CN103159168A - Method for determining metamaterial unit structure having maximum bandwidth characteristic - Google Patents

Abstract

The invention provides a method for determining a metamaterial unit structure having a maximum bandwidth characteristic. The method comprises the steps of: defining a design variable, setting the initial value and threshold value of the design variable, calculating the fitness of the design variable, estimating the probability of passing individuals genetically to the next generation, and carrying out crossing, mutation, judgment and other operations to determine the metamaterial unit structure having the maximum bandwidth characteristic. The method provided in the invention makes use of an improved genetic algorithm to conduct optimization selection on the initial value and conducts dynamic change on mutation probability, thus improving convergence of optimization methods and better obtaining a globally optimal solution. Thus, a locally optimal solution is avoided.

Description

A kind of method of determining to have the super material cell structure of maximum bandwidth characteristic

Technical field

The present invention relates to super Material Field, particularly relate to a kind of method of utilizing the structure of the super material cell of genetic algorithm optimization.

Background technology

At present, the super material cell of patch-type normally with the metal configuration printing of ad hoc structure on dielectric base plate, when electromagnetic wave incident, electric resonance and magnetic resonance will occur respectively in the metal configuration, near resonant frequency, wait dielectric constant and the equivalent permeability of metal configuration can show as negative value, and when the frequency that excites electric resonance and magnetic resonance overlapped, whole super material cell structure just showed negative refraction character.

When the super material cell structure of definite patch-type, 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 the design sheet metal at the distribution form of design section.The different topological structure of sheet metal can affect the characteristics such as electric resonance, magnetic resonance and bandwidth of sheet metal.For the electromagnetic optimization problem in super material cell, common target is to seek the structure of the super material cell of bandwidth maximum in a target frequency bands, and the negative index relevant with bandwidth is important variable.In the prior art, usually adopt gradient optimizing method to determine to have the structure of the super material cell of maximum bandwidth characteristic.But the convergence of gradient optimizing method depends on the selection of initial value greatly, and often is difficult to the initial configuration that provides suitable.And the convergence of existing optimization method is lower, and has many locally optimal solutions, thereby is difficult to design by existing optimization method the structure of super material.

Therefore, need to provide a kind of method of structure of the super material cell of determining to have the maximum bandwidth characteristic, low and have a problem of locally optimal solution to solve 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 of determining to have the super material cell structure of maximum bandwidth characteristic, can improve the convergence of optimum results and obtain better globally optimal solution.

For solving the problems of the technologies described above, the technical scheme that the present invention adopts is: a kind of method of determining to have the super material cell structure of maximum bandwidth characteristic is provided.Wherein, super material cell comprises dielectric base plate and is arranged on the sheet metal with ad hoc structure on dielectric base plate, and the method comprising the steps of:

Definition design variable: the design section of sheet metal is divided into a plurality of subelements that matrix is arranged that are, and whether be arranged with metal with binary coding representation on each subelement, and the corresponding architectural characteristic that characterizes each sheet metal with a binary coded matrix, the employing binary coded matrix is design variable; The random original group P that generates design variable, the individuality of setting in the P of group is that N is individual, the genetic algebra threshold value is T generation;

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

Interlace operation: enter the next generation according to two design variables of probability selection individual in the P of group, and select at random other four design variables to form together parent; Parent is intersected in twos with crossover probability P1 to generate two sons individual, and sub-individuality is deposited in default empty set Q;

Mutation operation: the partial design variable of choosing in the P of group according to probability individual in the P of group makes a variation with variation probability P 2, and the sub-individuality of variation that obtains after variation is also deposited in set Q;

Check individual quantity M1 in set Q, if M1 generates M2 new design variable at random less than N, wherein M1 and M2 sum equal N; The design variable assignment of set in Q to the P of group and empty set Q, recomputated fitness value to the design variable in the P of group, if do not satisfy the end condition that the genetic algebra threshold value is T, turn to the interlace operation step;

If satisfy end condition, export optimal solution.

Wherein, binary-coded value is 1 o'clock, is illustrated in and is arranged with metal on subelement, and binary-coded value is 0 o'clock, is illustrated in and is not arranged with metal on subelement.

