CN107357962A - A kind of antenna house rib cross-sectional size optimization method based on Adaptive proxy model - Google Patents
A kind of antenna house rib cross-sectional size optimization method based on Adaptive proxy model Download PDFInfo
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Abstract
The invention belongs to Radar Antenna System field, specifically discloses a kind of antenna house rib cross-sectional size optimization method based on Adaptive proxy model, and its main contents includes：In optimization process, two sampled points are chosen every time, and the global and local predictive ability of agent model is respectively increased；Then this method is applied in the electromechanical integrated optimization of metal truss formula antenna house rib sectional dimension, so as to reach the purpose for improving designing quality and optimization efficiency.The Adaptive proxy model method of the present invention can be very good to carry out approximation to complicated function；For the electromechanical integrated optimization of metal truss formula antenna house rib sectional dimension, the amount of calculation of whole process of optimization in the case where ensureing computational accuracy, can be substantially reduced, so as to improve computational efficiency and designing quality, there is higher practical implementation to be worth.
Description
Technical Field
The invention belongs to the technical field of radar antennas, and relates to an electromechanical integration optimization method for the rib section size of a metal truss type radome.
Background
The radome is a wave-transparent shell for protecting the antenna from the natural environment, and is a specially-shaped electromagnetic transparent window formed by a covering made of natural or artificial dielectric materials or a dielectric shell supported by a truss. The antenna housing with the excellent design has the functions of protectiveness, conductivity, reliability, concealment, decoration and the like, and can prolong the service life of each part of the whole system, reduce the service life cost and the operation cost, simplify the design, reduce the maintenance cost, ensure the accuracy of the surface and the position of the antenna, and create a good working environment for an antenna operator. However, the radome also affects the electromagnetic radiation of the desired antenna, which may reduce the electrical performance of the desired antenna.
With the progress of aviation, meteorological and military technologies and the development of military situation in China, research and manufacture of high-precision radars and high-gain antennas such as remote precision tracking and measuring radars becomes an urgent task. The natural environment of a special geographical position has a large influence on equipment, the antenna housing is required to be equipped to meet the requirements of the radars and the antennas, and the metal truss type antenna housing is popular due to good structural performance and electrical performance and is widely applied to antennas such as ground radars, ship-borne radars, radio astronomical telescopes and the like.
The influence of truss scattering in a metal truss type antenna cover on the far field of the antenna is analyzed in a book of a classic book radome telecommunication design method published in 1993 by a dua. The method has the following defects: the influence of the metal truss type antenna housing on the electrical performance of the antenna is only analyzed, and the electromechanical integration design is not considered.
An antenna electromechanical integrated technology and an antenna combined structure theory are researched in a thesis of 2008 by Wang, namely an electromechanical integrated design and analysis system for a large-scale reflector antenna structure, an antenna far-zone radiation electric field is analyzed by adopting an accurate PO method, a hierarchical structure of surface antenna parametric design is established, the problem of automatic division of a combined structure grid consisting of a back frame, a reflector, a central body and the like is solved, the electromechanical integrated design of the surface antenna structure is realized, and the electromechanical integrated design is not applied to a metal truss type antenna cover. However, when the antenna cover is optimized in electromechanical integration, in order to obtain the optimal mechanical structure and electromagnetic performance, multiple iterations among all discipline analysis models are needed, the overall calculation time is often increased sharply, and the calculation efficiency is low.
The proxy model technology has become a hot point of research at home and abroad as a method capable of effectively improving the calculation efficiency. The agent model is a mathematical model which is short in calculation period and small in calculation amount but has a calculation result similar to that of a simulation analysis model and is constructed according to a small amount of existing sample information under the condition of ensuring calculation accuracy. For the problem of black boxes with excessively complex expressions or generally no function expression, a proxy model can be used for determining the functional relationship between the input and the output of the system, and then the function is used for replacing time-consuming simulation calculation, so that the purposes of simplifying the optimization design process and improving the calculation efficiency are achieved. Commonly used surrogate model approximation algorithms include response surface, Kriging model, artificial neural network, radial basis function, and support vector regression. The proxy model technique has been reported in detail in the literature "Forrester A I J, Keane A J. percent advances in sulfate-based simulation. progress in Aerospace Science,2009,45(1):50-79. However, the current proxy model is mainly applied to the design of complex systems such as rockets and airplanes, and the research of applying the proxy model to the radome electromechanical integration optimization design has not been seen yet.
