A multilayer wave absorber design method based on a beta distribution model

Abstract

The application discloses a kind of based on Beta distribution model multilayer wave absorber design method, belong to electromagnetic absorption technical field, including: based on Beta distribution model, fixed total thickness encoding method, transmission line approximation method, construct multilayer homogeneous dielectric wave absorber model;According to the multilayer homogeneous dielectric wave absorber model, construct broadband optimization problem;For the broadband optimization problem constructed, genetic algorithm is used as optimization algorithm, and optimization solution is carried out;The estimated range of the to-be-optimized variable is determined, and several optimization results are obtained using the optimization algorithm, and the appropriate optimization result is selected as the combination scheme of the multilayer homogeneous dielectric wave absorber model.The application generates the dielectric constant frequency response curve of each layer equivalent homogeneous dielectric in the multilayer wave absorber using the Beta distribution model, greatly gets rid of the dependence on the material database, and can fully consider the frequency response characteristics of the material in a wide frequency range, which has important guiding significance for the design of multilayer broadband wave absorber.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromagnetic absorption, and in particular to a multilayer wave-absorbing body design method based on a Beta distribution model. BACKGROUND

[0002] To cope with the growing development of multi-radar, broadband radar detection systems, the development of multi-frequency, broadband wave-absorbing materials has become one of the research hotspots in the field of electromagnetic absorption. Traditional single-layer structure wave-absorbing bodies are difficult to achieve wideband matching with free space, and have narrow bandwidth; while multilayer structure wave-absorbing bodies can achieve wideband matching with free space by using flexible impedance characteristics, thereby expanding the bandwidth. Due to the large design dimension of the multilayer structure wave-absorbing body, intelligent algorithms are used as an effective means for optimization.

[0003] In the first prior art scheme, genetic algorithm is used for optimization of material combination and thickness of the multilayer wave-absorbing body based on a material database, and a low-frequency wave-absorbing body is designed; but the bandwidth is not good due to the limited number of material types and electromagnetic properties in the database. Similarly, in the second prior art scheme, genetic algorithm is used for optimization of material combination and thickness of the multilayer wave-absorbing body based on a material database, and a dynamic mutation probability is used to improve the algorithm performance, but the bandwidth is still not good. In the third prior art scheme, a honeycomb of thermoplastic polyester material doped with nano wave-absorbing particles is used as an equivalent dielectric layer, and the permittivity and permeability of the equivalent dielectric layer are adjusted by adjusting the size of the honeycomb and the doping concentration of the nano wave-absorbing particles, thereby expanding the design dimension, increasing the number of database materials, and using an improved genetic algorithm for optimization design; but the adjustment of the permittivity and permeability of the equivalent dielectric layer is limited, and the expansion of the database material types is small. In the fourth prior art scheme, different wide-thick ratio sheet-shaped materials of iron-silicon-aluminum are obtained by ball milling iron-silicon-aluminum at different times, thereby increasing the number of database materials, and using genetic algorithm for optimization design; but the expansion of the database material types is still limited. In the fifth prior art scheme, the mutation strategy of the genetic algorithm is improved, and an orthogonal table crossover algorithm is introduced in the later stage to avoid the algorithm falling into a local optimal solution; but the optimization process of the algorithm still depends on the material database.

[0004] Therefore, the existing multilayer composite wave-absorbing body optimization design method has the problems of poor bandwidth and dependence on and limitation by the material database in the optimization design process. SUMMARY

[0005] To at least partially solve one of the technical problems in the prior art, the purpose of the present application is to provide a multilayer wave-absorbing body design method based on a Beta distribution model.

[0006] The technical scheme adopted by the present application is as follows:

[0007] A multi-layer wave absorber design method based on a Beta distribution model, comprising the following steps:

[0008] Based on the Beta distribution model, the fixed total thickness coding method, and the transmission line approximation method, a multi-layer uniform dielectric wave absorber model is constructed.

[0009] According to the multi-layer uniform dielectric wave absorber model, a wideband optimization problem is constructed.

[0010] For the constructed wideband optimization problem, a genetic algorithm is used as an optimization algorithm for optimization solution.

[0011] The estimated range of the to-be-optimized variables is determined, a plurality of optimization results are obtained by using the optimization algorithm, and a suitable optimization result is selected as the combination scheme of the multi-layer uniform dielectric wave absorber model.

[0012] Further, the Beta distribution model includes a resonance peak Beta distribution model or a non-resonance peak Beta distribution model.

[0013] For the frequency domain electrical response characteristics of the uniform electric loss medium made of composite wave absorbing materials such as carbon-based polymers, a Beta distribution model is used to quantify the frequency response curve of the equivalent dielectric constant of the uniform electric loss medium.

[0014] If the frequency response curve of the equivalent dielectric constant of the uniform electric loss medium has a resonance peak, the calculation formula of the frequency response curve is as follows:

[0015]

[0016] Wherein, E is the sequence corresponding to the frequency response curve; F is the cumulative distribution function of the Beta probability distribution, and α and β are the independent variables of the function, which are used to adjust the curve steepness; A low , A high are the amplitude values of the frequency response curve at the lowest frequency and the highest frequency, respectively; is the probability density function of the Beta probability distribution normalized to [0, 1], and α r and β r are the independent variables of the function, which are used to adjust the peak width of the resonance peak and the position of the resonance peak on the frequency response curve; A r is the peak height value of the resonance peak; X is a sequence of any number of points taken at uniform intervals on the interval [0, 1], and ~X represents the reverse sequence of X;

[0017] If the frequency response curve of the equivalent dielectric constant of the uniform electric loss medium does not have a resonance peak, let A r = 0, and the calculation formula of the frequency response curve is degenerated as follows:

[0018] E = F(~X; α, β)·(A low -Ahigh )+A high

[0019] where the definitions of each function and variable remain unchanged.

