A multi-objective optimization design method for infrared stealth material film based on ML model

Abstract

The present invention discloses a multi-objective design method for infrared stealth material film layer based on ML model, including: (1) generating a population according to Latin hypercube sampling, simulating and evaluating the emissivity of the individual population in MATLAB and optical simulation software, and establishing a three-objective mathematical optimization model that minimizes the reflectivity error values ​​of three bands; (2) establishing a matching relationship between individuals and reference vectors according to angle values; (3) fusing angle information to construct a radial basis function machine learning model enhanced by angle information; (4) designing a sequential global and local evolution mechanism; (5) calculating real-time state parameters according to the individual improvement amount; (6) constructing a PF-driven screening function to determine the optimal offspring individual and perform simulation evaluation. If the design requirements are met, the optimal thickness value of each film layer is output, otherwise, return to step (2). The present invention designs an adaptive sequential global and local evolution mechanism for the multi-objective characteristics of infrared stealth material film layers, and the algorithm has strong adaptability.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence and swarm intelligence technology, and in particular to a multi-objective optimization design method for an infrared stealth material film layer based on an ML model. Background Art

[0002] In the current civilian field of avoiding infrared detection equipment tracking technology, infrared stealth technology occupies a pivotal position. In the civilian field, it can enhance the concealment of some special equipment in complex environments and meet the needs of specific scenarios. The core of infrared stealth technology is to effectively reduce, eliminate, simulate or change the difference in infrared radiation characteristics between the target and the background in the mid- and far-infrared atmospheric window, so as to avoid tracking by infrared detection equipment.

[0003] In the early days, the infrared stealth effect was mainly achieved by relying on low-emissivity materials. However, the limitations of such materials are extremely obvious. They cannot accurately control the emissivity of different bands according to actual needs, and it is difficult to meet the increasingly stringent stealth requirements in complex and changing application scenarios. In order to break through this dilemma, spectrally selective infrared stealth materials came into being and became the focus of research. By carefully designing the microstructure of the material and rationally adjusting the composition of the components, spectrally selective infrared stealth materials can accurately control infrared radiation in different bands to achieve an ideal stealth effect.

[0004] Accurately constructing simulation models is a key link in the in-depth study of spectrally selective infrared stealth materials. Generally speaking, this type of model is based on the Maxwell equations, integrates the electromagnetic parameters of the material, and is built with the help of numerical calculation methods such as the finite element method and the finite difference time domain method. By simulating the interaction between electromagnetic waves and materials by computer, key performance parameters such as the infrared emissivity of the material can be predicted in advance, thus providing an important reference for the design and optimization of the material.

[0005] When solving the multi-objective optimization problem of infrared stealth material film layers, the traditional multi-objective evolutionary algorithm uses selection, crossover and mutation operations that simulate biological evolution to search for the optimal solution in the solution space, taking into account the mutual influence between materials. However, this method has serious drawbacks. It requires a large number of simulation model calls, and a single simulation often takes several minutes or even longer. Such a huge amount of calculation and high time cost limit its practical application. Summary of the invention

[0006] In order to solve the limitations of the prior art or improve the technical needs, the present invention proposes a multi-objective optimization design method for infrared stealth material film layers based on ML models, introduces a proxy model in the multi-objective evolutionary algorithm, uses the ML (Machine Learning) model to quickly model complex simulation models, and provides reliable prediction values. The present invention greatly reduces the calculation amount and the number of times the simulation model is used by replacing the time-consuming simulation process with a proxy model, greatly shortens the calculation time while ensuring the solution accuracy, and can obtain a better design solution within an acceptable time range, showing significant superiority. Based on the time-consuming and complex simulation characteristics involved in the multi-objective optimization design of infrared stealth material film layers, and the design requirements of three optimization goals, the ideal selective emission infrared stealth material has an emissivity of 0 in two non-atmospheric window bands, namely 3µm-5µm and 8µm-14µm, and an emissivity of 1 in one atmospheric window band, namely 5µm-8µm, an angle information enhanced radial basis function machine learning model is proposed, in which the angle information and Euclidean distance information between population individuals are simultaneously integrated to comprehensively measure the correlation between any two population individuals. The present invention calculates the individual improvement amount according to the different optimization states of the current population individuals and the evolving individuals, and adjusts the real-time state parameters to match the optimization state of each generation by comparing the individual improvement amounts of the global and local evolutions; designs a PF-driven screening function to determine the best individual from the candidate set; and improves the optimization efficiency of the multi-objective optimization design of the infrared stealth material film layer.

[0007] To achieve the above object, according to one aspect of the present invention, a multi-objective optimization design method for an infrared stealth material film layer based on an ML model is provided, the method comprising:

[0008] Step (1): taking the thickness of each film layer of the infrared stealth material as an optimization design parameter, constructing a design space according to the maximum and minimum values ​​of the allowable thickness of each film layer, and taking the emissivity error values ​​of the infrared stealth material film layer in two non-atmospheric window bands and one atmospheric window band as three optimization targets; performing Latin hypercube sampling within the design space to obtain a population, wherein each population individual contains a specific value of the thickness of each film layer of the infrared stealth material, and generating 50 uniformly distributed reference vectors in the target space composed of the three optimization targets according to the simplex method; adding substrate properties to the optical simulation software, transferring the material structure of each film layer corresponding to each population individual into the optical simulation software through MATLAB, setting the grid division method and grid unit size, adding a plane wave source and setting the frequency range and polarization mode, adding monitors in the three bands respectively, running the optical simulation software to obtain the emissivity of the three bands corresponding to each population individual and calculating the corresponding emissivity error values; storing all population individuals and their corresponding emissivity error values ​​in a global database, initializing real-time state parameters, and establishing a three-target mathematical optimization model according to the characteristics of the design space and the target space;

