Graphene nanocomposite foam electromagnetic shielding multi-objective optimization model and application

Abstract

The application discloses a graphene nanocomposite foam material electromagnetic shielding multi-objective optimization model and application thereof. The model combines a graphene nanocomposite foam material electromagnetic constitutive model and a non-dominated sorting genetic algorithm, carries out multi-objective optimization calculation on high electromagnetic shielding efficiency and low cost, mainly considers the interactive influence of microstructure parameters such as a graphene mass fraction, material porosity and sample thickness on the electromagnetic shielding efficiency and cost, and optimizes the microstructure parameters to improve the electromagnetic shielding efficiency of the material and reduce the cost. The model can be applied to determining the minimum parameter of graphene in the graphene nanocomposite foam material, and has guiding significance for microstructure parameter design of a high-efficiency electromagnetic shielding device.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization model, specifically to a multi-objective optimization model and its application for electromagnetic shielding of graphene nanocomposite foam, belonging to the field of multi-objective optimization technology. Background Technology

[0002] Driven by the dual demands of controlling severe electromagnetic pollution and minimizing economic costs, high-efficiency electromagnetic shielding devices with high shielding effectiveness and low cost have attracted significant attention in modern industry. They have been widely applied in civilian and military fields, including electronic communications and precision measurement. Single-phase low-dimensional functional materials such as graphene or carbon nanotubes possess excellent electrical properties, but are difficult to directly use in production, thus failing to meet practical needs. Research has found that combining low-dimensional functional materials with porous polymer matrices can yield nanocomposite foam materials with superior performance, ensuring the excellent electrical properties of the low-dimensional functional materials while incorporating the good elastoplastic mechanical properties of the porous polymer matrix. Graphene or carbon nanotube-reinforced nanocomposite foam materials have been widely reported due to their excellent electromagnetic shielding effectiveness.

[0003] Furthermore, the manufacturing cost of electromagnetic shielding materials plays a crucial role in practical applications. The price of graphene is significantly higher than that of polymer matrices, necessitating a consideration of cost while pursuing high electromagnetic shielding effectiveness. High-efficiency electromagnetic shielding materials urgently need to overcome cost constraints to achieve high-performance, low-cost shielding. Therefore, electromagnetic shielding performance and cost are key to the design of graphene nanocomposite foam materials. However, microstructure parameters have varying impacts on the electromagnetic shielding effectiveness and cost of carbon-reinforced nanocomposites, making multi-objective optimization design for efficient electromagnetic shielding behavior essential. Microstructure parameters such as graphene mass fraction, porosity, and sample thickness have a significant influence on high-efficiency electromagnetic shielding materials. A set of optimal microstructure parameters for graphene nanocomposite foam materials is urgently needed to achieve both high electromagnetic shielding effectiveness and low cost. Summary of the Invention

[0004] To address the problems existing in the prior art, the first objective of this invention is to provide a multi-objective optimization model for electromagnetic shielding of graphene nanocomposite foam. This model optimizes the electromagnetic constitutive model of the effective electromagnetic shielding performance of low-dimensional nanocomposite foam materials by considering the effective medium approximation of functional interface effects, establishing a two-scale electromagnetic constitutive model for both shielding effectiveness and cost. Utilizing crowding distance and an elitist strategy, a multi-objective optimization model based on a non-dominated sorting genetic algorithm is established to address the requirements of high electromagnetic shielding effectiveness and low cost for graphene nanocomposite foam materials. This model is simple, easy to operate, and significantly improves the optimization effect, substantially reducing the preparation cost while ensuring electromagnetic shielding effectiveness.

[0005] The second objective of this invention is to provide an application of a multi-objective optimization model for electromagnetic shielding of graphene nanocomposite foam, used to determine the minimum parameter of graphene in graphene nanocomposite foam materials. The multi-objective optimization model provided by this invention utilizes a non-dominated sorting genetic algorithm to optimize the competitive relationship between electromagnetic shielding effectiveness and material cost of graphene nanocomposite foam materials from the perspective of microstructure parameters. It adjusts the microstructure material parameters to seek a compromise between high electromagnetic shielding and low cost. Testing shows that, under the same electromagnetic shielding effectiveness, the cost reduction can reach 76%; under the same cost, the electromagnetic shielding effectiveness improvement can reach 78%, and the overall effectiveness-cost improvement rate can reach 405%.

