CN106599331A - Antenna optimization method capable of combining moment method with confidence region space mapping algorithm - Google Patents

Abstract

The invention discloses an antenna optimization method capable of combining a moment method with a confidence region space mapping algorithm. The method comprises the following steps that: firstly, a rough model for an antenna space mapping algorithm is established, the construction of the rough model adopts a response surface approximation method based on a Kriging interpolation, the rough model is optimized, and the optimal design parameter of the rough model is determined; a fine model adopts a full wave analysis moment method, the response of the rough model is enabled to approach to the response of the fine model through parameter extraction, and a mapping relationship between a rough model parameter and a fine model parameter is established; and the optimal design parameter of the rough model and the inverse mapping of the established mapping relationship are utilized to obtain the predication parameter of the fine model, and if the predication parameter of the fine model does not meet design requirements, iterative update is carried out on the mapping relationship until the predication parameter of the fine model meets the design requirements. By use of the method, the parameter of the designed antenna is integrally optimized, and time is saved on the premise that accuracy is guaranteed.

Description

Moment method combines the antenna optimization method of confidence region space mapping algorithm

One technical field

The invention belongs to the technical field of antenna optimization design, day of particularly a kind of moment method with reference to confidence region space reflection Line optimization method.

Two background technologies

During Antenna Design, when antenna structure is complicated, when design parameters are more, the optimization time allows people to be difficult to receive, Sometimes even cannot get the antenna of desired properties.For these problems in Antenna Design, using space mapping algorithm, it The optimization problem that tradition is taken is converted into the optimization to alternative model rapidly and efficiently by mapping relations, avoids employing Time-consuming full-wave electromagnetic emulates the direct optimization to antenna model, can greatly shorten design time.

Due to antenna structure complexity, it is difficult to corresponding equivalent circuit or appropriate analytic equation are found, so on antenna It is relatively later that space mapping algorithm is used.Until space mapping algorithm in 2007 is just by Jiang Zhu, Natalia K. Nikolova et al. applies to (J.Zhu, J.W.Bandler, N.K.Nikolova, and S.Koziel. in Antenna Design Antenna optimization through space mapping.IEEE Transactions on Antennas and Propagation,2007,55(3):651-658), coarse grid method construct roughcast type is proposed, and it is successfully excellent with the method Change devises rectangular patch antenna.This kind of method not only can be used for optimizing the antenna of complexity, and to other roughcast types very The microwave structure that hardly possible is extracted is equally applicable, significantly enhances ability of the space mapping algorithm in microwave regime optimization design.

Three content of the invention

It is an object of the invention to provide a kind of moment method combines the antenna optimization method of confidence region space mapping algorithm, the party Method improves the convergence of space mapping algorithm.

The technical solution for realizing the object of the invention is：The antenna that a kind of moment method combines confidence region space mapping algorithm is excellent Change method, step is as follows：

1st step, sets up antenna model, is the return loss or voltage standing wave ratio of antenna according to design objective, determines antenna Initial parameter value x^init, the size of initial parameter value including aerial radiation paster, the thickness of substrate, the position of feed；

2nd step, using moment method, by arranging subdivision grid thickness, convergence precision size thick discrete model is obtained, right Roughcast type is optimized starting point x for obtaining space reflection⁽⁰⁾；

3rd step, apart from starting point x⁽⁰⁾N number of point, the basic point set of composition are randomly selected in the range of ± 20% X_B={ x⁽¹⁾,...,x^(N)}；

4th step, to basic point set X_B={ x⁽¹⁾,...,x^(N)In each basic engineering point x^(j), j=1 ..., N adopts Thick discrete model solution is carried out with moment method, is obtained and basic engineering point x^(j)Corresponding thick discrete model responds R_cd(x^(j))；

5th step, using basic engineering point x^(j)R is responded with corresponding thick discrete model_cd(x^(j)), with reference to gram in golden difference Roughcast type R of method construct space mapping algorithm_c；

6th step, arranges iterative steps i=1, and makesFor the value of consult volume of the thin model of ith iteration；

7th step is rightCarry out thin model emulation；

8th step, using confidence region space mapping algorithm the value of consult volume of the i+1 time thin model of iteration is predicted

9th step, judges whether to meet end conditionη values 10^-3, R_fRepresent thin The response of model, completes the optimization of antenna, if being unsatisfactory for return to step 7 if meeting.