[0009] Step (2): Normalize the objective function values ​​of all population individuals, loop through each reference vector, and match the population individual with the smallest angle with the reference vector until all reference vectors are matched with the population individuals;

[0010] Step (3): Calculate the angle cosine values ​​and Euclidean distance values ​​between all population individuals in the global database and construct angle information basis functions and Euclidean distance information basis functions respectively based on them, solve the weight vectors corresponding to the angle information basis functions and the Euclidean distance information basis functions in the radial basis function machine learning model architecture, and derive the radial basis function machine learning model with angle information enhancement;

[0011] Step (4): For each individual in the population, a global and local evolution mechanism driven by a feasible state is designed based on real-time state parameters to generate global and local candidate offspring individuals, and the Chebyshev function value and constraint violation value are sequentially compared to select the optimal global and local offspring individuals;

[0012] Step (5): Calculate the individual improvement of the optimal global and local offspring individuals relative to the population individuals, and calculate the real-time state parameters based on the individual improvement of the global and local evolution;

[0013] Step (6): Construct a PF-driven screening function to determine the optimal offspring individual from the optimal global and local offspring individuals, combine MATLAB and optical simulation software to simulate and evaluate the optimal offspring individuals, calculate the three-band reflectivity error values ​​corresponding to each optimal offspring individual, and update the global database. If the optimal offspring individual in the global database meets the design requirements, output the optimal thickness value of each film layer of the infrared stealth material, otherwise return to step (2).

[0014] Furthermore, in the step (1), Latin hypercube sampling is performed within the design space to obtain a population, wherein each population individual contains a specific value of the thickness of each film layer of the infrared stealth material, and 50 uniformly distributed reference vectors are generated according to the simplex method in the target space composed of three optimization objectives; the substrate and the material properties of each film layer are added in the optical simulation software, the thickness of each film layer corresponding to each population individual is transferred to the optical simulation software through MATLAB, the grid division method and the grid unit size are set, a plane wave source is added and the frequency range and polarization mode are set, monitors are added in three bands respectively, and the optical simulation software is run to obtain the emissivity of the three bands corresponding to each population individual and calculate the corresponding emissivity error value; all population individuals and their corresponding emissivity error values ​​are stored in a global database, the real-time state parameters are initialized, and a three-objective mathematical optimization model is established according to the characteristics of the design space and the target space, which specifically includes the following steps:

[0015] The first step is to determine the maximum and minimum thickness of each film layer according to the actual requirements for the thickness of the film layer, that is, to determine the upper and lower bounds of the optimization design parameters, use Latin hypercube sampling to generate 50 individuals as a population, and use the simplex method to generate 50 reference vectors in the target space;

[0016] The second step is to ensure that MATLAB and the optical simulation software can call each other to achieve data transmission and script execution;

[0017] The third step is to complete the simulation settings of the optical simulation software in MATLAB, including the following steps:

[0018] First, define the optimization variables, add a rectangular structure as the substrate, set the properties of the substrate, including position, size and material, and add the material properties and thickness of each film layer of the infrared stealth material through the setting command;

[0019] Then, set the boundary conditions of the simulation area, set the grid accuracy, and set the grid type to uniform type to ensure that the grid in the entire simulation area is uniform; dx, dy, and dz are set as the grid size to control the fineness of the grid;

[0020] Next, set the coordinate axis of the plane wave source to the z-axis, indicating that the plane wave propagates along the z-axis; set the direction of the plane wave source to backward, indicating that the plane wave propagates from the positive direction to the negative direction of the z-axis; set the frequency range, and set the wavelength start and end points to 3µm and 14µm respectively, indicating the simulation wavelength range; set the polarization mode to y, indicating that the polarization direction of the plane wave is in the y direction;

[0021] Finally, add three monitors to cover the wavelength ranges of 3µm-5µm, 5µm-8µm, and 8µm-14µm respectively; set the monitor type to 2D Z-normal, which means the monitor is on the XY plane; set the number of frequency points to 50, which means recording data at 50 frequency points in each band;

[0022] The fourth step is to simulate the 50 individuals generated by Latin hypercube sampling and obtain simulation data, which is then transferred to MATLAB for calculation and model building, including the following steps:

[0023] First, the emissivity in the three bands is calculated according to Kirchhoff’s law;

[0024] Then, the error value is calculated according to the emissivity of each band, and the emissivity error values ​​of all population individuals and their corresponding emissivity are stored in the global database. The real-time state parameters are initialized and a three-objective mathematical optimization model is established. The specific expression is as follows:

[0025] ,

[0026] In the above formula, F (x) is the target space composed of three optimization targets: the emissivity error values ​​of the infrared stealth material film layer in two non-atmospheric window bands and one atmospheric window band. f 1 (x) and f 2 (x) are the first objective function and the second objective function, namely, the emissivity error values ​​in the two non-atmospheric window bands, f 3 (x) is the third objective function, i.e., the error of the emissivity error value in an atmospheric window band, T is the transpose of the matrix, x refers to the thickness of each film material, Minimize To minimize the three optimization objectives, It refers to the design space constructed by the maximum and minimum allowable thickness of each film material. g j (x) is j A constraint function, j is a constraint function index, c is the number of constraint functions, subject to are constraints that need to be satisfied.

[0027] Furthermore, the step (2) specifically includes the following steps:

[0028] The first step is to use the Max-Min criterion to normalize the objective function values ​​of all population individuals to obtain the normalized objective function vector corresponding to each population individual;

[0029] In the second step, each reference vector is looped, and the angle between the reference vector and the normalized target function vector of the population individual is calculated in the target space. The population individual with the smallest angle with the reference vector is matched, and the matched reference vectors are deleted in the subsequent matching process to ensure that each reference vector is matched with only one individual.