Disclosure of Invention
The invention aims to provide an antenna cover rib section size optimization method based on a self-adaptive proxy model, aiming at the problems of overlarge calculated amount and lower calculation efficiency of the existing metal truss type antenna cover electromechanical integration optimization design during solving, so as to reduce the calculated amount, improve the design quality and the optimization efficiency, optimize the structural performance and the electrical performance of the antenna cover and improve the optimization efficiency.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for optimizing the cross section size of a radome rib based on an adaptive proxy model is characterized by comprising the following steps:
the method comprises the following steps of firstly, determining design variables and an initial design space, enabling the iteration number k to be 1, carrying out multi-objective weighting on the maximum value and the average value of the pointing error of the antenna with the cover, the maximum value and the average value of gain loss and the maximum value of the self weight and the node displacement of the antenna cover, and establishing the following electromechanical integrated optimization model of the metal truss type antenna cover structure to calculate the optimal rib size:
Min y(x(k))＝0.04·BSEmax+0.06·TLmax+0.04·BSEmean+0.06·TLmean+0.4·Defmax+0.4·Weight]
S.t.xL≤x(k)≤xU
in the formula, x(k)Design variables for the structure of a metal truss radome, including the rectangular cross-sectional width and height of each type of rib, BSEmaxFor maximum value of pointing error of shrouded antenna under all operating conditions, TLmaxBSE being the maximum value of the gain loss of the shrouded antenna under all operating conditionsmeanFor the mean value of the pointing error of the shrouded antenna under all operating conditions, TLmeanAverage value of gain loss of the shrouded antenna under all operating conditions, DefmaxIs the maximum value of the node displacement of the antenna housing under the action of load, Weight is the dead Weight of the antenna housing, and xLAnd xURespectively approximating a target function by using a self-adaptive agent model for a lower bound value and an upper bound value of a design variable;
and secondly, when k is equal to 1, setting a related design domain as the whole initial design space, and then selecting initial sample points in the initial design space by using a maximum-minimum Latin hypercube test design method, wherein the number n of the initial sample pointspComprises the following steps:
in the formula, nvRepresenting the number of design variables;
thirdly, calculating the corresponding real response values of the initial sample points, and storing the sample points and the response values thereof in a sample point database;
step four, extracting all sample points in the sample point database and corresponding response values thereof, and selecting a Kriging model to construct an agent model of the target function;
fifthly, selecting an optimization algorithm to solve a local sampling modelType, the optimal solution x obtained by using it(k,1)As an update point, calculating the response value y (x) corresponding to the optimal solution(k,1)) And storing the data into a sample point database; the local sampling model is as follows:
in the formula, x(k,1)Design variables for local sampling in the kth iteration;a proxy model corresponding to the objective function;andrespectively designing the lower bound and the upper bound of variables at the k-th iteration, wherein the lower bound and the upper bound are continuously changed in the iteration process, but the lower bound x cannot exceed the global boundLAnd a global upper bound xUThe sampling space at this time is the related design domain;
sixthly, an optimization algorithm is selected to solve the global sampling model, and the obtained optimal solution x is obtained(k,2)As an update point, calculating the response value y (x) corresponding to the optimal solution(k,2)) And storing the data into a sample point database; the global sampling model is:
S.T.xL≤x(k,2)≤xU
wherein,
fk-1(x(k,2))＝sk-1(x(k,2))min{|x(k,2)-xi||i＝1,2,…,ns}
in the formula, sk-1(x(k,2)) Is a design point x(k,2)The predicted standard deviation of (2); x is the number ofiFor an existing sample point, nsThe total number of the existing sample points; sigmf (x, [ ac ]]) The specific functional form is as follows:
seventhly, judging whether a convergence condition is met; when k is 1, directly switching to the eighth step; if the calculated times reach the set times or meet the convergence criterion, stopping iteration and outputting an optimal solution, otherwise, turning to the eighth step; wherein the convergence criterion is:
Δ1＝abs(y(xk)-y(xk-1))≤0.1Δa
in the formula, y (x)k) And y (x)k-1) Response values, delta, corresponding to the optimal solutions respectively obtained for the k-th time and the k-1-th time in the optimization processaFor some optimization problems with a globally optimal solution of 0, the iteration process needs to be terminated by using an absolute error Δ 1 and a proxy model approximation accuracy Δ 3, and for optimization problems with a globally optimal solution of other than 0, the iteration process needs to be terminated by using a relative error Δ and a proxy model approximation accuracy Δ 2;
and step eight, making k equal to k +1, updating the current sample point database and the related design domain, and turning to the step four.