Further, basic engineering point x is utilized described in the 5th step^(j)R is responded with corresponding thick discrete model_cd(x^(j)), With reference to gram in golden difference approach construct roughcast type R of space mapping algorithm_c, comprise the following steps that：

The i.e. basic point set X of one group of design vector is generated in (5.1) the 3rd steps_B={ x⁽¹⁾,...,x^(N), X_BMiddle basic engineering Point x^(j), j=1 ..., N, the thick discrete model response sets of correspondence

R_cd(X_B)=[R_cd(x⁽¹⁾),R_cd(x⁽²⁾),…,R_cd(x^(N))]^T；

(5.2) using gram in golden difference approach estimating definitiveness function f_pX ()=μ+ε (x), wherein μ are averages, ε It is error, it is independent variable to be contemplated to be 0, x, the Gauss correlation function form used is：

Wherein, x^(p),x^(q)Represent two different vectors in vector set, θ_kIt is the correlation coefficient for adjusting model,It is respectively vector x^(p),x^(q)Corresponding k-th element；

Roughcast type R based on Kriging regression_cX () is defined as：

R_c(x)=[R_c(x⁽¹⁾),R_c(x⁽²⁾),…,R_c(x^(N))]^T

R_c(x^(j)) represent X_BThe response of the corresponding roughcast type of each element, j=1,2 ..., N in set；

Wherein

Wherein, I is n dimension unit vectors；

f_i=[R_cd,i(x⁽¹⁾),R_cd,i(x⁽²⁾),…,R_cd,i(x^(N))]^T

R_cd,i(x^(j)) represent ith iteration when thick discrete model in j-th vectorial corresponding response；R is x and X_BIn it is each The associated vector of vector；

r^T(x)=[R (x, x⁽¹⁾),R(x,x⁽²⁾),…,R(x,x^(N))]^T

R(x,x^(j)) represent x and x^(j)Gauss correlation function；

M is X_BIn it is each vector between correlation matrix；

AverageIt is given by：

Correlation coefficient θ_kObtained by maximizing following formula：

Wherein variance

Further, the parameter of the i+1 time thin model of iteration is predicted using confidence region space mapping algorithm described in the 8th step ValueComprise the following steps that：

In space mapping algorithm, during ith iteration, make：

(B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾

Wherein, B⁽ⁱ⁾Roughcast shape parameter to the Jacobian matrixes of thin model parameter ith iteration approximate solution, parameter The selection of λ, it is ensured that | | h⁽ⁱ⁾| |≤δ, h⁽ⁱ⁾For correction to be asked,Represent that i ＆ lt parameter is carried The roughcast type value of consult volume for obtaining, δ is confidence interval radius；

The point of next iteration is remained asRepresent thin model parameter, the x of i+1 time_f ⁽ⁱ⁾Table Show the thin model parameter of i ＆ lt；

To x_f ⁽ⁱ⁺¹⁾Single-point parameter extraction is carried out, is obtained：

f⁽ⁱ⁺¹⁾The error residual of the secondary thick model parameter of expression i+1 and roughcast type optimal solution,Represent i+1 time ginseng Number extracts the roughcast type value of consult volume for obtaining；

If meeting the decision criteria of following formula, just receive new point x_f ⁽ⁱ⁺¹⁾It is credible；Otherwise it is assumed that parameter extraction process is not It is credible, residual error f⁽ⁱ⁺¹⁾Substitute into (B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾A new point is obtained, and the point is added in set Using multiple spot parameter extraction, new f is obtained⁽ⁱ⁺¹⁾：

(||f⁽ⁱ⁾||-||f⁽ⁱ⁺¹⁾||)≥0.01(||f⁽ⁱ⁾||-||f⁽ⁱ⁾+B⁽ⁱ⁾h⁽ⁱ⁾||)

By following formula, parameter extraction obtains the value of consult volume of new roughcast typeFurther byAsk Go out f⁽ⁱ⁺¹⁾：

Wherein, R_f(x_f) represent the response of thin model, x_fRepresent the value of consult volume of thin model, x_f ⁽ⁱ⁺¹⁾Represent i+1 time repeatedly For the value of consult volume of thin model.