[0030] Furthermore, the step (3) specifically includes the following steps:

[0031] The first step is to calculate the angle cosine values ​​between all population individuals in the global database and construct the angle information basis function, whose mathematical expression is as follows:

[0032] ,

[0033] in, It is i Individuals of a population, It is j Individuals of a population, and Respectively and The module length;

[0034] The second step is to calculate the Euclidean distance between all individuals in the global database and construct the Euclidean distance information basis function, whose mathematical expression is as follows:

[0035] ;

[0036] The third step is to solve the weight vector corresponding to the angle information basis function and the Euclidean distance information basis function in the radial basis function machine learning model architecture. The mathematical expression is as follows:

[0037] ,

[0038] ,

[0039] In the above formula, is the weight vector corresponding to the angle information basis function, is the weight vector corresponding to the distance information basis function, is the angle information weight corresponding to the first angle information basis function term, It is The angle information weight corresponding to the angle information basis function term is: is the distance information weight corresponding to the first Euclidean distance information basis function term, It is The distance information weight corresponding to the Euclidean distance information basis function term;

[0040] The fourth step is to derive the radial basis function machine learning model with angle information enhancement, which is expressed as follows:

[0041] ,

[0042] In the above formula, x is the new individual corresponding to the specific value of the thickness of each film layer material generated in the iterative process. Represents the predicted value of the radial basis function machine learning model with enhanced angle information for a new individual, and Respectively represent the calculation of the new individual x and the population individual through angle information and Euclidean distance The angle information basis function term and the Euclidean distance information basis function term, is the number of individuals in the population, and They are and The i-th weight value of Represents a first-order linear polynomial function.

[0043] Furthermore, the step (4) specifically includes the following steps:

[0044] In the first step, for each individual in the population, a global evolution mechanism driven by feasibility state is designed based on real-time state parameters to generate global candidate offspring individuals. The corresponding mathematical expression is as follows:

[0045] ,

[0046] In the above formula, TF is the trend function, For the population i The state parameter of each individual, max is the maximum value;

[0047] In the second step, DPM mutation is used for individuals in the population that meet the feasibility requirements. The mathematical expression is as follows:

[0048] ,

[0049] In the above formula, is the standard deviation of the DPM variation, is the reference number of the standard deviation, min is the minimum value, and Respectively represent the maximum and minimum allowable thickness of each film material. is the scaling parameter;

[0050] The third step is to use DE mutation for individuals in the population that do not meet the feasibility requirements, with the following parameters:

[0051] ,

[0052] In the above formula, is the scaling factor of DE variation, is the base number of the scaling factor, Represents a uniformly distributed random number between 0 and 1;

[0053] The fourth step is to sequentially compare the Chebyshev function value and the constraint violation value to select the best global offspring individual from the global candidate offspring individuals;

[0054] The fifth step is to design a feasibility state-driven local evolution mechanism based on real-time state parameters for each population individual to generate local candidate offspring individuals, and sequentially compare the Chebyshev function value with the constraint violation value to select the optimal local offspring individual from the local candidate offspring individuals.

[0055] Furthermore, the step (5) specifically includes the following steps:

[0056] In the first step, the calculation rule of individual improvement is as follows: when both the offspring individual and the population individual are feasible, the individual improvement is the Chebyshev function value of the population individual minus the Chebyshev function value of the offspring individual; otherwise, the individual improvement is the constraint violation value of the population individual minus the constraint violation value of the offspring individual;

[0057] The second step is to update the real-time status parameters according to the following rules AND :

[0058] First, when the real-time state parameter is positive and the individual improvement of the optimal global offspring individual is greater than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND = AND +1;

[0059] Second, when the real-time state parameter is positive and the individual improvement of the optimal global offspring individual is less than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND =-1;

[0060] Third, when the real-time state parameter is negative and the individual improvement of the optimal global offspring individual is greater than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND =1;

[0061] Fourth, when the real-time state parameter is negative and the individual improvement of the optimal global offspring individual is less than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND = AND -1.

[0062] Furthermore, the PF-driven screening function constructed in step (6) determines the optimal offspring individual from the optimal global and local offspring individuals, specifically comprising the following steps:

[0063] The first step is to set the optimal offspring individual candidate set to an empty set;

[0064] The second step is to store the corresponding optimal global and local offspring individuals into the optimal offspring individual candidate set for each population individual;

[0065] The third step is to construct the PF-driven screening function. The mathematical expression is as follows:

[0066] ,

[0067] In the above formula, Indicates the optimal offspring individual candidate set i Offspring individuals The calculated filtering function value, max means taking the maximum value, NXObj(i,k) represents the first i Individual The corresponding k target values, where the first and second target values ​​are the emissivity error values ​​in two non-atmospheric window bands, respectively, and the third target value is the error of the emissivity error value in an atmospheric window band. PF represents the Pareto front corresponding to the current iteration. j and k Both represent indexes;

[0068] The fourth step is to use the PF-driven screening function to calculate the screening function values ​​of all offspring individuals in the optimal offspring individual candidate set, and sort all offspring individuals from small to large according to the screening function value, and select the first two offspring individuals after sorting as the optimal offspring individuals.

[0069] In a second aspect, the present invention further provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the steps of a multi-objective design method for infrared stealth material film layers based on an ML model.

[0070] In a third aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a multi-objective design method for an infrared stealth material film layer based on an ML model.

[0071] In summary, compared with the prior art, the multi-objective design method of infrared stealth material film layer based on ML model provided by the present invention has the following improvements over the limitations of the prior art:

[0072] 1. Considering the limitation of the traditional radial basis function model that does not fully utilize the feature information between individuals, the angle information and Euclidean distance are combined to construct the radial basis function machine learning model with angle information enhancement, which enhances the adaptability of the radial basis function model to the multi-objective optimization design problem of infrared stealth material film layer;

[0073] 2. A parameter adaptive strategy based on individual improvement is constructed, in which the individual improvement is calculated according to the different optimization states of the current population individuals and the optimal global and local offspring individuals. By comparing the individual improvement of global and local evolution, the real-time state parameters are calculated to match the optimization state of each generation;

[0074] 3. A PF-driven screening function was designed to consider screening out the optimal offspring individuals from the optimal global and local offspring individuals, thereby accelerating the convergence speed of the algorithm for the multi-objective optimization design problem of infrared stealth material membrane layers;

[0075] 4. The present invention can optimize multi-objective problems involving complex simulations, thereby improving the optimization efficiency of complex simulations, and can optimize multiple objectives simultaneously to achieve overall optimality, which is beneficial to the optimization application of various complex structures and is practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 A simplified flow chart of a multi-objective design method for an infrared stealth material film layer based on an ML model provided by the present invention. DETAILED DESCRIPTION

[0077] In order to more clearly explain the purpose, technical solutions and advantages of the present invention, it will be described in detail below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit it. In addition, as long as the technical features in the following embodiments do not conflict with each other, they can be combined with each other.

[0078] See also Figure 1 The present invention provides a multi-objective design method for an infrared stealth material film layer based on an ML model, which is applicable to the multi-objective design optimization problem of an infrared stealth material film layer. Specifically, the method mainly includes the following steps (1) to (6).

[0079] Step (1): The thickness of each film layer of the infrared stealth material (e.g., the four film layers of metal layer-dielectric layer-metal layer-dielectric layer) is used as the optimization design parameter, and the design space is constructed according to the maximum and minimum allowable thickness values ​​of each film layer material. The emissivity error values ​​of the infrared stealth material film layers in two non-atmospheric window bands (i.e., 3µm-5µm and 8µm-14µm) and one atmospheric window band (i.e., 5µm-8µm) are used as three optimization targets; Latin hypercube sampling is performed within the design space to obtain a population, wherein each population individual contains specific values ​​of the thickness of each film layer of the infrared stealth material (e.g., the thickness of four film layers); 50 uniformly distributed reference vectors are generated in the target space composed of the three optimization targets according to the simplex method; in an optical simulation software (e.g., Ansys Lumerical The substrate properties were added in the optical FDTD software, the material structures of each film layer corresponding to each population individual were transferred to the optical simulation software through MATLAB, the grid division method and grid unit size were set, a plane wave source was added and the frequency range and polarization mode were set, monitors were added in three bands (including two non-atmospheric window bands and one atmospheric window band, the two non-atmospheric window bands corresponded to 3µm-5µm and 8µm-14µm, and the one atmospheric window band corresponded to 5µm-8µm), the optical simulation software was run to obtain the emissivity of the three bands corresponding to each population individual and calculate the corresponding emissivity error value; all population individuals and their corresponding emissivity error values ​​were stored in the global database, the real-time state parameters were initialized, and a three-objective mathematical optimization model was established according to the characteristics of the design space and the target space.

[0080] In step (1), Latin hypercube sampling is performed within the design space to obtain a population, wherein each population individual contains a specific value of the thickness of each film layer of the infrared stealth material, and 50 uniformly distributed reference vectors are generated in the target space composed of three optimization objectives according to the simplex method; the substrate and each film layer material properties are added in the optical simulation software, and the thickness of each film layer material corresponding to each population individual is transferred to the optical simulation software through MATLAB, the grid division method and the grid unit size are set, a plane wave source is added and the frequency range and polarization mode are set, monitors are added in three bands respectively, and the optical simulation software is run to obtain the emissivity of the three bands corresponding to each population individual and calculate the corresponding emissivity error value; all population individuals and their corresponding emissivity error values ​​are stored in a global database, the real-time state parameters are initialized, and a three-objective mathematical optimization model is established according to the characteristics of the design space and the target space, which specifically includes the following steps:

[0081] The first step is to determine the maximum and minimum thickness of each film layer according to the actual requirements for the thickness of the film layer, that is, to determine the upper and lower bounds of the optimization design parameters, use Latin hypercube sampling to generate 50 individuals as a population, and use the simplex method to generate 50 reference vectors in the target space;

[0082] The second step is to ensure that MATLAB and the optical simulation software can call each other to realize data transmission and script execution. In the specific implementation process, for example, when the optical simulation software uses Ansys Lumerical FDTD software, the following setting steps are used to ensure that MATLAB and Ansys Lumerical FDTD software can call each other: First, find and click "Matlab integration status" under "Help" in the toolbar above the Ansys Lumerical FDTD software; then, click select to find the libeng.dll file in the MATLAB installation directory; then, open the MATLAB software as an administrator, register the MATLAB COM component, and realize the interaction between the Ansys Lumerical FDTD software and MATLAB through the COM interface;

[0083] The third step is to complete the simulation settings of the optical simulation software in MATLAB, including the following steps:

[0084] First, define the optimization variables, add a rectangular structure as the substrate, set the properties of the substrate, including position, size and material, and add the material properties and thickness of each film layer of the infrared stealth material through the setting command;

[0085] Then, set the boundary conditions of the simulation area, set the grid accuracy, and set the grid type to uniform type to ensure that the grid in the entire simulation area is uniform; dx, dy, and dz are set as the grid size to control the fineness of the grid;

[0086] Next, set the coordinate axis position of the plane wave source to the z-axis, indicating that the plane wave propagates along the z-axis; set the direction of the plane wave source to backward, indicating that the plane wave propagates from the positive direction to the negative direction of the z-axis; set the frequency range, and set the wavelength start and end points to 3µm and 14µm respectively, indicating the simulation wavelength range; set the polarization mode to y, indicating that the polarization direction of the plane wave is in the y direction;

[0087] Finally, add three monitors to cover the wavelength ranges of 3µm-5µm, 5µm-8µm, and 8µm-14µm respectively; set the monitor type to 2D Z-normal, which means the monitor is on the XY plane; set the number of frequency points to 50, which means recording data at 50 frequency points in each band;

[0088] The fourth step is to simulate the 50 individuals generated by Latin hypercube sampling and obtain simulation data, which is then transferred to MATLAB for calculation and model building, including the following steps:

[0089] First, the emissivity in the three bands is calculated according to Kirchhoff’s law;

[0090] Then, the error value is calculated according to the emissivity of each band, and the emissivity error values ​​of all population individuals and their corresponding emissivity are stored in the global database. The real-time state parameters are initialized and a three-objective mathematical optimization model is established. The specific expression is as follows:

[0091] ,

[0092] In the above formula, F (x) is the target space composed of three optimization targets: the emissivity error values ​​of the infrared stealth material film layer in two non-atmospheric window bands and one atmospheric window band. f 1 (x) and f 2 (x) are the first objective function and the second objective function, namely, the emissivity error values ​​in the two non-atmospheric window bands, f 3 (x) is the third objective function, i.e., the error of the emissivity error value in an atmospheric window band, T is the transpose of the matrix, x refers to the thickness of each film material, Minimize To minimize the three optimization objectives, It refers to the design space constructed by the maximum and minimum allowable thickness of each film material. g j (x) is j A constraint function, j is a constraint function index, c is the number of constraint functions, subject to are constraints that need to be satisfied.

[0093] It should be noted that the optimization target in the two non-atmospheric window bands, namely the 3µm-5µm and 8µm-14µm bands, is the error between the emissivity and 0, and the optimization target in the one atmospheric window band, namely the 5µm-8µm band, is the error between the emissivity and 1.

[0094] Step (2): Normalize the objective function values ​​of all population individuals, loop through each reference vector, and match the population individual with the smallest angle with the reference vector until all reference vectors are matched with the population individuals.

[0095] Step (2) specifically includes the following steps:

[0096] The first step is to use the Max-Min criterion to normalize the objective function values ​​of all population individuals to obtain the normalized objective function vector corresponding to each population individual;

[0097] In the second step, each reference vector is looped, and the angle between the reference vector and the normalized target function vector of the population individual is calculated in the target space. The population individual with the smallest angle with the reference vector is matched, and the matched reference vectors are deleted in the subsequent matching process to ensure that each reference vector is matched with only one individual.

[0098] Step (3): Calculate the angle cosine values ​​and Euclidean distance values ​​between all population individuals in the global database and construct the angle information basis function and the Euclidean distance information basis function respectively based on them. Solve the weight vectors corresponding to the angle information basis function and the Euclidean distance information basis function in the radial basis function machine learning model architecture, and derive the radial basis function machine learning model with angle information enhancement.

[0099] Step (3) specifically includes the following steps:

[0100] The first step is to calculate the angle cosine values ​​between all population individuals in the global database and construct the angle information basis function, whose mathematical expression is as follows:

[0101] ,

[0102] in, It is i Individuals of a population, It is j Individuals of a population, and Respectively and The module length;

[0103] The second step is to calculate the Euclidean distance between all individuals in the global database and construct the Euclidean distance information basis function, whose mathematical expression is as follows:

[0104] ;

[0105] The third step is to solve the weight vector corresponding to the angle information basis function and the Euclidean distance information basis function in the radial basis function machine learning model architecture. The mathematical expression is as follows:

[0106] ,

[0107] ,

[0108] In the above formula, is the weight vector corresponding to the angle information basis function, is the weight vector corresponding to the distance information basis function, is the angle information weight corresponding to the first angle information basis function term, It is The angle information weight corresponding to the angle information basis function term is: is the distance information weight corresponding to the first Euclidean distance information basis function term, It is The distance information weight corresponding to the Euclidean distance information basis function term;

[0109] The fourth step is to derive the radial basis function machine learning model with angle information enhancement, which is expressed as follows:

[0110] ,

[0111] In the above formula, x is the new individual corresponding to the specific value of the thickness of each film layer material generated in the iterative process. Represents the predicted value of the radial basis function machine learning model with enhanced angle information for a new individual, and Respectively represent the calculation of the new individual x and the population individual through angle information and Euclidean distance The angle information basis function term and the Euclidean distance information basis function term, is the number of individuals in the population, and They are and The i-th weight value of Represents a first-order linear polynomial function.

[0112] Step (4): For each individual in the population, a feasibility state-driven global and local evolution mechanism is designed based on the real-time state parameters to generate global and local candidate offspring individuals, and the Chebyshev function value and constraint violation value are sequentially compared to screen the optimal global and local offspring individuals.

[0113] Step (4) specifically includes the following steps:

[0114] In the first step, for each individual in the population, a global evolution mechanism driven by feasibility state is designed based on real-time state parameters to generate global candidate offspring individuals. The corresponding mathematical expression is as follows:

[0115] ,

[0116] In the above formula, TF is the trend function, For the population i The state parameter of each individual, max is the maximum value;

[0117] In the second step, DPM mutation is used for individuals in the population that meet the feasibility requirements. The mathematical expression is as follows:

[0118] ,

[0119] In the above formula, is the standard deviation of the DPM variation, is the reference number of the standard deviation, min is the minimum value, and Respectively represent the maximum and minimum allowable thickness of each film material. is the scaling parameter;

[0120] The third step is to use DE mutation for individuals in the population that do not meet the feasibility requirements, with the following parameters:

[0121] ,

[0122] In the above formula, is the scaling factor of DE variation, is the base number of the scaling factor, Represents a uniformly distributed random number between 0 and 1;

[0123] The fourth step is to sequentially compare the Chebyshev function value and the constraint violation value to select the best global offspring individual from the global candidate offspring individuals;

[0124] The fifth step is to design a feasibility state-driven local evolution mechanism based on real-time state parameters for each population individual to generate local candidate offspring individuals, and sequentially compare the Chebyshev function value with the constraint violation value to select the optimal local offspring individual from the local candidate offspring individuals.

[0125] Step (5): Calculate the individual improvement of the optimal global and local offspring individuals relative to the population individuals respectively, and calculate the real-time state parameters based on the individual improvement of the global and local evolution.

[0126] Step (5) specifically includes the following steps:

[0127] In the first step, the calculation rule of individual improvement is as follows: when both the offspring individual and the population individual are feasible, the individual improvement is the Chebyshev function value of the population individual minus the Chebyshev function value of the offspring individual; otherwise, the individual improvement is the constraint violation value of the population individual minus the constraint violation value of the offspring individual;

[0128] The second step is to update the real-time status parameters according to the following rules AND :

[0129] First, when the real-time state parameter is positive and the individual improvement of the optimal global offspring individual is greater than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND = AND +1;

[0130] Second, when the real-time state parameter is positive and the individual improvement of the optimal global offspring individual is less than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND =-1;

[0131] Third, when the real-time state parameter is negative and the individual improvement of the optimal global offspring individual is greater than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND =1;

[0132] Fourth, when the real-time state parameter is negative and the individual improvement of the optimal global offspring individual is less than the individual improvement of the optimal local offspring individual, the state parameter is updated to AND = AND -1.

[0133] Step (6): Construct a PF-driven screening function to determine the optimal offspring individual from the optimal global and local offspring individuals, combine MATLAB and optical simulation software to simulate and evaluate the optimal offspring individuals, calculate the three-band reflectivity error values ​​corresponding to each optimal offspring individual, and update the global database. If the optimal offspring individual in the global database meets the design requirements, output the optimal thickness value of each film layer of the infrared stealth material, otherwise return to step (2).

[0134] In step (6), the PF-driven screening function is constructed to determine the optimal offspring individual from the optimal global and local offspring individuals, which specifically includes the following steps:

[0135] The first step is to set the optimal offspring individual candidate set to an empty set;

[0136] The second step is to store the corresponding optimal global and local offspring individuals into the optimal offspring individual candidate set for each population individual;

[0137] The third step is to construct the PF-driven screening function. The mathematical expression is as follows:

[0138] ,

[0139] In the above formula, Indicates the optimal offspring individual candidate set i Offspring individuals The calculated filtering function value, max means taking the maximum value, NXObj(i,k) represents the first i Individual The corresponding k target values, where the first and second target values ​​are the emissivity error values ​​in two non-atmospheric window bands, respectively, and the third target value is the error of the emissivity error value in an atmospheric window band. PF represents the Pareto front corresponding to the current iteration. j and k Both represent indexes;

[0140] The fourth step is to use the PF-driven screening function to calculate the screening function values ​​of all offspring individuals in the optimal offspring individual candidate set, and sort all offspring individuals from small to large according to the screening function value, and select the first two offspring individuals after sorting as the optimal offspring individuals.

[0141] Example

[0142] This embodiment uses the benchmark test function DC3-DTLZ1 to illustrate the optimization performance of a multi-objective optimization design method for infrared stealth material film layer based on the ML model provided in this embodiment, which has three optimization objectives ( m =3) is as follows:

[0143] ,

[0144] In the above formula, min means minimization. represents the first objective function, represents the second objective function, represents the third objective function, Represents an individual The first dimension value of Represents an individual The second dimension of , n represents the total dimension, Represents an individual No. m Dimension values, Represents an individual No. n Dimension values, For the auxiliary constructor, the expression is as follows:

[0145] ,

[0146] In the above formula, express The module length, Represents the individual i Dimension values;

[0147] The constraint function expression of DC3-DTLZ1 is as follows:

[0148] ,

[0149] In the above formula, Indicates j Constraint functions; Represents an individual No. j Dimension values;

[0150] The above-mentioned benchmark test function DC3-DTLZ1 is processed respectively through steps (1) to (6) of a multi-objective optimization design method for an infrared stealth material film layer based on an ML model provided by the present invention to obtain experimental results.

[0151] In order to illustrate this embodiment in more detail, the multi-objective optimization design method of the infrared stealth material film layer based on the ML model in this embodiment is compared with another Kriging-assisted multi-objective efficient global optimization algorithm, and the maximum number of simulation evaluations in this embodiment is set to 300 times, and the number of design variables is set to 30. The experimental results are shown in Table 1. The comparison method adopted is the average IGD value of 30 independent runs. When the number of simulations is the same, the method of this embodiment is significantly better than the Kriging-assisted multi-objective efficient global optimization algorithm. It can be considered that the method of this embodiment can solve the multi-objective optimization design problem of the infrared stealth material film layer.

[0152] Table 1: Comparison of optimization results of different algorithms

[0153]

[0154] The present invention provides a multi-objective optimization design method for an infrared stealth material film layer based on an ML model. A population is generated according to Latin hypercube sampling, and simulation evaluation is performed on the individual emissivity of the population in combination with MATLAB and Ansys Lumerical FDTD. A three-objective mathematical optimization model for minimizing the reflectivity error values ​​of three different bands is established. A matching relationship between individuals and reference vectors is established according to angle values. A radial basis function machine learning model enhanced with angle information is constructed by combining angle information and Euclidean distance information. A sequential global and local evolution mechanism is designed. Real-time state parameters are calculated according to individual improvement amounts. A PF-driven screening function is constructed to determine the optimal offspring individual and perform simulation evaluation. This method provides a systematic solution for the multi-objective optimization design of infrared stealth material film layers.

[0155] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of a multi-objective design method for an infrared stealth material film layer based on an ML model of the aforementioned embodiment are implemented.

[0156] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a multi-objective design method for an infrared stealth material film layer based on an ML model of the aforementioned embodiment.

[0157] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-objective optimization design method for infrared stealth material film based on ML model, characterized in that: The method comprises: Step (1): taking the thickness of each film layer of the infrared stealth material as an optimization design parameter, constructing a design space according to the maximum and minimum values ​​of the allowable thickness of each film layer, and taking the emissivity error values ​​of the infrared stealth material film layer in two non-atmospheric window bands and one atmospheric window band as three optimization targets; performing Latin hypercube sampling within the design space to obtain a population, wherein each population individual contains a specific value of the thickness of each film layer of the infrared stealth material, and generating 50 uniformly distributed reference vectors in the target space composed of the three optimization targets according to the simplex method; adding substrate properties to the optical simulation software, transferring the material structure of each film layer corresponding to each population individual into the optical simulation software through MATLAB, setting the grid division method and grid unit size, adding a plane wave source and setting the frequency range and polarization mode, adding monitors in the three bands respectively, running the optical simulation software to obtain the emissivity of the three bands corresponding to each population individual and calculating the corresponding emissivity error values; storing all population individuals and their corresponding emissivity error values ​​in a global database, initializing real-time state parameters, and establishing a three-target mathematical optimization model according to the characteristics of the design space and the target space; Step (2): Normalize the objective function values ​​of all population individuals, loop through each reference vector, and match the population individual with the smallest angle with the reference vector until all reference vectors are matched with the population individuals; Step (3): Calculate the angle cosine values ​​and Euclidean distance values ​​between all population individuals in the global database and construct angle information basis functions and Euclidean distance information basis functions respectively based on them, solve the weight vectors corresponding to the angle information basis functions and the Euclidean distance information basis functions in the radial basis function machine learning model architecture, and derive the radial basis function machine learning model with angle information enhancement; Step (4): For each individual in the population, a global and local evolution mechanism driven by a feasible state is designed based on real-time state parameters to generate global and local candidate offspring individuals, and the Chebyshev function value and constraint violation value are sequentially compared to select the optimal global and local offspring individuals; Step (5): Calculate the individual improvement of the optimal global and local offspring individuals relative to the population individuals, and calculate the real-time state parameters based on the individual improvement of the global and local evolution; Step (6): Construct a PF-driven screening function to determine the optimal offspring individual from the optimal global and local offspring individuals, combine MATLAB and optical simulation software to simulate and evaluate the optimal offspring individuals, calculate the three-band reflectivity error values ​​corresponding to each optimal offspring individual, and update the global database. If the optimal offspring individual in the global database meets the design requirements, output the optimal thickness value of each film layer of the infrared stealth material, otherwise return to step (2).

2. The method according to claim 1, characterized in that In the step (1), Latin hypercube sampling is performed within the design space to obtain a population, wherein each population individual contains a specific value of the thickness of each film layer of the infrared stealth material, and 50 uniformly distributed reference vectors are generated according to the simplex method in the target space composed of three optimization targets; the substrate and the material properties of each film layer are added in the optical simulation software, the thickness of each film layer corresponding to each population individual is transferred to the optical simulation software through MATLAB, the grid division method and the grid unit size are set, a plane wave source is added and the frequency range and polarization mode are set, monitors are added in three bands respectively, and the optical simulation software is run to obtain the emissivity of the three bands corresponding to each population individual and calculate the corresponding emissivity error value; all population individuals and their corresponding emissivity error values ​​are stored in a global database, the real-time state parameters are initialized, and a three-target mathematical optimization model is established according to the characteristics of the design space and the target space, which specifically includes the following steps: The first step is to determine the maximum and minimum thickness of each film layer according to the actual requirements for the thickness of the film layer, that is, to determine the upper and lower bounds of the optimization design parameters, use Latin hypercube sampling to generate 50 individuals as a population, and use the simplex method to generate 50 reference vectors in the target space; The second step is to ensure that MATLAB and the optical simulation software can call each other to achieve data transmission and script execution; The third step is to complete the simulation settings of the optical simulation software in MATLAB, including the following steps: First, define the optimization variables, add a rectangular structure as the substrate, set the properties of the substrate, including position, size and material, and add the material properties and thickness of each film layer of the infrared stealth material through the setting command; Then, set the boundary conditions of the simulation area, set the grid accuracy, and set the grid type to uniform type to ensure that the grid in the entire simulation area is uniform; dx, dy, and dz are set as the grid size to control the fineness of the grid; Next, set the coordinate axis of the plane wave source to the z-axis, indicating that the plane wave propagates along the z-axis; set the direction of the plane wave source to backward, indicating that the plane wave propagates from the positive direction to the negative direction of the z-axis; set the frequency range, and set the wavelength start and end points to 3µm and 14µm respectively, indicating the simulation wavelength range; set the polarization mode to y, indicating that the polarization direction of the plane wave is in the y direction; Finally, add three monitors to cover the wavelength ranges of 3µm-5µm, 5µm-8µm, and 8µm-14µm respectively; set the monitor type to 2D Z-normal, which means the monitor is on the XY plane; set the number of frequency points to 50, which means recording data at 50 frequency points in each band; The fourth step is to simulate the 50 individuals generated by Latin hypercube sampling and obtain simulation data, which is then transferred to MATLAB for calculation and model building, including the following steps: First, the emissivity in the three bands is calculated according to Kirchhoff’s law; Then, the error value is calculated according to the emissivity of each band, and the emissivity error values ​​of all population individuals and their corresponding emissivity are stored in the global database. The real-time state parameters are initialized and a three-objective mathematical optimization model is established. The specific expression is as follows: ， In the above formula, F (x) is the target space composed of three optimization targets: the emissivity error values ​​of the infrared stealth material film layer in two non-atmospheric window bands and one atmospheric window band. f 1(x) and f 2(x) are the first objective function and the second objective function, i.e., the emissivity error values ​​in the two non-atmospheric window bands. f 3(x) is the third objective function, i.e., the error of the emissivity error value in an atmospheric window band, T is the transpose of the matrix, x refers to the thickness of each film material, Minimize To minimize the three optimization objectives, It refers to the design space constructed by the maximum and minimum allowable thickness of each film material. g j (x) is j A constraint function, j is a constraint function index, c is the number of constraint functions, subject to are constraints that need to be satisfied.

3. The method according to claim 1, characterized in that The step (2) specifically includes the following steps: The first step is to use the Max-Min criterion to normalize the objective function values ​​of all population individuals to obtain the normalized objective function vector corresponding to each population individual; In the second step, each reference vector is looped, and the angle between the reference vector and the normalized target function vector of the population individual is calculated in the target space. The population individual with the smallest angle with the reference vector is matched, and the matched reference vectors are deleted in the subsequent matching process to ensure that each reference vector is matched with only one individual.

4. The method according to claim 1, characterized in that The step (3) specifically includes the following steps: The first step is to calculate the angle cosine values ​​between all population individuals in the global database and construct the angle information basis function, whose mathematical expression is as follows: ， in, It is i Individuals of a population, It is j Individuals of a population, and Respectively and The module length; The second step is to calculate the Euclidean distance between all individuals in the global database and construct the Euclidean distance information basis function, whose mathematical expression is as follows: ； The third step is to solve the weight vector corresponding to the angle information basis function and the Euclidean distance information basis function in the radial basis function machine learning model architecture. The mathematical expression is as follows: ， ， In the above formula, is the weight vector corresponding to the angle information basis function, is the weight vector corresponding to the distance information basis function, is the angle information weight corresponding to the first angle information basis function term, It is The angle information weight corresponding to the angle information basis function term is: is the distance information weight corresponding to the first Euclidean distance information basis function term, It is The distance information weight corresponding to the Euclidean distance information basis function term; The fourth step is to derive the radial basis function machine learning model with angle information enhancement, which is expressed as follows: ， In the above formula, x is the new individual corresponding to the specific value of the thickness of each film layer material generated in the iterative process. Represents the predicted value of the radial basis function machine learning model with enhanced angle information for a new individual, and Respectively represent the calculation of the new individual x and the population individual through angle information and Euclidean distance The angle information basis function term and the Euclidean distance information basis function term, is the number of individuals in the population, and They are and The i-th weight value of Represents a first-order linear polynomial function.

5. The method according to claim 1, characterized in that The step (4) specifically includes the following steps: In the first step, for each individual in the population, a global evolution mechanism driven by feasibility state is designed based on real-time state parameters to generate global candidate offspring individuals. The corresponding mathematical expression is as follows: ， In the above formula, TF is the trend function, For the population i The state parameter of each individual, max is the maximum value; In the second step, DPM mutation is used for individuals in the population that meet the feasibility requirements. The mathematical expression is as follows: ， In the above formula, is the standard deviation of the DPM variation, is the reference number of the standard deviation, min is the minimum value, and Respectively represent the maximum and minimum allowable thickness of each film material. is the scaling parameter; The third step is to use DE mutation for individuals in the population that do not meet the feasibility requirements, with the following parameters: ， In the above formula, is the scaling factor of DE variation, is the base number of the scaling factor, Represents a uniformly distributed random number between 0 and 1; The fourth step is to sequentially compare the Chebyshev function value and the constraint violation value to select the best global offspring individual from the global candidate offspring individuals; The fifth step is to design a feasibility state-driven local evolution mechanism based on real-time state parameters for each population individual to generate local candidate offspring individuals, and sequentially compare the Chebyshev function value with the constraint violation value to select the optimal local offspring individual from the local candidate offspring individuals.

6. The method according to claim 1, characterized in that The step (5) specifically includes the following steps: In the first step, the calculation rule of individual improvement is as follows: when both the offspring individual and the population individual are feasible, the individual improvement is the Chebyshev function value of the population individual minus the Chebyshev function value of the offspring individual; otherwise, the individual improvement is the constraint violation value of the population individual minus the constraint violation value of the offspring individual; The second step is to update the real-time status parameters according to the following rules ET : First, when the real-time state parameter is positive and the individual improvement of the optimal global offspring individual is greater than the individual improvement of the optimal local offspring individual, the state parameter is updated to ET = ET +1; Second, when the real-time state parameter is positive and the individual improvement of the optimal global offspring individual is less than the individual improvement of the optimal local offspring individual, the state parameter is updated to ET =-1; Third, when the real-time state parameter is negative and the individual improvement of the optimal global offspring individual is greater than the individual improvement of the optimal local offspring individual, the state parameter is updated to ET =1; Fourth, when the real-time state parameter is negative and the individual improvement of the optimal global offspring individual is less than the individual improvement of the optimal local offspring individual, the state parameter is updated to ET = ET -1.

7. The method according to claim 1, characterized in that The PF-driven screening function constructed in step (6) determines the optimal offspring individual from the optimal global and local offspring individuals, and specifically includes the following steps: The first step is to set the optimal offspring individual candidate set to an empty set; The second step is to store the corresponding optimal global and local offspring individuals into the optimal offspring individual candidate set for each population individual; The third step is to construct the PF-driven screening function. The mathematical expression is as follows: ， In the above formula, Indicates the optimal offspring individual candidate set i Offspring individuals The calculated filtering function value, max means taking the maximum value, NXObj(i,k) represents the first i Individual The corresponding k target values, where the first and second target values ​​are the emissivity error values ​​in two non-atmospheric window bands, respectively, and the third target value is the error of the emissivity error value in an atmospheric window band. PF represents the Pareto front corresponding to the current iteration. j and k Both represent indexes; The fourth step is to use the PF-driven screening function to calculate the screening function values ​​of all offspring individuals in the optimal offspring individual candidate set, and sort all offspring individuals from small to large according to the screening function value, and select the first two offspring individuals after sorting as the optimal offspring individuals.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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