The sixth step of optimization algorithm is a genetic algorithm or a particle swarm optimization algorithm or a global optimization algorithm.
In the eighth step, the updating method of the related design domain is as follows:
(8.1) determining the center point of the associated design Domain
In the formula, x(k-1,1)And x(k-1,2)Respectively local and global update points, y (x), obtained in the iteration of step k-1(k-1,2)) And min (Y) are each x(k-1,2)The corresponding response value and the smallest response value in the entire sample;
(8.2) calculating the relative error of the current optimal solution,
in the formula, xk-1Selecting an update point, y (x), with a smaller response value in the iteration of the step (k-1)k-1) Is xk-1The corresponding value of the response is set to,is xk-1Corresponding predicted values;
(8.3) determining a new control factor ζk，
ζk＝max(ζk,0.5)
In the formula, the allowable accuracy of the proxy modela＝0.01；
(8.4) determining the length V of the new correlation design fieldk，
In the formula, VkThe associated design field length obtained at the kth iteration, where k is greater than or equal to 2, thetai(i＝1,2,…,nv) Updating the hyper-parameters in the correlation function of the Kriging model along with the updating of the Kriging model;
(8.5) determining a new relevant design domain,
in the formula IkAnd k is a related design domain at the kth iteration and is more than or equal to 2.
The sixth step of optimization algorithm is a genetic algorithm or a particle swarm optimization algorithm or a global optimization algorithm.
The invention has the beneficial effects that: compared with the prior art, the invention has the following advantages:
(1) the sampling method can simultaneously improve the global and local prediction precision of the proxy model during each iteration, can accurately approximate complex problems, and finds out the global optimal solution of the original problems. In addition, in the optimization process, all data are stored in the form of sample points, and the analysis and the reutilization of the data are facilitated.
(2) For electromechanical integration optimization of the rib section size of the metal truss type antenna housing, the method provided by the invention can greatly reduce the calculation amount of the antenna housing in the optimization design process under the condition of ensuring the calculation precision, thereby improving the calculation efficiency and the design quality, and having higher practical application value.
Drawings
FIG. 1 is a general flow chart of an implementation of the present invention;
FIG. 2 is a flow chart of an antenna housing electromechanical integration optimization establishing process in the present invention;
fig. 3 is a schematic structural diagram of a conventional metal truss-type radome;
FIG. 4 is a schematic view of a metal truss radome;
FIG. 5 is a comparison of pointing errors for the front and rear shrouded antennas before and after optimization;
fig. 6 is a graph comparing gain loss for an optimized front and rear shrouded antenna.
Detailed Description
The invention is described in detail below with reference to the figures and the embodiments.
Referring to fig. 3, the metal truss-type radome comprises three parts, namely a rib, a central node and a skin, wherein the rib and the rib are connected together through the central node to form a triangle, the skin covers the rib and the central node, and fig. 4 is a finite element model of the metal truss-type radome.
Referring to fig. 1, a method for optimizing the cross-sectional dimension of a rib of a radome based on an adaptive proxy model includes the following steps:
in the first step, design variables, an initial design space and an optimized design model are determined, and the iteration number k is 1. Referring to fig. 2, an electromechanical integration optimization model of the cross-sectional dimension of the metal truss type antenna cover rib is established, and the specific steps are as follows,
(1.1) in commercial model analysis software, establishing a geometric model of a metal truss type radome skin according to the structural form of the radome, setting the side length of a grid as lambda, and carrying out grid division on the model;
(1.2) according to the structural parameters and the material parameters of the skin of the metal truss type antenna housing, calculating the transmission coefficients of all points on the skin by using a transmission line theoryAnd according to the known antenna aperture field E (x, y), calculating the aperture field after penetrating through the antenna housing:
(1.3) calculating a far field F '(θ, φ) generated by the diameter field after penetrating the skin, based on the diameter field E' (x, y) after penetrating the skin obtained in (1.2):
where θ and φ are spherical coordinate angles of the observation point in the rectangular coordinate system O-xyz, and k0In order to be a free-space propagation constant,according to the formulaCalculating, lambda is the wavelength of the antenna, according to the working frequency f and the speed of light c of the antenna, through a formulaAnd calculating to obtain s as the area of the integral unit.
