An antenna eigenmode topology optimization method based on topological connectivity constraints

Abstract

The application provides a kind of antenna eigenmode topology optimization method based on topological connectivity constraint, belong to antenna design technical field.The method includes: using the method of moments to the initial radiation structure of antenna is triangular mesh and unit pairing, constructs electromagnetic grid model;Establish the mapping relationship between binary array and triangle pair to generate initial population, and limit the length of continuous removal unit;Convert binary matrix into antenna structure after executing eigenmode analysis, obtain mode significance and radiation pattern and other performance parameters;Iterative optimization is carried out using NSGA-II algorithm, and topological connectivity constraint is applied in the links of cross variation, objective function value calculation and multi-objective selection;Output the optimal antenna topology structure after reaching the maximum iteration number.Topology cut point is identified based on graph theory and adaptive penalty term is introduced, and the crowding distance is corrected according to the number of cut points.The application can effectively suppress non-connected broken structure, reduce invalid iteration, and balance electromagnetic performance optimization and structural processability.

Description

Technical Field

[0001] This invention belongs to the field of antenna design technology and relates to an antenna eigenmode topology optimization method based on topological connectivity constraints. Background Technology

[0002] With the rapid development of satellite communication, next-generation mobile communication, and radar technologies, antennas are increasingly trending towards miniaturization, wide bandwidth, multi-frequency operation, conformal design, and high integration, placing more stringent demands on antenna overall performance and structural feasibility. Traditional analytical methods are only suitable for antennas with simple structures and cannot meet the needs of complex engineering applications. While commonly used simulation software such as FEKO, HFSS, and CST can perform accurate electromagnetic analysis, the design process is highly dependent on the designer's experience, lacks clear physical mechanism guidance, often requires repeated debugging, and results in long design cycles and low efficiency. Therefore, antenna topology optimization technology, which combines numerical calculation and intelligent optimization algorithms, has become an important research direction in the field of automated antenna design.

[0003] These optimization methods divide the antenna design area into several basic units, use binary encoding to represent the retention or removal of units, and then automatically search for the topology with the best electromagnetic performance through optimization algorithms. For example, the literature "Dong J, Li Q, Deng L. Design of Fragment-Type Antenna Structure Using an Improved BPSO [J].IEEE Transactions on Antennas and Propagation, 2018, 66 (2): 564-570." proposes an improved binary particle swarm optimization algorithm to design fragmented antenna structures, which can automatically complete the topology optimization of compact multi-frequency and ultra-wideband antennas. However, these topology optimization methods, which do not combine eigenmode analysis, only take electromagnetic performance indicators as optimization targets and lack radiation mechanism support. The optimized structure is often complex and irregular, with poor physical realizability, and is prone to forming fragmented, disconnected, and invalid topologies, which are difficult to meet actual processing requirements. At the same time, the feed position and type need to be set in advance, which restricts the degree of freedom of optimization. In high-dimensional design problems, it is easy to get trapped in local optima and cannot find the globally optimal antenna topology, resulting in obvious shortcomings in the electromagnetic performance of the optimized result.

[0004] Based on the method of moments, the characteristic mode theory can extract the antenna's own radiation modes, mode currents, and far-field radiation characteristics without pre-setting the feed. It can directly carry out mode control and mechanism analysis, providing clear theoretical support for antenna topology optimization. Topology optimization based on characteristic modes can directly target the intrinsic characteristics such as mode saliency and radiation orthogonality, and can achieve radiation performance control without relying on pre-set feed. The optimization direction is more reasonable and the physical mechanism is clearer. For example, the literature "Alroughani H, McNamara D A. The Shape Synthesis of Dielectric Resonator Antennas[J].IEEE Transactions on Antennas and Propagation, 2020, 68(8):5766-5777" proposes a topology optimization method for dielectric resonator antennas that combines characteristic modes. It can complete antenna topology optimization under irregular spatial constraints, but it still does not solve the problem of topology connectivity. Existing feature-modulus topology optimization methods generally lack topological connectivity constraints. During the optimization process, fragile structures (topological cut points) connected only by a single point or isolated metal fragments completely detached from the main body often appear, resulting in unprocessable invalid structures and a large amount of invalid computation. It is difficult to simultaneously ensure the topological connectivity of the structure and the optimization efficiency, resulting in poor overall engineering practicality.

