Method for determining coating area of wave-absorbing material cone structure based on multi-objective optimization

Abstract

The application discloses a method for determining a coating area of a wave-absorbing material cone structure based on multi-target optimization, and comprises the following steps: collecting geometric parameters and material attribute parameters of the cone structure through a data acquisition terminal; establishing an axial layered three-dimensional model of the cone structure through a modeling terminal; performing curvature self-adaptive unstructured tetrahedral mesh division on each layer through a mesh division terminal; dynamically optimizing a grid unit by calculating the curvature of a grid vertex; calculating electromagnetic response data of each grid unit in a target frequency band through a data analysis terminal by using a finite difference time domain method; iteratively searching a solution space while optimizing electromagnetic performance and economy by using a non-dominated sorting genetic algorithm with an elitist strategy through an optimization decision terminal, and outputting a Pareto front solution; and calculating a comprehensive evaluation value of each Pareto solution according to a preset weight coefficient, selecting a highest value scheme to generate a coating area coordinate mapping table, and solving the triangular contradiction of "precision-efficiency-cost" in coating of the cone structure wave-absorbing material.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of coating area optimization, and specifically discloses a method for determining a coating area of a wave-absorbing material conical structure based on multi-objective optimization. BACKGROUND

[0002] The conical structure is widely applied in the fields of aerospace, radar stealth and electronic countermeasure, and the special geometric shape thereof can effectively reduce the scattering intensity of electromagnetic waves. In order to improve the stealth performance of the conical body, a wave-absorbing material is often coated on the surface. However, the prior art has the following defects:

[0003] 1. The traditional method is to uniformly coat the whole area, which leads to excessive use of high-cost coating materials in low electromagnetic sensitive areas, and low material utilization rate.

[0004] 2. Simple partition coating relies on experience rules and does not quantify local electromagnetic characteristics, so it is difficult to accurately locate high scattering areas, resulting in insufficient coverage or redundancy in key areas.

[0005] 3. The curvature change of the conical body leads to highly non-uniform electromagnetic field distribution. The existing grid division method is not adaptive to the curvature characteristics, and calculation errors are easily generated in the curvature mutation area, affecting the reliability of the coating decision.

[0006] Therefore, it is necessary to invent a method for determining a coating area of a wave-absorbing material conical structure based on multi-objective optimization to solve the above problems. SUMMARY

[0007] In order to overcome the defects of the prior art, the application provides a method for determining a coating area of a wave-absorbing material conical structure based on multi-objective optimization. The geometric parameters and material attribute parameters of the conical structure are collected by a data acquisition terminal. An axial layered three-dimensional model of the conical structure is established by a modeling terminal. The curvature of each layer is adaptively divided into unstructured tetrahedral grids by a grid division terminal. The grid vertex curvature is calculated to dynamically optimize the grid elements. The electromagnetic response data of each grid element in the target frequency band is calculated by a data analysis terminal using the finite difference time domain method. The non-dominated sorting genetic algorithm with elitist strategy is used by an optimization decision terminal to iteratively search the solution space, simultaneously optimizing the electromagnetic performance and economy, and outputting the Pareto frontier solution. The comprehensive evaluation value of each Pareto solution is calculated according to the preset weight coefficient, the highest value scheme is selected to generate a coating area coordinate mapping table, and the problems mentioned in the background technology are effectively solved.

