CN113849945A - Submillimeter wave antenna back frame and transition structure optimization method - Google Patents

Submillimeter wave antenna back frame and transition structure optimization method Download PDF

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CN113849945A
CN113849945A CN202111112312.8A CN202111112312A CN113849945A CN 113849945 A CN113849945 A CN 113849945A CN 202111112312 A CN202111112312 A CN 202111112312A CN 113849945 A CN113849945 A CN 113849945A
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高婧婧
王海仁
左营喜
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Abstract

The invention discloses a submillimeter wave antenna back frame and a transition structure optimization method, which comprises the following steps: designing an initial model of the back frame structure; establishing an initial topological optimization model of a submillimeter wave antenna transition structure; performing static analysis on the initial topological optimization model, performing post-processing on an analysis result, extracting required parameters and establishing a corresponding optimization model; compressing the back frame of the antenna and the mass point units of the main panel thereof into interface nodes by adopting a hypercell method, and importing the compressed finite element model into a Workbench topology optimization module; performing distribution optimization by using a workbench optimization module, and outputting an optimization result to obtain an optimal solution model; and carrying out static analysis on the optimal solution model. The method can improve the structural rigidity as much as possible under the action of gravity to reduce the influence of the action of gravity on the surface shape precision of the antenna and obtain the optimal solution meeting the minimum surface shape error of the antenna.

Description

Submillimeter wave antenna back frame and transition structure optimization method
Technical Field
The invention relates to the technical field of design and optimization of large-scale precise antenna back frames and transition structures, in particular to a submillimeter wave antenna back frame and a transition structure optimization method.
Background
The sub-millimeter wave band is a new window for detecting the universe. In recent years, next generation large-caliber high-precision submillimeter-wave telescope antennas are planned and established internationally, including U.S. CCAT (25m), Japanese LST (50m), European AtLAST (50m), and the like. The submillimeter wave research group of China also puts forward a 60-meter submillimeter wave telescope assumption in recent years. The construction of next generation large-scale submillimeter wave astronomical observation facilities becomes a high consensus of the international astronomical community. For single-aperture millimeter wave and sub-millimeter wave antennas, the aperture required for the antenna is increasing to improve the sensitivity and resolution of the system. However, as the aperture of the large precise antenna is increased, the self weight of the structure of the large precise antenna generally increases exponentially, so that a higher requirement is provided for the structural rigidity of the large precise antenna, and if the self weight and the rigidity are mismatched, the inherent frequency of the structure is reduced, and the structure is seriously deformed, so that the precision of the reflecting surface of the antenna is seriously influenced. Therefore, when a large-aperture antenna structure is designed, the problem of mismatch of the self weight and the rigidity of the structure needs to be solved, an improvement scheme is pertinently provided through concept optimization design, and the overall structure of the antenna is developed.
The 60m submillimeter wave antenna is an advanced large-caliber and large-view-field submillimeter wave telescope, the caliber of a main reflecting surface is 60m, the working wavelength covers 0.65-3 mm, the diameter of a designed view field reaches 1 degree, the requirements on the precision and the pointing precision of the reflecting surface are strict, the surface type precision is required to be better than 30 micrometers, the tracking pointing precision is better than 2 arc seconds, and the precision is required to be kept stable for a long time. However, for a large-aperture antenna, in order to maintain the surface shape accuracy and the pointing accuracy, the self weight of the antenna and the structural distribution with a large span inevitably cause influences, and therefore, an optimal design means should be used to reduce the influences in the initial design stage of the structure.