[0020] Further, the fixed total thickness encoding method is as follows:

[0021] To facilitate the control of the total thickness of the multi-layer uniform electric loss medium wave absorber, a fixed total thickness encoding method based on binary encoding is adopted for the thickness of each layer of uniform electric loss medium, which is as follows:

[0022]

[0023] where d k is the thickness of the kth layer of uniform electric loss medium, is the corresponding binary encoding string of the kth layer, and m is the length of the encoding string; D and n are the total thickness and the number of layers of the multi-layer uniform electric loss medium wave absorber, respectively.

[0024] When the total thickness D is determined, the thickness d k of any layer is uniquely determined by the corresponding binary encoding string To ensure that the sum of the thicknesses of each layer is the total thickness D, i.e., D = d1+d2+...+d n , the following method is adopted:

[0025]

[0026] Then the binary encoding strings of the first layer to the nth layer are uniquely determined by the encoding string (b1,b2,...,b m );

[0027] Define the calculation process of formula (1) (2) as a function T, and the fixed total thickness encoding method is obtained as:

[0028] (d1,d2,...,d n )=Τ(b1,b2,...,b m ,D)

[0029] Further, the transmission line approximation method is as follows:

[0030] For a uniform electric loss medium made of carbon-based polymer composite wave absorbing material, the transmission line approximation method is used to calculate the scattering characteristics of the uniform electric loss medium.

[0031] For a layer of uniform electric loss medium, it is regarded as a section of uniform transmission line, then the calculation formulas of the complex propagation constant γ k and the characteristic impedance of the equivalent transmission line of the kth layer of uniform electric loss medium are as follows:

[0032]

[0033]

[0034] wherein, is the complex equivalent permittivity sequence of the kth layer of the uniform electric loss medium, F is the corresponding frequency sequence; c is the speed of light; η0is the wave impedance of air;

[0035] For the multilayer stack of uniform electric loss medium, it is regarded as a multi-section uniform transmission line, and the input impedance of each section of the transmission line is The calculation formula is as follows:

[0036]

[0037] wherein, d k is the thickness of the kth layer of the uniform medium; is the input impedance of the equivalent transmission line of the k-1th layer of the uniform electric loss medium; n is the total number of layers of the multilayer stack of the uniform electric loss medium;

[0038] When the k-1th layer is a metal plate, the metal plate impedance is 0 load, that is The calculation formula of the input impedance of the kth layer of the uniform electric loss medium is simplified as:

[0039]

[0040] By recursively calculating the input impedance of each section of the transmission line, the input impedance of the nth layer of the uniform medium in contact with the free space at the air contact surface is calculated and the reflection coefficient of the contact surface is calculated, and the calculation formula is:

[0041]

[0042] Further, the multilayer uniform dielectric wave absorber model is as follows:

[0043] For the multilayer stack of n layers (from the metal plate to the free space, the first layer to the nth layer) of the uniform electric loss medium made of the composite wave absorbing material based on carbon-based polymers and the like supported by the metal plate at the bottom, it has the effect of absorbing electromagnetic waves.

[0044] The electrical response characteristics of each layer are represented by the Beta distribution model, the thickness of each layer is represented by the fixed total thickness coding method, and finally the reflection coefficient RLof the contact surface with the free space is calculated by using the transmission line approximation method. The calculation process is defined as a function Ψ, and the multilayer uniform dielectric wave absorber model is obtained as follows:

[0045] 1) When the beta distribution model is equipped with the beta distribution model:

[0046] RL=Ψ(Φ1,T)

[0047] =Ψ{(α′,β′,A′ low ,A′ high )1,(a″,b″,A″ low "A" high )1,…,(α′,β′,A′ low ,A′ high ) n ,(a″,b″,A″ low "A" high ) n ,

[0048] [(α′1,β′1,A′1)1,(α″1,β″1,A″1)1,...,(α′ r ,b′ r ,A′ r )1,(a″ r ,b″ r "A" r )1],…,

[0049] [(α1′,β1′,A1′) n ,(α1″,β1″,A1″) n ,...,(a r ′,b r ′,A r ′) n ,(a r ″,b r ″,A r ″) n ],

[0050] (f low ,f high ),q,(b1,…,b m ),D},

[0051] stC1:α′,α″∈[1,+∞),C2:β′,β″∈[0,1],

[0052] C3:A′ low "A" low ,A′ high "A" high ∈[0,+∞],A′ low <A′ high "A" low <A″ high ,

[0053] C4:flow f high ∈(0,+∞),f low <f high ,

[0054] C5:q≥2∧q∈N * ,

[0055] C6:b1,…,b m ∈N * ,C7:D∈(0,+∞),

[0056] C8:n,m∈N * ,

[0057] C9:α′1,α″1,...,α′ r ,α″ r ∈(0,+∞),C10:β′1,β″1,,β′ r ,β″ r ∈(0,+∞),

[0058] C11:A′1,A″1,...,A′ r ,A″ r ∈(-∞,+∞),

[0059] C12:r∈N * .

[0060] 2) When the Beta distribution model is a resonance-free Beta distribution model:

[0061] RL=Ψ(Φ2,Τ)

[0062] =Ψ[(α′,β′,A l ′ ow ,A h ′ igh )1,(α″,β″,A l ′ o ′ w ,A h ″ igh )1,…,(α′,β′,A l ′ ow ,A h ′ igh ) n ,(α″,β″,A l ′ o ′ w ,A h ″ igh ) n ,

[0063] (f low ,f high), q, (b1, …, b m ), D],

[0064] s.t.C1:α′,α″∈[1,+∞),C2:β′,β″∈[0,1],

[0065] C3:A′ low ,A′ low ,A′ high ,A″ high ∈[0,+∞],A′ low <A′ high ,A″ low <A″ high ,

[0066] C4:f low ,f high ∈(0,+∞),f low <f high ,

[0067] C5:q≥2∧q∈N * ,

[0068] C6:b1,…,b m ∈N * ,C7:D∈(0,+∞),

[0069] C8:n,m∈N * .