[0008] To achieve the above purpose, the application provides the following technical scheme: a method for determining a coating area of a wave-absorbing material conical structure based on multi-objective optimization, comprising a data acquisition terminal, a modeling terminal, a grid division terminal, a data analysis terminal and an optimization decision terminal, specifically comprising the following steps:

[0009] S1, a data acquisition terminal acquires geometric parameters and material attribute parameters of the conical structure;

[0010] S2, a modeling terminal establishes an axial layered three-dimensional model of the conical structure in combination with the geometric parameters and the material attribute parameters;

[0011] S3, a meshing terminal performs curvature-adaptive meshing on each layer of the three-dimensional model, and divides each layer of the three-dimensional model into a plurality of mesh units;

[0012] S4, a data analysis terminal calculates electromagnetic response data of each mesh unit in a target frequency band [f min ,f max ] based on a finite-difference time-domain method;

[0013] S5, an optimization decision terminal adopts a non-dominated sorting genetic algorithm with elitism, takes the electromagnetic response data as a boundary condition, and iteratively searches a solution space through genetic operations of a crossover rate P c and a mutation rate P m , terminates iteration when a difference between optimal solutions of 20 consecutive generations is less than 1%, and outputs a Pareto front solution;

[0014] S6, a comprehensive evaluation value of each Pareto front solution is calculated according to a preset weight coefficient, and a solution with the highest comprehensive evaluation value is selected to generate a coating area coordinate mapping table.

[0015] Preferably, the geometric parameters include a cone angle θ, a height H, and a base radius R; the material attribute parameters include a complex permittivity ε r and a complex permeability μ r ; and the electromagnetic response data includes unit reflectivity, local electric field intensity distribution, and energy loss density.

[0016] Preferably, the modeling terminal establishes an axial layered three-dimensional model of the conical structure in the following process: a cylindrical coordinate system is established with a vertex of the cone as an origin; the cone is cut along a Z-axis direction at a step length of Δh, and the cone is divided into N layers.

[0017] Preferably, the meshing terminal performs curvature-adaptive meshing on each layer of the three-dimensional model in the following process: an initial mesh size is set based on a minimum wavelength of the target frequency band, each layer of the structure is divided into unstructured tetrahedral mesh units; a curvature a at a vertex of each mesh unit is calculated, and adaptive optimization is performed on all mesh units based on the curvature.

[0018] Preferably, the adaptive optimization is performed in the following specific manner:

[0019] A1, a local curvature radius r is calculated according to the curvature a at the vertex of the mesh unit, and if a side length L of the mesh unit is greater than β × r, the mesh unit is marked for refinement;

[0020] A2, binary refinement is performed on the grid cell to be marked, and the radius of curvature of the newly generated grid cell is recalculated;

[0021] A3, iteratively perform steps A1-A2 until all cells meet L < β × r or the maximum number of iterations n is reached max .

[0022] Preferably, the λ min is the free space wavelength corresponding to the highest frequency of the frequency band, λ min = c / f max , β is the curvature resolution factor, which is set according to the curvature size, and the value range is β ∈ [0.1, 0.2].

[0023] Preferably, the process of iteratively searching the solution space using genetic operations is:

[0024] B1, the coating state of each grid cell of the conical structure surface is binary coded: 1 represents that the cell needs to be coated with a wave-absorbing material, and 0 represents that it is not coated;

[0025] B2, randomly generate M initial individuals, each individual represents a possible coating scheme, and the binary value of the grid cell of each individual is determined by uniform distribution random;

[0026] B3, the electromagnetic performance and economy of each initial individual are evaluated, the average reflectivity integral value F1 of the coating scheme in the target frequency band is calculated, and the total area F2 of all grid cells marked as 1 is counted;

[0027] B4, randomly select m initial individuals to form a competition group each time, select the individual with the best fitness through tournament selection to enter the mating pool, and perform M times in total to obtain M parent chromosomes;

[0028] B5, randomly pair the individuals in the mating pool two by two, randomly generate two crossover points for each parent chromosome, exchange the binary values of the grid cells between the two crossover points, and the exchange probability is P c , obtain two child chromosomes, independently judge each grid cell of each child chromosome, change the binary value of the grid cell, and the change probability is P m ;

[0029] B6, combine the parent and child chromosomes, select M individuals as new generation parent chromosomes, continue to perform steps B3-B6, and continuously record the change rate for 20 generations, until the change rate is less than 1% continuously, and the iteration is terminated.