After the structural design of the high-precision large-caliber submillimeter-wave telescope is finished, the influence of gravity deformation on the precision of the main surface is corrected by adopting the active surface technology, but the correction precision range is limited, and certain design precision needs to be achieved during primary design, so that the precision requirement can be met by using the active surface technology afterwards. The design of the back frame of the prior antenna generally adopts a shape-preserving design, but the design of a transition structure is a great difficulty. At present, the following are probably available: for example, the 10mHHT millimeter wave telescope adopts a transition structure design of a cross steel sheet to connect the CFRP back frame and the steel material antenna pedestal, the design can reduce the influence of thermal deformation on the structural precision, but the structural rigidity of the telescope is seriously insufficient, so that the telescope is not suitable for large-caliber radio telescopes. A25 mCCAT submillimeter wave telescope planned and constructed in the United states is prepared to adopt a CFRP back frame structure, and a space truss type transition structure design is provided based on a heat preservation type theory, so that further research and verification are needed. The 50mLMT millimeter wave telescope adopts a transition structure design that a dual drive shaft is directly connected with a steel material back frame, connecting points are symmetrically distributed at 4 connecting positions of a 45-degree plane at the bottom layer of the back frame, the precision requirements of the optical field of view and the main surface shape of the telescope are lower than those of a 60m submillimeter wave antenna, but the structural design can be used as the design reference of the 60m submillimeter wave telescope.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a submillimeter wave antenna back frame and a transition structure optimization method, which can improve the structural rigidity as much as possible under the action of gravity to reduce the influence of the action of gravity on the surface shape precision of an antenna and obtain the optimal solution meeting the minimum surface shape error of the antenna.
In order to achieve the purpose, the invention adopts the following technical scheme:
a submillimeter wave antenna back frame and transition structure optimization method comprises the following steps:
s1, designing an initial model of the back frame structure by adopting a shape-preserving principle according to the design of a main panel of the 60m submillimeter wave antenna; establishing an initial topological optimization model of a 60m submillimeter wave antenna transition structure according to a topological optimization principle; performing static analysis on the initial topological optimization model, performing post-processing on an analysis result, extracting required parameters and establishing a corresponding optimization model;
s2, compressing the back frame of the antenna and the main panel particle unit thereof into an interface node by adopting a hypercell method, importing the compressed finite element model into a Workbench topology optimization module, and constructing an optimization model as follows:
find x＝[x1,x2,……,xn]T
min C(x)＝FTU(x)
s.t v(x)＝xTv-V*≤0
f≥fl
x∈χ,χ＝{x∈Rn,0≤x≤1}
wherein xiFor each cell assigned topological density variable, the objective function is the total compliance of the structure C (x); n is the total number of units in the optimized domain, F is the node load vector, U (x) is the displacement vector of the structure, V (x) is the optimized volume, V is the volume constraint, FlThe natural frequency and the natural frequency lower limit of the structure are respectively;
s3, performing distribution optimization by using a workbench optimization module, and outputting an optimization result to obtain an optimal solution model; and carrying out static analysis on the optimal solution model.
2. The submillimeter-wave antenna back frame and transition structure optimization method of claim 1, wherein in step S3, the process of performing distribution optimization by using a workbench optimization module comprises the following steps:
s31, selecting the reference point coordinates of the back frame as optimization variables, taking the deformation geometric error rmse of the antenna main surface pointed by the zenith as an objective function, and performing experimental analysis on the objective function by adopting a Genetic Aggregation response surface method in a Workbench optimization module, wherein the analysis model is as follows:
Figure BDA0003274273140000021
Figure BDA0003274273140000022
Figure BDA0003274273140000023
Figure BDA0003274273140000024
wherein r isjFor the design variable of the jth design point, NMFor the number of models used, wkWeight factor, y (r), for the kth iteration responsej) And
Figure BDA0003274273140000025
the output response and response prediction for the kth iteration respectively,
Figure BDA0003274273140000026
for the purpose of response prediction of the overall structure,
Figure BDA0003274273140000027
predicting the response of the integral structure without the jth design point; by making the root mean square error of the design experimental points
Figure BDA0003274273140000031
And cross-validation root mean square error
Figure BDA0003274273140000032
Minimizing to obtain the optimal weight value, namely the sensitivity result of each design variable;
s32, selecting a back frame coordinate parameter with high sensitivity as an optimization independent variable, taking an effective deformation error rmse of the antenna main surface pointed downwards by the zenith as a target function, and determining a value range of a design variable according to the spatial position of a back frame rod piece; optimizing by adopting a genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