[0070] In the formula, k and n are the layer sequence and the number of layers of the multilayer wave absorber, respectively; f low and f high are the lowest frequency and the highest frequency of the frequency response curve, respectively; r is the number of resonance peaks; α and β are parameters in the Beta distribution model that adjust the steepness of the frequency response curve; A low and A high are the amplitude of the frequency response curve at the lowest frequency and the highest frequency, respectively; α r and β r are parameters in the Beta distribution model that adjust the width of the resonance peak, and the ratio of α r and β r can adjust the position of the resonance peak in the frequency band; A r is the peak height value of the resonance peak.

[0071] D is the total thickness of the multilayer uniform electric loss medium wave absorber; q is the sequence length of the equivalent dielectric constant; (b1, b2, …, b m ) is a code string, and m is the length of the code string; N * is a set of positive integers.

[0072] Further, the wideband optimization problem is constructed according to the multi-layer uniform dielectric wave absorber model, and the wideband optimization problem includes:

[0073] To better evaluate the wideband performance of the optimization result, an evaluation method of setting different weights for different wave bands is adopted, and the evaluation of the wideband performance is divided into L, S, C, X and Ku wave bands for quantitative calculation, and the calculation formula of the evaluation index is:

[0074] fit=w L ·PCT L +w S ·PCT S +w C ·PCT C

[0075] +w X ·PCT X +w Ku ·PCT Ku

[0076] In the formula, w L =2, w S =2, w C =1, w X =1, w Ku =1 are the weights of the L, S, C, X and Ku wave bands respectively, and PCT L / S / C / X / Ku is the proportion of the number of frequency points meeting the target reflectivity requirement in the total number of frequency points in the L / S / C / X / Ku wave band, and the calculation formula is:

[0077]

[0078]

[0079] In the formula, RL L / S / C / X / Ku is the target reflectivity requirement of the L / S / C / X / Ku wave band; bool i is used to describe whether the reflection coefficient RL meets the target reflectivity requirement; N L / S / C / X / Ku is the total number of frequency points of the L / S / C / X / Ku wave band.

[0080] According to the calculation process of the evaluation index fit, fit depends on the function Ψ (i.e. the reflection coefficient RL), and the wideband optimization problem P1 is constructed as follows:

[0081]

[0082] s.t.C1:α′,α″∈[1,+∞),C2:β′,β″∈[0,1],

[0083] C3:A′ low ,A″low ,A′ high ,A″ high ∈[0,+∞],A′ low <A′ high ,A″ low <A″ high ,

[0084] C4:f low ,f high ∈(0,+∞),f low <f high ,

[0085] C5:q≥2∧q∈N * ,

[0086] C6:b1,…,b m ∈N * ,C7:D∈(0,+∞),

[0087] C8:n,m∈N * ,

[0088] C9:α′1,α″1,...,α′ r ,α″ r ∈(0,+∞),C10:β′1,β″1,...,β′ r ,β″ r ∈(0,+∞),

[0089] C11:A′1,A″1,...,A′ r ,A″ r ∈(-∞,+∞),

[0090] C12:r∈N * .

[0091] Further, the wideband optimization problem for construction adopts a genetic algorithm as an optimization algorithm to perform optimization solution, and the genetic algorithm comprises the following steps:

[0092] To improve the solution efficiency of the genetic algorithm for the optimization problem P1, a dynamic change of a crossover probability and a mutation probability is adopted, and a calculation formula is as follows:

[0093]

[0094] In the formula, r co and r mt are the crossover probability and the mutation probability respectively; fit is an evaluation index value of any individual in a population of the genetic algorithm; fit max is an evaluation index value of an individual with the highest evaluation index value in the population; and fit is an average value of evaluation index values of all individuals in the population.

[0095] Further, a population disaster mechanism is introduced in the solving process to avoid the genetic algorithm from falling into a local optimal solution in solving the optimization problem P1:

[0096] Wherein, the triggering condition of the population disaster mechanism is that when the evaluation indexes fit of all individuals in the population are equal;

[0097] The action mode of the population disaster mechanism is to retain 1% of the individuals in the population, regenerate and randomly initialize 99% of the individuals to form a new population.

[0098] Further, the estimated range of the to-be-optimized variable is determined, including:

[0099] On the basis of the constraint conditions C1-C12 of the optimization problem P1, the value range of all to-be-optimized variables is limited to a closed interval, so the following formula is used to limit the range of part of the to-be-optimized variables:

[0100]

[0101] In the formula, α min , α max are the minimum value and the maximum value of the α parameter in the Beta distribution model; β min , β max are the minimum value and the maximum value of the β parameter in the Beta distribution model; (A low ) min , (A low ) max are the minimum value and the maximum value of the A low parameter in the Beta distribution model; (A high ) min , (A high ) max are the minimum value and the maximum value of the A high parameter in the Beta distribution model; (A) min , (A) max are the minimum value and the maximum value of the A r parameter in the Beta distribution model.

[0102] Further, the optimization algorithm is used to obtain a plurality of optimization results, and a suitable optimization result is selected as the combination scheme of the multi-layer uniform dielectric wave absorber model, including:

[0103] Within the constraint conditions C1-C12 of the optimization problem P1, the value range of the to-be-optimized variable is defined as a closed interval, and the to-be-optimized variable is solved by using a genetic algorithm to obtain a group of solutions; the material electric response characteristics and physical size represented by the group of solutions are compared with the actual material to determine whether the group of solutions conforms to the physical law and engineering practice; if yes, the group of solutions is taken as the final scheme of the multilayer homogeneous dielectric wave absorber model; if not, the estimated range of the to-be-optimized variable is adjusted to perform solving again, and the above process is repeated.

[0104] Compared with the prior art, the present application can at least achieve the following beneficial effects:

[0105] (1) The multilayer wave absorber design method based on the Beta distribution model proposed in the present application quantifies the electric response characteristics of the dielectric constant of composite materials such as carbon-based polymers in the frequency domain based on the Beta distribution model, and fully considers the dielectric constant resonance characteristics, which can simultaneously fit the resonance peaks of the frequency response curve, and has strong versatility.

[0106] (2) The multilayer wave absorber design method based on the Beta distribution model proposed in the present application designs a fixed total thickness encoding method for the optimization process of the multilayer wave absorber, which is easy to control the profile and plays an important role in the optimization design of low-profile broadband multilayer wave absorbers.