Compared with prior art, its remarkable advantage is the present invention：(1) the parameter global optimization to designing：Reflect for space Algorithm is penetrated, the mapping relations in roughcast type and thin model parameter space need to be only found；(2) the optimization time is saved：Because handle is permitted Many Optimization Works are put in roughcast type to complete, and satisfied optimization effect is obtained with the thin model emulation number of times of minimum high cost Really, so this method greatlys save the time on the premise of result accuracy is ensured；(3) it is simple to operate：To being set up Two parameter spaces between mapping relations constantly updated, improved, while constantly new to thin model predictive designs ginseng Amount is verified, required until obtaining optimization design value satisfaction；(4) convergence is strong：Add on the basis of space mapping algorithm Enter confidence field technique, improve the convergence of space mapping algorithm.

Four description of the drawings

Fig. 1 is the micro-strip double loop antenna structure chart that the present invention is optimized.

Fig. 2 is the result figure for optimizing micro-strip double loop antenna in the embodiment of the present invention.

Five specific embodiments

Below in conjunction with the accompanying drawings and specific embodiment is described in further detail to the present invention.

Moment method of the present invention combines the antenna optimization method of confidence region space mapping algorithm, and step is as follows：

1st step, sets up antenna model, is the return loss or voltage standing wave ratio of antenna according to design objective, determines antenna Initial parameter value x^init, the size of initial parameter value including aerial radiation paster, the thickness of substrate, the position of feed；

2nd step, using moment method, by arranging subdivision grid thickness, convergence precision size thick discrete model is obtained, and is adopted Starting point x for obtaining space reflection is optimized to roughcast type with genetic algorithm or other intelligent optimization algorithms⁽⁰⁾；

3rd step, apart from starting point x⁽⁰⁾N number of point, the basic point set of composition are randomly selected in the range of ± 20% X_B={ x⁽¹⁾,...,x^(N)}；

4th step, to basic point set X_B={ x⁽¹⁾,...,x^(N)In each basic engineering point x^(j), j=1 ..., N adopts Thick discrete model solution is carried out with moment method, is obtained and basic engineering point x^(j)Corresponding thick discrete model responds R_cd(x^(j))；

5th step, using basic engineering point x^(j)R is responded with corresponding thick discrete model_cd(x^(j)), with reference to gram in golden difference Roughcast type R of method construct space mapping algorithm_c, comprise the following steps that：

The i.e. basic point set X of one group of design vector is generated in (5.1) the 3rd steps_B={ x⁽¹⁾,...,x^(N), X_BMiddle basic engineering Point x^(j), j=1 ..., N, the thick discrete model response sets of correspondence

R_cd(X_B)=[R_cd(x⁽¹⁾),R_cd(x⁽²⁾),…,R_cd(x^(N))]^T；

(5.2) using gram in golden difference approach estimating definitiveness function f_pX ()=μ+ε (x), wherein μ are averages, ε It is error, it is independent variable to be contemplated to be 0, x, the Gauss correlation function form used is：

Wherein, x^(p),x^(q)Represent two different vectors in vector set, θ_kIt is the correlation coefficient for adjusting model,It is respectively vector x^(p),x^(q)Corresponding k-th element；

Roughcast type R based on Kriging regression_cX () is defined as：

R_c(x)=[R_c(x⁽¹⁾),R_c(x⁽²⁾),…,R_c(x^(N))]^T (2)

R_c(x^(j)) represent X_BThe response of the corresponding roughcast type of each element, j=1,2 ..., N in set；

Wherein

Wherein, I is n dimension unit vectors；

f_i=[R_cd,i(x⁽¹⁾),R_cd,i(x⁽²⁾),…,R_cd,i(x^(N))]^T (4)

R_cd,i(x^(j)) represent ith iteration when thick discrete model in j-th vectorial corresponding response；R is x and X_BIn it is each The associated vector of vector；

r^T(x)=[R (x, x⁽¹⁾),R(x,x⁽²⁾),…,R(x,x^(N))]^T (5)

