CN103159168B - A kind of method determining the metamaterial modular construction with maximum bandwidth characteristic - Google Patents

Abstract

The invention provides a kind of method determining the metamaterial modular construction with maximum bandwidth characteristic, its method comprises step: definition design variable, the initial value of setting design variable and threshold value, calculate the fitness of design variable, assessment individual inheritance to follow-on probability, and operates through intersect, make a variation and judgement etc. the structure determining the metamaterial unit with maximum bandwidth characteristic.The present invention is in optimized selection initial value by utilizing follow-on genetic algorithm, and carries out dynamic change to mutation probability, improves the convergence of optimization and obtains globally optimal solution better, avoiding occurring locally optimal solution.

Description

A kind of method determining the metamaterial modular construction with maximum bandwidth characteristic

Technical field

The present invention relates to Meta Materials field, particularly relate to a kind of method utilizing the structure of genetic algorithm optimization metamaterial unit.

Background technology

At present, the metamaterial unit of patch-type normally by the metal configuration printing of ad hoc structure on the dielectric substrate, when electromagnetic wave incident, electric resonance and magnetic resonance will be there is respectively in metal configuration, near resonant frequency, wait dielectric constant and the equivalent permeability of metal configuration can show as negative value, and when exciting the frequency of electric resonance and magnetic resonance to overlap, whole metamaterial modular construction just shows negative refraction character.

When determining patch-type metamaterial modular construction, usually use for reference the thought of topological optimization.The both sides of dielectric base plate can be set as design section, and describe different topologys by design sheet metal at the distribution form of design section.The different topological structure of sheet metal can affect electric resonance, the characteristic such as magnetic resonance and bandwidth of sheet metal.For the electromagnetic optimization problem in metamaterial unit, common target is in a target frequency bands, find the structure of the maximum metamaterial unit of bandwidth, and the negative index relevant with bandwidth is important variable.In the prior art, gradient optimizing method is usually adopted to determine the structure of the metamaterial unit with maximum bandwidth characteristic.But the convergence of gradient optimizing method depends on the selection of initial value greatly, and be often difficult to provide suitable initial configuration.Further, the convergence of existing optimization method is lower, and there is many locally optimal solutions, is thus difficult to the structure being designed Meta Materials by existing optimization method.

Therefore, need to provide a kind of method determining the structure of the metamaterial unit with maximum bandwidth characteristic, to solve the low problem with there is locally optimal solution of convergence that prior art exists.

Summary of the invention

The technical problem that the present invention mainly solves is to provide a kind of method determining the metamaterial modular construction with maximum bandwidth characteristic, can improve the convergence of optimum results and obtain globally optimal solution better.

For solving the problems of the technologies described above, the technical scheme that the present invention adopts is: provide a kind of method determining the metamaterial modular construction with maximum bandwidth characteristic.Wherein, the sheet metal with ad hoc structure that metamaterial unit comprises dielectric base plate and arranges on the dielectric substrate, the method comprising the steps of:

Definition design variable: the subelement design section of sheet metal being divided into multiple arrangement in matrix, and on each subelement, whether be arranged with metal with binary coding representation, and correspondence characterizes the architectural characteristic of each sheet metal with a binary coded matrix, employing binary coded matrix is design variable; The original group P of stochastic generation design variable, the individuality in setting group P is N number of, genetic algebra threshold value is T generation;

Calculate the fitness value of each design variable in group P, and each individual inheritance of check and evaluation is to follow-on probability;

Interlace operation: enter the next generation according to probability selection two design variables individual in group P, and other four design variables of Stochastic choice form parent together; Parent is intersected generation two between two with crossover probability P1 individual, and by individual for the son empty set Q stored in presetting;

Mutation operation: make a variation with mutation probability P2 according to the partial design variable that probability individual in group P is chosen in group P, by the sub-individuality of variation obtained after variation also stored in gathering in Q;

Check quantity M1 individual in set Q, if M1 is less than N, the individual new design variable of stochastic generation M2, wherein M1 and M2 sum equals N; By set Q in design variable assignment to group P and empty set Q, recalculate fitness value to the design variable in group P, the end condition that genetic algebra threshold value is T if do not meet, then turn to interlace operation step;

If meet end condition, then export optimal solution.

Wherein, when binary-coded value is 1, represents and be arranged with metal on subelement, when binary-coded value is 0, represents and be not arranged with metal on subelement.

Wherein, when binary-coded value is 0, represents and be arranged with metal on subelement, when binary-coded value is 1, represents and be not arranged with metal on subelement.

Wherein, the initial value of crossover probability P1 is 0.7, and mutation probability P2 is set to 0 when first time variation, and mutation probability P2 increases along with the increase of iterations.

