CN105701297A - Multi-point adaptive proxy model based electromechanical coupling design method of reflector antenna - Google Patents

Abstract

The invention belongs to the technical field of antennae and particularly discloses a multi-point adaptive proxy model based electromechanical coupling design method of a reflector antenna. The method mainly comprises, in an optimization process, selecting two updating points by using established global and local sampling models during each iteration, so as to improve the global and local prediction capabilities of a proxy model at the same time; and then the method is applied to the electromechanical coupling optimization of the antenna, thus achieving the purpose of improving design quality and optimization efficiency. According to the multi-point adaptive proxy model based electromechanical coupling design method provided by the invention, the global prediction efficiency and the local prediction accuracy of the proxy model can be improved at the same time and a complicated function can be approximated very well; for the electromechanical coupling optimization of the reflector antenna, under the condition of ensuring calculation accuracy, the calculation amount can be reduced largely in the optimization process of the antenna, thus improving the calculation efficiency and the design quantity. Therefore, the method has relatively high actual application value.

Description

A kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model

Technical field

The invention belongs to antenna technical field, relate to reflector antenna mechanical-electric coupling method for designing, specifically a kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model。

Background technology

Tian Deng field, land, sea and air is had been widely used for as electromagnetic radiation and the microwave reflection surface antenna receiving device。Also exist between frame for movement (including heat) and the electromagnetism of reflector antenna influence each other, the relation of mutual dependence for existence, the successful realization of its electrical property depends not only upon design and the manufacture level of the subjects such as machinery, electromagnetism, heat transfer, being more dependent upon different interdisciplinary intersection and fusion, the development of its design mainly experienced by dynamo-electric separation, electric-mechanic control system to electrical and mechanical comprehensive three phases。

Dynamo-electric separate design method refers to that frame for movement separates with Electromagnetic Design and carries out, and when electronics working frequency range is relatively low, this method for designing can meet requirement。As document " Duan Baoyan. the current situation and development of electronics mechanical-electric coupling research. Chinese science: information science, 2015,45:299-312, doi:10.1360/N112014-00307. " in the method for the type is had been reported。But this dynamo-electric method for designing separated brings two problems, one is that frame for movement required precision is high, and two is that high-precision antenna structure not always meets all electrical performance indexes requirements。So often result in the serious problems such as product design cycle length, cost height, limited performance。

Electrical and mechanical comprehensive design is that it has recognized that electromechanics exists relation, also there has been relevant design experience by Machine Design and electrical property design simple superposition。As " Wang Congsi; Duan Baoyan; Chou Yuanying; Shao Xiaodong. towards the electrical and mechanical comprehensive design and analysis system of large-scale reflector antenna structure. aerospace journal, 2008,29 (6): 2041-2049. " and " horse big waves; Duan Baoyan; Wang Congsi. random parameter reflector antenna electromechanics Aggregation Robust Optimal Design. electric wave science journal, 2009,24 (6): 1065-1070. " in the type method is had been reported。But the method for designing of electrical and mechanical comprehensive does not have the chemical combination between research aircraft and electricity, also without the Influencing Mechanism of both considerations, lacking dynamo-electric relation formula, most dependence manually examination mode of gathering solves design problem。

Mechanical-electric coupling design refers to by the mechanism of action between exploration machine and electricity, under considering antenna electric performance index premise, provides the careful design of frame for movement precision。As document " Duan Baoyan; Wang Meng. the research of microwave antenna multi-field coupling theory model and Multidisciplinary Optimization. electronic letters, vol; 2013; 41 (10): 2051-2060. " and " cold state is pretty; Wang Wei, Duan Baoyan, Li Xiaoping. large-scale reflector antenna electromagnetic field and displacement field field coupling model and the application in the design of 65m aperture antenna thereof. mechanical engineering journal; 2012,48 (23): 1-9. " in have been reported。But when utilizing electromechanical Coupling Model that reflector antenna is optimized, owing to the coupled relation between every subjects is extremely complex, in order to obtain frame for movement and the electromagnetic performance of optimum, need successive ignition between each subject analytical model, the overall calculating time often sharply increases, and causes that computational efficiency is low。

Agent model technology, as a kind of method that can be effectively improved computational efficiency, has at home and abroad had become as the focus of research。Agent model refers to when ensureing computational accuracy, and the cycle is short, amount of calculation is little to construct a calculating according to existing a small amount of sample information, but the mathematical model that result of calculation is close with simulation analysis model。The black box problem of or typically no function expression excessively complicated for expression formula, agent model can be utilized to determine the functional relationship of system input and output, then this function is utilized to replace simulation calculation consuming time, thus reaching simplify process of optimization and improve the purpose of computational efficiency。Conventional agent model approximate data includes response surface, Kriging model, artificial neural network, RBF and support vector regression。Agent model technology there is detailed report by document " ForresterAIJ, KeaneAJ.Recentadvancesinsurrogate-basedoptimization.Prog ressinAerospaceScience, 2009,45 (1): 50-79. "。But current agent model is mainly used in the design of the complication system such as rocket, aircraft, the research being applied to by agent model in the design of reflector antenna mechanical-electric coupling was not also seen。

Summary of the invention

It is an object of the invention to for existing reflector antenna electromechanical Coupling Model amount of calculation when solving excessive, the problem that computational efficiency is relatively low, provide a kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model, to reduce amount of calculation, improve designing quality and optimize efficiency。

In order to realize above-mentioned target, the present invention adopts the following technical scheme that:

A kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model, comprises the following steps:

The first step, it is determined that design variable and initial designs space, makes iterations k=1, and during with the gain loss of antenna for optimization aim, the mathematical description of the mechanical-electric coupling optimization design of reflector antenna is as follows:

Findx=[x₁,x₂,…,x_m]^T

Miny(x)

S.T. $g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\Σ}}{\mathrm{\ρl}}^e{A}^e+W_{mb})-W_{max}\≤0$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

x_L≤x≤x_U

In formula, x is the structural design variable of antenna, and including physical dimension, shape, topology, type parameter, ρ is the density of backrest material, g₁X () retrains for quality, g₂X () is stress constraint, n1 is the rod member number of back frame structure, l^eIt is the length of e bar unit, A^eIt is the cross-sectional area of e bar unit, x_LAnd x_URespectively the floor value of design variable, upper dividing value, W_mbFor the quality of panel, W_maxFor the biggest quality that antenna allows, σ_eIt is the stress of e bar unit, σ_maxFor allowable stress value, the object function that y (x) is optimization design problem；Mechanical-electric coupling for reflector antenna designs, and y (x)=Δ G (x) represents the gain loss of antenna, uses Adaptive proxy model that object function is similar to；

Second step, as k=1, whole initial designs space is elected in initial significant design territory as, then, utilizes test design method to choose initial sample point, the number n of initial sample point in initial designs space_pFor:

$n_p=min\{\frac{(m+1)(m+2)}{2},5m\}$

In formula, m represents the number of design variable；

3rd step, calls electromechanical Coupling Model and calculates the response value that initial sample point is corresponding, and the response value of these sample points and correspondence thereof remained in sample point data base；

4th step, extracts the response value of all of sample point and correspondence thereof in sample point data base, chooses the agent model of Kriging algorithm construction object function；

5th step, chooses optimized algorithm and solves spot sampling's model, the optimal solution x obtained^(k,1)Update point as one, call electromechanical Coupling Model and calculate the response value y (x that this optimal solution is corresponding^(k,1)), and be saved in sample point data base；Spot sampling's model is:

Findx=[x₁,x₂,…,x_m]^T

Min

S.T. $g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\Σ}}{\mathrm{\ρl}}^e{A}^e+W_{mb})-W_{\max }\≤0$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

$x_L^k\≤x\≤x_U^k$

In formula,For the agent model that object function is corresponding,WithRespectively lower bound during kth time iteration and the upper bound, they are continually changing in an iterative process, but not can exceed that overall situation lower bound x_LWith overall situation upper bound x_U, the sampler space now is significant design territory；

6th step, chooses optimized algorithm and solves overall situation sampling pattern, the optimal solution x obtained^(k,2)Update point as one, call electromechanical Coupling Model and calculate the response value y (x that this optimal solution is corresponding^(k,2)), and be saved in sample point data base；Overall situation sampling pattern is:

Findx=[x₁,x₂,…,x_m]^T

Min $-\mathrm{\σ}\left(x\right)\mathrm{\φ}\left(\frac{y_{\min }-\hat{y}\left(x\right)}{\mathrm{\σ}\left(x\right)}\right)$

S.T. $g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\Σ}}{\mathrm{\ρl}}^e{A}^e+W_{mb})-W_{max}\≤0$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

x_L≤x≤x_U

In formula, σ (x) is the prediction variance of design point, Kriging model obtain, and φ is standard normal probabillity density function, y_minFor the minimum target response value in current sample point；

7th step, it may be judged whether meet the condition of convergence；As k=1, directly proceed to the 8th step；If the calculation times calling electromechanical Coupling Model reaches the number of times of setting or meets convergence criterion, then stop iteration, and export optimal solution, otherwise proceed to the 8th step；Wherein convergence criterion is:

$\mathrm{\Δ}=abs\left(\frac{y\left(x^k\right)-y\left(x^{k-1}\right)}{y\left(x^k\right)}\right)\≤{\mathrm{\Δ}}_a$

Δ 1=abs (y (x^k)-y(x^k-1))≤0.1Δ_a

In formula, y (x^k) and y (x^k-1) optimal solution required by kth time and kth-1 time is corresponding in respectively optimization process response value, Δ_a=0.005 is given convergence, is the optimization problem of 0 for some globally optimal solution, it is necessary to use absolute error Δ 1 to terminate iterative process, is not that the optimization problem of 0 then needs to use relative error Δ to terminate iterative process for globally optimal solution；

8th step, makes k=k+1, updates sample point data base and significant design territory, and turns to the 4th step。

In above-mentioned 5th step and the 6th step, optimized algorithm can use genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm and self adaptation covariance matrix evolution strategy；

In above-mentioned 8th step, the update method in significant design territory is as follows:

(8.1) central point in significant design territory is determined

$x_C^k=\left\{\begin{array}{cc}{x}^{(k-1,2)}& y\left(x^{(k-1,2)}\right)-y\left(x^{(k-1,1)}\right)\≤0\\ x^{(k-1,1)}& else\end{array}\right.$

In formula, x^(k-1,1)And x^(k-1,2)The local respectively obtained during kth-1 step iteration and the overall situation update point, y (x^(k-1,2)) and y (x^(k-1,1)) respectively x^(k-1,1)And x^(k-1,2)Corresponding response value；

(8.2) the relative error ε of currently most solution is calculated,

$\mathrm{\ϵ}=\left|\left(\frac{y\left(x^{k-1}\right)-\hat{y}\left(x^{k-1}\right)}{y\left(x^{k-1}\right)}\right)\right|$

In formula, x^k-1Choose the renewal point that response value during kth-1 step iteration is less, y (x^k-1) for x^k-1Corresponding response value,For x^k-1Corresponding predictive value；

(8.3) new controlling elements ζ is determined^k,

${\mathrm{\&zeta;}}^k=\left\{\begin{array}{cc}1/ln(\mathrm{\&epsiv;}/{\mathrm{\&epsiv;}}_a)& \mathrm{\&epsiv;}\&GreaterEqual;3{\mathrm{\&epsiv;}}_a\\ ln({\mathrm{\&epsiv;}}_a/\mathrm{\&epsiv;})& \mathrm{\&epsiv;}\&le;{\mathrm{\&epsiv;}}_a/3\\ 1& {\mathrm{\&epsiv;}}_a/3<\mathrm{\&epsiv;}<3{\mathrm{\&epsiv;}}_a\end{array}\right.$

In formula, the acceptable precision ε of agent model_a=0.01；

(8.4) the length V in new significant design region is determined^k,

V^k=max (ζ^kV^k-1,ζ_aV¹)

In formula, V^k-1The significant design length of field of gained, V during for-1 iteration of kth¹For initial designs siding-to-siding block length, the least dominated parameter ζ_a=0.05；

(8.5) new significant design region is determined,

$I_{IDD}^k=\left\{x\right|x_L^k\&le;x\&le;x_U^k\}$

$\begin{array}{cc}where& x_L^k=max(x_L,x_C^k-0.5V^k)\end{array}$

$x_U^k=\min (x_U,x_C^k+0.5V^k)$

In formula,Significant design territory during for kth time iteration。

Beneficial effects of the present invention: compared with prior art, present invention have the advantage that

(1) multiple spot Adaptive proxy model method can improve the global and local precision of prediction of agent model when each iteration simultaneously, it is possible to relatively accurately challenge is approached。

(2) for the mechanical-electric coupling optimization of reflector antenna, the method of the present invention can when ensureing computational accuracy, being substantially reduced antenna amount of calculation in process of optimization, thus improving computational efficiency and designing quality, there is higher actual application value。

Accompanying drawing explanation

Fig. 1 is reflector antenna mechanical-electric coupling design flow diagram of the present invention；

Fig. 2 is that in the present invention, electromechanical Coupling Model sets up process flow diagram flow chart；

Fig. 3 is that in the present invention, process flow diagram flow chart is set up in significant design territory；

Fig. 4 is that the present invention emulates reflecting surface antenna back frame structure diagram used；

Fig. 5 utilizes the inventive method to carry out front 100 iterative process schematic diagrams when mechanical-electric coupling optimizes during the present invention emulates；

Fig. 6 be after utilizing the inventive method to optimize during the present invention emulates gained Antenna Far Field directional diagram with the contrast schematic diagram of theoretical value。

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention done concrete introduction。

With reference to Fig. 1, a kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model, it comprises the following steps:

The first step, it is determined that design variable, initial designs space and mathematical optimization models, makes iterations k=1。With reference to Fig. 2, set up the mechanical-electric coupling mathematical optimization models of reflector antenna, comprise the following steps that,

(1.1) relevant parameter according to reflector antenna, sets up the FEM (finite element) model of reflector antenna structure, and applies external load and complete the static analysis of reflector antenna structure, is:

K δ (x)=F

In formula, K is structural stiffness matrix, and F is the load suffered by antenna, and δ (x) is antenna structure displacement, and x is the structural design variable of antenna, the parameter such as including physical dimension, shape, topology, type；

(1.2) from staticaanalysis results, extract coordinate and the displacement of node, then utilize formula below to obtain the radiated far field directional diagram of reflector antenna:

In formula,For far field direction of observation,For point of observation vector with the angle between z-axis,For the angle between the same x-axis on point of observation vector projection to xoy face,For Reflector Panel random error bore field phase affected item, γ is the parameter of the factors such as manufacturing process, A is the bore face area that reflecting surface projects on xoy face, ρ ' for zero with the direction vector of arbitrfary point on bore face, φ ' for ρ ' with the angle between x-axis；

(1.3) the far field Electric Field Distribution according to antenna, the gain calculating antenna is:

When δ (x), γ are zero, the gain G of ideal antenna can be obtained_ideal。The δ (x) calculated is substituted into above formula and can obtain the actual gain of antennaThe gain loss that now can obtain antenna is,

(1.4) when with the gain loss of antenna for optimization aim, the mathematical description of the mechanical-electric coupling optimization design of reflector antenna is as follows,

Findx=[x₁,x₂,…,x_m]^T

Miny (x)=Δ G (x)

S.T. $g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\&Sigma;}}{\mathrm{\&rho;l}}^e{A}^e+W_{mb})-W_{max}\&le;0$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

x_L≤x≤x_U

In formula, x is the structural design variable of antenna, and the parameter such as including physical dimension, shape, topology, type, ρ is the density of backrest material, g₁X () retrains for quality, g₂X () is stress constraint, n1 is the rod member number of back frame structure, l^eIt is the length of e bar unit, A^eIt is the cross-sectional area of e bar unit, x_LAnd x_URespectively the floor value of design variable, upper dividing value, W_mbFor the quality of panel, W_maxFor the biggest quality that antenna allows, σ_eIt is the stress of e bar unit, σ_maxFor allowable stress value；The gain loss that Δ G (x) is antenna, object function y (x) is function consuming time, it is necessary to object function is similar to, and constraint g (x) is simple function。

Second step, as k=1, whole initial designs space is elected in initial significant design territory as。Minimax Latin hypercube body test design method is utilized to choose initial sample point, the number n of initial sample point in initial designs space_pFor:

$n_p=min\{\frac{(m+1)(m+2)}{2},5m\}$

In formula, m represents the number of design variable；

3rd step, the electromechanical Coupling Model of call establishment calculates the gain loss value that initial sample point is corresponding, the gain loss value of these sample points and correspondence thereof is remained in sample point data base；

4th step, extracts the gain loss value of all of sample point and correspondence thereof in sample point data base, chooses Kriging algorithm and constructs the agent model of object function as approximate data, and its construction process is as follows,

(2.1) expression formula of Kriging algorithm is as follows:

$\hat{y}\left(x\right)={\mathrm{\&beta;}}^{T}q\left(x\right)+Z\left(x\right)$

In formula, β is regression parameter vector to be asked, and the column vector that q (x) is made up of polynomial basis function, Z (x) is an average is 0, and variance isStochastic process；Statistical nature is as follows:

E [Z (x)]=0

$Var\&lsqb;Z\left(x\right)\&rsqb;={\mathrm{\&sigma;}}_z^2$

$Cov\&lsqb;Z\left(x^i\right),Z\left(x^j\right)\&rsqb;={\mathrm{\&sigma;}}_z^2\&lsqb;R_{ij}(\mathrm{\&theta;},x^i,x^j)\&rsqb;$

In formula, xⁱ, x^jIt is any two sample point in sample set, R_ij(θ,xⁱ,x^j) it is Gauss correlation function, θ is parameter vector to be asked in Gauss correlation function；

(2.2) for arbitrfary point x⁰, utilize the predictive value of the agent model of Kriging algorithm construction and prediction variance to be expressed as:

$\hat{y}\left(x^0\right)={\widehat{\mathrm{\&beta;}}}^{T}q\left(x^0\right)+r^T{R}^{-1}(Y-Q\widehat{\mathrm{\&beta;}})$

${\mathrm{\&sigma;}}^2\left(x^0\right)={\widehat{\mathrm{\&sigma;}}}_z^2(1-r^T{R}^{-1}r+\frac{{(1-r^T{R}^{-1}r)}^2}{{\left(Q\widehat{\mathrm{\&beta;}}\right)}^T{R}^{-1}\left(Q\widehat{\mathrm{\&beta;}}\right)})$

In formula, Q is basic function matrix, and R is correlation function matrix, and other parameter expression is as follows:

$\widehat{\mathrm{\&beta;}}={\left(Q^T{R}^{-1}Q\right)}^{-1}{Q}^T{R}^{-1}Y$

${\widehat{\mathrm{\&sigma;}}}_z^2=\frac{{(Y-Q^T\mathrm{\&beta;})}^T{R}^{-1}(Y-Q^T\mathrm{\&beta;})}{n}$

r(x⁰)=[R (θ, x⁰,x¹),R(θ,x⁰,x²),…,R(θ,x⁰,xⁿ)]^T

In formula, xⁱBeing m dimensional vector, m is design variable number, and n is the number of existing sample point, and Y is the response value column vector that existing sample point is corresponding。

5th step, chooses genetic algorithm for solving spot sampling model, the optimal solution x obtained^(k,1)Update point as one, call electromechanical Coupling Model and calculate the response value y (x that this optimal solution is corresponding^(k,1)), and be saved in sample point data base。Spot sampling's model is:

Findx=[x₁,x₂,…,x_m]^T

Min

S.T. $g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\&Sigma;}}{\mathrm{\&rho;l}}^e{A}^e+W_{mb})-W_{\max }\&le;0$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

$x_L^k\&le;x\&le;x_U^k$

In formula,For the agent model that object function is corresponding,WithRespectively lower bound during kth time iteration and the upper bound, they are continually changing in an iterative process, but not can exceed that overall situation lower bound x_LWith overall situation upper bound x_U, the sampler space now is significant design territory；

6th step, chooses genetic algorithm for solving overall situation sampling pattern, the optimal solution x obtained^(k,2)Update point as one, call electromechanical Coupling Model and calculate the response value y (x that this optimal solution is corresponding^(k,2)), and be saved in sample point data base。Overall situation sampling pattern is:

Findx=[x₁,x₂,…,x_m]^T

Min $-\mathrm{\&sigma;}\left(x\right)\mathrm{\&phi;}\left(\frac{y_{\min }-\hat{y}\left(x\right)}{\mathrm{\&sigma;}\left(x\right)}\right)$

S.T. $g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\&Sigma;}}{\mathrm{\&rho;l}}^e{A}^e+W_{mb})-W_{\max }\&le;0$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

x_L≤x≤x_U

In formula, σ (x) is the prediction variance of design point, Kriging model obtain, and φ is standard normal probabillity density function, y_minFor the minimum target response value in current sample point；

7th step, it may be judged whether meet the condition of convergence；As k=1, directly proceed to the 8th step；If the calculation times calling electromechanical Coupling Model reaches the number of times of setting or meets convergence criterion, then stop iteration, and export optimal solution, otherwise proceed to the 8th step；Wherein convergence criterion is:

$\mathrm{\&Delta;}=abs\left(\frac{y\left(x^k\right)-y\left(x^{k-1}\right)}{y\left(x^k\right)}\right)\&le;{\mathrm{\&Delta;}}_a$

Δ 1=abs (y (x^k)-y(x^k-1))≤0.1Δ_a

In formula, y (x^k) and y (x^k-1) optimal solution required by kth time and kth-1 time is corresponding in respectively optimization process response value, Δ_aFor given convergence, it is the optimization problem of 0 for some globally optimal solution, it is necessary to use absolute error Δ 1 to terminate iterative process, is not that the optimization problem of 0 then needs to use relative error Δ to terminate iterative process for globally optimal solution；

8th step, makes k=k+1, updates sample point data base and significant design territory, and turns to the 4th step。With reference to Fig. 3, the update method in significant design territory is as follows:

(8.1) central point in significant design territory is determined

$x_C^k=\left\{\begin{array}{cc}{x}^{(k-1,2)}& y\left(x^{(k-1,2)}\right)-y\left(x^{(k-1,1)}\right)\&le;0\\ x^{(k-1,1)}& else\end{array}\right.$

In formula, x^(k-1,1)And x^(k-1,2)The local respectively obtained during kth-1 step iteration and the overall situation update point, y (x^(k-1,2)) and y (x^(k-1,1)) respectively x^(k-1,1)And x^(k-1,2)Corresponding response value；

(8.2) the relative error ε of currently most solution is calculated,

$\mathrm{\&epsiv;}=\left|\left(\frac{y\left(x^{k-1}\right)-\hat{y}\left(x^{k-1}\right)}{y\left(x^{k-1}\right)}\right)\right|$

In formula, x^k-1Choose the renewal point that response value during kth-1 step iteration is less, y (x^k-1) for x^k-1Corresponding response value,For x^k-1Corresponding predictive value；

(8.3) new controlling elements ζ is determined^k,

${\mathrm{\&zeta;}}^k=\left\{\begin{array}{cc}1/ln(\mathrm{\&epsiv;}/{\mathrm{\&epsiv;}}_a)& \mathrm{\&epsiv;}\&GreaterEqual;3{\mathrm{\&epsiv;}}_a\\ ln({\mathrm{\&epsiv;}}_a/\mathrm{\&epsiv;})& \mathrm{\&epsiv;}\&le;{\mathrm{\&epsiv;}}_a/3\\ 1& {\mathrm{\&epsiv;}}_a/3<\mathrm{\&epsiv;}<3{\mathrm{\&epsiv;}}_a\end{array}\right.$

In formula, the acceptable precision ε of agent model_a=0.01；

(8.4) the length V in new significant design region is determined^k,

V^k=max (ζ^kV^k-1,ζ_aV¹)

In formula, V^k-1The significant design length of field of gained, V during for-1 iteration of kth¹For initial designs siding-to-siding block length, the least dominated parameter ζ_a=0.05；

(8.5) new significant design region is determined,

$I_{IDD}^k=\left\{x\right|x_L^k\&le;x\&le;x_U^k\}$

$\begin{array}{cc}where& x_L^k=max(x_L,x_C^k-0.5V^k)\end{array}$

$x_U^k=\min (x_U,x_C^k+0.5V^k)$

In formula,Significant design territory during for kth time iteration。

Advantages of the present invention can be further illustrated by following l-G simulation test:

1. simulated conditions

The interarea bore of certain common 8m reflector antenna is 8m, and focal length is 3m, and during due to high frequency, the electrical property of antenna is more sensitive to the malformation of antenna, and therefore the operating frequency of analysis optimization elects 12.5GHz as。Due to the symmetry of antenna structure, Fig. 4 gives 1/4 part of whole back frame structure, and in figure, the unit of length is cm, has 97 rod members and 32 nodes, and back frame structure is steel construction, and the elastic modelling quantity of material is about 2.1 × 10⁵MPa, density is 7.85 × 10^-3kg/cm³；Reflection surface panel is aluminium alloy, and thickness is 4mm, and density is 2.73 × 10^-3kg/cm³。In order to reduce design variable number, being 12 class variables by 97 rod member merger, classification situation is as shown in table 1, using 12 class variables as design variable。The present invention only considers the impact that antenna gain is lost by the systematic error that the primary reflection surface deformation that antenna causes because of deadweight causes when looking up to heaven, and is left out feed and minor face during modeling。When utilizing the ANSYS FEM (finite element) model setting up antenna structure, Link8 elected as by rod member, and Shell163 elected as by panel。Utilize minimax Latin hypercube body test design method to choose 60 initial sample points simultaneously。

Bar cross-sectional area classification situation (square measure: the cm of table 1 reflecting surface antenna back frame structure²)

2. simulation result

Table 2 is adopt context of methods and directly utilize the Comparative result situation that genetic algorithm (not using agent model) carries out the mechanical-electric coupling optimization of 8m antenna。Fig. 5 utilizes the inventive method to carry out front 100 iterative process schematic diagrams when mechanical-electric coupling optimizes；Fig. 6 be after utilizing the inventive method to optimize gained Antenna Far Field directional diagram with the contrast schematic diagram of theoretical value。

Comprehensive Correlation (square measure: the cm of table 2 Different Optimization method²)

As shown in Table 2, the model call number of context of methods and operation time respectively may be about the 2.61% and 4.06% of genetic algorithm, model call number and operation time all greatly reduce, show that context of methods has higher optimization efficiency, as shown in Figure 5, the convergence of context of methods and local predictive ability are better simultaneously。The gain loss that context of methods obtains is more or less the same with genetic algorithm acquired results, and it will be appreciated from fig. 6 that context of methods gained far-field pattern is closer to theoretical value, illustrates that context of methods has good global prediction ability。

By means of the invention it is also possible to be substantially reduced antenna amount of calculation in process of optimization, thus improve computational efficiency and designing quality。

In present embodiment, the part of not narration in detail belongs to the known conventional means of the industry, does not describe one by one here。Exemplified as above is only illustration to the present invention, is not intended that the restriction to protection scope of the present invention, every belongs within protection scope of the present invention with the same or analogous design of the present invention。

Claims (3)

1. the reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model, it is characterised in that comprise the following steps:

The first step, it is determined that design variable and initial designs space, makes iterations k=1, and during with the gain loss of antenna for optimization aim, the mathematical description of the mechanical-electric coupling optimization design of reflector antenna is as follows:

Findx=[x₁,x₂,…,x_m]^T

Miny(x)

$\begin{array}{cc}S.T.& g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\&Sigma;}}{\mathrm{\&rho;l}}^e{A}^e+W_{mb})-W_{max}\&le;0\end{array}$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

x_L≤x≤x_U

In formula, x is the structural design variable of antenna, and including physical dimension, shape, topology, type parameter, ρ is the density of backrest material, g₁X () retrains for quality, g₂X () is stress constraint, n1 is the rod member number of back frame structure, l^eIt is the length of e bar unit, A^eIt is the cross-sectional area of e bar unit, x_LAnd x_URespectively the floor value of design variable, upper dividing value, W_mbFor the quality of panel, W_maxFor the biggest quality that antenna allows, σ_eIt is the stress of e bar unit, σ_maxFor allowable stress value, the object function that y (x) is optimization design problem；Mechanical-electric coupling for reflector antenna designs, and y (x)=Δ G (x) represents the gain loss of antenna, uses Adaptive proxy model that object function is similar to；

Second step, as k=1, whole initial designs space is elected in initial significant design territory as, then, chooses initial sample point, the number n of initial sample point in initial designs space_pFor:

$n_p=min\{\frac{(m+1)(m+2)}{2},5m\}$

In formula, m represents the number of design variable；

3rd step, calls electromechanical Coupling Model and calculates the response value that initial sample point is corresponding, and the response value of these sample points and correspondence thereof remained in sample point data base；

4th step, extracts the response value of all of sample point and correspondence thereof in sample point data base, chooses the agent model of Kriging algorithm construction object function；

5th step, chooses optimized algorithm and solves spot sampling's model, the optimal solution x obtained^(k,1)Update point as one, call electromechanical Coupling Model and calculate the response value y (x that this optimal solution is corresponding^(k,1)), and be saved in sample point data base；Spot sampling's model is:

Findx=[x₁,x₂,…,x_m]^T

$\begin{array}{cc}Min& \hat{y}\left(x\right)\end{array}$

$\begin{array}{cc}S.T.& g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\&Sigma;}}{\mathrm{\&rho;l}}^e{A}^e+W_{mb})-W_{max}\&le;0\end{array}$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

$x_L^k\&le;x\&le;x_U^k$

In formula,For the agent model that object function is corresponding,WithRespectively lower bound during kth time iteration and the upper bound, they are continually changing in an iterative process, but not can exceed that overall situation lower bound x_LWith overall situation upper bound x_U, the sampler space now is significant design territory；

6th step, chooses optimized algorithm and solves overall situation sampling pattern, the optimal solution x obtained^(k,2)Update point as one, call electromechanical Coupling Model and calculate the response value y (x that this optimal solution is corresponding^(k,2)), and be saved in sample point data base；Overall situation sampling pattern is:

Findx=[x₁,x₂,…,x_m]^T

$\begin{array}{cc}Min& -\mathrm{\&sigma;}\left(x\right)\mathrm{\&phi;}\left(\frac{y_{min}-\hat{y}\left(x\right)}{\mathrm{\&sigma;}\left(x\right)}\right)\end{array}$

$\begin{array}{cc}S.T.& g_1\left(x\right)=(\underset{e=1}{\overset{n1}{\&Sigma;}}{\mathrm{\&rho;l}}^e{A}^e+W_{mb})-W_{max}\&le;0\end{array}$

g₂(x)=σ_e-σ_max≤ 0, (e=1,2 ..., n1)

x_L≤x≤x_U

In formula, σ (x) is the prediction variance of design point, Kriging model obtain, and φ is standard normal probabillity density function, y_minFor the minimum target response value in current sample point；

7th step, it may be judged whether meet the condition of convergence；As k=1, directly proceed to the 8th step；If the calculation times calling electromechanical Coupling Model reaches the number of times of setting or meets convergence criterion, then stop iteration, and export optimal solution, otherwise proceed to the 8th step；Wherein convergence criterion is:

$\mathrm{\&Delta;}=abs\left(\frac{y\left(x^k\right)-y\left(x^{k-1}\right)}{y\left(x^k\right)}\right)\&le;{\mathrm{\&Delta;}}_a$

Δ 1=abs (y (x^k)-y(x^k-1))≤0.1Δ_a

In formula, y (x^k) and y (x^k-1) optimal solution required by kth time and kth-1 time is corresponding in respectively optimization process response value, Δ_a=0.005 is given convergence, is the optimization problem of 0 for some globally optimal solution, it is necessary to use absolute error Δ 1 to terminate iterative process, is not that the optimization problem of 0 then needs to use relative error Δ to terminate iterative process for globally optimal solution；

8th step, makes k=k+1, updates sample point data base and significant design territory, and turns to the 4th step。

2. a kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model according to claim 1, it is characterized in that, in the 5th step and the 6th step, optimized algorithm can use genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm and self adaptation covariance matrix evolution strategy。

3. a kind of reflector antenna mechanical-electric coupling method for designing based on multiple spot Adaptive proxy model according to claim 1, it is characterised in that in the 8th step, the update method in significant design territory is as follows:

(8.1) central point in significant design territory is determined

$x_C^k=\left\{\begin{array}{cc}{x}^{(k-1,2)}& y\left(x^{(k-1,2)}\right)-y\left(x^{(k-1,1)}\right)\&le;0\\ x^{(k-1,1)}& else\end{array}\right.$

In formula, x^(k-1,1)And x^(k-1,2)The local respectively obtained during kth-1 step iteration and the overall situation update point, y (x^(k-1,2)) and y (x^(k-1,1)) respectively x^(k-1,1)And x^(k-1,2)Corresponding response value；

(8.2) the relative error ε of currently most solution is calculated,

$\mathrm{\&epsiv;}=\left|\left(\frac{y\left(x^{k-1}\right)-\hat{y}\left(x^{k-1}\right)}{y\left(x^{k-1}\right)}\right)\right|$

In formula, x^k-1Choose the renewal point that response value during kth-1 step iteration is less, y (x^k-1) for x^k-1Corresponding response value,For x^k-1Corresponding predictive value；

(8.3) new controlling elements ζ is determined^k,

${\mathrm{\&zeta;}}^k=\left\{\begin{array}{cc}1/ln(\mathrm{\&epsiv;}/{\mathrm{\&epsiv;}}_a)& \mathrm{\&epsiv;}\&GreaterEqual;3{\mathrm{\&epsiv;}}_a\\ ln({\mathrm{\&epsiv;}}_a/\mathrm{\&epsiv;})& \mathrm{\&epsiv;}\&le;{\mathrm{\&epsiv;}}_a/3\\ 1& {\mathrm{\&epsiv;}}_a/3<\mathrm{\&epsiv;}<3{\mathrm{\&epsiv;}}_a\end{array}\right.$

In formula, the acceptable precision ε of agent model_a=0.01；

(8.4) the length V in new significant design region is determined^k,

V^k=max (ζ^kV^k-1,ζ_aV¹)

In formula, V^k-1The significant design length of field of gained, V during for-1 iteration of kth¹For initial designs siding-to-siding block length, the least dominated parameter ζ_a=0.05；

(8.5) new significant design region is determined,

$I_{IDD}^k=\left\{x\right|x_L^k\&le;x\&le;x_U^k\}$

$where{x}_L^k=max(x_L,x_C^k-0.5V^k)$

$x_U^k=min(x_U,x_C^k+0.5V^k)$

In formula,Significant design territory during for kth time iteration。