[0030] Preferably, the calculation formula of the average reflectivity integral value F1 is: In the formula, f min and f maxrespectively, are the lower and upper limit frequencies of the target frequency band, R avg (f) represents the average reflectivity of the cone surface at frequency f; the total area F2 of the grid cells is calculated by: In the formula, S i is the area of the i-th grid cell, x i is the binary value of the i-th grid cell.

[0031] Preferably, the calculation formula of the comprehensive evaluation value is: In the formula, V k is the comprehensive evaluation value of the k-th scheme, F 1k and F 2k are the evaluation values of the electromagnetic performance and economic evaluation in the k-th scheme, F 1min and F 1max are the minimum and maximum values of the evaluation values of the electromagnetic performance evaluation in the Pareto frontier solution, F 2min and F 2max are the minimum and maximum values of the evaluation values of the economic evaluation in the Pareto frontier solution, and w1 and w2 are weight coefficients determined according to the multi-objective optimization requirements.

[0032] Technical effects and advantages of the present application:

[0033] 1. The cone is layered along the Z-axis, combined with curvature-driven grid optimization, to ensure that the grid in the high-curvature area is encrypted, and to improve the calculation accuracy of the electric field strength distribution.

[0034] 2. The non-dominated sorting genetic algorithm with elitist strategy is used as the core to simultaneously optimize the reflectivity integral value and the material consumption, and output the Pareto optimal solution set to balance performance and cost.

[0035] 3. The grid cell binary coding dynamically identifies the coating area, and the weight coefficient is used to output the optimal coating coordinate mapping table to improve the material utilization efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0036] The present application is further illustrated by the accompanying drawings, but the embodiments in the drawings do not constitute any limitation on the present application. For ordinary skilled in the art, other drawings can be obtained without creative labor on the basis of the following drawings.

[0037] Figure 1 is a schematic diagram of the overall structure of the present application.

[0038] Figure 2 is a schematic diagram of the overall steps of the present application. DETAILED DESCRIPTION

[0039] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0040] The present application provides a method for determining a coating area of a wave-absorbing material cone structure based on multi-objective optimization, as shown in the formula: Figure 1 The method comprises a data acquisition terminal, a modeling terminal, a mesh division terminal, a data analysis terminal and an optimization decision terminal.

[0041] The present application will be described in detail below with reference to the drawings. Figure 2 The present application specifically comprises the following steps:

[0042] S1. The data acquisition terminal acquires geometric parameters and material attribute parameters of the cone structure.

[0043] Further, in the above technical solution, the geometric parameters include a cone angle θ, a height H and a base radius R; the material attribute parameters include a complex permittivity ε r and a complex permeability μ r .

[0044] S2. The modeling terminal establishes an axial layered three-dimensional model of the cone structure in combination with the geometric parameters and the material attribute parameters.

[0045] Further, in the above technical solution, the process of the modeling terminal for establishing the axial layered three-dimensional model of the cone structure is as follows: the modeling terminal establishes a cylindrical coordinate system with the apex of the cone as the origin; the cone is cut along the Z-axis direction with Δh as the step length, and the cone is divided into N layers.

[0046] It should be further explained that the determination of the number of layers is based on the height H and the free space wavelength λ min corresponding to the highest frequency of the target frequency band, and the calculation formula is N=8H / λ min , and the calculation result is rounded up, and the step length Δh=H / N.

[0047] S3. The mesh division terminal performs curvature adaptive mesh division on each layer of the three-dimensional model, and divides each layer of the three-dimensional model into a plurality of mesh units.

[0048] Further, in the technical scheme, the process that the grid division terminal performs curvature adaptive grid division on each layer structure of the three-dimensional model comprises: setting an initial grid size based on a minimum wavelength of a target frequency band, dividing each layer structure into unstructured tetrahedral grid units; calculating a curvature a at a vertex of each grid unit, and performing adaptive optimization on all grid units based on the curvature.

[0049] It should be further explained that the initial grid size is set in the following manner: λ min / 5.

[0050] Further, in the technical scheme, the adaptive optimization is performed in the following manner:

[0051] A1, calculating a local curvature radius r based on the curvature a at the vertex of the grid unit, and if a length L of the grid unit is greater than β×r, marking the grid unit as needing to be refined;

[0052] A2, performing two-part encryption on the grid unit marked as needing to be refined, and recalculating the curvature radius of the newly generated grid unit;

[0053] A3, iteratively performing steps A1-A2 until all units satisfy L<β×r or a maximum iteration number n max is reached.

[0054] In the preferred technical scheme of the present application, the maximum iteration number n max =5.

[0055] Further, in the technical scheme, the λ min is a free space wavelength corresponding to a highest frequency of the frequency band, the λ min =c / f max , and β is a curvature resolution factor, which is set according to the curvature size and has a value range of β∈[0.1, 0.2].

[0056] S4, the data analysis terminal calculates electromagnetic response data of each grid unit in a target frequency band [f min , f max ] based on a finite difference time domain method.

[0057] Further, in the technical scheme, the electromagnetic response data comprises unit reflectivity, local electric field intensity distribution and energy loss density.

[0058] It should be further explained that, in the embodiment, the target frequency band is [2, 18] GHz.

[0059] It should be further explained that the electromagnetic response data is calculated in the following manner: a plane wave excitation is applied to each grid unit, an incident direction is along an axis of the cone, a Gaussian pulse is set as an excitation waveform, and the target frequency band [f minf max ] is solved by discretization with finite-difference time-domain method: The electric field intensity distribution E(x, y, z, t) of each time step and the magnetic field intensity distribution H(x, y, z, t) of each time step are obtained, and then the electromagnetic response data is calculated according to the formula

[0060] In the formula, E is an electric field intensity vector, H is a magnetic field intensity vector, t is time, denotes the curl of the electric field intensity vector E, and is a key differential operator for describing the spatial variation characteristics of the electric field, denotes the curl of the magnetic field intensity vector H.

[0061] Further, in the formula, μ0 is the magnetic permeability of vacuum, ε0 is the dielectric constant of vacuum, μ r is the complex relative magnetic permeability, ε r is the complex relative dielectric constant, σ is the conductivity, E i is the incident field amplitude, ω is the angular frequency, and Im(x) denotes the imaginary part of the complex number x.

[0062] S5, the optimization decision terminal adopts a non-dominated sorting genetic algorithm with an elitist strategy, takes the electromagnetic response data as a boundary condition, and iteratively searches the solution space through genetic operations of a crossover rate P c and a mutation rate P m , terminates the iteration when the optimal solution difference is less than 1% for 20 consecutive generations, and outputs the Pareto frontier solution;

[0063] Further, in the above technical solution, the process of iteratively searching the solution space through genetic operations is:

[0064] B1, the coating state of each grid element of the conical structure surface is binary coded: 1 indicates that the element needs to be coated with a wave-absorbing material, and 0 indicates that it is not coated;

[0065] B2, M initial individuals are randomly generated, each individual represents a possible coating scheme, and the binary values of the grid elements of each individual are determined by uniform distribution randomization;

[0066] It should be further pointed out that after the initial individuals are generated, the grid elements are numbered in the order from top to bottom, and an index table of the individuals is established according to the numbering, including grid element number, individual index, grid element binary value, grid element area and layer index.

[0067] B3, the electromagnetic performance and economic efficiency of each initial individual are evaluated, the average reflectivity integral value F1 of the coating scheme in the target frequency band is calculated, and the total area F2 of all grid elements marked as 1 is counted;

[0068] ​B4, randomly select m initial individuals each time to form a competition group, select the individual with the optimal fitness through the tournament selection to enter the mating pool, perform M times, and obtain M parent chromosomes;

[0069] It should be further explained that the layer indexes of the selected initial individuals are the same, and in the preferred technical solution of the present application, m=4 and M=200.