min rmse
Figure BDA0003274273140000033
Figure BDA0003274273140000034
zcenl≤zcen≤zcenu
wherein xpq、zpqX-axis coordinates and z-axis coordinates of a reference point of the back frame under a main surface cylindrical coordinate system are respectively shown, p and q are the number of back frame layers and the number of rings respectively, and p is 1,2, … and 4; q is 1,2, …,7,
Figure BDA0003274273140000035
are respectively xpqThe upper and lower limits of (a) and (b),
Figure BDA0003274273140000036
are each zpqUpper and lower limits of (3), zcenl、zcenuThe upper limit and the lower limit of the gravity center position zcen of the whole structure are respectively; after obtaining the optimization result, bringing in a parameter result to reestablish the model required by the second-step optimization;
s33, selecting section parameters of the rod piece of the back frame and the transition structure as optimization independent variables, and taking an effective deformation error rmse of the antenna main surface and a gravity center position of the antenna main surface pointed downwards by the zenith as a target function; optimizing by adopting a multi-objective genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
minΠ(rmse,zcen)
Figure BDA0003274273140000037
Figure BDA0003274273140000038
Figure BDA0003274273140000039
Figure BDA00032742731400000310
wherein rbs ism、tbsmRespectively representThe outer diameter and the thickness of the back frame rod pieces, m is the type number of the back frame rod pieces, m is 1,2, …,5,
Figure BDA00032742731400000311
Figure BDA00032742731400000312
and
Figure BDA00032742731400000313
are each rbsm、tbsmUpper and lower limits of (rts)n、ttsnRespectively showing the outer diameter and the thickness of the transition structure rod piece, wherein n is the number of the transition structure rod piece types, n is 1,2,3,
Figure BDA00032742731400000314
and
Figure BDA00032742731400000315
are each rtsn、ttsnUpper and lower limits of (3). After obtaining the optimization result, bringing in a parameter result to reestablish a model required by the optimization in the third step;
s34, selecting the space positions of different component interfaces as optimization independent variables, and taking the effective deformation error rmse and the gravity center position zcen of the antenna main surface pointed downwards by the zenith as a target function; optimizing by adopting a multi-objective genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
minΠ(rmse,zcen)
Figure BDA0003274273140000041
Figure BDA0003274273140000042
Figure BDA0003274273140000043
Figure BDA0003274273140000044
wherein z is41And z43The reference point at the bottom layer of the back frame is corresponding to the coordinate value,
Figure BDA0003274273140000045
is z41And z43Corresponding lower and upper limits, h1The height of the driving wheel connecting platform is shown,
Figure BDA0003274273140000046
represents a sum of h1Lower and upper limits of, tcAnd c is the thickness of the steel plate of the driving wheel, and c is 1,2 and 3.
And S35, outputting a result after the optimization is completed, wherein the output data comprises an optimal solution, a constraint variable and a design variable.
Further, the antenna back frame of the 60m submillimeter wave antenna adopts a CFRP material rod piece.
Further, the transition structure of the 60m submillimeter wave antenna and the driving wheel are made of steel materials.
The back frame and the transition structure designed by the invention compress the back frame into a superunit at an interface node position by using a superunit method, simplify the annular entity transition structure into a space truss structure with good rigidity by using a topological optimization method, perform parametric modeling analysis on an antenna structure by using APDL (android package), and optimize the back frame and the transition structure by using a multi-objective genetic algorithm by calling an ANSYS Workbench optimization module, so that the antenna has the optimal main surface shape and the center of gravity position of the antenna is balanced under the action of gravity, and a final design result is obtained. The method can improve the structural rigidity as much as possible under the action of gravity to reduce the influence of the action of gravity on the surface shape precision of the antenna, obtains the initial design of the transition structure through topology optimization on the basis of the back frame shape-preserving design, and obtains the optimal solution meeting the minimum surface shape error of the antenna through a genetic algorithm.
The invention has the beneficial effects that:
(1) APDL is adopted for parameter modeling and analysis, and key variables such as model size, material characteristics and the like are parameterized so as to be convenient to view and modify.
(2) The topological optimization method is adopted to ensure the rigidity of the antenna transition structure and effectively reduce the influence of the gravity deformation of the structure on the surface shape precision of the antenna.
(3) The sensitivity of the parameters can be analyzed and optimized by using the test analysis result of ANSYS, and then the genetic algorithm of the Workbench optimization module is called to optimize the parameters of the whole model, so that the precision of the structure optimization design is improved.
(4) Variables and results of each iteration in the optimization process can be checked, and final output data comprise an optimal solution, constraint variables and design variables.
(5) The method is suitable for design and optimization of the large-scale submillimeter wave antenna back frame and the transition structure, and optimization processes and optimization variables can be chosen according to specific design.