Wherein, binary-coded value is 0 o'clock, is illustrated in and is arranged with metal on subelement, and binary-coded value is 1 o'clock, is illustrated in and is not arranged with metal on subelement.

Wherein, the initial value of crossover probability P1 is 0.7, and variation probability P 2 is made as 0 when making a variation for the first time, and variation probability P 2 increases along with the increase of iterations.

Wherein, crossover probability P1, variation probability P 2 and genetic algebra threshold value T satisfy following relational expression:

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

Wherein, t is iterations.

Wherein, the function of calculating fitness value is:

x＝(x ₁，x ₂，…，x _n) ^T

$\begin{array}{c}\mathrm{find}\\ \max \end{array}F=\frac{{\∫}_{f_{\min }}^{f_{\max }}H\left(n_{\mathrm{real}}\left(f\right)\right)\mathrm{df}}{f_{\max }-f_{\min }}$

s.t. x _i＝0，1，i＝1，2，…，n；

Wherein,

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

X is design variable, and F is the structure of the super material cell with maximum bandwidth characteristic in a target frequency bands, f _max, f _minThe upper limit, the lower limit of the corresponding target frequency bands of difference, H (n _Real(f)) formula is used for whether the refractive index of the super material cell of judgement is negative value, if H is (n _Real(f))=1, refractive index is for negative, if H is (n _Real(f))=0, refractive index is for 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 that is different from prior art, the present invention determines to have the method for super material cell structure of maximum bandwidth characteristic by utilizing follow-on genetic algorithm that initial value is in optimized selection, and the variation probability is carried out dynamic change, improved the convergence of optimum results and obtained better globally optimal solution, having avoided occurring locally optimal solution.

Description of drawings

Fig. 1 is the schematic flow sheet of the method for a kind of super material cell structure of determining to have the maximum bandwidth characteristic of the present invention;

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

Fig. 3 is the characteristic variations curve map of variation probability P 2 in the present invention.

The specific embodiment

See also Fig. 1, Fig. 1 is the schematic flow sheet of the method for a kind of super material cell structure of determining to have the maximum bandwidth characteristic of the present invention.

In the embodiment of the present invention, super material cell comprises dielectric base plate and is arranged on the sheet metal with ad hoc structure on dielectric base plate, and as shown in Figure 1, the method for structure of determining to have the super material cell of maximum bandwidth characteristic comprises the steps:

Step S1: definition design variable;

In the present invention, the design section of sheet metal is divided into a plurality of subelements that matrix is arranged that are, and whether be arranged with metal with binary coding representation on each subelement, and the corresponding architectural characteristic that characterizes each sheet metal with a binary coded matrix, the employing binary coded matrix is design variable.Thus, just can change design variable by a binary coding that changes in any binary coded matrix, thereby will obtain the architectural characteristic of another new super material cell, detailed design variable define method will describe in detail in Fig. 2 hereinafter.

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

The random original group P that generates design variable, the individuality of setting in the P of group is that N is individual, the genetic algebra threshold value is T generation.

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

Step S3: the fitness of calculation Design variable;

Namely calculate the fitness value of each design variable in the P of group; First built a fitness function before calculating fitness value, this fitness function is:

x＝(x ₁，x ₂，…，x _n) ^T

$\begin{array}{c}\mathrm{find}\\ \max \end{array}F=\frac{{\&Integral;}_{f_{\min }}^{f_{\max }}H\left(n_{\mathrm{real}}\left(f\right)\right)\mathrm{df}}{f_{\max }-f_{\min }}$

s.t. x _i＝0，1，i＝1，2，…，n；

Wherein,

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

In formula, x is design variable, and F is the structure of the super material cell with maximum bandwidth characteristic in a target frequency bands, f _max, f _minThe upper limit, the lower limit of the corresponding target frequency bands of difference, H (n _Real(f)) formula is used for whether the refractive index of the super material cell of judgement is negative value, if H is (n _Real(f))=1, refractive index is for negative, if H is (n _Real(f))=0, refractive index is for just.