(1.4) calculating the fringe field of the rib. Sequentially calculating the scattered field F of each rib of the metal truss type antenna housing according to the induced current rate theorysci(θ, φ), the fringe field F of each ribsci(theta, phi) are added to obtain the scattered field of all ribsWherein n is the total number of ribs of the metal truss type antenna housing.
And (1.5) adding the transmission field and the scattering field to obtain a covered antenna far field. The far field F' (theta, phi) generated by the aperture field after penetrating the skin obtained in (1.3) and the scattered field F caused by all the ribs obtained in (1.4) are comparedsca(θ, φ) to obtain the antenna far field after covering:
Ft(θ,φ)＝F′(θ,φ)+Fsca(θ,φ)。
according to the far field F of the covered antennatAnd (theta, phi) drawing a covered antenna far-field directional diagram, and extracting electrical performance indexes of gain and directional error from the directional diagram.
And (1.6) analyzing the node displacement of the metal truss type antenna housing under the action of load.
According to the structural parameters of the metal truss type antenna housing, a structural finite element model is established in commercial structural finite element analysis software, static analysis is carried out, the displacement of the deformed metal truss type antenna housing node is obtained, and the maximum value of the node displacement is extracted.
And (1.7) calculating the self weight of the metal truss type antenna housing.
And calculating the volume of each rib according to the cross section area and the length of each rib in the metal truss, wherein the product of the volume of each rib and the density of each rib is the self weight of each rib, and the sum of the self weights of all the ribs is the self weight of the radome.
(1.8) establishing the following electromechanical integrated optimization model of the metal truss type antenna housing structure to calculate the optimal rib size:
Min y(x(k))＝0.04·BSEmax+0.06·TLmax+0.04·BSEmean+0.06·TLmean+0.4·Defmax+0.4·Weight]
S.t.xL≤x(k)≤xU
in the formula, x(k)Design variables for the structure of a metal truss radome, including the rectangular cross-sectional width and height of each type of rib, BSEmaxFor maximum value of pointing error of shrouded antenna under all operating conditions, TLmaxBSE being the maximum value of the gain loss of the shrouded antenna under all operating conditionsmeanFor the mean value of the pointing error of the shrouded antenna under all operating conditions, TLmeanAverage value of gain loss of the shrouded antenna under all operating conditions, DefmaxIs the maximum value of the node displacement of the antenna housing under the action of load, Weight is the dead Weight of the antenna housing, and xLAnd xURespectively approximating a target function by using a self-adaptive agent model for a lower bound value and an upper bound value of a design variable;
secondly, when k is equal to 1, setting a related design domain as the whole initial design space, and then selecting initial sample points in the initial design space by using a maximum-minimum Latin hypercube test design method, wherein the number n of the initial sample pointspComprises the following steps:
in the formula, nvRepresenting the number of design variables;
thirdly, calling the established antenna housing electromechanical integration optimization model to calculate a target value y (x) corresponding to the initial sample point, and storing the target value y (x) into a sample point database;
fourthly, extracting all sample points in the sample point database and corresponding target values y (x), selecting a Kriging model as a proxy model of an approximate algorithm construction target function, wherein the construction process is as follows,
(4.1) the expression of the Kriging model is as follows:
wherein μ is an unknown constant, Z (x) is a mean of 0, and the variance isThe random process of (a); the statistical characteristics are as follows:
E[Z(x)]＝0
in the formula, xi，xjIs any two sample points, R, in the sample setij(θ,xi,xj) Is a Gaussian correlation function, and theta is a parameter vector to be solved in the Gaussian correlation function;
(4.2) for any point x to be measured, the Kriging agent model can provide a predicted value at the pointAnd the predicted variance s2(x) The following were used:
wherein:
r(θ,x,S)＝[R(θ,x,x(1)),R(θ,x,x(2)),…,R(θ,x,x(n))]T
the correlation function of the Kriging surrogate model can be taken as a Gaussian correlation function of the form:
in the above formula, nvThe dimension of x, i.e., the number of design variables;i. j is two sample points in the sample set, and n is the total number of the existing sample points; theta is a hyper-parameter of a correlation function in the Kriging agent model, thetal＞0,l＝1,2,…,nvThe value is found by optimization (maximum likelihood estimation) and updated with the sample points.