[0107] (3) The multilayer wave absorber design method based on the Beta distribution model proposed in the present application introduces dynamic crossover probability, mutation probability and population disaster mechanism in the genetic algorithm, which avoids the algorithm from falling into a local optimal solution and improves the local search and global search ability of the algorithm.

[0108] (4) The multilayer wave absorber design method based on the Beta distribution model proposed in the present application uses the Beta distribution model to generate the dielectric constant frequency response curve of the equivalent homogeneous dielectric in each layer of the multilayer wave absorber, which greatly gets rid of the dependence on the material database, and can fully consider the frequency response characteristics of the material in a wide frequency range, which has important guiding significance for the design of multilayer broadband wave absorbers. BRIEF DESCRIPTION OF DRAWINGS

[0109] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following introduces the drawings of the related technical solutions in the embodiments of the present application or the prior art. It should be understood that the drawings in the following introduction are only for the convenience of clearly describing part of the embodiments in the technical solutions of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0110] Figure 1Fig. 1 is a schematic diagram of fitting of dielectric constant of ferro-silicon aluminum material based on a Beta distribution model according to an embodiment of the present application, wherein (a) is the real part of the dielectric constant and its fitting, and (b) is the imaginary part of the dielectric constant and its fitting;

[0111] Table 1 is a parameter of Beta distribution model fitting of dielectric constant of ferro-silicon aluminum material based on a Beta distribution model according to an embodiment of the present application;

[0112] Figure 2 Fig. 2 is a schematic diagram of fitting of dielectric constant of carbon-based polymer material based on a Beta distribution model according to an embodiment of the present application, wherein (a) is the real part of the dielectric constant and its fitting, and (b) is the imaginary part of the dielectric constant and its fitting;

[0113] Table 2 is a parameter of Beta distribution model fitting of dielectric constant of carbon-based polymer material based on a Beta distribution model according to an embodiment of the present application;

[0114] Figure 3 Fig. 3 is a flowchart of a method for designing a multilayer wave absorber based on a Beta distribution model according to an embodiment of the present application;

[0115] Figure 4 Fig. 4 is a frequency response curve diagram of dielectric constant of each layer of a multilayer wave absorber according to an embodiment of the present application;

[0116] Figure 5 Fig. 5 is a frequency response curve diagram of reflection coefficient of a multilayer wave absorber according to an embodiment of the present application;

[0117] Figure 6 Fig. 6 is a step flowchart of a method for designing a multilayer wave absorber based on a Beta distribution model according to an embodiment of the present application. DETAILED DESCRIPTION

[0118] Embodiments of the present application are described in detail below with reference to the accompanying drawings, wherein the same or similar notations used throughout the drawings and the specification denote the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as a limitation of the present application. For the step numbers in the following embodiments, only the setting is for the convenience of explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0119] In the description of the present application, it should be understood that the orientation description, such as the orientation or position relationship indicated by the upper, lower, front, rear, left, right and the like, is based on the orientation or position relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0120] In the description of the present application, one or more is understood as one or more, two or more is understood as two or more, greater than, less than, more than, etc. are understood as not including the number, above, below, etc. are understood as including the number. If the first, second is described, it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of technical features indicated. In addition, the association relationship of the associated objects described by "and / or" indicates that there can be three kinds of relationships, for example, A and / or B can represent three cases of A alone, A and B together, and B alone. The character " / " generally represents an "or" relationship between the front and rear associated objects.

[0121] In the description of the present application, unless otherwise explicitly limited, the words such as setting, installing, connecting and the like should be broadly understood, and the person skilled in the art can reasonably determine the specific meaning of the above words in the present application in combination with the specific content of the technical solution.

[0122] Term explanation:

[0123] Beta distribution model: the Beta distribution model is a mathematical model for describing the electrical response characteristics of composite wave-absorbing materials such as carbon-based polymers in the frequency domain, such as dielectric constant. Through the Beta distribution model, the continuous frequency response curve formed by the above electrical response characteristics in the frequency domain can be described and calculated by several parameters, greatly reducing the optimization difficulty of the optimization algorithm; and the frequency response curve described by the Beta distribution model has high consistency with the actual material, and has the ability to implement engineering.

[0124] In view of the existing technical problems, the present application provides a multi-layer wave-absorbing body design method based on a Beta distribution model. First, for the electrical response characteristics of a uniform electrical loss medium made of composite wave-absorbing materials such as carbon-based polymers in the frequency domain, a mathematical model based on Beta distribution is proposed to quantify the frequency response curve; for the thickness of each layer of the multi-layer wave-absorbing body, a fixed total thickness coding method is proposed; further, the Beta distribution model and the fixed total thickness coding method are introduced into the genetic algorithm, and the transmission line approximation method is combined to optimize and design the multi-layer uniform electrical loss medium wave-absorbing body, and a wide frequency absorption bandwidth is realized.

[0125] As Figure 6As shown, the embodiment provides a multilayer wave absorber design method based on a Beta distribution model, including the following steps:

[0126] S1, based on the Beta distribution model, the fixed total thickness coding method, and the transmission line approximation method, a multilayer uniform dielectric wave absorber model is constructed.

[0127] As an optional implementation, the Beta distribution model in step S1 is a Beta distribution model with resonance peaks, and the Beta distribution model with resonance peaks is specifically:

[0128] For the frequency response curve with resonance peaks, the following parameters are taken to describe:

[0129]

[0130] Where k and n are the layer sequence and the total number of layers of the multilayer wave absorber, respectively; low , f high are the lowest frequency and the highest frequency of the frequency response curve, respectively; r is the number of resonance peaks.

