CN106599331B - The antenna optimization method of moment method combination confidence region space mapping algorithm - Google Patents

Abstract

The invention discloses a kind of antenna optimization methods of moment method combination confidence region space mapping algorithm.Step are as follows: initially set up the roughcast type of antenna space mapping algorithm, the construction of roughcast type uses the response surface approximation method based on Kriging regression, optimizes roughcast type and determines the optimal design parameter of roughcast type；Thin model uses full wave analysis moment method, makes the response of roughcast type approach the response of thin model by parameter extraction, establishes the mapping relations of thick model parameter Yu thin model parameter；The prediction parameter of thin model is obtained using the optimal design parameter of roughcast type and the inverse mapping of established mapping relations, if the prediction parameter of thin model is unsatisfactory for design requirement, update is iterated to mapping relations, until the prediction parameter of thin model meets design requirement.This method saves the time under the premise of guaranteeing accuracy to the parameter global optimization of designed antenna.

Description

The antenna optimization method of moment method combination confidence region space mapping algorithm

One technical field

The invention belongs to the technical field of antenna optimization design, especially a kind of moment method combination confidence region space reflection Antenna optimization method.

Two background techniques

During Antenna Design, when antenna structure complexity, when design parameters are more, the optimization time is difficult to accept, Sometimes it even cannot get the antenna of required performance.For these problems in Antenna Design, using space mapping algorithm, it will be passed The time-consuming optimization problem of system is converted into the optimization to alternative model rapidly and efficiently by mapping relations, avoids using 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 find corresponding equivalent circuit or appropriate analytic equation, so in antenna Upper space mapping algorithm uses relatively late.Until space mapping algorithm in 2007 is just by Jiang Zhu, Natalia K.Nikolova et al. applies in Antenna Design (J.Zhu, J.W.Bandler, N.K.Nikolova, and S.Koziel.Antenna optimization through space mapping.IEEE Transactions on Antennas and Propagation, 2007,55 (3): 651-658), propose coarse grid method construct roughcast type, and use The method success optimization design rectangular patch antenna.Such method can not only be used to optimize complicated antenna, but also to it Its roughcast type it is difficult to extract microwave structure it is equally applicable, significantly enhance space mapping algorithm in microwave regime optimization design Ability.

Three summary of the invention

The purpose of the present invention is to provide a kind of antenna optimization methods of moment method combination confidence region space mapping algorithm, should Method improves the convergence of space mapping algorithm.

The technical solution for realizing the aim of the invention is as follows: a kind of antenna of moment method combination confidence region space mapping algorithm Optimization method, steps are as follows:

Step 1 establishes antenna model, according to design objective, that is, antenna return loss or voltage standing wave ratio, determines antenna Initial parameter value x^init, initial parameter value includes the position of the size of aerial radiation patch, the thickness of substrate, feed；

Step 2 obtains thick discrete model by setting subdivision grid thickness, convergence precision size, to thick using moment method Model optimizes to obtain the starting point x of space reflection⁽⁰⁾；

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

Step 4, to basic point set X_B={ x⁽¹⁾,...,x^(N)Each of basic engineering point x^(j), j=1 ..., N, Thick discrete model solution is carried out using moment method, is obtained and basic engineering point x^(j)Corresponding thick discrete model responds R_cd(x^(j))；

Step 5 utilizes basic engineering point x^(j)R is responded with corresponding thick discrete model_cd(x^(j)), in conjunction with gram in golden difference side The roughcast type R of method construction space mapping algorithm_c；

Step 6 is arranged iterative steps i=1, and enablesFor the parameter value of the thin model of i-th iteration；

Step 7 is rightCarry out thin model emulation；

Step 8, using the parameter value of the thin model of confidence region space mapping algorithm prediction i+1 time iteration

Step 9 judges whether to meet termination conditionη value 10^-3, R_fIndicate thin model Response, if meet if complete the optimization of antenna, if being unsatisfactory for return step 7.