[0005] Therefore, traditional antenna topology optimization methods often lack effective constraints on structural connectivity when searching for high-performance structures, easily resulting in unmanufacturable topologies containing breaks or cut points. Furthermore, the optimization process lacks the physical guidance of characteristic mode theory, leading to numerous invalid iterations and making it difficult to balance electromagnetic performance and engineering feasibility. Current technologies cannot achieve end-to-end connectivity constraints in characteristic mode topology optimization, thus a method for antenna topology optimization that avoids breaks and cut points while balancing electromagnetic performance and engineering manufacturability is urgently needed. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide an antenna eigenmode topology optimization method based on topological connectivity constraints. This method introduces eigenmode analysis into the topology optimization process, directly utilizing the inherent mode characteristics of the antenna to guide the optimization direction without pre-setting the feed, thus avoiding blind searching. Simultaneously, strict topological connectivity constraints are applied during the optimization process: the length of continuously removed units is limited during initial population generation; large-area disconnected structures are rejected during the crossover and mutation stage; topological cut vertices are identified based on graph theory and adaptive penalties are applied during objective function value calculation; and the congestion distance is adjusted based on the number of cut vertices in the multi-objective selection stage. Through this series of topological connectivity constraints, the generation of broken structures is effectively suppressed, invalid iterations are reduced, and the optimization results not only meet the preset electromagnetic performance indicators but also possess complete physical manufacturability, thereby enhancing the engineering practical value of antenna topology optimization.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for antenna eigenmode topology optimization based on topological connectivity constraints, the method specifically includes the following steps: S1. The initial radiating structure of the antenna is discretized using the method of moments, dividing the initial structure into 2... K The triangular units are combined into K Using pairs of triangles, an electromagnetic mesh model suitable for characteristic mode analysis is constructed; S2. Import the discretized electromagnetic mesh model into the numerical computation platform and establish a mapping relationship between the binary array and triangle pairs: where element "1" indicates that triangle pairs are retained, and element "0" indicates that triangle pairs are removed; generate the size N × K binary matrix [ X The maximum length of consecutive "0"s removed from each row of the matrix is ​​limited to a preset threshold. Q ,in Q It is a positive integer greater than or equal to 1, and Q The value of and the number of columns in the binary matrix K related; S3, convert the binary matrix [ X The data is converted into the corresponding antenna electromagnetic grid structure, and characteristic mode analysis is performed using full-wave simulation software to obtain the characteristic mode performance parameters of the population. S4. Based on the feature pattern performance parameters and the preset objective function, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to iteratively optimize the initial population. The parent selection adopts a dynamic adaptive linear ranking mechanism to improve population diversity. Topological connectivity constraints are applied in the crossover mutation, objective function value calculation and multi-objective selection stages. S5. Determine whether the number of iterations has reached the preset maximum value Tmax. If it has, terminate the optimization and output the optimal antenna topology. If it has not, return to step S3 and repeat the process.

[0008] Furthermore, step S1 specifically includes the following steps: S11. Determine the initial radiation structure of the antenna: First, determine the radiation structure, geometric dimensions, dielectric parameters and operating frequency band of the antenna to be optimized, and clarify the calculation objects of the method of moments discretization and characteristic mode analysis. S12. Triangular mesh partitioning: Based on the numerical solution requirements of the electric field integral equation, the antenna radiation structure is partitioned into a full triangular mesh. The partitioned mesh satisfies the constraints of shared edges, no overlap, and no gaps to ensure current continuity. The size of the triangular mesh has a significant impact on the optimization of the antenna objective function: a larger mesh size results in higher electromagnetic simulation efficiency, but coarser control over the antenna structure, which reduces the optimization effect of the objective function; a smaller mesh size allows for finer structural control and expands the optimization space, but reduces the solution efficiency. Typically, an electromagnetic mesh subdivision accuracy of about one-tenth of the wavelength is chosen to meet the numerical solution accuracy requirements of the method of moments and eigenmode analysis.

[0009] S13. Define RWG basis functions on the common side of adjacent triangular elements to realize the discrete expansion of the antenna surface current and ensure the continuity of the normal current. S14. Based on the RWG basis function matching rule, two triangles sharing the same edge are combined into a triangle pair, and the resulting 2 K The triangular units are combined as follows K A set of triangle pairs is used to ensure that each grid cell corresponds to a basis function.

[0010] Furthermore, in step S13, specifically: RWG basis functions are defined on the common edge of adjacent triangular elements. The RWG basis functions are vector basis functions specific to the method of moments. These basis functions exhibit non-zero values ​​only within a pair of triangular elements sharing a common edge. They are used to achieve discrete expansion of the antenna surface current and ensure the continuity of the normal current, satisfying the numerical solution requirements of the electric field integral equation. The RWG basis functions are as follows: (12) In the formula: l n For the first n Length of the common side; T n + , T n These are two triangular units adjacent to each other on a common side; A n+ , A n This represents the area of ​​the corresponding triangle. r n + , r n Let be the coordinates of the free vertices of the two triangles.

[0011] Furthermore, step S2 specifically includes the following steps: S21. Mesh Model Import: Import the electromagnetic mesh model discretized by the method of moments into the numerical computing platform to provide a basis for subsequent topology coding; S22, Binary Mapping Construction: Constructing 1× K 3D binary arrays and K A one-to-one mapping relationship is established between pairs of triangles; the following mapping relationship is established: when an element in the array is "0", it means to remove the corresponding triangle pair; when an element is "1", it means to keep the corresponding triangle pair. S23. Initial population generation: N sets of 1×K dimensional binary arrays are randomly generated in the numerical computing platform to form a matrix [X] of size N×K, which is the optimized initial population. Each row of the matrix corresponds to an antenna topology. S24. Connectivity constraint check: Check the initial population matrix [ X Perform connectivity checks, limiting the maximum length of consecutive "0"s removed from each row of the matrix to no more than a preset threshold. Q The threshold Q The number of triangle pairs K is set as follows: Q = 0.1 × K, that is, Q is equal to one-tenth of K, rounded down; individuals that do not meet the constraints are removed and regenerated to ensure that the initial population has no large-area disconnected structure.

[0012] Furthermore, step S3 specifically includes the following steps: S31, Encoding to Structure: Converting matrices that satisfy connectivity constraints [ X ] Convert to N An antenna electromagnetic grid structure controls the retention and removal of triangle pairs; S32. Characteristic mode full-wave simulation: Based on the electromagnetic mesh structure generated by the aforementioned method of moments, the characteristic mode solver is called after importing it into the full-wave simulation software to complete the solution of the electric field integral equation and the decomposition of the characteristic modes, and to extract the characteristic mode performance parameters of the antenna. S33. Performance Parameter Extraction: Key parameters such as eigenvalues, mode significance (MS), and radiation patterns of each topology are extracted from the simulation results for subsequent objective function calculation. MS represents the ability of a specific mode to be effectively excited, with a variation range of [0,1]. The closer MS is to the maximum value of 1, the stronger the mode's resonance state and the easier it is to be effectively excited; conversely, the closer MS is to 0, the more the mode is in a storage state and the more difficult it is to be effectively excited. The radiation pattern describes the radiation distribution of the mode in space, intuitively reflecting key indicators such as the main radiation direction and polarization orthogonality. By comparing the shape and direction of the mode patterns at different frequencies, the radiation independence of each mode during dual-frequency operation can be determined, providing an intuitive basis for optimization objectives.

[0013] Furthermore, step S4 specifically includes the following steps: S41. Parent Selection: Sort the individuals in the current iteration population linearly according to their objective function values ​​to obtain their objective function value ranking numbers. i A linear ranking selection mechanism based on iterative algebraic dynamic adaptive adjustment is introduced. A dynamic linear probability allocation formula assigns a parent generation selection probability to each individual. The selection probability is linearly positively correlated with the individual's objective function ranking. This dynamic linear probability allocation formula uses a dynamic upper limit coefficient that adaptively changes with the iterative algebraic number. η + ( t ) and dynamic lower limit coefficient η - ( t Real-time adjustment of selection pressure avoids excessive concentration of dominant individuals, balancing population diversity and algorithm convergence; S42. Crossover and Mutation Operations: In the crossover operation, after generating offspring individuals, the matrix needs to be checked. X The longest consecutive "0" sequence length in each line of the array; if this length exceeds a preset threshold. Q If the current crossover result is invalid, the crossover operation will be re-executed to generate new offspring individuals; in the mutation operation, when bit-flip mutation is used, the flipped matrix must be evaluated in advance. X The longest consecutive "0" sequence length in the []; if this length exceeds the threshold Q If the threshold value is not met, the mutation operation is rejected. Q Based on the number of triangle pairs K The settings are as follows: Q = 0.1 × K ,Right now Q equal K One-tenth of the original value, rounded down; S43. Objective Function Calculation: Introducing a penalty term for disconnected regions in the topology, and using graph theory, transforming the electromagnetic triangular mesh of the antenna into an undirected graph of vertices and edges in mathematics. G The undirected graph refers to a graph in which each vertex in the antenna triangle mesh is mapped to a vertex of the graph, and the connection relationship of each triangle edge in the mesh is mapped to an undirected edge. S44. In the process of non-dominated ranking and crowding distance calculation, the original non-dominated ranking level of individuals remains unchanged, and topological constraints are guided by crowding distance. Non-dominated ranking refers to the stratification of individuals in the population according to the dominance relationship in multi-objective optimization. Individuals not dominated by any other individuals constitute the first frontier, and subsequent frontiers are determined in sequence. The smaller the level, the better the individual. Crowding distance is a measure of the distribution density of other individuals around an individual in the same frontier. The larger the distance, the sparser the individuals, which is more conducive to maintaining frontier diversity.

[0014] Furthermore, in step S41, the dynamic linear probability allocation formula is: (13) in, i =1,2,…, N , N For population size, i Rank the individual objective function values. t Let the current iteration algebra be... η + ( t ) represents the dynamic upper limit coefficient. η - ( t ) represents the dynamic lower bound coefficient; the dynamic coefficient changes linearly and adaptively with the iterative algebra, satisfying: , , T max This is the preset maximum number of iterations.