Fifthly, selecting a genetic algorithm to solve a local sampling model, and obtaining an optimal solution x(k,1)As an update point, calculating the response value y (x) corresponding to the optimal solution(k,1)) And storing the data into a sample point database; the local sampling model is as follows:
in the formula, x(k,1)Design variables for local sampling in the kth iteration;a proxy model corresponding to the objective function;andrespectively designing the lower bound and the upper bound of variables at the k-th iteration, wherein the lower bound and the upper bound are continuously changed in the iteration process, but the lower bound x cannot exceed the global boundLAnd a global upper bound xUThe sampling space at this time is the related design domain;
sixthly, selecting a genetic algorithm to solve the global sampling model, and obtaining an optimal solution x(k,2)As an update point, calculating the response value y (x) corresponding to the optimal solution(k,2)) And storing the data into a sample point database; the global sampling model is:
S.T.xL≤x(k,2)≤xU
wherein,
fk-1(x(k,2))＝sk-1(x(k,2))min{|x(k,2)-xi||i＝1,2,…,ns}
in the formula, sk-1(x(k,2)) Is a design point x(k,2)The predicted standard deviation of (2); x is the number ofiFor an existing sample point, nsThe total number of existing sample points. sigmf (x, [ ac ]]) The specific functional form is as follows:
seventhly, judging whether a convergence condition is met; when k is 1, directly switching to the eighth step; if the calculation times reach the set times or meet the convergence criterion, stopping iteration and outputting an optimal solution, otherwise, turning to the eighth step; wherein the convergence criterion is:
Δ1＝abs(y(xk)-y(xk-1))≤0.1Δa
in the formula, y (x)k) And y (x)k-1) Response values, delta, corresponding to the optimal solutions respectively obtained for the k-th time and the k-1-th time in the optimization processaFor some optimization problems with a globally optimal solution of 0, the iteration process needs to be terminated by using an absolute error Δ 1 and a proxy model approximation accuracy Δ 3, and for optimization problems with a globally optimal solution of other than 0, the iteration process needs to be terminated by using a relative error Δ and a proxy model approximation accuracy Δ 2;
and step eight, making k equal to k +1, updating the current sample point database and the related design domain, and turning to the step four.
In the eighth step, the updating method of the related design domain is as follows:
(8.1) determining the center point of the associated design Domain
In the formula, x(k-1,1)And x(k-1,2)Respectively local and global update points, y (x), obtained in the iteration of step k-1(k-1,2)) And min (Y) is the response value corresponding to x (k-1,2) and the minimum response value in the whole sample;
(8.2) calculating the relative error of the current optimal solution,
in the formula, xk-1Selecting an update point, y (x), with a smaller response value in the iteration of the step (k-1)k-1) Is xk-1The corresponding value of the response is set to,corresponding predicted values;
(8.3) determining a new control factor ζk，
ζk＝max(ζk,0.5)
In the formula, the allowable accuracy of the proxy modela＝0.01；
(8.4) determining the length V of the new correlation design fieldk，
In the formula, VkThe associated design field length obtained at the kth iteration, where k is greater than or equal to 2, thetai(i＝1,2,…,nv) Updating the hyper-parameters in the correlation function of the Kriging model along with the updating of the Kriging model;
(8.5) determining a new relevant design domain,
in the formula IkAnd k is a related design domain at the kth iteration and is more than or equal to 2.
The advantages of the present invention can be further illustrated by the following simulation tests:
1. simulation parameters
The aperture of a certain parabolic antenna is 50 meters, the focal length is 20 meters, the working frequency is 2.3GHz, the antenna outer cover is a metal truss type antenna cover with the diameter of 70 meters, the structural form of the antenna cover is shown in figure 3, the truss material is aluminum, the dielectric constant of the skin material is 4, the dielectric loss tangent is 0.015, the thickness of the skin is 1 millimeter, the section of the rib is rectangular, and the size of the rib is divided into 3 types according to the height.