[0006] To achieve the above technical objectives, this invention provides a multi-objective optimization model for electromagnetic shielding of graphene nanocomposite foam materials, characterized by the following steps: 1) obtaining characteristic parameters of graphene nanocomposite foam materials; 2) establishing a dual-scale constitutive model for electromagnetic shielding and cost of graphene nanocomposite foam materials based on the characteristic parameters; 3) establishing a multi-objective optimization model based on the dual-scale constitutive model; and 4) testing and correcting the multi-objective optimization model.

[0007] The multi-optimization model provided by this invention establishes a dual-scale electromagnetic constitutive model of electromagnetic shielding effectiveness and cost, and uses a non-dominated sorting genetic algorithm to optimize the competitive relationship between electromagnetic shielding effectiveness and material cost of graphene nanocomposite foam materials from the perspective of microstructure parameters. By adjusting the microstructure material parameters, the optimal solution between high electromagnetic shielding effectiveness and low cost is sought, thereby achieving a significant improvement in overall effectiveness-cost.

[0008] As a preferred embodiment, the characteristic parameters of the graphene nanocomposite foam material include: graphene aspect ratio α, graphene thickness λ, interface layer thickness d, distance r between the electromagnetic wave source and the graphene nanocomposite foam material, angular frequency ω of the electromagnetic wave, in-plane conductivity σ1, dielectric constant ε1, and permeability μ1 of graphene, out-of-plane conductivity σ3, dielectric constant ε3, and permeability μ3 of graphene, conductivity σ0, dielectric constant ε0, and permeability μ0 of the polymer, and graphene ρ. g and the mass density ρ of the polymer m Conductivity in vacuum σ v Dielectric constant ε v and permeability μ v The unit price of graphene is p g and polymer unit price p m .

[0009] As a preferred embodiment, the characteristic parameters of the graphene nanocomposite foam material also include: the conductivity of the original interface. Dielectric constant magnetic permeability μ(int) tunneling effect scaling parameter γ σ Maxwell polarization scaling parameter γ ε .

[0010] As a preferred embodiment, the process for establishing the dual-scale constitutive model for electromagnetic shielding and cost of the graphene nanofoam composite material is as follows:

[0011] 1) Establish the graphene mass fraction (wt%) and material porosity (c) v A correlation model between sample thickness h and electromagnetic shielding effectiveness;

[0012] 2) Establish the graphene mass fraction (wt%) and material porosity (c). v A correlation model between sample thickness h and cost.

[0013] As a preferred embodiment, the process for establishing the correlation model of electromagnetic shielding effectiveness is as follows:

[0014]

[0015]

[0016]

[0017] Formula 4: S 33 =1-2S 11 ;

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Equation 15: Z w=1 / (ωε) v r);

[0030]

[0031] Equation 17: SE(c v ,h,wt%)=R dB +A dB +M dB ;

[0032] In equations 1 to 17: c g The value represents the volume fraction of graphene, which is dimensionless. S represents the micropore volume concentration in polymer foam, dimensionless; 11 and S 33 It is a depolarization tensor, which is dimensionless; The seepage threshold is dimensionless. For resistance function; σ is the Cauchy cumulative function; (int) ε is the interfacial conductivity after tunneling effect and Maxwell polarization, with dimensions (S / m); (int) c is the dielectric constant after tunneling effect and Maxwell polarization, with dimensions (F / m); int The interfacial volume concentration of the coated graphene is dimensionless. The electrical conductivity, dielectric constant, and magnetic permeability of the coated graphene with functional interface effects are expressed in units of (S / m), (F / m), and (N / A), respectively. 2 );χ f The electrical conductivity, dielectric constant, and magnetic permeability of the polymer foam are given by (S / m), (F / m), and (N / A), respectively. 2 );χ e The electrical conductivity, dielectric constant, and magnetic permeability of the graphene nanocomposite foam material are given in units of (S / m), (F / m), and (N / A), respectively. 2 );σ e ε represents the electrical conductivity of the graphene nanocomposite foam material, with dimensions in (S / m); e The dielectric constant of the graphene nanocomposite foam material is given by dimensions (F / m); μ e The dimensionless permeability of graphene nanocomposite foam material is expressed in N / A. 2 j is an imaginary constant, dimensionless; γ e β v η e and η v Intermediate process parameters, dimensionless; R dB Electromagnetic shielding reflection loss, in dB; A dB The absorption loss is expressed in dB; M dB The loss due to multiple reflections is expressed in dB.

