CN117421874A - Reflection surface antenna radiation Liang Tapu optimal design method based on conformal constraint - Google Patents
Reflection surface antenna radiation Liang Tapu optimal design method based on conformal constraint Download PDFInfo
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Abstract
The invention discloses a reflection surface antenna radiation Liang Tapu optimal design method based on shape-preserving constraint, and relates to the technical field of reflection surface antenna structure design; the method comprises the following steps: determining the design domain and boundary condition of an antenna radiation beam; establishing a topology optimization model based on the conformal constraint; calculating sensitivity information of the objective function and the constraint; solving a topology optimization model based on a gradient method; the validity of the numerical value case verification method; in the step S1, a topology optimization design domain omega is constructed aiming at the condition that an upper chord node of a radiation beam of the reflecting surface antenna is positioned on a parabola and supported at a lower chord node, and the surface type precision of the upper chord node of the radiation beam is realized by optimizing the material distribution in the design domain. The invention can realize the surface type precision of the winding node of the radiation beam by constructing the topology optimization model of the conformal constraint; a topological optimization model is established by adopting a variable density method, so that density variables in a design domain can be effectively processed.
Description
Technical Field
The invention relates to the technical field of reflector antenna structure design, in particular to a reflector antenna radiation Liang Tapu optimal design method based on conformal constraint.
Background
In the field of design of reflecting surface antenna structures, designing structures to meet the surface type accuracy of the antenna is called conformal design. In order to meet the electrical performance of an antenna, it is necessary to limit the degree of deviation of its profile, for example, for a radio telescope, the profile accuracy is better than one sixteenth of its operating wavelength. When the traditional antenna is designed, the topological structure is usually determined manually, and then the size and shape parameters are optimized, so that the freedom degree of structural design is limited. The topology optimization technology has great potential in reducing the weight of the structure and improving the performance of the structure, and since the introduction of the topology optimization technology by Bendsoe and Kikuchi in 1988, the topology optimization technology is widely applied to the fields of aerospace, automobiles, buildings, bridge construction, new material design and the like.
In recent years, researchers have also explored the topology optimization design of the reflector antenna radiation beam. For example, by amplifying the influence of deformation at the upper chord node on the flexibility index, a weighted flexibility index is established, and the deformation at the upper chord node can be restrained by minimizing the index. Or a weighted compliance index that takes into account electrical performance. Such as the patent application numbers CN201911261289.1, CN202011395516.2, etc., essentially both of the above strategies improve the antenna accuracy or electrical performance from an indirect point of view by reducing the deformation at the upper chord node of the beam. Because the weighted compliance index is not equivalent to the design objective of antenna shape retention, the topology optimization result does not necessarily satisfy the constraint of antenna shape retention. Based on the above, the invention provides an antenna radiation Liang Tapu optimization method directly taking a shape-preserving index as a constraint.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides an optimization design method for reflecting surface antenna radiation Liang Tapu based on conformal constraint.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a reflection surface antenna radiation Liang Tapu optimal design method based on conformal constraint comprises the following steps:
s1: determining the design domain and boundary condition of an antenna radiation beam;
s2: establishing a topology optimization model based on the conformal constraint;
s3: calculating sensitivity information of the objective function and the constraint;
s4: solving a topology optimization model based on a gradient method;
s5: the validity of the numerical value case verification method;
in the step S1, a topology optimization design domain omega is constructed aiming at the condition that an upper chord node of a radiation beam of the reflecting surface antenna is positioned on a parabola and supported at a lower chord node, and the surface type precision of the upper chord node of the radiation beam is realized by optimizing the material distribution in the design domain.
Preferably: in the step S2, a topological optimization model is established by adopting a variable density method, when the topological optimization model is established, firstly, the design domain is subjected to grid division, and each grid is allocated with a density variable x, wherein the value range of x is more than or equal to 0 and less than or equal to 1; to avoid checkerboard and reduce gray scale cells, the density variable x is typically filtered and projected to obtain the physical density x corresponding to the cell e The unit elastic modulus is obtained by interpolation of physical density, and a specific calculation formula of the unit elastic modulus is as follows:
E e (x e )＝E min +x e p (E 0 -E min )
wherein E is 0 And E is min Modulus of elasticity of the solid units, respectively, and E min ＜＜E 0 The method comprises the steps of carrying out a first treatment on the surface of the p is a penalty factor.
Preferably: in the step S2, the plane type accuracy of the reflecting plane antenna is expressed as a root mean square value of a caliber plane half-optical path difference, and the caliber plane half-optical path difference formula is specifically as follows:
where ρ is a half-path difference vector of the aperture plane, and W is a weight considering an irradiation function or the like.