2. Simulation content and results
The rib section size of the antenna housing is subjected to electromechanical integration optimization by using the optimization method based on the adaptive proxy model, the pointing error, the gain loss, the maximum node displacement and the self weight of the antenna system with the housing before and after optimization are respectively calculated under the frequency of 2.3GHz, the simulation result is shown in fig. 5 and 6, and the simulation data is shown in table 1. As can be seen from fig. 5, the pointing error of the optimized rear-shroud antenna system is significantly improved, and as can be seen from fig. 6, the gain loss of the optimized rear-shroud antenna system is also significantly improved.
TABLE 1 indices of the system before and after optimization
As can be seen from Table 1, after the antenna system with the cover is designed by the method, the gain loss and the pointing error of the antenna system with the cover are obviously improved, the structural deformation of the cover body is reduced, the self weight is also obviously reduced, and the cost is greatly reduced. In addition, compared with a random optimization algorithm PSO, the result is very close, but the number of model calling times is greatly reduced compared with that of a PSO method, so that the optimization efficiency is greatly improved.
The simulation data prove that the electrical performance and the structural performance of the metal truss type antenna housing can be effectively improved, the efficiency of the whole optimization process can be improved, and a satisfactory target can be obtained.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.
Claims (4)
1. A method for optimizing the cross section size of a radome rib based on an adaptive proxy model is characterized by comprising the following steps:
the method comprises the following steps of firstly, determining design variables and an initial design space, enabling the iteration number k to be 1, carrying out multi-objective weighting on the maximum value and the average value of the pointing error of the antenna with the cover, the maximum value and the average value of gain loss and the maximum value of the self weight and the node displacement of the antenna cover, and establishing the following electromechanical integrated optimization model of the metal truss type antenna cover structure to calculate the optimal rib size:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mi>i</mi> <mi>n</mi> <mi>d</mi> </mrow> </mtd> <mtd> <mrow> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <msubsup> <mi>x</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <mn>2</mn> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>x</mi> <msub> <mi>n</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
Min y(x(k))＝0.04·BSEmax+0.06·TLmax+0.04·BSEmean+0.06·TLmean+0.4·Defmax+0.4·Weight]
S.t.xL≤x(k)≤xU
in the formula, x(k)Design variables for the structure of a metal truss radome, including the rectangular cross-sectional width and height of each type of rib, BSEmaxFor maximum value of pointing error of shrouded antenna under all operating conditions, TLmaxBSE being the maximum value of the gain loss of the shrouded antenna under all operating conditionsmeanFor the mean value of the pointing error of the shrouded antenna under all operating conditions, TLmeanAverage value of gain loss of the shrouded antenna under all operating conditions, DefmaxIs the maximum value of the node displacement of the antenna housing under the action of load, Weight is the dead Weight of the antenna housing, and xLAnd xURespectively approximating a target function by using a self-adaptive agent model for a lower bound value and an upper bound value of a design variable;
and secondly, when k is equal to 1, setting a related design domain as the whole initial design space, and then selecting initial sample points in the initial design space by using a maximum-minimum Latin hypercube test design method, wherein the number n of the initial sample pointspComprises the following steps:
<mrow> <msub> <mi>n</mi> <mi>p</mi> </msub> <mo>=</mo> <mi>min</mi> <mo>{</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mi>v</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>(</mo> <msub> <mi>n</mi> <mi>v</mi> </msub> <mo>+</mo> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </mfrac> <mo>,</mo> <mn>5</mn> <msub> <mi>n</mi> <mi>v</mi> </msub> <mo>}</mo> </mrow>
in the formula, nvRepresenting the number of design variables;
thirdly, calculating the corresponding real response values of the initial sample points, and storing the sample points and the response values thereof in a sample point database;
step four, extracting all sample points in the sample point database and corresponding response values thereof, and selecting a Kriging model to construct an agent model of the target function;
fifthly, selecting an optimization algorithm to solve the local sampling model, and obtaining an optimal solution x(k,1)As an update point, calculating the response value y (x) corresponding to the optimal solution(k,1)) And storing the data into a sample point database; the local sampling model is as follows:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mi>i</mi> <mi>n</mi> <mi>d</mi> </mrow> </mtd> <mtd> <mrow> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>x</mi> <msub> <mi>n</mi> <mi>v</mi> </msub> </msub> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>M</mi> <mi>i</mi> <mi>n</mi> </mrow> </mtd> <mtd> <mrow> <msup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>S</mi> <mo>.</mo> <mi>T</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>x</mi> <mi>L</mi> <mi>k</mi> </msubsup> <mo>&le;</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>&le;</mo> <msubsup> <mi>x</mi> <mi>U</mi> <mi>k</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced>
in the formula, x(k,1)Design variables for local sampling in the kth iteration;a proxy model corresponding to the objective function;andrespectively designing the lower bound and the upper bound of variables at the k-th iteration, wherein the lower bound and the upper bound are continuously changed in the iteration process, but the lower bound x cannot exceed the global boundLAnd a global upper bound xUThe sampling space at this time is the related design domain;
sixthly, an optimization algorithm is selected to solve the global sampling model, and the obtained optimal solution x is obtained(k,2)As an update point, calculating the response value y (x) corresponding to the optimal solution(k,2)) And storing the data into a sample point database; the global sampling model is:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mi>i</mi> <mi>n</mi> <mi>d</mi> </mrow> </mtd> <mtd> <mrow> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>x</mi> <msub> <mi>n</mi> <mi>v</mi> </msub> </msub> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>M</mi> <mi>i</mi> <mi>n</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msup> <mi>f</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>g</mi> <mi>m</mi> <mi>f</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>P</mi> <mi>B</mi> <mi>S</mi> </mrow> </msub> </mrow> <mrow> <msup> <mi>s</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <mo>&lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> <mo>&rsqb;</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
S.T.xL≤x(k,2)≤xU
wherein,
fk-1(x(k,2))＝sk-1(x(k,2))min{|x(k,2)-xi||i＝1,2,…,ns}
in the formula, sk-1(x(k,2)) Is a design point x(k,2)The predicted standard deviation of (2); x is the number ofiFor an existing sample point, nsThe total number of the existing sample points; sigmf (x, [ ac ]]) The specific functional form is as follows:
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mi>c</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>a</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <mi>c</mi> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow>
seventhly, judging whether a convergence condition is met; when k is 1, directly switching to the eighth step; if the calculated times reach the set times or meet the convergence criterion, stopping iteration and outputting an optimal solution, otherwise, turning to the eighth step; wherein the convergence criterion is:
<mrow> <mi>&Delta;</mi> <mo>=</mo> <mi>a</mi> <mi>b</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>&Delta;</mi> <mi>a</mi> </msub> </mrow>
Δ1＝abs(y(xk)-y(xk-1))≤0.1Δa
<mrow> <mi>&Delta;</mi> <mn>2</mn> <mo>=</mo> <mi>a</mi> <mi>b</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>&Delta;</mi> <mi>a</mi> </msub> </mrow>
<mrow> <mi>&Delta;</mi> <mn>3</mn> <mo>=</mo> <mi>a</mi> <mi>b</mi> <mi>s</mi> <mrow> <mo>(</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> <mo>-</mo> <mi>y</mi> <mo>(</mo> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> <mo>&le;</mo> <mn>0.1</mn> <msub> <mi>&Delta;</mi> <mi>a</mi> </msub> </mrow>
in the formula, y (x)k) And y (x)k-1) Response values, delta, corresponding to the optimal solutions respectively obtained for the k-th time and the k-1-th time in the optimization processa0.01 is given yieldThe convergence standard is that for some optimization problems with the global optimal solution being 0, the iteration process needs to be terminated by using an absolute error delta 1 and a proxy model approximation accuracy delta 3, and for the optimization problems with the global optimal solution being not 0, the iteration process needs to be terminated by using a relative error delta and a proxy model approximation accuracy delta 2;
and step eight, making k equal to k +1, updating the current sample point database and the related design domain, and turning to the step four.
2. The method for optimizing the rib section size of the antenna cover based on the adaptive proxy model according to claim 1, wherein the sixth optimization algorithm is a genetic algorithm, a particle swarm optimization algorithm or a global optimization algorithm.
3. The method for optimizing the rib section size of the antenna cover based on the adaptive proxy model according to claim 1, wherein in the eighth step, the updating method of the related design domain is as follows:
(8.1) determining the center point of the associated design Domain
<mrow> <msubsup> <mi>x</mi> <mi>C</mi> <mi>k</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>&le;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>e</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
In the formula, x(k-1,1)And x(k-1,2)Respectively local and global update points, y (x), obtained in the iteration of step k-1(k-1,2)) And min (Y) are each x(k-1,2)The corresponding response value and the smallest response value in the entire sample;
(8.2) calculating the relative error of the current optimal solution,
<mrow> <mi>&epsiv;</mi> <mo>=</mo> <mo>|</mo> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>|</mo> </mrow>
in the formula, xk-1Selecting an update point, y (x), with a smaller response value in the iteration of the step (k-1)k-1) Is xk-1The corresponding value of the response is set to,is xk-1Corresponding predicted values;
(8.3) determining a new control factor ζk，
<mrow> <msup> <mi>&zeta;</mi> <mi>k</mi> </msup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>/</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&epsiv;</mi> <mo>/</mo> <msub> <mi>&epsiv;</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>&epsiv;</mi> <mo>&GreaterEqual;</mo> <mn>3</mn> <msub> <mi>&epsiv;</mi> <mi>a</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>&epsiv;</mi> <mi>a</mi> </msub> <mo>/</mo> <mi>&epsiv;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>&epsiv;</mi> <mo>&le;</mo> <msub> <mi>&epsiv;</mi> <mi>a</mi> </msub> <mo>/</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>&epsiv;</mi> <mi>a</mi> </msub> <mo>/</mo> <mn>3</mn> <mo><</mo> <mi>&epsiv;</mi> <mo><</mo> <mn>3</mn> <msub> <mi>&epsiv;</mi> <mi>a</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
ζk＝max(ζk,0.5)
In the formula, the allowable accuracy of the proxy modela＝0.01；
(8.4) determining the length V of the new correlation design fieldk，
<mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> </mrow> </msqrt> </mfrac> <mo>,</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <msub> <mi>&theta;</mi> <mn>2</mn> </msub> </mrow> </msqrt> </mfrac> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mn>2</mn> <msub> <mi>&theta;</mi> <msub> <mi>n</mi> <mi>v</mi> </msub> </msub> </mrow> </msqrt> </mfrac> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow>
In the formula, VkThe associated design field length obtained at the kth iteration, where k is greater than or equal to 2, thetai(i＝1,2,…,nv) Updating the hyper-parameters in the correlation function of the Kriging model along with the updating of the Kriging model;
(8.5) determining a new relevant design domain,
<mrow> <msup> <mi>I</mi> <mi>k</mi> </msup> <mo>=</mo> <mo>{</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>|</mo> <msubsup> <mi>x</mi> <mi>L</mi> <mi>k</mi> </msubsup> <mo>&le;</mo> <msup> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>&le;</mo> <msubsup> <mi>x</mi> <mi>U</mi> <mi>k</mi> </msubsup> <mo>}</mo> </mrow>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>w</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>e</mi> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>x</mi> <mi>L</mi> <mi>k</mi> </msubsup> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>L</mi> </msub> <mo>,</mo> <msubsup> <mi>x</mi> <mi>C</mi> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>&zeta;</mi> <mi>k</mi> </msup> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mrow> <msubsup> <mi>x</mi> <mi>U</mi> <mi>k</mi> </msubsup> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>U</mi> </msub> <mo>,</mo> <msubsup> <mi>x</mi> <mi>C</mi> <mi>k</mi> </msubsup> <mo>+</mo> <msup> <mi>&zeta;</mi> <mi>k</mi> </msup> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>)</mo> </mrow> </mrow>
in the formula IkAnd k is a related design domain at the kth iteration and is more than or equal to 2.
4. The method of claim 1, wherein the computing software used in the third, fifth and sixth steps is ANSYS15.0 and MATLABR2013 b.
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| CN113065268A (en) * | 2021-03-30 | 2021-07-02 | 中国科学院光电技术研究所 | Rapid multi-objective space reflector optimization design method based on proxy model |
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Application publication date: 20171117 |