Wherein, crossover probability P1, mutation probability P2 and genetic algebra threshold value T meet following relational expression:

$P2=\frac{(1-P1)\×ln\left(t\right)}{\ln \left(T\right)}$

Wherein, t is iterations.

Wherein, the function calculating fitness value is:

$\begin{array}{cc}\mathrm{find}& x={(x_i,x_2,...,x_n)}^T\\ \max & F=\frac{{\∫}_{f_{\min }}^{f_{\max }}H\left(n_{\mathrm{real}}\left(f\right)\right)\mathrm{df}}{f_{\max }-f_{\min }}\\ s.t.& x_i=\mathrm{0,1},i=\mathrm{1,2},...,n\end{array};$

Wherein,

$H\left(n_{real}\left(f\right)\right)=\left\{\begin{array}{cc}1& n_{real}<0\\ 0& n_{real}>0\end{array}\right.,$

X is design variable, and F is the structure with the metamaterial unit of maximum bandwidth characteristic in a target frequency bands, f _max, f _minthe upper limit, the lower limit of corresponding target frequency bands respectively, H (n _real(f)) formula is for judging whether the refractive index of metamaterial unit is negative value, if H is (n _real(f))=1, then refractive index is negative, if H is (n _real(f))=0, then refractive index is just.

Wherein, the value of N is 50.

Wherein, genetic algebra threshold value T is 100.

The invention has the beneficial effects as follows: the situation being different from prior art, the present invention determines that the method for the metamaterial modular construction with maximum bandwidth characteristic is in optimized selection initial value by utilizing follow-on genetic algorithm, and dynamic change is carried out to mutation probability, improve the convergence of optimum results and obtain globally optimal solution better, avoiding occurring locally optimal solution.

Accompanying drawing explanation

Fig. 1 is a kind of schematic flow sheet determining the method for the metamaterial modular construction with maximum bandwidth characteristic of the present invention;

Fig. 2 is a kind of schematic diagram defining the embodiment of design variable of the present invention;

Fig. 3 is the characteristic variations curve map of mutation probability P2 in the present invention.

Detailed description of the invention

Refer to Fig. 1, Fig. 1 is a kind of schematic flow sheet determining the method for the metamaterial modular construction with maximum bandwidth characteristic of the present invention.

In the embodiment of the present invention, the sheet metal with ad hoc structure that metamaterial unit comprises dielectric base plate and arranges on the dielectric substrate, as shown in Figure 1, determines that the method for the structure of the metamaterial unit with maximum bandwidth characteristic comprises the steps:

Step S1: definition design variable;

In the present invention, the design section of sheet metal is divided into the subelement of multiple arrangement in matrix, and on each subelement, whether be arranged with metal with binary coding representation, and correspondence characterizes the architectural characteristic of each sheet metal with a binary coded matrix, employing binary coded matrix is design variable.Thus, just can change design variable by the binary coding changed in any binary coded matrix, thus the architectural characteristic of another new metamaterial unit will be obtained, detailed design variable define method, will describe in detail in hereafter Fig. 2.

Step S2: the initial value of setting design variable and threshold values;

The original group P of stochastic generation design variable, the individuality in setting group P is N number of, genetic algebra threshold value is T generation.

The value that the present embodiment gets N is the value of 50, T is 100.Certainly, individual quantity N and genetic algebra threshold values T can also be set according to actual needs.

Step S3: the fitness calculating design variable;

Namely the fitness value of each design variable in group P is calculated; Before calculating fitness value, first build a fitness function, this fitness function is:

$\begin{array}{cc}\mathrm{find}& x={(x_i,x_2,...,x_n)}^T\\ \max & F=\frac{{\&Integral;}_{f_{\min }}^{f_{\max }}H\left(n_{\mathrm{real}}\left(f\right)\right)\mathrm{df}}{f_{\max }-f_{\min }}\\ s.t.& x_i=\mathrm{0,1},i=\mathrm{1,2},...,n\end{array};$

Wherein,

$H\left(n_{real}\left(f\right)\right)=\left\{\begin{array}{cc}1& n_{real}<0\\ 0& n_{real}>0\end{array}\right.,$

In formula, x is design variable, and F is the structure with the metamaterial unit of maximum bandwidth characteristic in a target frequency bands, f _max, f _minthe upper limit, the lower limit of corresponding target frequency bands respectively, H (n _real(f)) formula is for judging whether the refractive index of metamaterial unit is negative value, if H is (n _real(f))=1, then refractive index is negative, if H is (n _real(f))=0, then refractive index is just.

In other designs of Meta Materials, if the target property determined is different, constructed fitness function is also different, does not repeat them here.