Further, basic engineering point x is utilized described in step 5^(j)R is responded with corresponding thick discrete model_cd(x^(j)), knot The roughcast type R of golden difference approach construction space mapping algorithm in conjunction gram_c, the specific steps are as follows:

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

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 estimate certainty function f_p(x)=μ+ε (x), wherein μ is mean value, and ε is Error, being contemplated to be 0, x is independent variable, the Gauss correlation function form used are as follows:

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

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

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

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

Wherein

Wherein, I is n dimension unit vector；

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

R_cd,i(x^(j)) indicate the corresponding response of j-th of vector in thick discrete model when i-th iteration；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)) indicate x and x^(j)Gauss correlation function；

M is X_BIn correlation matrix between each vector；

Mean valueIt is given by:

Related coefficient θ_kIt is obtained by maximizing following formula:

Wherein variance

Further, using the parameter of the thin model of confidence region space mapping algorithm prediction i+1 time iteration described in step 8 ValueSpecific step is as follows:

In space mapping algorithm, when i-th iteration, make:

(B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾

Wherein, B⁽ⁱ⁾It is approximate solution of the roughcast shape parameter to the Jacobian matrix of thin model parameter in i-th iteration, ginseng The selection of number λ, guarantees | | h⁽ⁱ⁾| |≤δ, h⁽ⁱ⁾For correction amount to be asked,Indicate that i-th parameter mentions The roughcast type parameter value obtained, δ are confidence interval radius；

The point of next iteration remains asIndicate thin model parameter, the x of i+1 time_f ⁽ⁱ⁾Table Show the thin model parameter of i-th；

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

f⁽ⁱ⁺¹⁾The error residual of expression i+1 secondary thick model parameter and roughcast type optimal solution,Indicate i+1 time The roughcast type parameter value that parameter extraction obtains；

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 and is used Multiple spot parameter extraction obtains new f⁽ⁱ⁺¹⁾:

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

By following formula, parameter extraction obtains the parameter value of new roughcast typeFurther byIt asks F out⁽ⁱ⁺¹⁾:

Wherein, R_f(x_f) indicate the response of thin model, x_fIndicate the parameter value of thin model, x_f ⁽ⁱ⁺¹⁾Indicate i+1 time iteration The parameter value of thin model.

Compared with prior art, the present invention its remarkable advantage are as follows: (1) to the parameter global optimization of design: being reflected for space Algorithm is penetrated, the mapping relations of roughcast type and thin model parameter space need to be only found；(2) the optimization time is saved: due to many excellent Chemical industry is put into roughcast type and completes, and obtains satisfied effect of optimization, institute with the least high thin model emulation number of cost The time is greatly saved under the premise of guaranteeing result accuracy with this method；(3) easy to operate: empty to two parameters established Between between mapping relations constantly updated, improved, while predictive designs parameter constantly new to thin model is verified, directly It is met the requirements to optimization design value is obtained；(4) convergence is strong: joined confidence field technique on the basis of space mapping algorithm, mentions The high convergence of space mapping algorithm.

Four Detailed description of the inventions

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

With reference to the accompanying drawing and specific embodiment present invention is further described in detail.

The antenna optimization method of moment method combination confidence region space mapping algorithm of the present invention, steps are as follows:

Step 1 establishes antenna model, according to design objective, that is, antenna return loss or voltage standing wave ratio, determines antenna Initial parameter value x^init, initial parameter value includes the position of the size of aerial radiation patch, the thickness of substrate, feed；

Step 2 is obtained thick discrete model by setting subdivision grid thickness, convergence precision size, is used using moment method Genetic algorithm or other intelligent optimization algorithms optimize roughcast type to obtain the starting point x of space reflection⁽⁰⁾；

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

Step 4, to basic point set X_B={ x⁽¹⁾,...,x^(N)Each of basic engineering point x^(j), j=1 ..., N, Thick discrete model solution is carried out using moment method, is obtained and basic engineering point x^(j)Corresponding thick discrete model responds R_cd(x^(j))；

Step 5 utilizes basic engineering point x^(j)R is responded with corresponding thick discrete model_cd(x^(j)), in conjunction with gram in golden difference side The roughcast type R of method construction space mapping algorithm_c, the specific steps are as follows:

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

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 estimate certainty function f_p(x)=μ+ε (x), wherein μ is mean value, and ε is Error, being contemplated to be 0, x is independent variable, the Gauss correlation function form used are as follows:

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

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

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

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

Wherein

Wherein, I is n dimension unit vector；

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

R_cd,i(x^(j)) indicate the corresponding response of j-th of vector in thick discrete model when i-th iteration；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)) indicate x and x^(j)Gauss correlation function；

M is X_BIn correlation matrix between each vector；

Mean valueIt is given by:

Related coefficient θ_kIt is obtained by maximizing following formula:

Wherein variance

Step 6 is arranged iterative steps i=1, and enablesFor the parameter value of the thin model of i-th iteration；

Step 7 is rightCarry out thin model emulation；

Step 8, using the parameter value of the thin model of confidence region space mapping algorithm prediction i+1 time iterationSpecific step It is rapid as follows:

In space mapping algorithm, when i-th iteration, make:

(B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾ (10)

Wherein, B⁽ⁱ⁾It is approximate solution of the roughcast shape parameter to the Jacobian matrix of thin model parameter in i-th iteration, ginseng The selection of number λ, guarantees | | h⁽ⁱ⁾| |≤δ, h⁽ⁱ⁾For correction amount to be asked,Indicate that i-th parameter mentions The roughcast type parameter value obtained, δ are confidence interval radius；

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

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

f⁽ⁱ⁺¹⁾The error residual of expression i+1 secondary thick model parameter and roughcast type optimal solution,Indicate i+1 time The roughcast type parameter value that parameter extraction obtains；

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 process It is insincere, residual error f⁽ⁱ⁺¹⁾Substitution formula (10) obtains a new point, and the point is added in set and uses multiple spot parameter extraction, obtains New f⁽ⁱ⁺¹⁾:

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

By formula (13), the parameter value that parameter extraction obtains new roughcast type is further found out by formula (11)

Wherein, R_f(x_f) indicate the response of thin model, x_fIndicate the parameter value of thin model, x_f ⁽ⁱ⁺¹⁾Indicate i+1 time iteration The parameter value of thin model.

Step 9 judges whether to meet termination conditionη value 10^-3, R_fIndicate thin model Response, if meet if complete the optimization of antenna, if being unsatisfactory for return step 7.

Embodiment 1

In order to verify the correctness and validity of context of methods, it is as shown in Figure 1 that micro-strip double loop antenna is optimized below.Micro-strip There are three dielectric layers for double loop antenna, and relative dielectric constant from top to bottom is other are as follows: ε_r1=2.2, ε_r2=1.07, ε_r3=2.2, Each layer of dielectric loss is δ=0.001 tan, ring-like microband paste with a thickness of 0.05mm.Optimization design variable is annular The interior outer radius of micro-strip, the feed placement of probe, the thickness of the first second medium layer and the length of dielectric layer, are indicated with variable For x=[a₁ a₂ b₁ b₂ ρ d₁ d₂ l₁ l₂]^T.The radius of probe and top layer's dielectric layer with a thickness of fixed value, respectively For 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 are as follows:

The bicyclic microstrip antenna of the micro-strip is optimized using moment method combination confidence region space mapping algorithm, algorithm changes by 4 times Generation, 5 thin model emulations.Fig. 2 is the return loss S11 figure that micro-strip double loop antenna meets design objective, this is also sufficiently demonstrated The validity of moment method combination confidence region space mapping algorithm optimization antenna.

In conclusion the antenna optimization method basic procedure of moment method combination confidence region space mapping algorithm of the present invention is such as Under: the roughcast type of antenna space mapping algorithm is initially set up, the construction of roughcast type is close using the response surface based on Kriging regression Like method, optimizes roughcast type and determine the optimal design parameter of roughcast type；Thin model uses full wave analysis moment method, passes through parameter It extracts so that the response of roughcast type approaches the response of thin model, establishes the mapping relations of thick model parameter Yu thin model parameter；Benefit The prediction parameter of thin model is obtained with the optimal design parameter of roughcast type and the inverse mapping of established mapping relations, if thin model Prediction parameter be unsatisfactory for design requirement, update is iterated to mapping relations, until thin model prediction parameter meet design It is required that.This method saves the time under the premise of guaranteeing accuracy to the parameter global optimization of design.

Claims (3)

1. a kind of antenna optimization method of moment method combination confidence region space mapping algorithm, which is characterized in that steps are as follows:

Step 1 establishes antenna model, according to design objective, that is, antenna return loss or voltage standing wave ratio, determines the first of antenna Beginning parameter value x^init, initial parameter value includes the position of the size of aerial radiation patch, the thickness of substrate, feed；

Step 2 obtains thick discrete model by setting subdivision grid thickness, convergence precision size, to roughcast type using moment method It optimizes to obtain the starting point x of space reflection⁽⁰⁾；

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

Step 4, to basic point set X_B={ x⁽¹⁾,...,x^(N)Each of basic engineering point x^(j), j=1 ..., N, using square Amount method carries out thick discrete model solution, obtains and basic engineering point x^(j)Corresponding thick discrete model responds R_cd(x^(j))；

Step 5 utilizes basic engineering point x^(j)R is responded with corresponding thick discrete model_cd(x^(j)), in conjunction with gram in golden difference approach structure Make the roughcast type R of space mapping algorithm_c；

Step 6 is arranged iterative steps i=1, and enables For the parameter value of the thin model of i-th iteration；

Step 7 is rightCarry out thin model emulation；

Step 8, using the parameter value of the thin model of confidence region space mapping algorithm prediction i+1 time iteration

Step 9 judges whether to meet termination conditionη value 10^-3, R_fIndicate the sound of thin model It answers, the optimization of antenna is completed if meeting, if being unsatisfactory for return step 7.

2. the antenna optimization method of moment method combination confidence region space mapping algorithm according to claim 1, which is characterized in that Basic engineering point x is utilized described in step 5^(j)R is responded with corresponding thick discrete model_cd(x^(j)), in conjunction with gram in golden difference approach Construct the roughcast type R of space mapping algorithm_c, the specific steps are as follows:

(5.1) the i.e. basic point set X of one group of design vector is generated in step 3_B={ x⁽¹⁾,...,x^(N), X_BMiddle basic engineering point x^(j), J=1 ..., N, corresponding thick discrete model response sets 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 estimate certainty function f_p(x)=μ+ε (x), wherein μ is mean value, and ε is error, Being contemplated to be 0, x is independent variable, the Gauss correlation function form used are as follows:

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

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

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

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

Wherein

Wherein, I is n dimension unit vector；

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

R_cd,i(x^(j)) indicate the corresponding response of j-th of vector in thick discrete model when i-th iteration；R is x and X_BIn each vector Associated vector；

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

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

M is X_BIn correlation matrix between each vector；

Mean valueIt is given by:

Related coefficient θ_kIt is obtained by maximizing following formula:

Wherein variance

3. the antenna optimization method of moment method combination confidence region space mapping algorithm according to claim 1, which is characterized in that Using the parameter value of the thin model of confidence region space mapping algorithm prediction i+1 time iteration described in step 8Specific steps are such as Under:

In space mapping algorithm, when i-th iteration, make:

(B^(i)TB⁽ⁱ⁾+λI)h⁽ⁱ⁾=-B^(i)Tf⁽ⁱ⁾ (10)

Wherein, B⁽ⁱ⁾Roughcast shape parameter to the Jacobian matrix of thin model parameter i-th iteration approximate solution, parameter lambda Selection guarantees | | h⁽ⁱ⁾| |≤δ, h⁽ⁱ⁾For correction amount to be asked, Indicate that i-th parameter extraction obtains Roughcast type parameter value, δ be confidence interval radius；

The point of next iteration remains as x_f ⁽ⁱ⁺¹⁾=x_f ⁽ⁱ⁾+h⁽ⁱ⁾, x_f ⁽ⁱ⁺¹⁾Indicate thin model parameter, the x of i+1 time_f ⁽ⁱ⁾Indicate i-th Secondary thin model parameter；

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

f⁽ⁱ⁺¹⁾The error residual of expression i+1 secondary thick model parameter and roughcast type optimal solution,Indicate that i+1 subparameter mentions The roughcast type parameter value obtained；

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 process can not Letter, residual error f⁽ⁱ⁺¹⁾Substitution formula (10) obtains a new point, and the point is added in set and uses multiple spot parameter extraction, obtains 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 parameter value of new roughcast typeFurther found out by formula (11)

Wherein, R_f(x_f) indicate the response of thin model, x_fIndicate the parameter value of thin model, x_f ⁽ⁱ⁺¹⁾Indicate the thin mould of i+1 time iteration The parameter value of type.