R(x,x^(j)) represent x and x^(j)Gauss correlation function；

M is X_BIn it is each vector between correlation matrix；

AverageIt is given by：

Correlation coefficient θ_kObtained by maximizing following formula：

Wherein variance

6th step, arranges iterative steps i=1, and makesFor the value of consult volume of the thin model of ith iteration；

7th step is rightCarry out thin model emulation；

8th step, using confidence region space mapping algorithm the value of consult volume of the i+1 time thin model of iteration is predictedConcrete step It is rapid as follows：

In space mapping algorithm, during ith iteration, make：

(B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾ (10)

Wherein, B⁽ⁱ⁾Roughcast shape parameter to the Jacobian matrixes of thin model parameter ith iteration approximate solution, parameter The selection of λ, it is ensured that | | h⁽ⁱ⁾| |≤δ, h⁽ⁱ⁾For correction to be asked,Represent that i ＆ lt parameter is carried The roughcast type value of consult volume for obtaining, δ is confidence interval radius；

The point of next iteration remains as x_f ⁽ⁱ⁺¹⁾=x_f ⁽ⁱ⁾+h⁽ⁱ⁾, x_f ⁽ⁱ⁺¹⁾Represent thin model parameter, the x of i+1 time_f ⁽ⁱ⁾Table Show the thin model parameter of i ＆ lt；

To x_f ⁽ⁱ⁺¹⁾Single-point parameter extraction is carried out, is obtained：

f⁽ⁱ⁺¹⁾The error residual of the secondary thick model parameter of expression i+1 and roughcast type optimal solution,Represent i+1 time ginseng Number extracts the roughcast type value of consult volume for obtaining；

If meeting the decision criteria of formula (12), just receive new point x_f ⁽ⁱ⁺¹⁾It is credible；Otherwise it is assumed that parameter extraction mistake Journey is insincere, residual error f⁽ⁱ⁺¹⁾Substitution formula (10) obtains a new point, and the point is added using multiple spot parameter extraction in set, Obtain new f⁽ⁱ⁺¹⁾：

(||f⁽ⁱ⁾||-||f⁽ⁱ⁺¹⁾||)≥0.01(||f⁽ⁱ⁾||-||f⁽ⁱ⁾+B⁽ⁱ⁾h⁽ⁱ⁾||) (12)

By formula (13), parameter extraction obtains the value of consult volume of new roughcast typeFurther obtained by formula (11)

Wherein, R_f(x_f) represent the response of thin model, x_fRepresent the value of consult volume of thin model, x_f ⁽ⁱ⁺¹⁾Represent i+1 time repeatedly For the value of consult volume of thin model.

9th step, judges whether to meet end conditionη values 10^-3, R_fRepresent thin The response of model, completes the optimization of antenna, if being unsatisfactory for return to step 7 if meeting.

Embodiment 1

In order to verify the correctness and effectiveness of context of methods, micro-strip double loop antenna is optimized below as shown in Figure 1.Micro-strip Double loop antenna has three dielectric layers, and relative dielectric constant from top to bottom is not to be：ε_r1=2.2, ε_r2=1.07, ε_r3=2.2, Each layer of dielectric loss is tan δ=0.001, and the thickness of ring-like microband paste is 0.05mm.Optimization design variable is The interior outer radius of annular micro-strip, the feed placement of probe, the thickness of the first second medium layer, and the length of dielectric layer, use Variable is expressed as x=[a₁ a₂ b₁ b₂ ρ d₁ d₂ l₁ l₂]^T.The radius of probe and the thickness of the superiors' dielectric layer are fixed value, Respectively r₀=0.325mm, d₃=0.254mm.Design initial value x^init=[10,15,30,30,20,6,8,100,100]^Tmm

The design object of micro-strip double loop antenna is：

The bicyclic microstrip antenna of the micro-strip is optimized with reference to confidence region space mapping algorithm using moment method, algorithm through 4 iteration, 5 thin model emulations.Fig. 2 is the return loss S11 figure that micro-strip double loop antenna meets design objective, and this is also fully proved Moment method combines the effectiveness that confidence region space mapping algorithm optimizes antenna.

