Improved particle swarm optimization algorithm-based variable-thickness wave-absorbing material performance optimization design method
By improving the particle swarm algorithm, using the Levy flight strategy and α-Trimmed model lateral constraints, the thickness parameters of variable thickness absorbing materials are optimized, and the problem of limited bandwidth of one-dimensional structure in existing absorbing materials is solved, and broadband absorbing design is realized, which is suitable for engineering applications.
Patent Information
- Application Number
- CN202411520249.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-29
- Publication Date
- 2025-02-28
AI Technical Summary
The effective absorbing bandwidth of the one-dimensional structure in existing absorbing materials is limited by the Kramers–Kronig principle, making it difficult to achieve bandwidth expansion, and optimization algorithms are difficult to take into account both speed and accuracy.
Using an improved particle swarm algorithm, the thickness parameters of variable thickness absorbing materials are optimized by introducing Levy flight strategy and α-Trimmed model lateral constraints, and the optimization efficiency of the algorithm and the lateral continuity of the model are improved.
The three-dimensional structure variable thickness optimization design has been realized, the wave absorption frequency band has been significantly expanded, the technical bottleneck of traditional one-dimensional layered structure design has been broken, and the engineering application potential is available.
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Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of microwave detection and provides an optimization design method for variable thickness absorbing materials based on an improved particle swarm algorithm. Background Art
[0002] With the advancement of microwave detection technology and its application in engineering practice, higher requirements are placed on the stealth performance of new weapons and equipment. Since the microwave detection frequency band often ranges from several GHz to tens of GHz, the research on broadband absorbing and shielding materials has gradually become a research hotspot. Whether based on dielectric loss or magnetic loss, existing absorbing materials usually adopt a one-dimensional layered structure. The impedance matching characteristics are determined by adjusting the material properties and material thickness to determine the center frequency and bandwidth of the absorbing material. The effective absorbing bandwidth of one-dimensional layered absorbing materials is limited by the Kramers–Kronig principle, and it is difficult to achieve a breakthrough without changing the structure.
[0003] In electromagnetics, bandwidth expansion research is relatively common and is in principle the same. For example, in the design of frequency-selective absorber units, bandwidth expansion is achieved by enriching the resonant structure in the unit structure. Similarly, changing the one-dimensional structure in the absorber material to a three-dimensional variable thickness structure design can also increase the bandwidth of the absorption. Due to the complexity and multi-solution nature of the variable thickness three-dimensional absorber structure, it is difficult for the current optimization algorithm to take both speed and accuracy into account at the same time. According to the model-driven optimization algorithm, the gradient optimization algorithm has a fast optimization speed but is prone to fall into a local optimal solution. The intelligent optimization algorithm is more suitable for solving complex multi-solution problems and has achieved certain results in electromagnetic optimization design. In response to the above problems, the traditional particle swarm algorithm still needs to be further improved. On the one hand, it is necessary to optimize the driving mode of the algorithm and improve the optimization efficiency of the algorithm. On the other hand, it is necessary to increase the constraints between parameters and improve the lateral continuity in the variable thickness model design. Summary of the invention
[0004] In view of the above problems, the present invention provides a performance optimization design method for variable thickness absorbing materials based on an improved particle swarm algorithm.
[0005] The technical solution adopted by the present invention is as follows:
[0006] A performance optimization design method for variable thickness absorbing materials based on an improved particle swarm algorithm comprises the following steps:
[0007] Obtaining actual values of dielectric loss parameters and magnetic loss parameters of the absorbing material;
[0008] Taking the spatial thickness distribution of absorbing materials as the optimization target and the absorbing characteristics of each frequency point in the absorbing frequency band as the fitness function, the thickness parameters of the gridded absorbing materials are optimized based on the improved particle swarm algorithm to obtain the thickness parameters of the absorbing materials that vary with spatial position.