[0033] The graphene nanocomposite foam material addressed in this invention, at the microscale, features spherical micropores uniformly distributed within the polymer, forming a porous polymer binary composite material. Graphene is surrounded by an ultrathin, imperfect interface layer, forming a coating nanofiller. At the macroscale, the porous polymer and graphene constitute a monolithic binary composite material. Therefore, the dual-scale electromagnetic constitutive model for electromagnetic shielding effectiveness and cost established in this invention fully considers the tunneling effect and Maxwellian polarization, effectively unifying the micro- and macro-scales, and achieving a higher degree of fit with actual conditions.

[0034] As a preferred approach, the process for establishing the cost correlation model is as follows:

[0035] Formula 18: M g =c g hsρ g ;

[0036] Formula 19: M m =(1-c g -c v )hsρ m ;

[0037] Equation 20: COST = M g p g +M m p m ;

[0038] In equations 18-20: M g M represents the mass of graphene, with dimensions in kg. m s is the mass of the polymer, in kg; s is the bottom area of ​​the foam material, in m². 2 ;p g This is the unit price of graphene, with dimensions in dollars per kilogram; p m The unit price of the polymer is expressed in units of $ / kg.

[0039] As a preferred embodiment, the multi-objective optimization model employs a non-dominated sorting genetic algorithm, and its establishment process is as follows:

[0040] 1) Determine the objective function and optimization variables:

[0041]

[0042] Electromagnetic shielding effectiveness and cost are the objective functions, with maximizing electromagnetic shielding effectiveness and minimizing cost as the optimization objectives; graphene mass fraction (wt%) and material porosity (c) are also considered. v The sample thickness h is the optimization variable;

[0043] 2) Determine the parameters of the non-dominated sorting genetic algorithm, including: population size N, maximum number of generations G, and crossover probability η. c Probability of mutation η m ;

[0044] 3) Obtaining the optimal solution set for electromagnetic shielding effectiveness and cost, the process includes:

[0045] a) Using a random algorithm, several sets of micro-parameters are randomly generated within a reasonable parameter range to produce the initial population of the multi-objective algorithm for graphene nanocomposite foam materials; calculate the two objective function values ​​of electromagnetic shielding effectiveness and cost for each individual, and store the micro-parameter values ​​and objective function values ​​in the individual;

[0046] b) Using simulated binary crossover and polynomial mutation operators, crossover and mutation operations are performed on the parent population to generate offspring. The calculation process is as follows:

[0047]

[0048]

[0049]

[0050]

[0051] Equation 26: Q3 = P3 + (P max -P min )δ;

[0052] c) Employ an elite strategy to merge the parent and offspring generations into an intermediate generation; perform non-dominated ranking of the intermediate generation individuals based on the objective function value, dividing them into several non-dominated fronts; calculate the crowding distance of the i-th individual within each non-dominated front, and further rank the individuals based on the crowding distance; select the individuals with higher rankings to enter the next generation. The calculation process for the crowding distance is as follows:

[0053]

[0054] d) Repeat steps b and c until the evolutionary generation calculation reaches the maximum generation G, which is the result;

[0055] In equations 22-27: β is the random algorithm parameter, dimensionless; u is a random number, dimensionless; η c η is the crossover probability, dimensionless; δ is the small perturbation of the random algorithm, dimensionless; m P represents the mutation probability, dimensionless; Q1, Q2, and Q3 are the new offspring individuals, dimensionless; P1, P2, and P3 are the parent individuals, dimensionless; P max and P minThese are the supremum and infimum of the objective function in the parent individual, respectively, and are dimensionless.

[0056] As a preferred embodiment, the population size N is 300.

[0057] As a preferred embodiment, the maximum algebra G is 300.

[0058] As a preferred option, the crossover probability η c It is 0.95.

[0059] As a preferred option, the mutation probability η m It is 0.05.

[0060] High electromagnetic shielding effectiveness and low cost are two important performance indicators of graphene nanocomposite foam materials, and are key parameters for multi-objective optimization algorithms to obtain high-efficiency electromagnetic shielding performance. This invention defines electromagnetic shielding effectiveness (SE) and cost (COST) as objective functions, selecting maximizing electromagnetic shielding effectiveness and minimizing cost as the optimization objectives of this method, and selecting graphene mass fraction (wt%) and porosity (c) as the optimization parameters. v The sample thickness h is used as an optimization variable, and the reasonable optimization range of each optimization variable is determined.

[0061] As a preferred embodiment, the testing process of the multi-objective optimization model is as follows: 1500 individuals are randomly generated within the selectable range of optimization variables, and the two objective function values ​​of electromagnetic shielding effectiveness and cost for each individual are calculated and compared with the obtained Pareto optimal solution set; if the Pareto optimal solution set is a non-dominated solution compared with the random individuals, the correctness of the multi-objective optimization result can be proven.

