutation operations on individuals in the new population to obtain offspring individuals; S8. Merge the parent and offspring populations, calculate the fitness of all individuals in the population, perform non-dominated sorting and calculate crowding distance, and select individuals to enter the next generation based on fitness. S9. Repeat steps S4-S8 until the maximum number of iterations is satisfied; The optimization objective in step S1 is: ； Where V represents the antenna volume and db represents the antenna bandwidth. This indicates the antenna gain flatness, and X represents the maximum frequency within the antenna's operating frequency band. The constraints in step S1 include: (1) The origin coincides with the centroid of the polygon: ； Where (0, 0) are the coordinates of the origin, () represents the coordinates of the i-th vertex of the polygon, and n is the number of vertices of the polygon; (2) The distance f between the center of the feed point and the origin is less than or equal to the average distance f from the vertices of the polygon to the origin: ； (3) The sides of a polygon are connected only from the vertex with the smaller argument to the vertex with the larger argument: ； The argument of the i-th vertex is represented by the following. Calculated using the following formula: ； (4) The side length of the polygonal antenna substrate shall not be less than twice the average distance from the vertex of the polygon to the origin: 。 2. The method as described in claim 1, characterized in that, The antenna volume, antenna bandwidth, and antenna gain flatness are obtained in the following way: S11. Use HFSS three-dimensional electromagnetic simulation software to construct an irregular polygon patch antenna model for electromagnetic simulation, and obtain the return loss and gain of the irregular polygon patch antenna. S12. Calculate the antenna volume V: ； Where L is the side length of the antenna dielectric substrate, and h is the thickness of the antenna dielectric substrate; S13. Calculate the antenna bandwidth bd: ; Where fre(S11<-10) represents the frequency band in which the input return loss is less than -10dB within the operating frequency band, max{fre(S11<-10)} represents the maximum frequency within the frequency band, and min{fre(S11<-10)} represents the minimum frequency within the frequency band; S14. Calculate antenna gain flatness : ; in, This represents the antenna gain in a fixed direction within a frequency band where the input return loss is less than -10dB, max{ } represents the maximum gain within that frequency range, min{ } represents the minimum gain at that frequency.

3. The method as described in claim 1, characterized in that, In step S2, each individual in the initial population represents the geometric parameters of the irregular polygon patch antenna, which include: the side length of the dielectric substrate, the distance between the centroid of the feed point and the origin, and the coordinates of each vertex. Furthermore, in step S2, randomly generating an initial population that satisfies the constraints specifically includes: S21. For each individual in the population, randomly generate the side length of the dielectric substrate that satisfies the following constraints. L : L min< L < L max； in, L min and L max These are the minimum and maximum allowable values ​​for the substrate side length; S22. Initialize the feeder point position; S23. Based on the number of sides N of the polygon, generate the angle of each vertex according to a uniform angle distribution; S24. Apply a random perturbation to the angle of each vertex to obtain the initialized argument of each vertex. And according to the size of the substrate L Randomly generated radius : ； ； S25. Based on the generated angle and radius, obtain the coordinates of each vertex through polar coordinate transformation, and calculate the geometric center of all vertices based on the obtained coordinates of each vertex. : ； S26. Translate each vertex based on its geometric center: ； in, and Let represent the coordinates of the i-th vertex before and after translation, respectively; S27. Calculate the distance from each vertex to the origin after translation, and determine whether the distance exceeds the maximum allowable radius. If it exceeds the limit, the entire polygon will be uniformly scaled. ； in, and These represent the distances from the i-th vertex to the origin before and after scaling, respectively. ; S28. Check each vertex P i Its adjacent vertex P i-1 P i+1 internal angle formed If the size of the interior angle is less than the preset minimum interior angle value, then adjust vertex P. i Location; S29. Calculate the argument of each vertex. The vertices are sorted according to their arguments to ensure that the vertex order satisfies either clockwise or counterclockwise direction.

4. The method as described in claim 3, characterized in that, In step S28, vertex P is adjusted. i The locations specifically include: S281, Calculate vertex P i Angle bisector direction : ； in, and Vertex P i Two adjacent vectors; S282. Adjust the vertex coordinates along the angle bisector.

5. The method as described in claim 1, characterized in that, Step S5, which updates the particle position based on quantum behavior, specifically involves employing a dual dynamic search evolution strategy to update the particle position, including: S51. Set the evolutionary process control parameter ω: ； Where t represents the current iteration number, Maxlt represents the maximum iteration number, and rand represents a random number between 0 and 1. As the iteration number increases, the overall trend of ω becomes smaller and smaller. S52, When ω is less than At that time, the particle position is updated using the principle of local search priority. The particle position update formula is: ； When ω is greater than At that time, the particle position is updated using the global search priority principle, and the particle position update formula is: ； in, For a pre-set threshold, gbest(t) is the global optimal position of the current particle. Let be the optimal position of the i-th particle at time t, β be the expansion coefficient used to control the convergence speed of the algorithm, and μ be a random number between 0 and 1. and Let be the solutions for the i-th particle at time t and time t+1, respectively, and let mbest(t) be the average optimal position of the current particle, calculated as follows: ； Where m is the total number of particles and D is the dimension of the particles.

6. The method as described in claim 5, characterized in that, In step S7, individuals in the new population are crossovered using a dynamic crossover method. Specifically: When ω is less than When ω is greater than ω, the particle's position is crossed with the average optimal position of the individual. At that time, the particle is crossed with the global optimal position; The crossover rate is dynamically adjusted based on the algorithm's iterative algebraic progression. The formula for calculating the crossover rate is as follows: ； in, Let k be the initial crossover rate, and k be the current generation. This represents the maximum number of iterations.

7. The method as described in claim 6, characterized in that, In step S7, an adaptive mutation mechanism is used to perform mutation operations on individuals in the new population. Specifically: The mutation rate is adjusted according to the iterative algebraic rules of the algorithm, and the formula for calculating the mutation rate is: ； in, Let k be the initial mutation rate, and k be the current generation. This represents the maximum number of iterations.

8. A design device for an irregular polygonal patch antenna based on the improved NSGA-II, characterized in that, The device includes: The optimization target setting module is used to set the optimization target and constraints for irregular polygon patch antennas; The initialization population generation module is used to set the population size M and the number of sides N of the irregular polygon patch antenna, and randomly generate an initial population that satisfies the constraints. The initialization parameter setting module is used to initialize the relevant parameters of the NSGA II algorithm, including the maximum number of iterations, external archive size, crossover rate, and mutation rate. The iterative optimization module is used to calculate the population fitness, perform non-dominated sorting on the initial population, update the individual extreme value of each particle, calculate the crowding distance, select the global optimal solution based on the crowding distance, calculate the average value of the individual optimal solutions of the population, and establish an external profile. The offspring population is obtained by updating the particle positions based on quantum behavior. Calculate the individual fitness of the offspring population, merge the parent and offspring populations, perform non-dominated sorting and calculate crowding distance, and update the external profile; Select, crossover, and mutate individuals in the new population to obtain offspring individuals; Merge the parent and offspring populations, calculate the fitness of all individuals in the population, perform non-dominated sorting and calculate crowding distance, and select individuals to enter the next generation based on fitness. Repeat the above steps until the maximum number of iterations is met; The optimization objective in the optimization objective setting module is: ； Where V represents the antenna volume and db represents the antenna bandwidth. This indicates the antenna gain flatness, and X represents the maximum frequency within the antenna's operating frequency band. The constraints in the optimization target setting module include: (1) The origin coincides with the centroid of the polygon: ； Where (0, 0) are the coordinates of the origin, () represents the coordinates of the i-th vertex of the polygon, and n is the number of vertices of the polygon; (2) The distance f between the center of the feed point and the origin is less than or equal to the average distance f from the vertices of the polygon to the origin: ； (3) The sides of a polygon are connected only from the vertex with the smaller argument to the vertex with the larger argument: ； The argument of the i-th vertex is represented by the following. Calculated using the following formula: ； (4) The side length of the polygonal antenna substrate shall not be less than twice the average distance from the vertex of the polygon to the origin: 。

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