In other designs of super material, if the target property of determining is different, constructed fitness function is also different, does not repeat them here.

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

Here said individual inheritance 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 two design variables of probability selection individual in the P of group, and select at random other four design variables to form together parent.Parent is intersected in twos with crossover probability P1 to generate two sons individual, and sub-individuality is deposited in default empty set Q.

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

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, can improve like this convergence of optimum results.Certainly, also can change as the case may be the number of the design variable that forms parent, not repeat them here.

Step S6: mutation operation;

The partial design variable of choosing in the P of group according to probability individual in the P of group makes a variation with variation probability P 2, and the sub-individuality of variation that obtains after variation is also deposited in set Q.

Variation probability P 2 is made as 0 when making a variation for the first time, and increases along with the increase of iterations.

Crossover probability P1, variation probability P 2 and genetic algebra threshold value T satisfy following relational expression:

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

Wherein, t is iterations.

Because variation probability P 2 is dynamically changes, actively generation is new individual, makes individuality away from regional area, reduces super individual to the impact of Evolution of Population, makes the Xie Buhui of acquisition converge to prematurely locally optimal solution, has improved ability of searching optimum.

Step S7: decision operation;

Check individual quantity M1 in set Q, if M1 generates M2 new design variable at random less than N, wherein M1 and M2 sum equal N;

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

By the way, when the structure of the super material cell of determining to have the maximum bandwidth characteristic by utilizing follow-on genetic algorithm that initial value is in optimized selection, and the variation probability is carried out dynamic change, improved the convergence of optimum results and obtained better globally optimal solution, having avoided occurring locally optimal solution.

Particularly, in step S1 of the present invention, adopt a kind of method that defines design variable as shown in Figure 2.See also Fig. 2, the both sides of dielectric base plate are set as design section, and describe different topologys by the design sheet metal at the distribution form of design domain.For example, adopt the medium substrate of FR4 material, its relative dielectric constant is 4.4, get the one side of medium substrate and be the design section of super material cell, as shown in Fig. 2 left part, design section is divided into the discrete grid block structure, it comprises a plurality of subelements that matrix is arranged that are, and whether be arranged with metal with binary coding representation on each subelement, and the corresponding architectural characteristic that characterizes each super material cell with a binary coded matrix.For example, in the embodiment as Fig. 2, design section is divided into 25 subelements, this moment, binary-coded value was to represent that subelement arranged metal at 1 o'clock, and binary-coded value is to represent that subelement do not arrange metal at 0 o'clock.Thus, the structure of the super material cell of Fig. 2 left part can represent with 0,1 matrix on Fig. 2 right side.That is: by the way, the structure of super material cell just is converted into 0 and 1 integer programming.So the structural design of the super material cell that each is different can be used as utilizes genetic algorithm to be optimized item chromosome in processing, method is simple.When incidence wave is propagated along z direction in Fig. 2, and the direction of electric field is along x axle, magnetic direction during along the y axle, just can calculate each super material cell equivalent electric magnetic parameter according to the matrix variables method for expressing that provides in the part of Fig. 2 right side, and then determine to have the structure of the super material cell of maximum bandwidth characteristic.

Certainly, also can binary-coded value in the present invention be to represent that subelement do not arrange metal at 1 o'clock, binary-coded value is to represent that subelement arranged metal at 0 o'clock.

See also Fig. 3, Fig. 3 is the characteristic variations curve map of variation probability P 2 in the present invention, the variation characteristic of variation probability P 2 when the curve in Fig. 3 represents to increase with iterations t.As shown in Figure 3, the initial value of variation probability P 2 when making a variation for the first time is made as 0, value curved increase along with the increase of iterations t of variation probability P 2, and when iterations t equaled predefined genetic algebra threshold value T, the value of variation probability P 2 was maximum.In the present embodiment, crossover probability P1, variation probability P 2 and genetic algebra threshold value T satisfy following relational expression:

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

Wherein, t is iterations.

Changed along with the change of crossover probability P1, iterations t and genetic algebra threshold values T by make a variation the as can be known value of probability P 2 of above-mentioned relation formula.