Step S4: assessment individual inheritance is to follow-on probability;

Individual inheritance mentioned here can be assessed according to the fitness value of design variable to follow-on probability, also can not assess according to the fitness value of design variable.Be determined on a case-by-case basis.

Step S5: interlace operation;

Enter the next generation according to probability selection two design variables individual in group P, and other four design variables of Stochastic choice form parent together.Parent is intersected generation two between two with crossover probability P1 individual, and by individual for the son empty set Q stored in presetting.

The value of crossover probability P1 used in the present invention is 0.7.Different crossover probability values can be set as the case may be.

There are two to be with the probability correlation of individuality in six design variables of parent, have four to be irrelevant with the probability of individuality, the convergence of optimum results can be improved like this.Certainly, also can change the number of the design variable of composition parent as the case may be, not repeat them here.

Step S6: mutation operation;

Make a variation with mutation probability P2 according to the partial design variable that probability individual in group P is chosen in group P, by the sub-individuality of variation obtained after variation also stored in gathering in Q.

Mutation probability P2 is set to 0 when first time variation, and increases along with the increase of iterations.

Crossover probability P1, mutation probability P2 and genetic algebra threshold value T meet following relational expression:

$P2=\frac{(1-P1)\&times;\ln \left(t\right)}{\ln \left(T\right)}$

Wherein, t is iterations.

Because mutation probability P2 dynamically changes, actively produce new individual, make individual away from regional area, reduce super individual to the impact of Evolution of Population, make the solution obtained can not converge to locally optimal solution prematurely, improve ability of searching optimum.

Step S7: judge operation;

Check quantity M1 individual in set Q, if M1 is less than N, the individual new design variable of stochastic generation M2, wherein M1 and M2 sum equals N;

By set Q in design variable assignment to group P and empty set Q, recalculate fitness value to the design variable in group P, the end condition that genetic algebra threshold value is T if do not meet, then turn to interlace operation step; If meet end condition, then export optimal solution.

By the way, when determining the structure of the metamaterial unit with maximum bandwidth characteristic by utilizing follow-on genetic algorithm to be in optimized selection initial value, and dynamic change is carried out to mutation probability, improve the convergence of optimum results and obtain globally optimal solution better, avoiding occurring locally optimal solution.

Specifically, in step S1 of the present invention, adopt a kind of method defining design variable as shown in Figure 2.Refer to Fig. 2, the both sides of dielectric base plate are set as design section, and describe different topologys by design sheet metal at the distribution form of design domain.Such as, adopt the medium substrate of FR4 material, its relative dielectric constant is 4.4, the one side of getting medium substrate is the design section of metamaterial unit, as shown in Fig. 2 left part, design section is divided into discrete grid block structure, it comprises the subelement of multiple arrangement in matrix, and on each subelement, whether be arranged with metal with binary coding representation, and correspondence characterizes the architectural characteristic of each metamaterial unit with a binary coded matrix.Such as, as in the embodiment of Fig. 2, design section is divided into 25 subelements, represents subelement arrangement metal when now binary-coded value is 1, when binary-coded value is 0, represent that subelement does not arrange metal.Thus, the structure of the metamaterial unit of Fig. 2 left part can represent with 0,1 matrix on the right side of Fig. 2.That is: by the way, the structure of metamaterial unit is just converted into 0 and 1 integer programming.So the structural design of each different metamaterial unit can be used as and utilizes genetic algorithm to be optimized item chromosome in process, and method is simple.When incidence wave is propagated along z direction in Fig. 2, and when the direction of electric field is along x-axis, magnetic direction along y-axis, just according to the matrix variables method for expressing provided in Fig. 2 right part to calculate each metamaterial unit effective electromagnetic parameter, and then the structure of the metamaterial unit with maximum bandwidth characteristic can be determined.

Certainly, also binary-coded value can represent that subelement does not arrange metal when being 1 in the present invention, when binary-coded value is 0, represent subelement arrangement metal.

Refer to Fig. 3, Fig. 3 is the characteristic variations curve map of mutation probability P2 in the present invention, and the curve in Fig. 3 represents the variation characteristic of mutation probability P2 when increasing with iterations t.As shown in Figure 3, the initial value of mutation probability P2 when first time variation is set to 0, and value curved increase along with the increase of iterations t of mutation probability P2, when iterations t equals the genetic algebra threshold value T preset, the value of mutation probability P2 is maximum.In the present embodiment, crossover probability P1, mutation probability P2 and genetic algebra threshold value T meet following relational expression:

$P2=\frac{(1-P1)\&times;\ln \left(t\right)}{\ln \left(T\right)}$

Wherein, t is iterations.