Drawings
Fig. 1 is a flowchart of a method for optimizing a submillimeter-wave antenna backing frame and a transition structure according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of an antenna transition structure topology optimization design according to an embodiment of the present invention; fig. 2(a) is a schematic diagram of an initial design of topology optimization, and fig. 2(b) is a schematic diagram of a final design of topology optimization.
Fig. 3 is a schematic diagram of a topology optimization process of a transition structure according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of the analysis result of the back frame reference point coordinate test according to the embodiment of the invention.
FIG. 5 is a schematic diagram of an iterative process of genetic algorithm optimization according to an embodiment of the present invention; fig. 5(a) is a schematic diagram of optimizing the reference point coordinates of the back frame, fig. 5(b) is a schematic diagram of optimizing the section parameters of the rod, and fig. 5(c) is a schematic diagram of optimizing the parameters of the spatial position of the interface.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
It should be noted that the terms "upper", "lower", "left", "right", "front", "back", etc. used in the present invention are for clarity of description only, and are not intended to limit the scope of the present invention, and the relative relationship between the terms and the terms is not limited by the technical contents of the essential changes.
Fig. 1 is a flowchart of a method for optimizing a submillimeter-wave antenna backing frame and a transition structure according to an embodiment of the present invention. Referring to fig. 1, the optimization method includes the steps of:
s1, designing an initial model of the back frame structure by adopting a shape-preserving principle according to the design of a main panel of the 60m submillimeter wave antenna; establishing an initial topological optimization model of a 60m submillimeter wave antenna transition structure according to a topological optimization principle; and (4) carrying out static analysis on the initial topological optimization model, carrying out post-processing on an analysis result, and extracting required parameters to establish a corresponding optimization model.
S2, compressing the back frame of the antenna and the main panel particle unit thereof into an interface node by adopting a hypercell method, importing the compressed finite element model into a Workbench topology optimization module, and constructing an optimization model as follows:
find x＝[x1,x2,……,xn]T
min C(x)＝FTU(x)
s.t v(x)＝xTv-V*≤0
f≥fl
x∈χ,χ＝{x∈Rn,0≤x≤1}
wherein xiFor each cell assigned topological density variable, the objective function is the total compliance of the structure C (x); n is the total number of units in the optimized domain, F is the node load vector, U (x) is the displacement vector of the structure, V (x) is the optimized volume, V is the volume constraint, FlThe natural frequency and the natural frequency lower limit of the structure are respectively.
S3, performing distribution optimization by using a workbench optimization module, and outputting an optimization result to obtain an optimal solution model; and carrying out static analysis on the optimal solution model.
The invention aims to improve the structural rigidity as much as possible under the action of gravity so as to reduce the influence of the action of gravity on the antenna surface shape precision, and therefore, the invention provides an antenna back frame based on topological optimization and genetic algorithm and a transition structure optimization design method. The specific design process is as follows:
(1) according to the design of a main panel of a 60m submillimeter wave antenna, an initial model of a back frame structure is designed by adopting a shape-preserving principle. And establishing an initial topological optimization model of the 60m submillimeter wave antenna transition structure according to a topological optimization principle. And after the integral model is established, performing static analysis on the integral model, performing post-processing on an analysis result, extracting required parameters and establishing an optimization model.
(2) Considering that a finite element model has a large number of non-optimization domain units, firstly, a dorsal frame of an antenna and a main panel particle unit thereof are compressed into interface nodes by adopting a hypercell method so as to reduce the optimization iterative computation scale. And then importing the compressed finite element model into a topology optimization module of Workbench, wherein the constructed optimization model is as follows:
find x＝[x1,x2,……,xn]T
min C(x)＝FTU(x)
s.t v(x)＝xTv-V*≤0
f≥fl
x∈χ,χ＝{x∈Rn,0≤x≤1}
wherein xiFor each cell assigned topological density variable, the objective function is the total compliance of the structure C (x); n is the total number of units in the optimized domain, F is the node load vector, U (x) is the displacement vector of the structure, V (x) is the optimized volume, V is the volume constraint, FlThe natural frequency and the natural frequency lower limit of the structure are respectively. Optimizing the model by adopting a variable density method, then deriving an optimized model result, converting the optimized model result into an optimizable space truss structure, and carrying out multi-step optimization after establishing a parameter finite element model.
(3) Selecting reference point coordinates of a back frame as an optimization variable, taking a deformation geometric error rmse of a main surface of an antenna pointed by a zenith as an objective function, firstly carrying out experimental analysis on the objective function, wherein the analysis method is a Genetic Aggregation response surface method in a Workbench optimization module, and the analysis model is as follows:
Figure BDA0003274273140000061
Figure BDA0003274273140000062
Figure BDA0003274273140000063
Figure BDA0003274273140000064
wherein r isjFor the design variable of the jth design point, NMFor the number of models used, wkWeight factor, y (r), for the kth iteration responsej) And
Figure BDA0003274273140000065
the output response and response prediction for the kth iteration respectively,
Figure BDA0003274273140000066
for the purpose of response prediction of the overall structure,
Figure BDA0003274273140000067
predicting the response of the integral structure without the jth design point; by making the root mean square error of the design experimental points
Figure BDA0003274273140000068
And cross-validation root mean square error
Figure BDA0003274273140000069
Minimized to obtain the optimal weight values, i.e., sensitivity results for the respective design variables.
And selecting a back frame coordinate parameter with high sensitivity as an optimization independent variable, taking an effective deformation error rmse of the antenna main surface under the direction of the zenith as a target function, and determining a value range of a design variable according to the spatial position of the back frame rod piece. Optimizing by adopting a genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
min rmse
Figure BDA0003274273140000071
Figure BDA0003274273140000072
zcenl≤zcen≤zcenu
wherein xpq、zpqX-axis coordinates and z-axis coordinates of a reference point of the back frame under a main surface cylindrical coordinate system are respectively shown, p and q are the number of back frame layers and the number of rings respectively, and p is 1,2, … and 4; q is 1,2, …,7,
Figure BDA0003274273140000073
are respectively xpqThe upper and lower limits of (a) and (b),
Figure BDA0003274273140000074
are each zpqUpper and lower limits of (3), zcenl、zcenuThe upper limit and the lower limit of the gravity center position zcen of the whole structure are respectively; and after the optimization result is obtained, bringing the parameter result into the optimization result to reestablish the model required by the second step of optimization.
(4) The rod section parameters (including the outer diameter and the thickness of the rod) of the back frame and the transition structure are selected as optimization independent variables, and the effective deformation error rmse of the main surface of the antenna with the zenith pointing downwards and the gravity center position are taken as objective functions. Optimizing by adopting a multi-objective genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
minΠ(rmse,zcen)
Figure BDA0003274273140000075
Figure BDA0003274273140000076
Figure BDA0003274273140000077
Figure BDA0003274273140000078
wherein rbs ism、tbsmRespectively shows the outer diameter and the thickness of the back frame rod piece, m is the number of the back frame rod piece types, m is 1,2, …,5,
Figure BDA0003274273140000079
Figure BDA00032742731400000710
and
Figure BDA00032742731400000711
are each rbsm、tbsmUpper and lower limits of (rts)n、ttsnRespectively showing the outer diameter and the thickness of the transition structure rod piece, wherein n is the number of the transition structure rod piece types, n is 1,2,3,
Figure BDA00032742731400000712
and
Figure BDA00032742731400000713
are each rtsn、ttsnUpper and lower limits of (3). And after the optimization result is obtained, bringing the parameter result into the optimization result to reestablish the model required by the optimization in the third step.
(5) Selecting the space positions of interfaces of different components as optimization independent variables, and taking the effective deformation error rmse of the antenna main surface and the gravity center position zcen of the antenna with the zenith pointing downwards as objective functions. Optimizing by adopting a multi-objective genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
minΠ(rmse,zcen)
Figure BDA00032742731400000714
Figure BDA00032742731400000715
Figure BDA00032742731400000716
Figure BDA00032742731400000717
wherein z is41And z43The reference point at the bottom layer of the back frame is corresponding to the coordinate value,
Figure BDA00032742731400000718
is z41And z43Corresponding lower and upper limits, h1The height of the driving wheel connecting platform is shown,
Figure BDA0003274273140000081
represents a sum of h1Lower and upper limits of, tcAnd c is the thickness of the steel plate of the driving wheel, and c is 1,2 and 3. And outputting a result after the optimization is completed.
(6) And according to the optimization result, establishing an antenna model based on the optimal result, and analyzing the whole antenna.