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, be limited to 1-P1=0-3 on the probability P that can make a variation 2, hence one can see that, although variation probability P 2 increases along with the increase of iterations t, is no more than 1-P1.

Certainly, crossover probability P1 and genetic algebra threshold value T also can get other values, make variation probability P 2 obtain other values.

By the way, 2 dynamic changes of variation probability P have actively produced new individuality, make individual away from regional area, reduce super individual to the impact of Evolution of Population, thereby avoid the optimum results of genetic algorithm Premature Convergence to occur, improve the genetic algorithm ability of searching optimum.

In sum, the present invention is by utilizing follow-on genetic algorithm that initial value is in optimized selection, and the variation probability is carried out dynamic change, improved the convergence of optimum results and obtained better globally optimal solution, avoids occurring locally optimal solution.

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

Claims (8)

1. method of determining to have the super material cell structure of maximum bandwidth characteristic, described super material cell comprise dielectric base plate and be arranged on the sheet metal with ad hoc structure on dielectric base plate, and it is characterized in that, described method comprises step:

Definition design variable: the design section of sheet metal is divided into a plurality of subelements that matrix is arranged that are, and whether be arranged with metal with binary coding representation on each described subelement, and the corresponding architectural characteristic that characterizes each described sheet metal with a binary coded matrix, adopting described binary coded matrix is design variable;

The random original group P that generates described design variable, the individuality of setting in the described P of group is that N is individual, the genetic algebra threshold value is T generation;

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

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

Described parent is intersected in twos with crossover probability P1 to generate two sons individual, and described sub-individuality is deposited in default empty set Q;

Mutation operation: the described design variable of part of choosing in the P of group according to probability individual described in the described P of group makes a variation with variation probability P 2, and the sub-individuality of the variation that obtains after described variation is also deposited in described set Q;

Check individual quantity M1 in described set Q, if M1 generates M2 new design variable at random less than N, wherein M1 and M2 sum equal N;

Described design variable assignment in described set Q is given the described P of group and emptied described set Q, described design variable in the described P of group is recomputated fitness value, if the end condition that not satisfy described genetic algebra threshold value be T turns to described interlace operation step; If satisfy described end condition, export optimal solution.

2. method according to claim 1, is characterized in that, described binary-coded value is 1 o'clock, is illustrated on described subelement and is arranged with metal, and described binary-coded value is 0 o'clock, is illustrated on described subelement and is not arranged with metal.

3. method according to claim 1, is characterized in that, described binary-coded value is 0 o'clock, is illustrated on described subelement and is arranged with metal, and described binary-coded value is 1 o'clock, is illustrated on described subelement and is not arranged with metal.

4. according to claim 2 or 3 described methods, is characterized in that, the initial value of described crossover probability P1 is 0.7, and described variation probability P 2 is made as 0 when making a variation for the first time, and described variation probability P 2 increases along with the increase of iterations.

5. method according to claim 4, is characterized in that, described crossover probability P1, described variation probability P 2 and described genetic algebra threshold value T satisfy following relational expression:

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

Wherein, t is iterations.

6. according to claim 2 or 3 described methods, is characterized in that, the function that calculates described fitness value is:

x＝(x ₁，x ₂，…，x _n) ^T

$\begin{array}{c}\mathrm{find}\\ \max \end{array}F=\frac{{\&Integral;}_{f_{\min }}^{f_{\max }}H\left(n_{\mathrm{real}}\left(f\right)\right)\mathrm{df}}{f_{\max }-f_{\min }}$

s.t. x _i＝0，1，i＝1，2，…，n；

Wherein,

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

X is described design variable, and F is the structure of the super material cell with maximum bandwidth characteristic in a target frequency bands, f _max, f _minThe upper limit, the lower limit of the corresponding described target frequency bands of difference, H (n _Real(f)) formula is used for judging whether the refractive index of described super material cell is negative value, if H is (n _Real(f))=1, refractive index is for negative, if H is (n _Real(f))=0, refractive index is for 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.

Images