Preferably: in the S2, the caliber plane half-optical path difference formula adopts a quadratic form, and the following conformal constraint is introduced into the standard topology optimization model:
wherein,is the upper limit of the face type error;
based on the following linear relationship existing between the half optical path difference vector and the displacement u:
ρ＝Ru
the R matrix is only related to the coordinates of the reflecting surface nodes; modifying the conformal constraint function to be:
preferably: in S2, an antenna radiation Liang Tapu optimization model is established taking into account the conformal constraints as follows:
0≤x≤1
Ku＝P
wherein c is structural flexibility, u and P are allLocal displacement and force vectors, K is a global stiffness matrix; u (u) e For unit displacement vector, k 0 Is the unit stiffness matrix under the Young's modulus of unit, N is the unit number, V (x) e ) And V 0 The material volume and the design domain volume, respectively, f is a given volume fraction, v 0e The volume of the domain is designed for the cell.
Preferably: in the step S3, in the topology optimization based on the gradient algorithm, sensitivity information of the objective function and the constraint is necessary, and the derivative of the conformal constraint function with respect to the physical density is expressed as:
where λ is a solution satisfying the following accompanying equation:
preferably: in the S3As a virtual load vector, applying the virtual load vector to a structure to obtain an accompanying variable lambda; the derivatives of P and K compared with the design variable can be obtained through an interpolation model; wherein if the structure is loaded independently of the design variables, then: />
Next, according to the formulaObtaining the derivative of the shape-preserving constraint function on the physical density; since the physical density is obtained by filtering and projecting the density variable, the sensitivity of the conformal constraint to the density variable is finally obtained based on the chained derivation criterion for different filtering and projecting functions>
Preferably: in the step S4, after the sensitivity information of the objective function and the constraint is obtained in the step S3, an optimization model is solved by adopting a gradient-based optimization algorithm; the GCMMA/MMA algorithm was used.
Preferably: in the step S5, a numerical value case is implemented to obtain a radiation Liang Tapu optimization result under the consideration of the shape retention constraint, and the radiation Liang Tapu optimization result is compared with a traditional standard topology optimization result; the effectiveness of the method is verified by comparing the flexibility and the shape retention performance index between the two designs.
The beneficial effects of the invention are as follows:
1. the invention can realize the surface type precision of the winding node of the radiation beam by constructing the topology optimization model of the conformal constraint; a topological optimization model is established by adopting a variable density method (SIMP method), so that density variables in a design domain can be effectively processed.
2. The invention introduces a shape-preserving constraint function, and can realize the control of the upper limit of the face type error while maintaining the flexibility of the structure; the optimization model can be effectively solved by adopting a gradient-based optimization algorithm (GCMMA/MMA algorithm); the validity of the method is demonstrated by numerical case verification.
Drawings
Fig. 1 is a schematic diagram of a topological optimization design domain of an antenna radiation beam structure in a reflection surface antenna radiation Liang Tapu optimization design method based on conformal constraint;
fig. 2 is a schematic diagram of calculation of optical path difference of aperture surface of a reflecting surface antenna in a method for optimizing design of reflecting surface antenna radiation Liang Tapu based on conformal constraint;
FIG. 3 is a diagram of a feed source irradiation function in a method for optimizing design of reflector antenna radiation Liang Tapu based on conformal constraint;
FIG. 4 is a graph showing the variation of plane type accuracy with iteration in a method for optimizing the design of the reflection plane antenna radiation Liang Tapu based on the conformal constraint;
fig. 5 is a graph showing the variation of structural flexibility with iteration in the optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint;
FIG. 6 is a graph showing the comparison of the half-path difference distribution of two caliber surfaces in the optimization design method of the reflecting surface antenna radiation Liang Tapu based on the conformal constraint;
fig. 7 is a diagram showing the comparison of parameters related to two designs in the optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint.
Detailed Description
The technical scheme of the patent is further described in detail below with reference to the specific embodiments.
Example 1:
a reflection surface antenna radiation Liang Tapu optimal design method based on conformal constraint comprises the following steps:
s1: determining the design domain and boundary condition of an antenna radiation beam;
s2: establishing a topology optimization model based on the conformal constraint;
s3: calculating sensitivity information of the objective function and the constraint;
s4: solving a topology optimization model based on a gradient method;
s5: the validity of the numerical case verification method.
In general, in the S1, the upper chord node of the radiation beam of the reflecting surface antenna is on a parabola and supported at the lower chord node, so that a topology optimization design domain Ω as shown in fig. 1 can be constructed, and the surface type accuracy of the upper chord node of the radiation beam is realized by optimizing the material distribution in the design domain.
In the step S2, a topological optimization model is established by adopting a variable density method (SIMP method), firstly, the design domain is subjected to grid division, and a density variable x is distributed for each grid, wherein the value range of x is more than or equal to 0 and less than or equal to 1; to avoid checkerboard and reduce gray scale cells, the density variable x is typically filtered and projected to obtain the physical density x corresponding to the cell e The unit elastic modulus is interpolated from the physical density, for example:
E e (x e )＝E min +x e p (E 0 -E min )
wherein E is 0 And E is min Modulus of elasticity of the solid units, respectively, and E min ＜＜E 0 The method comprises the steps of carrying out a first treatment on the surface of the p is a penalty factor (typically 3).
The plane type accuracy of the reflection plane antenna can be expressed as a root mean square value of a caliber plane half optical path difference, and is specifically as follows:
where ρ is the half-path difference vector of the aperture plane, its physical meaning is shown in fig. 2, and w is the weight considering the irradiation function, etc.
Considering convenience of sensitivity derivation, the invention writes the above formula into a quadratic form, and introduces the following conformal constraint in a standard topology optimization model:
is the upper limit of the face type error;
since there is a simple linear relationship between the half optical path difference vector and the displacement u:
ρ＝Ru
the R matrix is only related to the coordinates of the reflecting surface nodes; the conformal constraint function can be further written as:
in summary, an optimization model of antenna radiation Liang Tapu can be built that takes into account the conformal constraints as follows:
0≤x≤1
Ku＝P
wherein c is the structural flexibility, u and P are global displacement and force vectors, and K is a global stiffness matrix; u (u) e For unit displacement vector, k 0 Is the unit stiffness matrix under the Young's modulus of unit, N is the unit number, V (x) e ) And V 0 The material volume and the design domain volume, respectively, f is a given volume fraction, v 0e The volume of the domain is designed for the cell.
In the step S3, in the topology optimization based on the gradient algorithm, the sensitivity information of the objective function and the constraint is necessary, the sensitivity information of the compliance function and the volume function may be referred to related documents, which are not described herein again, and only the sensitivity of the conformal constraint function to the design variables is given. The derivative of the conformal constraint function with respect to physical density can be expressed as:
where λ is a solution satisfying the following accompanying equation:
will beAs a virtual load vector, the virtual load vector is applied to a structure, and then an accompanying variable lambda can be obtained; the derivatives of P and K compared with the design variable can be obtained through an interpolation model; in particular if the structure is loadedThe load is independent of the design variables, then: />Next, according to the formula->Obtaining the derivative of the conformal constraint function on the physical density; as the physical density is obtained by filtering and projecting the density variable, the sensitivity of the conformal constraint to the density variable can be finally obtained based on the chained derivation criterion for different filtering and projecting functions>
In the step S4, after the sensitivity information of the objective function and the constraint is obtained by the step S3, an optimization model is solved by adopting a gradient-based optimization algorithm; the GCMMA/MMA algorithm was used.
In S5, the numerical case is implemented to obtain the optimization result of the radiation Liang Tapu under the constraint of considering the shape retention, and the optimization result is compared with the traditional standard topology optimization result. The effectiveness of the method provided by the invention is verified by comparing the flexibility and the shape-keeping performance index between the two designs.
A simple example is given below to illustrate the effectiveness of the method according to the invention:
in the calculation example, the antenna is in an overhead working condition, the caliber D=6000 mm, the focal length F=0.3D=1800 mm, the supporting point distance L=0.25D=1500 mm,11 vertical downward concentrated loads are uniformly distributed on the upper chord node of the radiation beam, the size is 50N, the height h of the radiation beam=2500 mm, and the thickness t=1 mm. Elastic modulus e0=1gpa, emin=1pa, poisson ratio μ=0.3, volume constraint of 0.25, face accuracy constraint of 0.2mm, the influence of the feed source irradiation function as shown in fig. 3 is considered in the weight W;
FIGS. 4 and 5 show an iterative curve comparison of face accuracy and compliance for conformal topology optimization versus standard topology optimization; FIG. 6 shows a comparison of the half-path difference distribution of the aperture surfaces of two designs; FIG. 7 shows a comparison of the relevant parameters for both designs; as can be seen from fig. 7, the conformal design sacrifices stiffness (7.423-7.145)/7.423 =3.75% but the area accuracy improves (0.813-0.2)/0.2= 306.5% for the same volume, indicating the effectiveness of the method of the present invention.
The data in fig. 7 are as follows:
| optimization model | Conformal topology optimization | Standard topology optimization |
| Compliance c/J | 7.423 | 7.145 |
| Surface accuracy sigma/mm | 0.200 | 0.813 |
| Volume fraction | 0.250 | 0.250 |
| Gain loss/dB * | -3.0473 | -50.3695 |
| Anastomotic focal length/mm | 1724.71 | 1731.57 |
* Based on the rule formula.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (9)
1. The optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint is characterized by comprising the following steps:
s1: determining the design domain and boundary condition of an antenna radiation beam;
s2: establishing a topology optimization model based on the conformal constraint;
s3: calculating sensitivity information of the objective function and the constraint;
s4: solving a topology optimization model based on a gradient method;
s5: the validity of the numerical value case verification method;
in the step S1, a topology optimization design domain omega is constructed aiming at the condition that an upper chord node of a radiation beam of the reflecting surface antenna is positioned on a parabola and supported at a lower chord node, and the surface type precision of the upper chord node of the radiation beam is realized by optimizing the material distribution in the design domain.
2. The optimization design method for the reflector antenna radiation Liang Tapu based on the conformal constraint of claim 1, wherein in the step S2, a topological optimization model is built by adopting a variable density method, when the topological optimization model is built, a design domain is firstly grid-divided, and each grid is allocated with a density variable x, wherein the value range of x is more than or equal to 0 and less than or equal to 1; to avoid checkerboard and reduce gray scale cells, the density variable x is typically filtered and projected to obtain the physical density x corresponding to the cell e The unit elastic modulus is obtained by interpolation of physical density, and a specific calculation formula of the unit elastic modulus is as follows:
E e (x e )＝E min +x e p (E 0 -E min )
wherein E is 0 And E is min Modulus of elasticity of the solid units, respectively, and E min ＜＜E 0 The method comprises the steps of carrying out a first treatment on the surface of the p is a penalty factor.
3. The optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint of claim 2, wherein in S2, the surface type accuracy of the reflector antenna is expressed as a root mean square value of a caliber surface half-optical path difference, and the caliber surface half-optical path difference formula is specifically as follows:
where ρ is a half-path difference vector of the aperture plane, and W is a weight considering an irradiation function or the like.
4. The optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint of claim 3, wherein in the step S2, a caliber plane half-path difference formula adopts a quadratic form, and the following conformal constraint is introduced into a traditional topology optimization model:
wherein,is the upper limit of the face type error;
based on the following linear relationship existing between the half optical path difference vector and the displacement u:
ρ＝Ru
the R matrix is only related to the coordinates of the reflecting surface nodes; modifying the conformal constraint function to be:
5. the optimization design method for the reflector antenna radiation Liang Tapu based on the conformal constraint according to claim 4, wherein in S2, an antenna radiation Liang Tapu optimization model is established by taking the conformal constraint into consideration as follows:
0≤x≤1
Ku＝P
wherein c is the structural flexibility, u and P are global displacement and force vectors, and K is a global stiffness matrix; u (u) e For unit displacement vector, k 0 Is the unit stiffness matrix under the Young's modulus of unit, N is the unit number, V (x) e ) And V 0 The material volume and the design domain volume, respectively, f is a given volume fraction, v 0e The volume of the domain is designed for the cell.
6. The optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint according to claim 5, wherein in S3, in the topology optimization based on the gradient algorithm, the sensitivity information of the objective function and the constraint is necessary, and the derivative of the conformal constraint function to the physical density is expressed as:
where λ is a solution satisfying the following accompanying equation:
7. the optimization design method for the reflector antenna radiation Liang Tapu based on the conformal constraint of claim 6, wherein in S3, the following is performedAs a virtual load vector, applying the virtual load vector to a structure to obtain an accompanying variable lambda; the derivatives of P and K compared with the design variable can be obtained through an interpolation model; wherein if the structure is loaded independently of the design variables, then: />
Next, according to the formulaObtaining the derivative of the shape-preserving constraint function on the physical density; since the physical density is obtained by filtering and projecting the density variable, the sensitivity of the conformal constraint to the density variable is finally obtained based on the chained derivation criterion for different filtering and projecting functions>
8. The optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint of claim 7, wherein in the step S4, after the objective function and the constrained sensitivity information are obtained by the step S3, the optimization model is solved by adopting a gradient-based optimization algorithm; the GCMMA/MMA algorithm was used.
9. The optimization design method of the reflector antenna radiation Liang Tapu based on the conformal constraint according to claim 8, wherein in S5, by implementing a numerical case, a radiation Liang Tapu optimization result considering the conformal constraint is obtained and compared with a traditional topology optimization result; the effectiveness of the method is verified by comparing the flexibility and the shape retention performance index between the two designs.
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