Taking a 60 m-caliber submillimeter wave antenna as an example, the antenna back frame is made of a CFRP material rod, the transition structure and the driving wheel are made of steel materials, the antenna transition structure is designed by adopting a topological optimization method, models before and after design are shown in figure 2, the arrow points are transition structure optimization areas, the transition structure optimization areas are simplified into a ring-shaped solid structure, a final design structure is obtained through topological optimization and conversion, and the optimization process is shown in figure 3.
According to the optimization model established in the step (2), the antenna main surface deformation geometric error rmse is taken as a main objective function, sensitivity analysis of the back frame contact point reference coordinate is performed in the step (3), and the analysis result is shown in fig. 4. In the optimization process in the steps (4) and (5), the structure gravity center position zcen is added as a secondary target parameter, the optimization process takes the reference coordinate of the connection point of the back frame, the section parameters of the back frame and the transition structure rod piece and the interface position as design variables, genetic algorithm optimization is carried out on the designed structure step by step, a target function and design variable values corresponding to the optimal result of each step are output to establish an optimization parameter model of the next step, and data in an output file are extracted to obtain an iterative process capable of obtaining the target function rmse and the structure gravity center position zcen, as shown in fig. 5.
And finally, the maximum evolution algebra is reached and the algorithm converges to obtain the optimal solution, namely under the action of gravity, the deformation geometric error of the main surface of the antenna is 135.6 mu m, and the barycentric coordinate is 0.029 m. The analysis results of the optimized front and rear structures are compared, the deformation error of the main surface of the antenna under the same gravity load is reduced by 61.1%, and the barycentric coordinate is very close to an ideal position. Compared with the optimization result of the reference LMT design structure, the deformation error of the main surface of the antenna is reduced by 48.3%, and the barycentric coordinate is closer to the ideal position.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (4)

1. A submillimeter wave antenna back frame and transition structure optimization method is characterized by comprising the following steps:
s1, designing an initial model of the back frame structure by adopting a shape-preserving principle according to the design of a main panel of the 60m submillimeter wave antenna; establishing an initial topological optimization model of a 60m submillimeter wave antenna transition structure according to a topological optimization principle; performing static analysis on the initial topological optimization model, performing post-processing on an analysis result, extracting required parameters and establishing a corresponding optimization model;
s2, compressing the back frame of the antenna and the main panel particle unit thereof into an interface node by adopting a hypercell method, importing the compressed finite element model into a Workbench topology optimization module, and constructing an optimization model as follows:
find x＝[x1,x2,……,xn]T
min C(x)＝FTU(x)
s.t v(x)＝xTv-V*≤0
f≥fl
x∈χ,χ＝{x∈Rn,0≤x≤1}
wherein xiFor each cell assigned topological density variable, the objective function is the total compliance of the structure C (x); n is the total number of units in the optimized domain, F is the node load vector, U (x) is the displacement vector of the structure, V (x) is the optimized volume, V is the volume constraint, FlThe natural frequency and the natural frequency lower limit of the structure are respectively;
s3, performing distribution optimization by using a workbench optimization module, and outputting an optimization result to obtain an optimal solution model; and carrying out static analysis on the optimal solution model.