[0062] As a preferred embodiment, the correction process of the multi-objective optimization model includes: 1) selecting an optimal data point as a reference benchmark based on the test data of the electromagnetic shielding effectiveness of graphene nanocomposite foam material;

[0063] 2) Find the optimal solution in the Pareto optimal solution set that is close to the electromagnetic shielding effectiveness of the optimal data point, and calculate the percentage difference in cost between the optimal solution and the optimal data point.

[0064] 3) Find the optimal solution in the Pareto optimal solution set that is close to the cost of the optimal data point, and calculate the percentage difference between the electromagnetic shielding effectiveness of the optimal solution and the optimal data point.

[0065] 4) Calculate the ratio ρ of electromagnetic shielding effectiveness and cost between the experimental optimal data point and the Pareto optimal solution set. SE =SE / COST, find ρ in the optimal solution set SE Find the optimal solution with the largest value, and calculate the percentage difference between this optimal solution and the optimal data point.

[0066] As a preferred embodiment, the electromagnetic shielding effectiveness test process of the graphene nanocomposite foam material is as follows: the graphene nanocomposite foam sample is placed in a vector network analyzer, and the electromagnetic shielding effectiveness of the sample at different graphene concentrations is measured in a frequency range of 100MHz. The distance r between the electromagnetic wave emission source and the sample is measured or obtained, and the cost of the graphene nanocomposite foam material at different graphene concentrations is obtained.

[0067] The present invention also provides an application of a multi-objective optimization model for electromagnetic shielding of graphene nanocomposite foam materials, used to determine the minimum parameter of graphene in graphene nanocomposite foam materials.

[0068] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0069] 1) The multi-objective optimization model for electromagnetic shielding of graphene nanocomposite foam materials provided in this invention is based on a two-scale electromagnetic constitutive model of graphene-reinforced nanocomposite foam materials to optimize electromagnetic shielding effectiveness and cost. Utilizing crowding distance and elitist strategies, a multi-objective optimization model based on a non-dominated sorting genetic algorithm is established to address the requirements of high electromagnetic shielding effectiveness and low cost for graphene nanocomposite foam materials.

[0070] 2) In the technical solution provided by the present invention, a dual-scale electromagnetic constitutive model of electromagnetic shielding effectiveness and cost is established, and a non-dominated sorting genetic algorithm is used to optimize the competitive relationship between electromagnetic shielding effectiveness and material cost of graphene nanocomposite foam material from the perspective of microstructure parameters. The microstructure material parameters are adjusted to seek the optimal solution between high electromagnetic shielding and low cost, thereby achieving a significant improvement in overall effectiveness-cost.

[0071] 3) In the technical solution provided by this invention, a non-dominated sorting genetic algorithm is used to optimize the competitive relationship between electromagnetic shielding effectiveness and material cost of graphene nanocomposite foam material from the perspective of microstructure parameters. The microstructure material parameters are adjusted to seek a compromise between high electromagnetic shielding and low cost. Tests show that under the same electromagnetic shielding effectiveness, the cost can be reduced by up to 76%; under the same cost, the electromagnetic shielding effectiveness can be improved by up to 78%, and the overall effectiveness-cost improvement rate can reach 405%. Attached Figure Description

[0072] Figure 1 A schematic diagram of a dual-scale homogenization scheme for graphene nanocomposite foam materials;

[0073] Figure 2 A schematic diagram illustrating the electromagnetic shielding effectiveness and cost of graphene nanocomposite foam materials;

[0074] Figure 3Flowchart of a multi-objective optimization method for efficient electromagnetic shielding in graphene nanocomposite foam materials;

[0075] Figure 4 Comparison of optimization results between random point and non-dominated sorting genetic algorithms;

[0076] Figure 5 A comparison of Pareto optimal solution set and experimental data for electromagnetic shielding effectiveness and cost of graphene nanocomposite foam materials.

[0077] Figure 6 Comparison of calculation results between multi-objective non-dominated sorting genetic algorithm and multi-objective particle swarm optimization algorithm for graphene nanocomposite foam materials. Detailed Implementation

[0078] The following specific embodiments are merely detailed explanations of the technical solutions of the present invention. The present invention is not limited to the following embodiments. Those skilled in the art should understand that any improvements or substitutions made based on the above principles and spirit on the basis of the present invention should be within the protection scope of the present invention.