[0070] B5, randomly pair the individuals in the mating pool two by two, randomly generate two crossover points for each parent chromosome, exchange the binary values of the grid cells between the two crossover points, and the exchange probability is P c , obtain two child chromosomes, independently determine each grid cell of each child chromosome, change the binary value of the grid cell, and the change probability is P m .

[0071] In the preferred technical solution of the present application, P c =0.85 and P m =0.08.

[0072] B6, combine the parent and child to select M individuals as new generation parent chromosomes, continue to perform steps B3-B6, and continuously record the change rate of 20 generations until the iteration is terminated when the change rate is continuously less than 1%.

[0073] Further, in the above technical solution, the calculation formula of the average reflectivity integral value F1 is: In the formula, f min and f max are the lower and upper frequencies of the target frequency band, respectively, R avg (f) represents the average reflectivity of the surface of the cone at a frequency of f; and the calculation formula of the total area F2 of the grid cells is: In the formula, S i is the area of the i-th grid cell, and x i is the binary value of the i-th grid cell.

[0074] S6, calculate the comprehensive evaluation value of each Pareto front solution according to the preset weight coefficient, and select the solution with the highest comprehensive evaluation value to generate a coating area coordinate mapping table.

[0075] Further, in the above technical solution, the calculation formula of the comprehensive evaluation value is: In the formula, V k is the comprehensive evaluation value of the k-th scheme, F 1k and F 2k are the evaluation values of the electromagnetic performance and economic evaluation in the k-th scheme, respectively, F 1min and F 1maxMin and Max of the evaluation value of the electromagnetic performance evaluation in the Pareto frontier solution, F 2min and F 2max Min and Max of the evaluation value of the economic evaluation in the Pareto frontier solution, w1 and w2 are weight coefficients, which are determined according to the multi-objective optimization requirement.

[0076] Finally, it should be noted that: the above only for the preferred embodiments of the present application, and not for the purpose of limiting the present application, although the foregoing detailed description of the present application has been made with reference to the foregoing embodiments, for those skilled in the art, it still can be modified, or part of the technical features of the equivalent replacement, within the spirit and principles of the present application, any modification, equivalent replacement, improvement, etc., should be included within the scope of the present application.

Claims

1. A method for determining the coating region of a cone-shaped structure for absorbing materials based on multi-objective optimization, characterized in that, It includes a data acquisition terminal, a modeling terminal, a grid generation terminal, a data analysis terminal, and an optimization decision-making terminal, and specifically includes the following steps: S1. The data acquisition terminal acquires the geometric parameters and material property parameters of the conical structure; S2. The modeling terminal combines geometric parameters and material property parameters to establish an axially layered three-dimensional model of the conical structure; S3. The mesh generation terminal performs curvature adaptive mesh generation on each layer of the 3D model, dividing each layer of the 3D model into multiple mesh units. S4. The data analysis terminal calculates the frequency of each grid cell in the target frequency band [f] based on the finite-difference time-domain method. min ,f max Electromagnetic response data; S5. The optimized decision-making terminal employs a non-dominated sorting genetic algorithm with an elitist strategy, using electromagnetic response data as boundary conditions and a crossover rate P. c Variation rate P m The genetic operation iteratively searches the solution space. The iteration terminates when the difference between the optimal solutions for 20 consecutive generations is <1%, and the Pareto front solution is output. S6. Calculate the comprehensive evaluation value of each Pareto front solution according to the preset weight coefficients, and select the solution with the highest comprehensive evaluation value to generate the coating area coordinate mapping table.

2. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 1, characterized in that: The geometric parameters include the cone angle θ, height H, and base radius R; the material property parameters include the complex permittivity ε. r and complex permeability μ r The electromagnetic response data includes unit reflectivity, local electric field intensity distribution, and energy loss density.

3. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 1, characterized in that: The process of establishing an axially layered three-dimensional model of the cone structure by the modeling terminal is as follows: a cylindrical coordinate system is established with the cone vertex as the origin; the cone is cut along the Z-axis with a step size of Δh, and the cone is divided into N layers.

4. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 1, characterized in that: The process of the mesh generation terminal performing curvature adaptive mesh generation for each layer of the 3D model is as follows: the initial mesh size is set based on the minimum wavelength of the target frequency band, and each layer of the structure is divided into unstructured tetrahedral mesh units; Calculate the curvature 'a' at the vertex of each mesh element, and perform adaptive optimization on all mesh elements based on the curvature.

5. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 4, characterized in that: The specific method of adaptive optimization is as follows: A1. Calculate the local radius of curvature r based on the curvature a at the vertex of the mesh cell. If the side length L of the mesh cell is greater than β×r, then mark the mesh cell as needing to be refined. A2. Perform binary search on the marked mesh cells that need refinement, and recalculate the radius of curvature of the newly generated mesh cells; A3. Iterate through steps A1-A2 until all units satisfy L < β × r or the maximum number of iterations n is reached. max .

6. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 5, characterized in that: The λ min λ is the free-space wavelength corresponding to the highest frequency in the frequency band. min =c / f max β is the curvature resolution factor, which is set according to the curvature and takes values ​​in the range [0.1, 0.2].

7. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 1, characterized in that: The process of iteratively searching the solution space using genetic operations is as follows: B1. Encode the coating status of each grid cell on the surface of the conical structure in binary form: use 1 to indicate that the cell needs to be coated with absorbing material, and 0 to indicate that it is not coated. B2. Randomly generate M initial individuals, each representing a possible coating scheme. The binary value of the grid cell of each individual is randomly determined by a uniform distribution. B3. Evaluate the electromagnetic performance and economic efficiency of each initial individual, calculate the average reflectivity integral value F1 of the coating scheme in the target frequency band, and count the total area F2 of all grid cells marked as 1. B4. Each time, m initial individuals are randomly selected to form a competition group. The individual with the best fitness is selected through a tournament to enter the mating pool. This process is repeated M times to obtain M parent chromosomes. B5. Randomly pair individuals in the mating pool. For each parent chromosome, randomly generate two crossover points and exchange the binary values ​​of the grid cells between the two crossover points. The exchange probability is P. c Two offspring chromosomes are obtained. Each grid cell of each offspring chromosome is independently evaluated, and the binary value of the grid cell is changed with a probability of P. m ; B6. Merge the parent and offspring generations, select M individuals as the new generation of parent chromosomes, and continue to execute steps B3-B6. Record the change rate for 20 generations continuously until the change rate is consistently less than 1%, at which point the iteration is terminated.

8. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 7, characterized in that: The formula for calculating the integral value of average reflectivity F1 is as follows: In the formula f min and f max These are the lower and upper frequency limits of the target frequency band, respectively. avg (f) represents the average reflectivity of the cone surface at frequency f; the formula for calculating the total area F2 of the grid cells is: In the formula, S i Let x be the area of ​​the i-th grid cell. i It is the binary value of the i-th grid cell.

9. The method for determining the coating area of ​​a cone-shaped structure of absorbing material based on multi-objective optimization as described in claim 1, characterized in that: The formula for calculating the comprehensive evaluation value is as follows: V in the formula k Let F be the comprehensive evaluation value of the k-th scheme. 1k and F 2k These are the evaluation values ​​of electromagnetic performance and economic efficiency for the k-th scheme, respectively, F. 1min and F 1max These are the minimum and maximum values ​​of the electromagnetic performance evaluation values ​​in the Pareto front solution, respectively, F. 2min and F 2max These are the minimum and maximum values ​​of the economic evaluation in the Pareto front solution, respectively. w1 and w2 are weighting coefficients, determined according to the multi-objective optimization requirements.

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