[0009] Furthermore, the actual values of the dielectric loss parameter and the magnetic loss parameter of the absorbing material are obtained by using a reflectivity testing system.
[0010] Furthermore, the fitness function is expressed as:
[0011]
[0012] Where n is the frequency number, A i is the absorption rate at each frequency point.
[0013] Furthermore, the improved particle swarm algorithm uses a joint call of matlab and CST to obtain the wave-absorbing characteristics of the wave-absorbing material that vary with frequency.
[0014] Furthermore, the improved particle swarm algorithm comprises the following steps:
[0015] Step 1: Obtain the absorption frequency band range and select the absorption rates of N frequency points to calculate the fitness function;
[0016] Step 2: Set the optimization parameter values, including the model size and how to segment and refine. Assume that the thickness parameter dimension of the segmented model is D, the number of particle swarm individuals is M, the maximum number of iterations is T, the α-Trimmed filter window width is n and the trimming parameter is α, assign P_num=1, M_num=1, k=0, where a particle refers to a single model parameter and a particle swarm refers to multiple model parameters;
[0017] Step 3: Randomly generate the initial model in the particle swarm algorithm in the model parameter space in represents the model parameter, i.e., thickness;
[0018] Step 4: Calculate the fitness of all particles in the P_num model, update the global optimal solution G of each parameter model, and calculate the Euclidean distance between other particles and the global optimal solution;
[0019] Step 5: Calculate the Levy flight strategy step length L of the P_num point in turn, and update the model correction information and current model of the particle swarm;
[0020] Step 6: Carry out the α-Trimmed method to perform lateral constraints on the model, increase the lateral continuity of the variable thickness model, and update all model parameters.
[0021] Step 7: Determine whether the global optimal solution meets the target value or whether the number of iterations reaches the upper limit. If the conditions are met, the optimization ends and the optimal value of the variable thickness design is obtained. If the conditions are not met, continue to modify the model.
[0022] The beneficial effects of the present invention are as follows:
[0023] Aiming at the limitation of absorption bandwidth of single-layer absorbing materials in design, the present invention improves the particle swarm algorithm by adopting flight strategy and lateral constraint strategy to realize the optimization design of variable thickness three-dimensional structure. On the one hand, the introduction of levy strategy constraint gradient corrects the model update formula, which significantly improves the optimization ability of particle swarm algorithm. On the other hand, the lateral constraint of the model is used to improve the optimization efficiency, while improving the lateral continuity of the final design model, laying a solid foundation for engineering application. The improved particle swarm algorithm retains the richness and smoothness of the resonant structure to the maximum extent. Under certain constraints, a broadband absorbing structure is optimized and designed according to the method proposed in this patent, which can achieve broadband absorption at 6 to 18 GHz. This patent opens up a new way for the design of variable thickness three-dimensional absorbing structures, breaking through the technical bottleneck in the design of traditional one-dimensional layered structures. BRIEF DESCRIPTION OF THE DRAWINGS
[0024] Figure 1 is the α-Trimmed model with lateral constraints (n=5, α=0.25).
[0025] Figure 2 It is the wave absorption characteristic curve under different thickness.
[0026] Figure 3 It is the optimization design model result of the improved particle swarm algorithm.
[0027] Figure 4 It is a comparison of the absorption curves of the final model of the traditional particle swarm algorithm and the improved particle swarm algorithm. DETAILED DESCRIPTION
[0028] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below through specific embodiments.
[0029] In view of the problems existing in the prior art, the present invention discloses a method for optimizing the design of variable thickness absorbing materials based on an improved particle swarm algorithm. The method comprises the following steps:
[0030] The actual values of the dielectric loss parameters and magnetic loss parameters of the absorbing material are obtained by using the reflectivity test system;
[0031] Taking the spatial thickness distribution of absorbing materials as the optimization target and the absorbing characteristics of each frequency point in the absorbing frequency band as the fitness function, the thickness parameters of the gridded absorbing materials are optimized based on the improved particle swarm algorithm to obtain the thickness parameters of the absorbing materials that vary with spatial position.