[0079] Example 1

[0080] The following is a complete description of the multi-objective optimization method for electromagnetic shielding effectiveness and cost of the graphene nanocomposite foam material of the present invention, with reference to this embodiment. Specifically, it includes the following steps:

[0081] 1. Obtain the microscopic parameters of each component material.

[0082] Graphene and polydimethylsiloxane were selected as the component materials. The aspect ratio of graphene was measured to be α = 5 × 10⁻⁶. - 5 m, the graphene thickness is λ=8×10 -8 m, density ρ of polydimethylsiloxane m =1200kg / m 3 The density ρ of graphene g =1900kg / m 3 The conductivity of polydimethylsiloxane is σ0 = 2.5 × 10⁻⁶. -13 S / m, dielectric constant ε0=2.38ε v and permeability μ0=μ v The in-plane conductivity of graphene, σ1, is 1.0 × 10⁻⁶. 8 S / m, dielectric constant ε1=15ε v And permeability μ1=1.01μ v The out-of-plane conductivity of graphene is σ³ = 1.0 × 10⁻⁶. 5 S / m, dielectric constant ε3=10ε v And permeability μ3=1.0μ vThe conductivity σ in vacuum is obtained by referring to the table. v =8×10 -15 S / m, vacuum dielectric constant ε v =8.85×10 -12 F / m, permeability μ in vacuum v =4π×10 -7 N / A 2 Research was conducted to obtain the unit price p of graphene. g =133448$ / kg and the unit price p of polydimethylsiloxane m = $148.28 / kg.

[0083] 2. Preparation of graphene nanocomposite foam material samples

[0084] Graphene nanocomposite foam materials with graphene mass fractions of 0.4%, 0.6%, and 0.8% (wt%) were fabricated using graphene and polydimethylsiloxane as raw materials via chemical vapor deposition. The sample thickness was measured to be h = 0.001 μm, and the porosity was c. v =0.937, base area s =0.02m 2 .

[0085] 3. Measurement of electromagnetic shielding experimental data for graphene nanocomposite foam materials

[0086] The electromagnetic shielding effectiveness (SE) of each graphene nanocomposite foam sample was measured in a vector analyzer at an incident electromagnetic wave frequency of f = 100 MHz. Simultaneously, the distance between the field source and the nanocomposite material was measured to be r = 0.01 m. The cost (COST) and ratio (ρ) of each sample were calculated according to formula (4). SE The experimental data obtained are shown in Table 1 below.

[0087] Table 1. Experimental data on electromagnetic shielding and cost of sample materials with different graphene mass fractions.

[0088]

[0089] 4. Determine the remaining parameters of the electromagnetic constitutive model.

[0090] Experimental data from some graphene nanocomposite foam materials were incorporated into the electromagnetic constitutive model established in step one, and the remaining model parameters, including interfacial conductivity, were determined through data fitting. Interfacial relative permittivity Interfacial relative permeability Maxwell polarization scaling parameter γ ε =1×10 -12 tunneling effect scaling parameter γ σ =0.00018.

[0091] 5. Establish a multi-objective optimization model and specify the optimization parameters.

[0092] The optimization objectives are to maximize electromagnetic shielding effectiveness and minimize cost, with the optimization variables being the graphene mass fraction (wt%) and porosity (c). v The sample thickness h is shown in Table 2, and the multi-objective optimization parameters are shown in Table 3. A multi-objective optimization model for the high-efficiency electromagnetic shielding performance of graphene nanocomposite foam materials is established as follows:

[0093]

[0094] Table 2 Range of values ​​for optimization variables

[0095] Variable name Graphene mass fraction wt% <![CDATA[Porosity c v > Sample thickness h (m) Variable range <![CDATA[10 -5 -0.1]]> <![CDATA[10 -5 -0.99]]> <![CDATA[10 -5 -0.01]]>

[0096] Table 3 Parameters of the multi-objective optimization method for graphene nanocomposite foam materials

[0097] Population size, N 300 Maximum Algebra, G 300 <![CDATA[Cross probability, η c > 0.95 <![CDATA[Mutation probability, η m > 0.05

[0098] 6. Conduct multi-objective optimization calculations to obtain the Pareto optimal solution set.

[0099] 1) Initialize the population by randomly generating an initial population of 300 individuals, calculating the electromagnetic shielding effectiveness and cost of each individual, and storing the optimization variable values ​​and objective function values ​​in the individuals.

[0100] 2) Perform crossover and mutation operations on the parent population to generate offspring. Crossover and mutation are performed using the simulated binary crossover operator and the polynomial mutation operator, respectively.