[0131] In formula (1), (α′,β′,A′ low ,A′ high ) k , (α″,β″,A″ low ,A″ high ) k and (α′1,β′1,A′1) k ,(α″1,β″1,A″1) k ,...,(α r ′,β r ′,A r ′) k ,(α r ″,β r ″,A r ″) k are used to calculate the real part sequence E′k and the imaginary part sequence E′k′ of the equivalent dielectric constant of the kth layer, and the calculation formula is:

[0132]

[0133] Where (A′ low )k and (A″ low )k are the amplitude values of the real part and the imaginary part of the equivalent dielectric constant of the kth layer at the lowest frequency f low , (A′ high ) k and (A″ high ) k are the amplitude values of the real part and the imaginary part of the equivalent dielectric constant of the kth layer at the highest frequency f highThe amplitude value of the phase of the first harmonic; (A1′) k ,...,(A r k ,...,(A1″) k ,...,(A r k The real part and the imaginary part of the equivalent dielectric constant, respectively, the peak height of the first to the rth resonance peak, when the peak height is negative, then the resonance peak is converted into a resonance valley.

[0134] X is a one-dimensional sequence of q points on [0, 1] with uniform spacing (q affects the quantization accuracy of the curve), ~X is the reverse sequence of X; F is the cumulative distribution function of the Beta distribution, and its definition is:

[0135]

[0136] is the probability density function of the Beta distribution normalized to [0, 1], that is:

[0137]

[0138] The definition of the probability density function of the Beta distribution is:

[0139]

[0140] Г in formula (3) (5) is the gamma function, and its definition is:

[0141]

[0142] Further, the real part sequence E′ k and the imaginary part sequence E′ k ′ of the equivalent dielectric constant of the kth layer are calculated by the following formula:

[0143]

[0144] The complex equivalent dielectric constant sequence

[0145] (f low ,f high ) in formula (1) is used to obtain the frequency point sequence F corresponding to the complex equivalent dielectric constant sequence by de-normalization, and the calculation formula is:

[0146] F=X·(f high -f low )+f low (8)

[0147] ​​Through the above process, the frequency point sequence F is calculated, and the complex equivalent dielectric constant sequence E corresponding to the frequency point sequence F is calculated k , which is used to describe the electrical response characteristics of a uniform electrical loss medium in the frequency domain, is defined as a function Φ1, as follows:

[0148]

[0149] As shown in Figure 1 , Figure 1 is the fitting effect of the resonant peak Beta distribution model on the real and imaginary parts of the dielectric constant of the iron-silicon-aluminum material. As can be seen, Figure 1 , the real and imaginary parts of the dielectric constant of the iron-silicon-aluminum material shown in (a) and (b) have obvious resonant peaks, and the Beta distribution model has good fitting effect. Table 1 is the parameter of the fitting curve of the resonant peak Beta distribution model on the real and imaginary parts of the dielectric constant of the iron-silicon-aluminum material, corresponding to the parameters of formula (1). Among them, R 2 is the determination coefficient for evaluating the fitting effect, and the calculation formula is:

[0150]

[0151] Among them, ε i is the dielectric constant sample value, is the mean of the dielectric constant sample value, is the fitting value.

[0152] R 2 is closer to 1, the better the fitting effect. As can be seen from Table 1, the values of R 2 are close to 1, indicating that the resonant peak Beta distribution model has good fitting effect on the real and imaginary parts of the dielectric constant of the iron-silicon-aluminum material. The model has engineering significance.

[0153] Table 1

[0154]

[0155] As another optional implementation, the step S1 Beta distribution model is a non-resonant peak Beta distribution model, and the non-resonant peak Beta distribution model is specifically:

[0156] For the frequency response curve without resonant peak, the parameters (α1′, β1′, A1′) k ,(α1″, β1″, A1″) k ,...,(α r ′,β r ′,A r ′) k ,(α r ″,β r ″,A r ″)k Remove, so the formula (1) is simplified as:

[0157] [(α′,β′,A l ′ ow ,A h ′ igh ) k ,(α″,β″,A l ′ o ′ w ,A h ″ igh ) k ,(f low ,f high )],k=1,2,...,n.(11) Where k, n are the layer sequence, the total number of layers of the multilayer wave absorber; f low , f high are the lowest frequency, the highest frequency of the frequency response curve.

[0158] (α′,β′,A′ low ,A′ high ) k and (α″,β″,A″ low ,A″ high ) k for calculating the real part sequence E′ k , the imaginary part sequence E′ k ′ of the equivalent dielectric constant of the kth layer, then the calculation formula (2) is simplified as:

[0159]

[0160] The function in formula (12) and the variable definition are the same as formula (3) (6).

[0161] Via formula (7) (8), the frequency point sequence F and the complex equivalent dielectric constant sequence for describing the electrical response characteristics of the uniform lossy medium in the frequency domain, defined as the function Φ2, as follows:

[0162]

[0163] As shown in Figure 2 , the fitting effect of the Beta distribution model without resonance peak on the real part and imaginary part of the dielectric constant of the carbon-based polymer material. As can be seen, Figure 2 The fitting effect of the Beta distribution model shown in (a) and (b) on the real part and imaginary part of the dielectric constant of the carbon-based polymer material is good. Table 2 is the parameter of the fitting curve of the real part and imaginary part of the dielectric constant of the iron-silicon-aluminum material by the Beta distribution model with resonance peak, corresponding to each parameter of formula (1).

[0164] As the above embodiment, the R 2 value is close to 1, which shows that the no resonance peak Beta distribution model has good fitting effect on the real part and imaginary part of the dielectric constant of iron silicon aluminum material. The model has engineering significance. 2

[0165] Table 2

[0166]

[0167]

[0168] In some optional embodiments, the fixed total thickness encoding method is as follows:

[0169] In order to conveniently control the total thickness of the multi-layer uniform electric loss medium wave absorber, the fixed total thickness encoding method based on binary encoding is adopted for the thickness of each layer of uniform electric loss medium, as follows:

[0170]

[0171] Wherein, d k is the thickness of the kth layer of uniform electric loss medium, is the corresponding binary encoding string of the kth layer, and m is the length of the encoding string; D and n are the total thickness and the number of layers of the multi-layer uniform electric loss medium wave absorber, respectively.