[0015] Furthermore, step S43 specifically includes: 1) In this undirected graph, edges only represent connections between two points and do not have directionality, thus preserving the original connectivity information of the antenna structure: (14) (15) (16) in, V This is the set of vertices, corresponding to all nodes in the mesh; E Let be the set of edges, corresponding to the common edges shared by triangles; t p, t q For the first p , No. q One triangular unit, ; indicates that two triangles share a side, that is, they share two vertices, 2 K This represents the total number of triangular elements in the antenna grid. Based on graph theory principles, the connection state of the structure is analyzed, and a mapping relationship between nodes and their corresponding triangular elements is established. : (17) This enables the association and retrieval of nodes and units, and filters core nodes accordingly; where: v m For the first m One grid node; T The set consisting of all triangular units; M This represents the total number of grid nodes. 2) Construct a triangular cell adjacency matrix based on shared common edges [A]: (18) in, A pq The adjacency matrix of triangular units is the first... p Line 1 q Column elements; A pq =1 indicates a triangular unit. t p and t q Share a common edge; A pq =0 indicates that the two units are not adjacent; 3) Use connected component analysis algorithm for undirected graphs G Perform topology analysis to identify topological cut points. v c A cut point is a critical node in the mesh that, when removed, would cause the overall radiating structure to split into multiple unconnected parts, corresponding to a fracture defect in the antenna structure that makes it impossible to actually manufacture; the cut point v c Criterion satisfied: (19) This means that removing this node increases the number of connected components in the undirected graph, resulting in a break in the corresponding antenna structure, making it impossible to actually manufacture; where: v c The topological cut vertex to be determined; G v c To remove a node vc The undirected graph after; ω ( G () is an undirected graph G The total number of connected components; ω( G v c The total number of connected components after removing node v is denoted as ; if the original graph G is a connected graph, then Then the cut point satisfies If the original graph itself is not connected If removing a node causes a connected component to split further, the inequality still applies. 4) Introducing an adaptive penalty coefficient that is dynamically adjusted as the iteration progresses: In the early stages of iteration, a smaller penalty value is used to maintain population diversity and avoid prematurely eliminating potentially superior structures; in the later stages of iteration, the penalty value is gradually increased to strengthen the constraint on topological break structures; the penalty term is constructed as follows: First, the topological cut points in the current antenna structure are identified and their number is counted. N C Then, the penalty value is calculated according to the exponential rule: (20) The penalty value is added to the objective function to degrade the objective function value of individuals containing cut points; this design protects the exploratory nature in the early stages of the search and guides the algorithm to converge to a fracture-free, workable topology in the later stages; the adaptive penalty coefficient is set as follows: (twenty one) In the formula, α ( t ) indicates the first t The adaptive penalty coefficient in the next iteration; α min This is the initial penalty coefficient; α max This is the final penalty coefficient; T max This is the preset maximum number of iterations.

[0016] Furthermore, in step S44, for individuals within the same frontal line, the crowding distance is adjusted based on the number of cut points, using the following formula: (twenty two) in, d i ′ For the first i Individually corrected crowding distance; d i For the first i The original crowding distance of each individual; N c,i For the first iThe total number of cut points for each individual; the more cut points, the smaller the corrected crowding distance, and the lower the priority in selection at the same level; individuals without cut points have their crowding distance unchanged and are given priority to be selected for the next generation of the population.

[0017] Furthermore, in step S5, specifically: using a preset maximum number of iterations... T max The termination condition is that if the maximum number of iterations is not reached, the next generation of binary matrix will be generated. X 1] As a new population, return the feature mode analysis step; when the maximum number of iterations is reached, select the individual with the optimal objective function value, no topological cut points, and complete structural connectivity from the final population, and output the corresponding antenna topology file and feature mode performance parameters.

[0018] The beneficial effects of this invention are as follows: This invention proposes an antenna eigenmode topology optimization method based on topological connectivity constraints. This method combines eigenmode analysis with end-to-end topological connectivity constraints to achieve efficient antenna topology optimization. By performing triangular mesh partitioning and element pairing according to the electric field integral equation in the initial stage, optimization is carried out based on eigenmode analysis, eliminating the need for additional feed structures and effectively improving design freedom and optimization efficiency. During the optimization process, the NSGA-II algorithm is employed, applying strict topological connectivity constraints in the crossover mutation, objective function value calculation, and multi-objective selection stages. This effectively identifies structural cut points, eliminates invalid non-connected structures, significantly reduces invalid iterations, and improves optimization stability. This method ensures the connectivity and physical manufacturability of the antenna topology throughout the entire process from structure generation to iterative optimization. While guaranteeing electromagnetic performance optimization, it also considers optimization efficiency and engineering feasibility, possessing high engineering application value.

[0019] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the overall process of the antenna eigenmode topology optimization method based on topological connectivity constraints of the present invention; Figure 2 The following is a schematic diagram of the initial structure of the optimized dual-frequency microstrip antenna in an embodiment of the present invention: (a) top view, (b) side view. Figure 3This is a schematic diagram of the triangular mesh partitioning of the initial antenna radiation structure in an embodiment of the present invention; Figure 4 This invention improves NSGA II Algorithm and Traditional NSGA Comparison curves of the number of cut points during the iteration process of Algorithm II; Figure 5 The mode significance curve for the initial antenna structure; Figure 6 This is a schematic diagram of the optimized antenna topology in an embodiment of the present invention; Figure 7 The mode significance curve of the optimized antenna; Figure 8 To optimize the 3D mode radiation pattern of the antenna; Figure 9 This is a graph showing the S-parameters of the optimized antenna after loading and feeding in an embodiment of the present invention. Figure 10 This is the 3D radiation pattern of the antenna after optimized loading and feeding in this embodiment of the invention; Figure 11 Simulated radiation patterns of the proposed antenna at 5.22 GHz and 5.81 GHz; (a) E-plane radiation pattern at 5.22 GHz; (b) H-plane radiation pattern at 5.22 GHz; (c) E-plane radiation pattern at 5.81 GHz; (d) H-plane radiation pattern at 5.81 GHz; Figure 12 This is a graph showing the optimized antenna gain in an embodiment of the present invention. Detailed Implementation

[0021] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0022] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0023] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0024] In this embodiment, a dual-band microstrip patch antenna operating in the 5G Wi-Fi band is optimized. Specifically, the target frequency bands are 5.15 GHz-5.25 GHz and 5.75 GHz-5.85 GHz. To facilitate characteristic mode analysis and optimization, the center frequencies of 5.2 GHz and 5.8 GHz for each band are selected as the design frequencies. The NSGA-II population size is 100, the number of iterations is 50, the crossover probability is 80%, and the mutation probability is... Then, the proposed optimization method is used to design the antenna, such as... Figure 1 As shown, the specific steps are as follows: Step 1: Initial sampling.