In sum, moment method of the present invention is as follows with reference to the antenna optimization method basic procedure of confidence region space mapping algorithm： The roughcast type of antenna space mapping algorithm is initially set up, the construction of roughcast type is approximate using the response surface based on Kriging regression Method, optimizes roughcast type and determines the optimal design parameter of roughcast type；Thin model adopts full wave analysis moment method, by ginseng Number extraction causes the response of roughcast type to approach the response of thin model, and the mapping for setting up thick model parameter and thin model parameter is closed System；Using roughcast type optimal design parameter and set up the inverse mapping of mapping relations and obtain the prediction parameter of thin model, such as The prediction parameter of the thin model of fruit is unsatisfactory for design requirement, and mapping relations are iterated with renewal, until the prediction of thin model is joined Amount meets design requirement.The method saves the time to the parameter global optimization for designing on the premise of accuracy is ensured.

Claims (3)

1. a kind of moment method combines the antenna optimization method of confidence region space mapping algorithm, it is characterised in that step is as follows：

1st step, sets up antenna model, is the return loss or voltage standing wave ratio of antenna according to design objective, determines antenna Initial parameter value x^init, the size of initial parameter value including aerial radiation paster, the thickness of substrate, the position of feed；

2nd step, using moment method, by arranging subdivision grid thickness, convergence precision size thick discrete model is obtained, right Roughcast type is optimized starting point x for obtaining space reflection⁽⁰⁾；

3rd step, apart from starting point x⁽⁰⁾N number of point, the basic point set of composition are randomly selected in the range of ± 20% X_B={ x⁽¹⁾,...,x^(N)}；

4th step, to basic point set X_B={ x⁽¹⁾,...,x^(N)In each basic engineering point x^(j), j=1 ..., N adopts Thick discrete model solution is carried out with moment method, is obtained and basic engineering point x^(j)Corresponding thick discrete model responds R_cd(x^(j))；

5th step, using basic engineering point x^(j)R is responded with corresponding thick discrete model_cd(x^(j)), with reference to gram in golden difference Roughcast type R of method construct space mapping algorithm_c；

6th step, arranges iterative steps i=1, and makes For the value of consult volume of the thin model of ith iteration；

7th step is rightCarry out thin model emulation；

8th step, using confidence region space mapping algorithm the value of consult volume of the i+1 time thin model of iteration is predicted

9th step, judges whether to meet end conditionη values 10^-3, R_fRepresent thin The response of model, completes the optimization of antenna, if being unsatisfactory for return to step 7 if meeting.

2. according to claim 1 moment method combines the antenna optimization method of confidence region space mapping algorithm, its feature It is that basic engineering point x is utilized described in the 5th step^(j)R is responded with corresponding thick discrete model_cd(x^(j)), with reference to gram in Golden difference approach constructs roughcast type R of space mapping algorithm_c, comprise the following steps that：

The i.e. basic point set X of one group of design vector is generated in (5.1) the 3rd steps_B={ x⁽¹⁾,...,x^(N), X_BMiddle basic engineering Point x^(j), j=1 ..., N, the thick discrete model response sets of correspondence

R_cd(X_B)=[R_cd(x⁽¹⁾),R_cd(x⁽²⁾),…,R_cd(x^(N))]^T；

(5.2) using gram in golden difference approach estimating definitiveness function f_pX ()=μ+ε (x), wherein μ are averages, ε It is error, it is independent variable to be contemplated to be 0, x, the Gauss correlation function form used is：

$R(x^{\left(p\right)},x^{\left(q\right)})=\exp \[\underset{k=1}{\overset{N}{\Σ}}{\mathrm{\θ}}_k{\left|x_k^{\left(p\right)}-x_k^{\left(q\right)}\right|}^2\]---\left(1\right)$

Wherein, x^(p),x^(q)Represent two different vectors in vector set, θ_kIt is the correlation coefficient for adjusting model,It is respectively vector x^(p),x^(q)Corresponding k-th element；

Roughcast type R based on Kriging regression_cX () is defined as：

R_c(x)=[R_c(x⁽¹⁾),R_c(x⁽²⁾),…,R_c(x^(N))]^T (2)

R_c(x^(j)) represent X_BThe response of the corresponding roughcast type of each element, j=1,2 ..., N in set；