[0172] Based on formula (14), when the total thickness D is determined, any layer thickness d k can be uniquely determined by the corresponding binary encoding string In order to ensure that the sum of the thicknesses of each layer is the total thickness D, i.e. D = d1+d2+...+d n , the following method is adopted:

[0173]

[0174] Then the binary encoding string corresponding to the first layer to the nth layer can be uniquely determined by the encoding string (b1, b2,..., b m ). Define the calculation process of formula (8) (9) as a function T, and then the fixed total thickness encoding method is obtained as:

[0175] (d1, d2,..., d n ) = T(b1, b2,..., b m , D) (16)

[0176] In some optional embodiments, the transmission line approximation method is as follows:

[0177] ​For homogeneous electrical loss dielectrics made from composite absorbing materials such as carbon-based polymers, the scattering characteristics are calculated using the transmission line approximation method.

[0178] For a single layer of uniformly lossy dielectric material, it can be considered as a uniform transmission line. The complex propagation constant γ of the equivalent transmission line of the k-th layer of uniformly lossy dielectric material is then... k and characteristic impedance The calculation formula is:

[0179]

[0180] in, It is the sequence of complex equivalent dielectric constants of the k-th layer of uniform electrical loss dielectric, F is the corresponding frequency sequence, which can be represented by equation (8); c is the speed of light, c = 3 × 10 8 m / s; η0 is the wave impedance of air, η0=120πΩ.

[0181] For a multilayer stacked uniform loss dielectric, it can be regarded as multiple segments of uniform transmission lines, each segment having an input impedance of... The calculation formula is:

[0182]

[0183] Where, γ k , It can be calculated from equations (17) and (18); d k It is the thickness of the k-th homogeneous medium, which can be represented by equation (14); is the input impedance of the equivalent transmission line of the (k-1)th layer of uniform loss dielectric; n is the total number of layers of the multilayer stacked uniform loss dielectric.

[0184] When the (k-1)th layer is a metal plate, the load with zero impedance of the metal plate is... The formula for calculating the input impedance of the k-th layer of uniform electrical loss dielectric material simplifies to:

[0185]

[0186] By recursively calculating the input impedance of each transmission line segment according to equations (19) and (20), the input impedance of the nth layer of homogeneous medium in contact with free space at the air contact surface can be calculated. The reflection coefficient of the contact surface was calculated using the following formula:

[0187]

[0188] Specifically, the constructed multilayer homogeneous dielectric absorber model is as follows:

[0189] For a multi-layer uniform electric loss medium made of carbon-based polymer composite wave-absorbing material supported by a metal plate at the bottom, n layers are stacked (from the metal plate to the free space, the first layer to the nth layer), which has the effect of absorbing electromagnetic waves. The electrical response characteristics of each layer can be represented by functions Φ1 or Φ2 based on the Beta distribution model, as shown in equations (9) and (12); the thickness of each layer can be represented by function T based on the fixed total thickness coding method, as shown in equation (15); and finally, the reflection coefficient RL of the interface with the free space is calculated by equations (11)-(15) using the transmission line approximation method. Defining the above process as function Ψ, the multi-layer uniform medium wave-absorbing body model is obtained as follows:

[0190]

[0191] or

[0192]

[0193] S2, constructing a wideband optimization problem based on the multi-layer uniform electric medium wave-absorbing body model.

[0194] As an optional implementation, in order to better evaluate the wideband performance of the optimization result, an evaluation method of setting different weights for different wave bands is adopted, and the evaluation of the wideband performance is divided into L, S, C, X, Ku, a total of 5 wave bands for quantitative calculation. The calculation formula of the evaluation index is:

[0195]

[0196] where w L = 2, w S = 2, w C = 1, w X = 1, w Ku = 1 are the weights of L, S, C, X, and Ku wave bands respectively, and PCT L / S / C / X / Ku is the proportion of the number of frequency points meeting the target reflectivity requirement in the total number of frequency points in each L / S / C / X / Ku wave band. The calculation formula is:

[0197]

[0198] where RL L / S / C / X / Ku is the target reflectivity requirement of L / S / C / X / Ku wave band, with unit of dB; bool i is used to describe whether the reflection coefficient RL obtained by equation (22) or equation (23) meets the target reflectivity requirement; and N L / S / C / X / Ku is the total number of frequency points in each L / S / C / X / Ku wave band.

[0199] According to the calculation process of the above evaluation index fit, fit depends on the function Ψ (i.e. the reflection coefficient RL), and the wideband optimization problem (P1) can be constructed as follows:

[0200]

[0201] The constraint conditions C1-C5 in the optimization problem (P1) ensure that the real part sequence E' of the equivalent permittivity obtained by the Beta distribution model described in claim 2 k and the imaginary part sequence E" k are non-negative sequences that decrease with increasing corresponding frequency; the constraint conditions C6-C7 ensure that the thickness of each layer of the multilayer homogeneous dielectric wave absorber is a non-negative number; the constraint condition C8 ensures that the total number of layers of the multilayer homogeneous dielectric wave absorber is greater than 1; and the constraint conditions C9-C12 ensure that the number of resonance peaks is greater than or equal to 0.

[0202] In the considered optimization problem (P1), there are two types of variables:

[0203] ① Preset variables, specifically: the lowest frequency f low and the highest frequency f high , the sequence length q of the equivalent permittivity, the encoding string length m of the fixed total thickness encoding method, the total number of layers n and the total thickness D of the multilayer homogeneous dielectric wave absorber, and the number of resonance peaks r;

[0204] ② Variables to be optimized, specifically: the parameters of the electrical response characteristics of each layer of the homogeneous dielectric represented by the Beta distribution model the encoding string (b1,…,b m ) of the fixed total thickness encoding method.

[0205] According to the variable type, the optimization problem (P1) is divided into two steps: first, determine the preset variables according to user requirements; second, use an optimization algorithm to find the optimal variables to be optimized.

[0206] S3, for the wideband optimization problem of the multilayer homogeneous dielectric wave absorber model, a genetic algorithm is used as the optimization algorithm, and the parameters of the genetic algorithm are initialized, including: population size N p , maximum number of iterations G max , crossover probability and genetic probability, and a population disaster mechanism is introduced.