[0032] The theoretical calculation value of the absorptivity is obtained by theoretical simulation of the dielectric loss parameter and the magnetic loss parameter of the absorbing material. The theoretical calculation formula of the absorptivity of the variable thickness absorbing material is as follows:
[0033]
[0034] Where A represents the absorption rate, S 21 represents the transmittance, S 11 Indicates reflectivity.
[0035] Among them, the expression of the fitness function is:
[0036]
[0037] Among them, n is the number of frequency sampling points (referred to as frequency points), A i is the absorption rate at each frequency point.
[0038] The method of optimizing the thickness parameters of the gridded absorbing material based on the improved particle swarm algorithm and obtaining the absorbing characteristics of the absorbing material that vary with frequency by using a joint call of matlab and CST comprises the following steps:
[0039] Step 1: Obtain the absorption frequency band range and select the absorption rates of N frequency points to calculate the fitness function.
[0040] Step 2: Set the optimization parameter values, including the model size and how to segment and refine. Assume that the model thickness parameter dimension after segmentation is D, the number of particle swarm individuals is M, the maximum number of iterations is T, the α-Trimmed filter window width is n, and the trimming parameter is α. Assign P_num=1, M_num=1, k=0. Among them, a particle refers to a single model parameter, and a particle swarm refers to multiple model parameters.
[0041] Step 3: Randomly generate the initial model in the particle swarm algorithm in the model parameter space in Represents model parameters (thickness).
[0042] Step 4: Calculate the fitness of all particles in the P_num model, update the global optimal solution G (i.e., the global optimal particle) of each parameter model according to formulas (3)-(4), and calculate the Euclidean distance between other particles and the global optimal particle.
[0043] The model correction information and thickness parameter formula of the improved particle swarm algorithm are as follows:
[0044]
[0045]
[0046] in, represents the model correction amount (i.e. the amount of thickness correction), represents the model parameters (i.e. thickness), γ 1 and γ 2 are all random numbers in the range [0,1]; ω is the velocity inertia factor; α 1 and α 2 are the individual and social acceleration coefficients respectively. Where i is the particle number, k is the current iteration number, P i and G are the individual optimal solution and the global optimal solution respectively. k represents the weighted parameter in the kth iteration, and w increases with the number of iterations. k Gradually decays from 1 to 0. L is the step length in the levy flight strategy. The individual optimal solution refers to the optimal solution of a single model in the optimization process.
[0047] Step 5: Calculate the Levy flight strategy step length L of the P_num model in turn according to formulas (5)-(8), and update the model correction information and current model of the particle swarm according to formula (3).
[0048] In order to calculate the step length L required in the improved particle swarm algorithm, it is necessary to calculate the Levy distribution. A variety of algorithms can be used to achieve this. Here, the more classic Mantegna algorithm is used to generate a symmetric and stable Levy distribution. The step length L is expressed as follows:
[0049]
[0050] The exponential factor β∈(1,2) is the parameter of the Levy function, which can be used to generate the Levy flight step. At the same time, the standard deviations of U and V are σ u and σ v , and its calculation formula is:
[0051]
[0052] Set the minimum step size L 0 As the threshold parameter, when L>L 0 When the Levy function obeys the above distribution, L 0 Typically the value is from 0.1 to 1.
[0053] Step 6: Carry out the α-Trimmed method to perform lateral constraints on the model, increase the lateral continuity of the variable thickness model, and update all model parameters.