Wherein

$R_c\left(x^{\left(i\right)}\right)={\stackrel{\‾}{\mathrm{\μ}}}_i+r^T\left(x\right)M^{-1}(f_i-I{\stackrel{\‾}{\mathrm{\μ}}}_i)---\left(3\right)$

Wherein, I is n dimension unit vectors；

f_i=[R_cd,i(x⁽¹⁾),R_cd,i(x⁽²⁾),…,R_cd,i(x^(N))]^T (4)

R_cd,i(x^(j)) represent ith iteration when thick discrete model in j-th vectorial corresponding response；R is x and X_BIn it is each The associated vector of vector；

r^T(x)=[R (x, x⁽¹⁾),R(x,x⁽²⁾),…,R(x,x^(N))]^T (5)

R(x,x^(j)) represent x and x^(j)Gauss correlation function；

M is X_BIn it is each vector between correlation matrix；

AverageIt is given by：

${\stackrel{\‾}{\mathrm{\μ}}}_i={\left(I^T{M}^{-1}I\right)}^{-1}{I}^T{M}^{-1}{f}_i---\left(7\right)$

Correlation coefficient θ_kObtained by maximizing following formula：

$-\[Nln\left({\stackrel{\‾}{\mathrm{\σ}}}^2\right)+ln\left|M\right|\]/2---\left(8\right)$

Wherein variance

${\stackrel{\‾}{\mathrm{\σ}}}_i^2={(f_i-I{\stackrel{\‾}{\mathrm{\μ}}}_i)}^T{M}^{-1}(f_i-I{\stackrel{\‾}{\mathrm{\μ}}}_i)/N---\left(9\right).$

3. according to claim 1 moment method combines the antenna optimization method of confidence region space mapping algorithm, its feature It is to predict the value of consult volume of the i+1 time thin model of iteration described in the 8th step using confidence region space mapping algorithm Comprise the following steps that：

In space mapping algorithm, during ith iteration, make：

(B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾ (10)

Wherein, B⁽ⁱ⁾Roughcast shape parameter to the Jacobian matrixes of thin model parameter ith iteration approximate solution, parameter The selection of λ, it is ensured that | | h⁽ⁱ⁾| |≤δ, h⁽ⁱ⁾For correction to be asked, Represent that i ＆ lt parameter is carried The roughcast type value of consult volume for obtaining, δ is confidence interval radius；

The point of next iteration is remained as Represent thin model parameter, the x of i+1 time_f ⁽ⁱ⁾Table Show the thin model parameter of i ＆ lt；

To x_f ⁽ⁱ⁺¹⁾Single-point parameter extraction is carried out, is obtained：

$f^{(i+1)}=x_c^{(i+1)}-x^{\left(0\right)}---\left(11\right)$

f⁽ⁱ⁺¹⁾The error residual of the secondary thick model parameter of expression i+1 and roughcast type optimal solution,Represent i+1 time ginseng Number extracts the roughcast type value of consult volume for obtaining；

If meeting the decision criteria of formula (12), just receive new point x_f ⁽ⁱ⁺¹⁾It is credible；Otherwise it is assumed that parameter extraction mistake Journey is insincere, residual error f⁽ⁱ⁺¹⁾Substitution formula (10) obtains a new point, and the point is added using multiple spot parameter extraction in set, Obtain new f⁽ⁱ⁺¹⁾：

(||f⁽ⁱ⁾||-||f⁽ⁱ⁺¹⁾||)≥0.01(||f⁽ⁱ⁾||-||f⁽ⁱ⁾+B⁽ⁱ⁾h⁽ⁱ⁾||) (12)

By formula (13), parameter extraction obtains the value of consult volume of new roughcast typeFurther obtained by formula (11) $f^{(i+1)}=x_c^{(i+1)}-x^{\left(0\right)}:$

$\underset{x_c^{(i+1)}}{min}\left|\right|R_c(x_c^{(i+1)}+B^{\left(i\right)}(x_f-{x_f}^{(i+1)}\left)\right)-R_f\left(x_f\right)\left|\right|---\left(13\right)$

Wherein, R_f(x_f) represent the response of thin model, x_fRepresent the value of consult volume of thin model, x_f ⁽ⁱ⁺¹⁾Represent i+1 time repeatedly For the value of consult volume of thin model.