[0207] As an optional implementation, the crossover probability and mutation probability are as follows:

[0208] To improve the solving efficiency of the genetic algorithm for the optimization problem (P1), the crossover probability and mutation probability are dynamically changed, and the calculation formula is:

[0209]

[0210] wherein, r co and r mt are the crossover probability and mutation probability, respectively; fit is the evaluation index value of any individual in the population of the genetic algorithm; fit max is the evaluation index value of the individual with the highest evaluation index value in the population; and is the average value of the evaluation index values of all individuals in the population.

[0211] As an optional embodiment, a population disaster mechanism is introduced, specifically as follows:

[0212] To avoid the solution of the genetic algorithm for the optimization problem (P1) falling into a local optimal solution, a population disaster mechanism is introduced.

[0213] The triggering condition of the population disaster mechanism is that the evaluation index fit of all individuals in the population is equal.

[0214] The action mode of the population disaster mechanism is to retain 1% of the individuals in the population, re-generate and randomly initialize 99% of the individuals, and form a new population.

[0215] S4, determine the estimated range of the to-be-optimized variable, obtain a plurality of optimization results by using an optimization algorithm, and select a suitable optimization result as the combination scheme of the multilayer uniform dielectric wave absorber model.

[0216] Specifically, the determination of the value range of the to-be-optimized variable in step S4 is as follows:

[0217] On the basis of the constraint conditions C1-C12 of the optimization problem (P1), the value range of all to-be-optimized variables is limited to a closed interval, so the following formula is used to limit the range of part of the to-be-optimized variables:

[0218]

[0219] Within the constraint conditions C1-C12 of the optimization problem (P1), the value range of the to-be-optimized variable is limited to a closed interval, and the genetic algorithm is used to solve the to-be-optimized variable to obtain a group of solutions. The material electrical response characteristics and physical size represented by the group of solutions are compared with the actual material to determine whether the group of solutions conforms to the physical law and engineering practice: if yes, the group of solutions is used as the final scheme of the multilayer uniform dielectric wave absorber model; if no, the estimated range of the to-be-optimized variable is adjusted for solving again, and the above process is repeated.

[0220] The above method is explained and described in detail in combination with the drawings and specific embodiments.

[0221] In some embodiments, referring to Figure 3Before entering the genetic algorithm process, a non-resonant peak Beta distribution model is selected as the optimization model, the minimum frequency and the maximum frequency are set to 0.3 GHz and 18 GHz, the total thickness is 30 mm, and the number of layers is 5, to obtain a set of solutions in accordance with physical laws and engineering practices, as shown in Figure 4 . Among them, from the metal back plate to the free space, each layer is L1, L2, L3, L4, and L5, and the thickness of each layer is d1=12 mm, d2=9 mm, d3=4 mm, d4=3 mm, and d5=2 mm. The equivalent dielectric constant of each layer is substituted into the commercial electromagnetic simulation software HFSS to obtain the simulation results, as shown in Figure 5 . Among them, Figure 5 (a) is the simulation model, Figure 5 (b) is the algorithm optimization result and the simulation result, and the results are consistent. The reflection coefficient is less than -10 dB in the frequency band range of 1.29-18 GHz, and the profile height is 0.133 L (λ L is the wavelength corresponding to the lowest frequency in the -10 dB bandwidth range), which has good performance of a low profile and a wide absorption band.

[0222] In the above description of the present specification, the description of the terms "one embodiment", "another embodiment", or "some embodiments" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiments or examples are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the described specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0223] Although the embodiments of the present application have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, replacements and variations can be made to these embodiments without departing from the principles and purposes of the present application, and the scope of the present application is defined by the claims and their equivalents.

[0224] The above is a specific description of the preferred embodiments of the present application, but the present application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the present application, and these equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A method for designing a multilayer wave absorber based on a Beta distribution model, characterized in that, The method comprises the following steps: A multi-layer uniform dielectric wave absorber model is constructed based on a Beta distribution model, a fixed total thickness encoding method and a transmission line approximation method; A broadband optimization problem is constructed according to the multi-layer uniform dielectric wave absorber model; The genetic algorithm is used as an optimization algorithm to solve the broadband optimization problem; The estimated range of the to-be-optimized variables is determined, and a plurality of optimization results are obtained by using the optimization algorithm, and a suitable optimization result is selected as the combination scheme of the multi-layer uniform dielectric wave absorber model; The Beta distribution model comprises a resonance peak Beta distribution model or a non-resonance peak Beta distribution model; The Beta distribution model is used to quantify the frequency response curve of the equivalent permittivity of the uniform electric loss medium according to the electric response characteristics of the uniform electric loss medium made of the composite wave absorbing material in the frequency domain. If the frequency response curve of the equivalent permittivity of the uniform electric loss medium has a resonance peak, the calculation formula of the frequency response curve is as follows: wherein, is a sequence corresponding to the frequency response curve; is a cumulative distribution function of a Beta probability distribution, is an argument of the function, used to adjust the steepness of the curve; are the amplitude values of the frequency response curve at the lowest and highest frequencies, respectively; is a probability density function of a Beta probability distribution normalized to [0, 1], is an argument of the function, used to adjust the peak width of the resonance peak and the position of the resonance peak on the frequency response curve; is the peak height value of the resonance peak; is a sequence of arbitrary number of points taken at uniform intervals on the interval [0, 1], denotes the reverse sequence of If the frequency response curve of the equivalent dielectric constant of the uniform electric loss medium does not have a resonance peak, let , the calculation formula of the frequency response curve degenerates into the following form: Wherein the definitions of the functions and variables remain unchanged.

2. The method of claim 1, wherein, The fixed total thickness encoding method is as follows: In order to conveniently control the total thickness of the multi-layer uniform electric loss medium wave absorber, a fixed total thickness encoding method based on binary encoding is adopted for the thickness of each layer of uniform electric loss medium, which is as follows: （1） In the formula, is the thickness of the kth layer of uniform electric loss medium, is the binary code string corresponding to the kth layer, is the length of the code string; n are the total thickness and the number of layers of the multilayer uniform electric loss medium wave absorber, respectively; is a set of positive integers; when the total thickness determining the thickness of any layer from the corresponding binary coded string uniquely determined; to ensure that the sum of the thicknesses of the layers is the total thickness i.e. The following method is adopted: （2） The binary code string corresponding to the 1st layer to the nth layer The code string is determined by the code string Unique determination; The calculation process of formula (1) (2) is defined as a function The fixed total thickness encoding method is obtained as follows: 。 3. The method of claim 1, wherein, The transmission line approximation method is as follows: The transmission line approximation method is used to calculate the scattering characteristics of the uniform electric loss medium made of the composite wave absorbing material. For a uniform electric loss medium, it is regarded as a uniform transmission line, the calculation formula of the complex propagation constant of the equivalent transmission line of the kth uniform electric loss medium is and the characteristic impedance ​ wherein is a sequence of complex equivalent permittivity of the kth uniform electric loss medium, F is a corresponding sequence of frequency points; c is the speed of light; is the wave impedance of air; For a multilayer stack of uniform electrically lossy media, consider it as a multi-section uniform transmission line, the input impedance of each section of the transmission line is calculated as follows: Zin = Z0 + jX0 wherein Zin(k) is the input impedance of the equivalent transmission line of the kth uniform electrically lossy medium; When the k-1th layer is a metal plate, the metal plate impedance is a load of 0, i.e. The calculation formula of the input impedance of the kth uniform electric loss medium is simplified as follows: The input impedance of the air contact surface of the nth uniform medium layer in contact with free space is calculated by recursively calculating the input impedance of each transmission line and the reflection coefficient of the contact surface is calculated, and the calculation formula is: 。 4. The method of claim 1, wherein, The multi-layer uniform dielectric wave absorber model is as follows: For the n-layer stacked multilayer uniform electric loss medium made of composite wave-absorbing material supported by metal plate at the bottom, the effect of absorbing electromagnetic wave is achieved, the electric response characteristics of each layer are represented by Beta distribution model, the thickness of each layer is represented by fixed total thickness coding method, and finally the reflection coefficient RL of the contact surface between the multilayer uniform electric loss medium and free space is calculated by using transmission line approximation method; the calculation process is defined as a function Therefore, the multilayer uniform medium wave-absorbing body model is as follows: 1) When the Beta distribution model is a resonance peak Beta distribution model: 2) When the Beta distribution model is a non-resonance peak Beta distribution model: wherein, , are the lowest frequency and the highest frequency of the frequency response curve, respectively; r is the number of resonance peaks; is a parameter in the Beta distribution model that adjusts the steepness of the frequency response curve; is a parameter in the Beta distribution model that adjusts the width of the resonance peaks, and the ratio of the two parameters adjusts the position of the resonance peaks in the frequency band; is the peak height value of the resonance peak; is the sequence length of the equivalent permittivity.

5. The method of claim 4, wherein, The broadband optimization problem is constructed according to the multi-layer uniform dielectric wave absorber model, which comprises: In order to better evaluate the broadband performance of the optimization result, an evaluation method of setting different weights for different wave bands is adopted, and the evaluation of the broadband performance is divided into L, S, C, X and Ku wave bands for quantitative calculation, and the calculation formula of the evaluation index is as follows: In the formula, w L = 2, w S = 2, w C = 1, w X = 1, w Ku = 1 respectively are weights corresponding to L, S, C, X, Ku bands, is the proportion of the number of frequency points meeting the target reflectivity requirement in the total number of frequency points in L / S / C / X / Ku bands, and the calculation formula is: In the formula, is the target reflectivity requirement of each band of L / S / C / X / Ku; is used to describe whether the reflection coefficient RL meets the target reflectivity requirement; is the total number of frequency points of each band of L / S / C / X / Ku; According to the evaluation index fit The calculation process can be known, fit Depending on the function Then the wideband optimization problem P1 is constructed as follows: 。 6. The method of claim 5, wherein, The genetic algorithm is used as an optimization algorithm to solve the broadband optimization problem, which comprises: In order to improve the solving efficiency of the genetic algorithm for the optimization problem P1, the crossover probability and the mutation probability are dynamically changed, and the calculation formula is as follows: wherein, and are the crossover probability and mutation probability, respectively; is the evaluation index value of any individual in the population of the genetic algorithm; is the evaluation index value of the individual with the highest evaluation index value in the population; is the average of the evaluation index values of all individuals in the population.

7. The method of claim 6, wherein, A population disaster mechanism is introduced in the solving process to avoid the local optimal solution of the genetic algorithm for the optimization problem P1: Wherein, the triggering condition of the population disaster mechanism is: when the evaluation index value of all individuals in the population is equal equal; The action mode of the population disaster mechanism is to retain 1% of the individuals in the population, randomly initialize 99% of the individuals, and form a new population.

8. The method of claim 5, wherein, The estimated range of the to-be-optimized variables is determined, which comprises: On the basis of the constraint conditions C1-C12 of the optimization problem P1, the value range of all to-be-optimized variables is limited to a closed interval, so that the range of part of the to-be-optimized variables is limited by using the following formula: wherein is the minimum value of the parameter is the maximum value of the parameter is the minimum value of the parameter is the maximum value of the parameter is the minimum value of the parameter is the maximum value of the parameter is the minimum value of the parameter is the maximum value of the parameter is the minimum value of the parameter is the maximum value of the parameter 9. The method of claim 5, wherein, The genetic algorithm is used as an optimization algorithm to solve the broadband optimization problem, which comprises: In the constraint conditions C1-C12 of the optimization problem P1, the value range of the to-be-optimized variable is defined as a closed interval, and the genetic algorithm is used to solve the to-be-optimized variable to obtain a group of solutions; the material electric response characteristics and physical size represented by the group of solutions are compared with the actual material to determine whether the group of solutions conforms to the physical law and engineering practice; if yes, the group of solutions is taken as the final scheme of the multilayer homogeneous dielectric wave absorber model; if not, the estimated range of the to-be-optimized variable is adjusted for solving again, and the above process is repeated.

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