By the known mutation probability P2 of above-mentioned relation formula value along with crossover probability P1, iterations t and genetic algebra threshold values T change and change.

In the present embodiment, crossover probability P1 value is 0.7, and genetic algebra threshold value T value is 100, utilize above-mentioned relational expression, the upper limit that can obtain mutation probability P2 is 1-P1=0.3, it can thus be appreciated that, although mutation probability P2 increases along with the increase of iterations t, be no more than 1-P1.

Certainly, crossover probability P1 and genetic algebra threshold value T also can get other values, makes mutation probability P2 obtain other values.

By the way, mutation probability P2 dynamic change, actively creates new individuality, make individual away from regional area, reduce super individual to the impact of Evolution of Population, thus avoid the optimum results of genetic algorithm to occur Premature Convergence, improve genetic algorithm ability of searching optimum.

In sum, the present invention is in optimized selection initial value by utilizing follow-on genetic algorithm, and carries out dynamic change to mutation probability, improves the convergence of optimum results and obtains globally optimal solution better, avoiding occurring locally optimal solution.

The foregoing is only embodiments of the invention; not thereby the scope of the claims of the present invention is limited; every utilize description of the present invention and accompanying drawing content to do equivalent structure or equivalent flow process conversion; or be directly or indirectly used in other relevant technical fields, be all in like manner included in scope of patent protection of the present invention.

Claims (8)

1. determine a method for the metamaterial modular construction with maximum bandwidth characteristic, the sheet metal with ad hoc structure that described metamaterial unit comprises dielectric base plate and arranges on the dielectric substrate, it is characterized in that, described method comprises step:

Definition design variable: the subelement design section of sheet metal being divided into multiple arrangement in matrix, and so that whether binary coding representation subelement described in each is arranged with metal, and correspondence characterizes the architectural characteristic of sheet metal described in each with a binary coded matrix, described binary coded matrix is adopted to be design variable;

The original group P of design variable described in stochastic generation, the individuality set in described group P is N number of, genetic algebra threshold value is T generation;

Calculate the fitness value of each described design variable in described group P, and check and evaluation individual inheritance described in each is to follow-on probability;

Interlace operation: enter the next generation according to probability selection two described design variables individual in described group P, and other four described design variables of Stochastic choice form parent together;

Described parent is intersected generation two between two with crossover probability P1 individual, and by individual for the described son empty set Q stored in presetting;

Mutation operation: make a variation with mutation probability P2 according to the described design variable of part that probability individual described in described group P is chosen in group P, by the sub-individuality of variation that obtains after described variation also stored in described set Q;

Check quantity M1 individual in described set Q, if M1 is less than N, the individual new design variable of stochastic generation M2, wherein M1 and M2 sum equals N;

Described design variable assignment in described set Q is given described group P and emptied described set Q, fitness value is recalculated to the described design variable in described group P, if not meeting described genetic algebra threshold value is the end condition of T, then turn to described interlace operation step; If meet described end condition, then export optimal solution.

2. method according to claim 1, is characterized in that, when described binary-coded value is 1, represents and be arranged with metal on described subelement, when described binary-coded value is 0, represents and be not arranged with metal on described subelement.

3. method according to claim 1, is characterized in that, when described binary-coded value is 0, represents and be arranged with metal on described subelement, when described binary-coded value is 1, represents and be not arranged with metal on described subelement.

4. according to the method in claim 2 or 3, it is characterized in that, the initial value of described crossover probability P1 is 0.7, and described mutation probability P2 is set to 0 when first time variation, and described mutation probability P2 increases along with the increase of iterations.

5. method according to claim 4, is characterized in that, described crossover probability P1, described mutation probability P2 and described genetic algebra threshold value T meet following relational expression:

$P2=\frac{(1-P1)\&times;h\left(t\right)}{ln\left(T\right)}$

Wherein, t is iterations.

6. according to the method in claim 2 or 3, it is characterized in that, the function calculating described fitness value is:

x＝(x ₁,x ₂,…,x _n) ^T

Wherein,

$H\left(n_{real}\right(f\left)\right)=\{\begin{array}{ccc}1& n_{real}& <0\\ 0& n_{real}& >0\end{array},$

X is described design variable, and F is the structure with the metamaterial unit of maximum bandwidth characteristic in a target frequency bands, f _max, f _minthe upper limit, the lower limit of corresponding described target frequency bands respectively, H (n _real(f)) formula is for judging whether the refractive index of described metamaterial unit is negative value, if H is (n _real(f))=1, then refractive index is negative, if H is (n _real(f))=0, then refractive index is just.

7. method according to claim 1, is characterized in that, the value of described N is 50.

8. method according to claim 1, is characterized in that, described genetic algebra threshold value T is 100.