[0101] 3) After generating offspring, an elite strategy is used to merge the parent and offspring generations into an intermediate generation. The intermediate generation is then non-dominated and ranked according to the objective function value, and the crowding distance for each individual is calculated. Individuals with higher rankings are selected to enter the next generation.

[0102] 4) Repeat steps 2) and 3) until the evolutionary generation reaches the maximum generation G = 300. The multi-objective algorithm for graphene nanocomposite foam materials then terminates, obtaining the Pareto optimal solution set for the electromagnetic shielding effectiveness and cost of the graphene nanocomposite foam material. Figure 4 As shown.

[0103] 6. Verify the correctness of the Pareto optimal solution set for graphene nanocomposite foam materials.

[0104] Within the range of selectable optimization variables, 1500 individuals were randomly generated, and the objective function values ​​of electromagnetic shielding effectiveness and cost for each individual were calculated. The results of the randomized individuals were compared with the Pareto optimal solution set. Figure 4As shown, the Pareto optimal solution set is non-dominated compared to the random individual, proving the correctness of the results of this multi-objective optimization method.

[0105] 7. Analyze the results of multi-objective optimization.

[0106] Experimental data 1 is selected as reference point A. In the Pareto optimal solution set, point Q1, with electromagnetic shielding effectiveness similar to point A, and point Q2, with cost similar to point A, are found, along with ρ... SE The data for point P, which has the largest value, is shown in Table 4. Analysis reveals that, under the same electromagnetic shielding effectiveness (31 dB), the cost at point Q1 decreases from $1.68 to $0.40 compared to reference point A, a reduction of 76%. Under the same low cost ($1.68), the electromagnetic shielding effectiveness at point Q2 increases from 31.15 dB to 55.58 dB compared to reference point A, an increase of 78%. At point P, compared to reference point A, the cost from ρ... SE The value increased from 18.54 dB / $ to 93.55 dB / $, an increase of 405%.

[0107] Table 4. Optimal solutions for high electromagnetic shielding effectiveness and low cost in graphene nanocomposite foam materials.

[0108] Optimal solution P <![CDATA[Q1]]> <![CDATA[Q2]]> <![CDATA[Porosity, c v > 0.9945 0.9875 0.9527 Graphene mass fraction, wt% 0.0899 0.0850 0.0854 Sample thickness, h (m) 0.0001 0.0001 0.0001 Cost ($) 0.19 0.40 1.68 Electromagnetic shielding effectiveness (EMI SE, dB) 17.73 30.91 55.58 <![CDATA[Electromagnetic shielding effectiveness / cost, ρ SE (dB / $)]]> 93.55 77.92 32.96

[0109] The above multi-objective optimization results demonstrate that, based on the method of this invention, the electromagnetic shielding effectiveness of graphene nanocomposite foam materials can be improved while reducing costs through optimized calculation of microstructure parameters. This solves the problem of designing microstructure parameters for low-cost, high-efficiency electromagnetic shielding devices under the constraints of severe electromagnetic pollution and limited budget.

[0110] Comparative Example 1

[0111] The multi-objective optimization algorithm of this invention will be described below with reference to the comparative example. By comparing the calculation results of the non-dominated sorting multi-objective optimization algorithm and the particle swarm optimization algorithm of this invention regarding the high-efficiency electromagnetic shielding performance of graphene nanocomposite foam materials, the advantages and disadvantages of the optimization method of this invention will be discussed. The specific steps are as follows:

[0112] 1. The non-dominated sorting multi-objective optimization algorithm and related parameters for the high-efficiency electromagnetic shielding performance of the graphene nanocomposite foam material of this invention have been given in Example 1. The obtained optimal solution set is as follows: Figure 6 The data points are shown in the middle square.

[0113] 2. Combine the electromagnetic model of the graphene nanocomposite foam material established in Step 1 with the particle swarm optimization algorithm to establish a corresponding multi-objective optimization model; wherein, the objective function and optimization variables are the same as in Example 1, and the relevant parameters used in the multi-objective particle swarm optimization process are shown in Table 5 below; carry out multi-objective particle swarm optimization calculations and obtain the optimal solution set of electromagnetic shielding effectiveness and cost, as shown below. Figure 6 The data points are shown in a circular pattern.

[0114] Table 5 shows the optimization parameters used in the multi-objective particle swarm optimization algorithm.