[0025] First, the initial structure diagram of the microstrip patch antenna before optimization is given, such as... Figure 2 As shown, the dielectric substrate has a thickness of H The substrate is 1.524 mm thick Rogers RO4003 with a relative permittivity of 3.55. The substrate length is... L =45mm, width W =32mm; Metal patch length L 1 = 20mm, width W 1 = 15mm.

[0026] Then, the antenna's radiation structure is discretized using the method of moments (MoM) to create an electromagnetic mesh. The initial antenna radiation structure is divided into a triangular mesh structure with 304 meshes and 178 nodes. Figure 3 As shown.

[0027] Finally, the meshed model is converted into a .nas file.

[0028] Step 2: Construct the initial population.

[0029] Based on the .nas file from step 1, import it into MATLAB and control the distribution of '1' and '0'. In MATLAB, a set of 1×152 binary arrays corresponds to a triangle. 100 different binary arrays are generated using random sampling, forming a 100×152 binary matrix. X ], corresponding to 100 populations of NSGA-II, while limiting the matrix [ X The maximum length of consecutive "0"s in each line is no more than 15, in order to avoid large areas of disconnected regions in the initial population and reduce the proportion of invalid iterations in subsequent optimization processes.

[0030] In step 3, the binary array obtained in step 2 needs to be converted into the electromagnetic grid structure of the antenna. In this example, a binary matrix is ​​used. X Step 1 controls the generation of different electromagnetic grid structures from the CTRIA line in the .nas file. The full-wave simulation software FEKO is used to perform eigenmode analysis to obtain population-related eigenmode performance parameters. The solution frequency band is set to 4.5 GHz–6.5 GHz, and the number of frequency points is set to 100. This embodiment is mainly based on mode saliency and mode radiation patterns.

[0031] The antenna design objective of this invention is to maximize the MS values ​​at 5.2 GHz and 5.8 GHz. Simultaneously, it is desired that the antenna excites a dominant characteristic mode at each of these two frequencies, with the spatial radiation patterns of the two modes exhibiting an orthogonal relationship, to reduce mutual interference during dual-frequency operation. The specific objective function is: (twenty three) (twenty four) in, obj 1 represents objective function 1, with a value range of [2, +∞], and MS1 represents the MS value of the dominant mode at the current frequency. f 1 is set to 5.2 GHz. f 2 is set to 5.8 GHz. The optimization focuses on minimizing objective function 1. obj The smaller the value of 1, the larger the MS value at the two frequencies, and the better the resonance performance. Objective function obj 2 is a normalized correlation coefficient based on radiation pattern sampling, used to quantify the spatial orthogonality between the dominant characteristic modes of the antenna at two operating frequencies. Its value ranges from [0, 1]. A normalized correlation coefficient is defined as follows: when the electric field vectors of the two modes are perpendicular to each other everywhere in all sampling directions, i.e., the dot product at every point is zero. obj When the electric field vectors of the two modes reach a minimum value of 0, they are completely orthogonal. Conversely, if the electric field vectors of the two modes are exactly the same or proportional in all directions, obj A value of 2 approaches 1, indicating a perfect correlation.

[0032] In this embodiment, the two frequency points are set to 5.2 GHz and 5.8 GHz, respectively, in order to minimize the correlation between the far-field electric fields of the two modes in three-dimensional space, thereby reducing mode coupling and mutual interference when the two frequencies are working simultaneously. N θ This represents the number of sampling points in the vertical plane direction, which is set to 37 here. N This is the number of sampling points in the horizontal plane, set to 73 here; E 1( θ i , j ) for frequency point f 1 down, elevation angle θ i Azimuth j The mode electric field vector at that location; E 2( θi, j ) for frequency point f 2 down, elevation angle θ i Azimuth j The mode electric field vector at that location.

[0033] To suppress the generation of disconnected topologies during optimization, this invention introduces an adaptive penalty term based on the number of cut vertices into the objective function. The final optimized objective function is defined as follows: (25) (26) in, N c This represents the total number of cut points in the current antenna topology. α (t) is a penalty coefficient that increases adaptively with the number of iterations, and its value ranges from [0.1, 5].

[0034] In step 4, the improved NSGA-II algorithm based on topological connectivity constraints is used to process a 100×152 binary matrix. X Optimize the elements in []. Dynamic upper limit. η + ( t The coefficient ranges from [1, 2] and increases gradually with the number of iterations in increments of 0.02. The dynamic lower limit coefficient is... η - ( tThe value range is [0, 1]. This coefficient gradually decreases with the number of iterations by a step size of 0.02. The optimized matrix of size 100×152 is defined as [ X 1).