2. The submillimeter-wave antenna back frame and transition structure optimization method of claim 1, wherein in step S3, the process of performing distribution optimization by using a workbench optimization module comprises the following steps:
s31, selecting the reference point coordinates of the back frame as optimization variables, taking the deformation geometric error rmse of the antenna main surface pointed by the zenith as an objective function, and performing experimental analysis on the objective function by adopting a Genetic Aggregation response surface method in a Workbench optimization module, wherein the analysis model is as follows:
Figure FDA0003274273130000011
Figure FDA0003274273130000012
Figure FDA0003274273130000013
Figure FDA0003274273130000014
wherein r isjFor the design variable of the jth design point, NMFor the number of models used, wkWeight factor, y (r), for the kth iteration responsej) And
Figure FDA0003274273130000015
the output response and response prediction for the kth iteration respectively,
Figure FDA0003274273130000016
for the purpose of response prediction of the overall structure,
Figure FDA0003274273130000017
predicting the response of the integral structure without the jth design point; by making the root mean square error of the design experimental points
Figure FDA0003274273130000021
And cross-validation root mean square error
Figure FDA0003274273130000022
Minimizing to obtain the optimal weight value, namely the sensitivity result of each design variable;
s32, selecting a back frame coordinate parameter with high sensitivity as an optimization independent variable, taking an effective deformation error rmse of the antenna main surface pointed downwards by the zenith as a target function, and determining a value range of a design variable according to the spatial position of a back frame rod piece; optimizing by adopting a genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
min rmse
Figure FDA0003274273130000023
Figure FDA0003274273130000024
zcenl≤zcen≤zcenu
wherein xpq、zpqX-axis coordinates and z-axis coordinates of a reference point of the back frame under a main surface cylindrical coordinate system are respectively shown, p and q are the number of back frame layers and the number of rings respectively, and p is 1,2, … and 4; q is 1,2, …,7,
Figure FDA0003274273130000025
are respectively xpqThe upper and lower limits of (a) and (b),
Figure FDA0003274273130000026
are each zpqUpper and lower limits of (3), zcenl、zcenuThe upper limit and the lower limit of the gravity center position zcen of the whole structure are respectively; after obtaining the optimization result, bringing in a parameter result to reestablish the model required by the second-step optimization;
s33, selecting section parameters of the rod piece of the back frame and the transition structure as optimization independent variables, and taking an effective deformation error rmse of the antenna main surface and a gravity center position of the antenna main surface pointed downwards by the zenith as a target function; optimizing by adopting a multi-objective genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
minΠ(rmse,zcen)
Figure FDA0003274273130000027
Figure FDA0003274273130000028
Figure FDA0003274273130000029
Figure FDA00032742731300000210
wherein rbs ism、tbsmRespectively shows the outer diameter and the thickness of the back frame rod piece, m is the number of the back frame rod piece types, m is 1,2, …,5,
Figure FDA00032742731300000211
Figure FDA00032742731300000212
and
Figure FDA00032742731300000213
are each rbsm、tbsmUpper and lower limits of (rts)n、ttsnRespectively showing the outer diameter and the thickness of the transition structure rod piece, wherein n is the number of the transition structure rod piece types, n is 1,2,3,
Figure FDA00032742731300000214
and
Figure FDA00032742731300000215
are each rtsn、ttsnUpper and lower limits of (d); after obtaining the optimization result, bringing in a parameter result to reestablish a model required by the optimization in the third step;
s34, selecting the space positions of different component interfaces as optimization independent variables, and taking the effective deformation error rmse and the gravity center position zcen of the antenna main surface pointed downwards by the zenith as a target function; optimizing by adopting a multi-objective genetic algorithm of a Workbench optimizing module, wherein the constructed optimizing model is as follows:
minΠ(rmse,zcen)
Figure FDA0003274273130000031
Figure FDA0003274273130000032
Figure FDA0003274273130000033
Figure FDA0003274273130000034
wherein z is41And z43The reference point at the bottom layer of the back frame is corresponding to the coordinate value,
Figure FDA0003274273130000035
is z41And z43Corresponding lower and upper limits, h1The height of the driving wheel connecting platform is shown,
Figure FDA0003274273130000036
represents a sum of h1Lower and upper limits of, tcThe thickness of the steel plate of the driving wheel is shown, c is the thickness type number of the steel plate of the driving wheel, and c is 1,2 and 3;
and S35, outputting a result after the optimization is completed, wherein the output data comprises an optimal solution, a constraint variable and a design variable.
3. The submillimeter-wave antenna back frame and transition structure optimization method of claim 1, wherein the antenna back frame of the 60m submillimeter-wave antenna is made of a CFRP (carbon fiber reinforced plastics) material rod.
4. The submillimeter-wave antenna back frame and transition structure optimization method of claim 1, wherein the transition structure and the driving wheel of the 60m submillimeter-wave antenna are made of steel.
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CN116702391A (en) * 2023-05-15 2023-09-05 东莞理工学院 Regularization-based conformal topology optimization design method

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Publication number Priority date Publication date Assignee Title
CN114707380A (en) * 2022-04-07 2022-07-05 中国科学院紫金山天文台 Method for adjusting actuator of main reflecting surface of submillimeter-wave telescope and calculating precision
CN114707380B (en) * 2022-04-07 2024-03-22 中国科学院紫金山天文台 Method for adjusting actuator of main reflecting surface of submillimeter wave telescope and calculating accuracy
CN116702391A (en) * 2023-05-15 2023-09-05 东莞理工学院 Regularization-based conformal topology optimization design method
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