[0115] Population size, N 300 Maximum Algebra, G 300 <![CDATA[Learning factor 1, C1]]> 2 <![CDATA[Learning factor 2, C2]]> 2 <![CDATA[Maximum inertia coefficient, W max > 0.9 <![CDATA[Minimum inertia coefficient, W min > 0.4

[0116] 3. Analyze and compare the optimization results of non-dominated sorting genetic algorithm and multi-objective particle swarm optimization algorithm.

[0117] The results of non-dominated sorting genetic algorithms and multi-objective particle swarm optimization algorithms are compared to, for example Figure 6 As shown, the Pareto solution set trends of the non-dominated sorting genetic algorithm and the multi-objective particle swarm optimization algorithm are consistent, indicating a competitive relationship between electromagnetic shielding effectiveness and cost. This further verifies the correctness of the multi-objective optimization algorithm described in this paper. Furthermore, the multi-objective particle swarm optimization algorithm performs poorly in maintaining population diversity. Compared to the multi-objective particle swarm optimization algorithm, the non-dominated sorting genetic algorithm proposed in this paper exhibits good convergence and robustness, and the resulting Pareto solution set is more uniformly distributed. Therefore, the non-dominated sorting genetic algorithm for electromagnetic shielding effectiveness of graphene nanofoam composite materials established in this paper is superior to the multi-objective particle swarm optimization algorithm.

Claims

1. A multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials, characterized in that: Includes the following steps: 1) Obtain the characteristic parameters of graphene nanocomposite foam material; 2) Establish a dual-scale constitutive model of electromagnetic shielding and cost of graphene nanocomposite foam material based on the characteristic parameters; 3) Establish a multi-objective optimization model based on the dual-scale constitutive model; 4) Test and revise the multi-objective optimization model. The process of establishing the dual-scale constitutive model for electromagnetic shielding and cost of the graphene nanofoam composite material is as follows: 1) Establish the graphene mass fraction Material porosity and sample thickness Correlation model of electromagnetic shielding effectiveness; 2) Establish the graphene mass fraction Material porosity and sample thickness A correlation model regarding costs; The process of establishing the correlation model of electromagnetic shielding effectiveness is as follows: Formula 1: ; Formula 2: ; Formula 3: ; Formula 4: ; Formula 5: ; Formula 6: ; Formula 7: ; Formula 8: ; Formula 9: ; Formula 10: ; Formula 11: ; Formula 12: ; Formula 13: ； Formula 14: , , , ; Formula 15: ; Formula 16: , , Formula 17: ; In equations 1 to 17: The value represents the volume fraction of graphene, which is dimensionless. The micropore volume concentration in the polymer foam is dimensionless. and It is a depolarization tensor, which is dimensionless; The seepage threshold is dimensionless. For resistance function; It is the Cauchy accumulator function; The interfacial conductivity after tunneling effect and Maxwell polarization is expressed in units of (S / m). is the dielectric constant after tunneling effect and Maxwell polarization, with dimensions (F / m); The interfacial volume concentration of the coated graphene is dimensionless. The electrical conductivity, dielectric constant, and magnetic permeability of the coated graphene with functional interface effects are expressed in units of (S / m), (F / m), and (N / A), respectively. 2 ); The electrical conductivity, dielectric constant, and magnetic permeability of the polymer foam are given by (S / m), (F / m), and (N / A), respectively. 2 ); The electrical conductivity, dielectric constant, and magnetic permeability of the graphene nanocomposite material are given, with dimensions of (S / m), (F / m), and (N / A), respectively. 2 ); The electrical conductivity of the graphene nanocomposite foam material is expressed in units of (S / m). is the dielectric constant of the graphene nanocomposite foam material, with dimensions of (F / m); The conductivity of the graphene nanocomposite foam material is expressed in N / A. 2 ); It is an imaginary constant, dimensionless; , , and Intermediate process parameters are dimensionless. This is the electromagnetic shielding reflection loss, with dimensions in dB; The unit of measurement is dB, representing the absorption loss. The loss due to multiple reflections is expressed in dB.

2. The multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials according to claim 1, characterized in that: The characteristic parameters of the graphene nanocomposite foam material include: graphene aspect ratio. Graphene thickness Interface layer thickness The distance between the electromagnetic wave source and the graphene nanocomposite foam material angular frequency of electromagnetic waves In-plane conductivity of graphene Dielectric properties and permeability Graphene's external conductivity Dielectric properties and permeability The electrical conductivity of polymers Dielectric properties and permeability The mass density of graphene and the mass density of the polymer Conductivity in a vacuum Dielectric constant and permeability Graphene unit price and polymer unit price .