[0054] According to the spatial constraints of the global optimal particles in each model on other particles, the α-Trimmed method is proposed to carry out the lateral model constraints of the global optimal particles of the adjacent models. First, the global optimal particles G corresponding to each model are integrated into an optimal model matrix m D,N , where D is the number of models and N is the number of model parameters. Then, a fixed window width n is selected according to the horizontal constraint scale (number of models), and the matrix data is read using a sliding window. The selected data is sorted from small to large to obtain a new sequence:
[0055] m(1:D,αn+1+j)≤m(1:D,αn+2+j)...≤m(1:D,n-αn+j) (7)
[0056] Where m represents the model, and 1:D represents from the 1st model to the Dth model. Then select the clipping parameter α and cut off the same number of model parameters in the first and second segments of the sequence, and finally take the average value of the remaining model parameters instead of the value of the sliding window center point.
[0057]
[0058] Figure 1 Schematic diagram of lateral constraint of an α-Trimmed model in one embodiment of the present invention, wherein n=5 and α=0.25.
[0059] Step 7: Determine whether the global optimal solution meets the target value or whether the number of iterations reaches the upper limit. If the conditions are met, the optimization ends and the optimal value of the variable thickness design is obtained. If the conditions are not met, continue to modify the model.
[0060] The key points of the present invention are:
[0061] Key point 1: Driven by the improved particle swarm algorithm, the matlab and CST joint calling technology is used to realize the optimal design of variable thickness absorbing materials, breaking the limitation of the absorbing frequency band in the design of traditional one-dimensional single-layer absorbing materials, and realizing the automated design of variable thickness broadband absorbing materials.
[0062] Key point 2: In view of the complexity and multi-solution problems of the optimization design of variable thickness absorbing materials, the levy strategy is used to improve the traditional particle swarm algorithm. After the improvement, the difference between models of the particle swarm algorithm is increased, and the ability to jump out of the local optimal solution is significantly improved. It has a stronger optimization ability and overcomes the disadvantage of low optimization efficiency of the traditional particle swarm algorithm in multi-parameter optimization problems.
[0063] Key point 3: In order to solve the problem of lateral continuity of the model, the a-Trimmed method is proposed as the lateral constraint of the model, which maximizes the richness and smoothness of the resonant structure, is conducive to the realization of broadband absorbing design, overcomes the model discontinuity problem caused by randomness in the traditional particle swarm optimization algorithm, and ensures the structural richness in the design results.
[0064] In one embodiment of the present invention, a dielectric absorber is used to carry out specific simulation work. Figure 2 is the absorptivity diagram of a single-layer microwave absorber. Figure 2 It can be seen from the figure that the absorption bandwidth is relatively limited when the thickness of the layer is fixed. The absorption characteristic curves of the absorber with a thickness from 1mm to 5mm are shown in Figure 2 In the figure, we can see the variation of the central absorption frequency and absorption bandwidth under different thicknesses. Due to the constraints of the Kramers-Kronig relationship, the design upper limit of its broadband bandwidth is strictly limited.
[0065] Taking the unit with a period size of 24mm as an example, the model is divided into a 12×12 network structure, a central symmetric structure is adopted, and the thickness parameters are 36. The initial model is a 4mm thickness model, the number of models is 1200, the optimization target frequency range is 6GHz to 18GHz, the absorption rate exceeds 90%, and the stop condition is set to the fitting residual reaching 10-3 or the fitting error no longer changes.
[0066] Figure 3 It is the optimization design model result of the improved particle swarm algorithm of the present invention. Figure 4 This is a comparison of the absorption curves of the final model of the traditional particle swarm algorithm (PSO) and the improved particle swarm algorithm (MPSO). The final design result achieves ultra-wideband absorption from 5.9GHz to 18GHz. It breaks the constraints of the Kramers-Kronig relationship of the traditional single-layer absorber and expands the upper limit of the effective absorption bandwidth. It provides a new solution for the broadband design of absorbing materials. This technology is suitable for most absorbers at present and has the potential for engineering applications.
[0067] Although the existing gradient algorithms can also complete the design process of variable thickness absorbing materials, such as gradient descent algorithm, conjugate gradient algorithm or quasi-Newton algorithm, etc., which can quickly achieve thickness parameter optimization design, the design results are heavily dependent on the initial model and parameter settings, and designers need to have sufficient knowledge reserves to get a better result. In short, the existing gradient algorithms are not suitable for solving complex and multi-solution problems, and are prone to fall into local optimal solutions.