[0035] In step 5, the convergence condition for the iteration can be set to the number of iterations of NSGA-II. In this example, the number of iterations is 50.

[0036] Figure 4 To improve NSGA II Algorithm and Traditional NSGA The comparison of the number of cut points during the iteration process of the II algorithm shows that each algorithm underwent 5 independent optimization simulations, and the average number of cut points for the Pareto optimal population and the entire population was statistically analyzed. As can be seen from the figure, the average number of cut points in the improved NSGA-II algorithm decreases rapidly with the number of iterations and approaches 0, while the average number of cut points in the traditional NSGA-II algorithm remains at a high level. This indicates that the topological connectivity constraint of the present invention can effectively reduce the number of cut points in the antenna structure and improve the structural connectivity.

[0037] Figure 5 The MS curves corresponding to the initial antenna structure are presented. The initial antenna structure exhibits only one resonant mode (mode 1) at the center frequency of 5.3 GHz; the MS values ​​for other modes are very small and difficult to excite. This implies that mode 1 is the dominant operating mode for the antenna in the current frequency band, failing to meet the requirement of two resonant modes.

[0038] Figure 6 This is a diagram of an antenna structure representing a typical optimization result of the present invention. Figure 7 , Figure 8 The images show the optimized MS curve and mode pattern, respectively. Compared to the initial antenna's single operating mode, this invention, through structural optimization, enables the antenna to excite two characteristic modes at 5.2 GHz and 5.8 GHz, namely Mode 1 and Mode 2. Combined with... Figure 8 As shown in the pattern diagram, the main lobe directions of the radiation patterns of Mode 1 and Mode 2 at their respective resonant frequencies are orthogonal to each other, and the spatial radiation field components are vertically distributed, effectively realizing the orthogonal radiation characteristics at the dual frequency points. The optimization results meet the requirements of the set objective function.

[0039] Figure 9 The S-parameter parameters after feeding are given. Probe feeding was performed at locations with relatively strong electric fields at the center frequency of 5.2 GHz and 5.8 GHz. The specific feeding locations are as follows: x =3.5mm, y=2.6mm. According to the S-parameter specifications, the resonant frequencies of Mode 1 and Mode 2 show a slight shift, with Mode 1 shifting to 5.22 GHz and Mode 2 shifting to 5.81 GHz. Their |S... 11 All values ​​are less than -10dB, covering the 5.2 GHz and 5.8 GHz frequency bands. Figure 10 The 3D radiation pattern after feeding is given, and the pattern still satisfies orthogonality. Figure 11 Simulation radiation patterns show that, compared to a fully symmetrical antenna structure, the asymmetric topology introduced in the optimized design introduces certain cross-polarization components, making it impossible to achieve optimal low cross-polarization performance. At 5.22 GHz, the cross-polarization levels in the E-plane and H-plane main radiation directions of this antenna are both below -18 dB, and at 5.81 GHz, the corresponding cross-polarization level is below -17 dB. Even with the inherent characteristics of the asymmetric structure, cross-polarization radiation can still be effectively suppressed. Figure 12 The figure shows the antenna gain versus frequency curve. The antenna achieves a peak gain of 6.75 dBi at 5.22 GHz and a gain of 6.23 dBi at 5.81 GHz, achieving high radiation gain at both operating points.

[0040] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for antenna eigenmode topology optimization based on topological connectivity constraints, characterized in that, The method specifically includes the following steps: S1. The initial radiating structure of the antenna is discretized using the method of moments, dividing the initial structure into 2... K The triangular units are combined into K Using pairs of triangles, an electromagnetic mesh model suitable for characteristic mode analysis is constructed; S2. Import the discretized electromagnetic mesh model into the numerical computation platform and establish a mapping relationship between the binary array and triangle pairs: where element "1" indicates that triangle pairs are retained, and element "0" indicates that triangle pairs are removed; generate the size N × K binary matrix [ X The maximum length of consecutive "0"s removed from each row of the matrix is ​​limited to a preset threshold. Q ,in Q It is a positive integer greater than or equal to 1, and Q The value of and the number of columns in the binary matrix K related; S3, convert the binary matrix [ X The data is converted into the corresponding antenna electromagnetic grid structure, and characteristic mode analysis is performed using full-wave simulation software to obtain the characteristic mode performance parameters of the population. S4. Based on the feature pattern performance parameters and the preset objective function, the non-dominated sorting genetic algorithm II is used to iteratively optimize the initial population. The parent selection adopts a dynamic adaptive linear ranking mechanism to improve population diversity. Topological connectivity constraints are applied in the crossover mutation, objective function value calculation and multi-objective selection stages. S5. Determine whether the number of iterations has reached the preset maximum value Tmax. If it has, terminate the optimization and output the optimal antenna topology. If it has not, return to step S3 and repeat the process.

2. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11. Determine the initial radiation structure of the antenna: First, determine the radiation structure, geometric dimensions, dielectric parameters and operating frequency band of the antenna to be optimized, and clarify the calculation objects of the method of moments discretization and characteristic mode analysis. S12. Triangular mesh partitioning: Based on the numerical solution requirements of the electric field integral equation, the antenna radiation structure is partitioned into a full triangular mesh. The partitioned mesh satisfies the constraints of shared edges, no overlap, and no gaps to ensure current continuity. S13. Define RWG basis functions on the common side of adjacent triangular elements to realize the discrete expansion of the antenna surface current and ensure the continuity of the normal current. S14. Based on the RWG basis function matching rule, two triangles sharing the same edge are combined into a triangle pair, and the resulting 2 K The triangular units are combined as follows K A set of triangle pairs is used to ensure that each grid cell corresponds to a basis function.

3. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 2, characterized in that, In step S13, specifically: RWG basis functions are defined on the common edge of adjacent triangular elements. The RWG basis functions are vector basis functions specific to the method of moments. These basis functions exhibit non-zero values ​​only within a pair of triangular elements sharing a common edge. They are used to achieve discrete expansion of the antenna surface current and ensure the continuity of the normal current, satisfying the numerical solution requirements of the electric field integral equation. The RWG basis functions are as follows: (1) In the formula: l n For the first n Length of the common side; T n + , T n These are two triangular units adjacent to each other on a common side; A n + , A n This represents the area of ​​the corresponding triangle. r n + , r n Let be the coordinates of the free vertices of the two triangles.

4. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 3, characterized in that, Step S2 specifically includes the following steps: S21. Mesh Model Import: Import the electromagnetic mesh model discretized by the method of moments into the numerical computing platform to provide a foundation for subsequent topology coding; S22, Binary Mapping Construction: Constructing 1× K 3D binary arrays and K A one-to-one mapping relationship is established between pairs of triangles; the following mapping relationship is established: when an element in the array is "0", it means to remove the corresponding triangle pair; when an element is "1", it means to keep the corresponding triangle pair. S23. Initial population generation: N sets of 1×K dimensional binary arrays are randomly generated in the numerical computing platform to form a matrix [X] of size N×K, which is the optimized initial population. Each row of the matrix corresponds to an antenna topology. S24. Connectivity constraint check: Check the initial population matrix [ X Perform connectivity checks, limiting the maximum length of consecutive "0"s removed from each row of the matrix to no more than a preset threshold. Q The threshold Q The number of triangle pairs K is set as follows: Q = 0.1 × K, that is, Q is equal to one-tenth of K, rounded down; individuals that do not meet the constraints are removed and regenerated to ensure that the initial population has no large-area disconnected structure.

5. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 4, characterized in that, Step S3 specifically includes the following steps: S31, Encoding to Structure: Converting matrices that satisfy connectivity constraints [ X ] Convert to N An antenna electromagnetic grid structure controls the retention and removal of triangle pairs; S32. Characteristic mode full-wave simulation: Based on the electromagnetic mesh structure generated by the aforementioned method of moments, the characteristic mode solver is called after importing it into the full-wave simulation software to complete the solution of the electric field integral equation and the decomposition of the characteristic modes, and to extract the characteristic mode performance parameters of the antenna. S33. Performance Parameter Extraction: Key parameters such as eigenvalues, mode saliency (MS), and radiation patterns of each topology are extracted from the simulation results for subsequent objective function calculation. MS represents the effective excitation capability of a specific mode, with a variation range of [0,1]. The closer MS is to the maximum value of 1, the stronger the mode's resonance state and the easier it is to excite; conversely, the closer MS is to 0, the more the mode primarily exhibits an energy storage state and the more difficult it is to excite. The radiation pattern describes the radiation distribution of the mode in space, intuitively reflecting key indicators such as the main radiation direction and polarization orthogonality. By comparing the shape and direction of the mode radiation patterns at different frequencies, the radiation independence of each mode during dual-frequency operation can be determined, providing an intuitive basis for optimization objectives.

6. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 5, characterized in that, Step S4 specifically includes the following steps: S41. Parent Selection: Sort the individuals in the current iteration population linearly according to their objective function values ​​to obtain their ranking numbers based on objective function values. i A linear ranking selection mechanism based on iterative algebraic dynamic adaptive adjustment is introduced. A dynamic linear probability allocation formula is used to assign parent generation selection probabilities to each individual. The selection probability is linearly positively correlated with the individual's objective function ranking. This dynamic linear probability allocation formula uses a dynamic upper limit coefficient that adaptively changes with the iterative algebraic number. η + ( t ) and dynamic lower limit coefficient η - ( t Real-time adjustment of selection pressure avoids excessive concentration of dominant individuals, balancing population diversity and algorithm convergence; S42. Crossover and Mutation Operations: In the crossover operation, after generating offspring individuals, the matrix needs to be checked. X The longest consecutive "0" sequence length in each line of the array; if this length exceeds a preset threshold. Q If the current crossover result is invalid, the crossover operation will be re-executed to generate new offspring individuals; in the mutation operation, when bit-flip mutation is used, the flipped matrix must be evaluated in advance. X The longest consecutive "0" sequence length in the [database name]; if this length exceeds the threshold. Q If the threshold value is not met, the mutation operation is rejected. Q Based on the number of triangle pairs K The settings are as follows: Q = 0.1 × K ,Right now Q equal K One-tenth of the original value, rounded down; S43. Objective Function Calculation: Introducing a penalty term for disconnected regions in the topology, and using graph theory, transforming the electromagnetic triangular mesh of the antenna into an undirected graph of vertices and edges in mathematics. G The undirected graph refers to a graph in which each vertex in the antenna triangle mesh is mapped to a vertex of the graph, and the connection relationship of each triangle edge in the mesh is mapped to an undirected edge. S44. In the process of non-dominated ranking and crowding distance calculation, the original non-dominated ranking level of individuals remains unchanged, and topological constraints are guided by crowding distance. Non-dominated ranking refers to the stratification of individuals in the population according to the dominance relationship in multi-objective optimization. Individuals not dominated by any other individuals constitute the first frontier, and subsequent frontiers are determined in sequence. The smaller the level, the better the individual. Crowding distance is a measure of the distribution density of other individuals around an individual in the same frontier. The larger the distance, the sparser the individuals, which is more conducive to maintaining frontier diversity.

7. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 6, characterized in that, In step S41, the dynamic linear probability allocation formula is: (2) in, i =1,2,…, N , N For population size, i Rank the individual objective function values. t Let the current iteration algebra be... η + ( t ) represents the dynamic upper limit coefficient. η - ( t ) is the dynamic lower bound coefficient; the dynamic coefficient changes linearly and adaptively with the iterative algebra, satisfying: , , T max This is the preset maximum number of iterations.

8. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 7, characterized in that, Step S43 specifically includes: 1) In this undirected graph, edges only represent connections between two points and do not have directionality, thus preserving the original connectivity information of the antenna structure: (3) (4) (5) in, V This is the set of vertices, corresponding to all nodes in the mesh; E Let be the set of edges, corresponding to the common edges shared by triangles; t p , t q For the first p , No. q Triangular units, ; indicates that two triangles share a side, that is, they share two vertices, 2 K This represents the total number of triangular elements in the antenna grid. Based on graph theory principles, the connection state of the structure is analyzed, and a mapping relationship between nodes and their corresponding triangular elements is established. : (6) This enables the association and retrieval of nodes and units, and filters core nodes accordingly; where: v m For the first m One grid node; T The set consisting of all triangular units; M This represents the total number of grid nodes. 2) Construct a triangular cell adjacency matrix based on shared common edges [A]: (7) in, A pq The adjacency matrix of triangular units is the first... p Line number q Column elements; A pq =1 indicates a triangular unit. t p and t q Share a common edge; A pq =0 indicates that the two units are not adjacent; 3) Use connected component analysis algorithm for undirected graphs G Perform topology analysis to identify topological cut points. v c A cut point is a critical node in the mesh that, when removed, would cause the overall radiating structure to split into multiple unconnected parts, corresponding to a fracture defect in the antenna structure that makes it impossible to actually manufacture; the cut point v c Criterion satisfied: (8) This means that removing this node increases the number of connected components in the undirected graph, resulting in a break in the corresponding antenna structure, making it impossible to actually manufacture; where: v c The topological cut vertex to be determined; G v c To remove a node v c The undirected graph after; ω ( G () is an undirected graph G The total number of connected components; ω( G v c The total number of connected components after removing node v is denoted as ; if the original graph G is a connected graph, then Then the cut point satisfies If the original graph itself is not connected If removing a node causes a connected component to split further, the inequality still applies. 4) Introducing an adaptive penalty coefficient that is dynamically adjusted as the iteration progresses: In the early stages of iteration, a smaller penalty value is used to maintain population diversity and avoid prematurely eliminating potentially superior structures; in the later stages of iteration, the penalty value is gradually increased to strengthen the constraint on topological break structures; the penalty term is constructed as follows: First, the topological cut points in the current antenna structure are identified and their number is counted. N C Then, the penalty value is calculated according to the exponential rule: (9) The penalty value is added to the objective function to degrade the objective function value of individuals containing cut points; this design protects the exploratory nature in the early stages of the search and guides the algorithm to converge to a fracture-free, workable topology in the later stages; the adaptive penalty coefficient is set as follows: (10) In the formula, α ( t ) indicates the first t The adaptive penalty coefficient in the next iteration; α min This is the initial penalty coefficient; α max This is the final penalty coefficient; T max This is the preset maximum number of iterations.

9. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 8, characterized in that, In step S44, for individuals within the same frontal line, the crowding distance is adjusted based on the number of cut points, using the following formula: (11) in, d i ′ For the first i Individually corrected crowding distance; d i For the first i The original crowding distance of each individual; N c,i For the first i The total number of cut points for each individual; the more cut points, the smaller the corrected crowding distance, and the lower the priority in selection at the same level; individuals without cut points have their crowding distance unchanged and are given priority to be selected to enter the next generation of the population.

10. The antenna eigenmode topology optimization method based on topological connectivity constraints according to claim 9, characterized in that, In step S5, specifically: using a preset maximum number of iterations... T max This is a termination condition; If the maximum number of iterations has not been reached, the next generation of binary matrix will be [ X 1] This is a step in the analysis of the returned eigenmodels of a new population; When the maximum number of iterations is reached, select the individual with the optimal objective function value, no topological cut points, and fully connected structure from the final population, and output the corresponding antenna topology file and characteristic mode performance parameters.

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