3. The multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials according to claim 2, characterized in that: The characteristic parameters of the graphene nanocomposite foam material also include: the conductivity of the original interface. dielectric constant magnetic permeability tunneling effect scaling parameters Maxwell polarization scaling parameters .

4. The multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials according to claim 1, characterized in that: The process of establishing the cost correlation model is as follows: Formula 18: ; Formula 19: ; Formula 20: ; In equations 18-20: The mass of graphene is expressed in kg. The mass of the polymer is expressed in kg. Let m be the base area of ​​the foam material, with dimensions in m. 2 ; This is the unit price of graphene, with dimensions in dollars per kilogram. The unit price of the polymer is expressed in units of $ / kg.

5. The multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials according to claim 1, characterized in that: The multi-objective optimization model employs a non-dominated sorting genetic algorithm, and its establishment process is as follows: 1) Determine the objective function and optimization variables: Equation 21: ; Electromagnetic shielding effectiveness and cost are the objective functions, with maximizing electromagnetic shielding effectiveness and minimizing cost as the optimization objectives; graphene mass fraction. Material porosity and sample thickness To optimize variables; 2) Determine the parameters of the non-preparative sorting genetic algorithm, including: population size. Maximum Algebra Crossover probability Probability of mutation ; 3) Obtaining the optimal solution set for electromagnetic shielding effectiveness and cost, the process includes: a) Using a random algorithm, several sets of micro-parameters are randomly generated within a reasonable parameter range to produce the initial population of the multi-objective algorithm for graphene nanocomposite foam materials; calculate the two objective function values ​​of electromagnetic shielding effectiveness and cost for each individual, and store the micro-parameter values ​​and objective function values ​​in the individual; b) Using simulated binary crossover and polynomial mutation operators, crossover and mutation operations are performed on the parent population to generate offspring. The calculation process is as follows: Equation 22: ; Equation 23: ; Formula 24: ; Formula 25: ; Equation 26: ; c) Employ an elite strategy to merge parent and offspring generations into an intermediate generation; perform non-dominated ranking of intermediate generation individuals based on the objective function value, dividing them into several non-dominated fronts; calculate the crowding distance of the i-th individual within each non-dominated front, and further rank individuals based on the crowding distance; select individuals with higher ranking levels to enter the next generation. The calculation process for the crowding distance is as follows: Equation 27: ; d) Repeat steps b and c until the maximum number of generations is reached. That is, you get it; In equations 22-27: These are the parameters of the random algorithm, and are dimensionless. These are random numbers, dimensionless. The crossover probability is dimensionless. The perturbation is a small, dimensionless disturbance in the random algorithm. It is the probability of mutation, which is dimensionless; , , Each of these represents a new offspring individual, dimensionless; , , Each is a parent individual, dimensionless; and These are the supremum and infimum of the parent individual's objective function, respectively, and are dimensionless.

6. The multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials according to claim 5, characterized in that: The testing process for the multi-objective optimization model is as follows: 1500 individuals are randomly generated within the selectable range of optimization variables. The electromagnetic shielding effectiveness and cost of each individual are calculated and compared with the obtained Pareto optimal solution set. If the Pareto optimal solution set is a non-dominated solution compared with the random individuals, the correctness of the multi-objective optimization result can be proven.

7. The multi-objective optimization model method for electromagnetic shielding of graphene nanocomposite foam materials according to claim 5, characterized in that: The correction process of the multi-objective optimization model includes: 1) Selecting an optimal data point as a reference benchmark based on the test data of the electromagnetic shielding effectiveness of graphene nanocomposite foam material; 2) Find the optimal solution in the Pareto optimal solution set that is close to the electromagnetic shielding effectiveness of the optimal data point, and calculate the percentage difference in cost between the optimal solution and the optimal data point. 3) Find the optimal solution in the Pareto optimal solution set that is close to the cost of the optimal data point, and calculate the percentage difference between the electromagnetic shielding effectiveness of the optimal solution and the optimal data point. 4) Calculate the ratio of electromagnetic shielding effectiveness to cost between the experimental optimal data point and the Pareto optimal solution set. Find in the optimal solution set Find the optimal solution with the largest value, and calculate the percentage difference between this optimal solution and the optimal data point.

8. An application system for a multi-objective optimization model of electromagnetic shielding for graphene nanocomposite foam materials as described in any one of claims 1 to 7, characterized in that: Used to determine the minimum amount of graphene in graphene nanocomposite foam materials.

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