[0068] The specific embodiments of the present invention disclosed above are intended to help understand the content of the present invention and implement it accordingly. It can be understood by those skilled in the art that various replacements, changes and modifications are possible without departing from the spirit and scope of the present invention. The present invention should not be limited to the contents disclosed in the embodiments of this specification, and the scope of protection of the present invention shall be subject to the scope defined in the claims.
Claims
1. A performance optimization design method for variable thickness absorbing materials based on improved particle swarm algorithm, characterized in that: The following steps are involved: Obtaining actual values of dielectric loss parameters and magnetic loss parameters of the absorbing material; Taking the spatial thickness distribution of absorbing materials as the optimization target and the absorbing characteristics of each frequency point in the absorbing frequency band as the fitness function, the thickness parameters of the gridded absorbing materials are optimized based on the improved particle swarm algorithm to obtain the thickness parameters of the absorbing materials that vary with spatial position.
2. The method according to claim 1, characterized in that The actual values of the dielectric loss parameter and the magnetic loss parameter of the absorbing material are obtained by using a reflectivity testing system.
3. The method according to claim 1, characterized in that The expression of the fitness function is: Where n is the frequency number, A i is the absorption rate at each frequency point.
4. The method according to claim 1, characterized in that: The improved particle swarm algorithm uses a joint call of matlab and CST to obtain the wave absorbing characteristics of the wave absorbing material that vary with frequency.
5. The method according to claim 1, characterized in that The improved particle swarm algorithm comprises the following steps: Step 1: Obtain the absorption frequency band range and select the absorption rates of N frequency points to calculate the fitness function; Step 2: Set the optimization parameter values, including the model size and how to segment and refine. Assume that the thickness parameter dimension of the segmented model is D, the number of particle swarm individuals is M, the maximum number of iterations is T, the α-Trimmed filter window width is n and the trimming parameter is α, assign P_num=1, M_num=1, k=0, where a particle refers to a single model parameter and a particle swarm refers to multiple model parameters; Step 3: Randomly generate the initial model in the particle swarm algorithm in the model parameter space i∈[1,M], where represents the model parameter, i.e., thickness; Step 4: Calculate the fitness of all particles in the P_num model, update the global optimal solution G of each parameter model, and calculate the Euclidean distance between other particles and the global optimal solution; Step 5: Calculate the Levy flight strategy step length L of the P_num point in turn, and update the model correction information and current model of the particle swarm; Step 6: Carry out the α-Trimmed method to perform lateral constraints on the model, increase the lateral continuity of the variable thickness model, and update all model parameters. Step 7: Determine whether the global optimal solution meets the target value or whether the number of iterations reaches the upper limit. If the conditions are met, the optimization ends and the optimal value of the variable thickness design is obtained. If the conditions are not met, continue to modify the model.
6. The method according to claim 6, characterized in that: Step 4 updates the global optimal solution G of each parameter model according to the following formula: in, Indicates the model correction amount, that is, the amount of thickness correction; represents the model parameter, i.e., thickness; γ1 and γ2 are both random numbers in the range [0,1]; ω is the velocity inertia factor; α1 and α2 are the individual and social acceleration coefficients, respectively; i is the particle number, k is the current number of iterations, P i and G are the individual optimal solution and the global optimal solution respectively; w k represents the weighted parameter in the kth iteration, and w increases with the number of iterations. k Gradually decays from 1 to 0; L is the step length in the levy flight strategy.
7. The method according to claim 6, characterized in that Step 5: Calculate the Levy flight strategy step length L according to the following formula: The exponential factor β∈(1,2) is the parameter of the Levy function, and the standard deviations of U and V are σ u and σ v , and its calculation formula is: