CN106785470B - Electromechanical integration manufacturing method for framework type antenna cable net - Google Patents

Electromechanical integration manufacturing method for framework type antenna cable net Download PDF

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CN106785470B
CN106785470B CN201611134912.3A CN201611134912A CN106785470B CN 106785470 B CN106785470 B CN 106785470B CN 201611134912 A CN201611134912 A CN 201611134912A CN 106785470 B CN106785470 B CN 106785470B
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谢靓
张树新
方栋
杨东武
杨癸庚
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Xidian University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/14—Reflecting surfaces; Equivalent structures
    • H01Q15/141—Apparatus or processes specially adapted for manufacturing reflecting surfaces
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
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Abstract

The invention discloses a method for mechanically and electrically integrating and manufacturing a framework type antenna cable net, which is based on a particle swarm algorithm and uses the tension balance condition of a cable net structure and the upper limit and the lower limit of the tension of a cable section to form a fitness function; and solving the cable net structure mechanical model with the geometric nonlinear characteristics by using an optimization algorithm, and searching for a vertical span structure at the cable net boundary of the module. According to the invention, the constraint problem is converted into an unconstrained problem by constructing a proper fitness function, so that a PSO algorithm can be selected for solving. The invention can design the cable net mechanical structure of the antenna, ensure the mechanical property of the cable net to be within the allowable range and greatly reduce the influence of the reflecting surface gap on the electrical property of the antenna.

Description

Electromechanical integration manufacturing method for framework type antenna cable net
Technical Field
The invention belongs to the technical field of a framework type antenna, and particularly relates to an electromechanical integration manufacturing method of a cable net of the framework type antenna.
Background
The framework type expandable antenna consists of a plurality of space units and is a reticular reflector antenna; the unique modular design concept can effectively meet the requirements of large caliber and high precision of the antenna structure. The framework type expandable antenna is composed of an upper metal cable net and a lower back frame. The modules are designed and debugged respectively in the early stage of the integral assembly of the antenna, and nodes on the boundary of the module cable net need to retract inwards under the condition of cable tension balance so as to form a vertical span structure form. Due to the existence of the vertical span ratio, the area of the cord net triangular patch at the boundary is defective, and gaps appear among modules on the reflecting surface. The existence of the gap can affect the electrical performance of the antenna, and then, how to solve the problem brought by the gap, namely designing the cable-net vertical span ratio of each module, becomes the key of the cable-net design of the framework type antenna. If the vertical span ratio is small, the tension of the border cable net unit is increased, whereas if the vertical span ratio is large, the reflecting surface is lost, and the gain of the antenna is further influenced.
In summary, the conventional frame-type antenna cable network has lower antenna electrical performance due to gaps between modules on the reflecting surface.
Disclosure of Invention
The invention aims to provide an electromechanical integration manufacturing method of a framework type antenna cable net, and aims to solve the problem that the existing framework type antenna cable net is low in antenna electrical performance caused by gaps among modules on a reflecting surface.
The invention is realized in this way, a method for manufacturing the electromechanical integration of the framework type antenna cable net, which is based on the particle swarm algorithm and uses the tension balance condition of the cable net structure and the upper and lower limits of the cable section tension to form a fitness function; and solving the cable net structure mechanical model with the geometric nonlinear characteristics by using an optimization algorithm, and searching for a vertical span structure at the cable net boundary of the module.
Further, the electromechanical integration manufacturing method of the framework type antenna cable net comprises the following steps:
firstly, analyzing the electrical property of the framework type antenna, and mathematically describing the gain of the antenna;
secondly, carrying out mechanical analysis on the cable net structure, and designing the balance tension of each cable section in the cable net;
then, an optimized mathematical model of the electromechanical integration design of the framework type antenna cable network is established through analysis;
and finally, providing a truss type antenna cable net electromechanical integrated design method based on a particle swarm optimization algorithm based on a tension balance condition and a fitness function of the upper and lower limits of the cable section tension.
Furthermore, the tension value T of the cable net part can be obtained by constructing a force balance equation of the cable net structureNUME×1。
Further, the optimized mathematical model is:
Findρ＝[ρ1，ρ2，…，ρNUMM]T
Figure BDA0001176804010000021
ρj∈[ρjl,ρju],j＝1,…,NUMM
further, the fitness function is,
Figure BDA0001176804010000022
wherein f ismaxIs the fitness value of the worst feasible individual in the population;
Figure BDA0001176804010000023
further, the directional coefficients of the reflector antenna are:
Figure BDA0001176804010000024
wherein the content of the first and second substances,
Figure BDA0001176804010000025
representing the radiation power of the feed source;
and after performing integral calculation on each patch on the reflecting surface to obtain the far-zone radiation electric field of each unit, overlapping all patches in a far field to obtain the far-zone radiation electric field of the whole antenna.
Will D1Substituting the gain formula of the antenna:
G＝D1η。
further, the force balance equation of a certain node i on the space cable network structure balance configuration in the x, y and z directions is as follows:
Figure BDA0001176804010000031
Figure BDA0001176804010000032
Figure BDA0001176804010000033
wherein, tijIs cable force,. lijIs the length, x, of the cord segment unit iji,yi,zi,xj,yj,zjIs a node coordinate value, fix,fiy,fizThe external force applied to the node i in the x, y and z directions.
Further, each unconstrained node equation in the cable network is integrated into a matrix form, and a cable network balance equation is obtained as follows,
A3(NUMC-NUMU)×NUMETNUME×1＝03(NUMC-NUMU)×1；
in the formula, A3(NUMC-NUMU)×NUMEAs a balanced matrix of nets, TNUME×1The pre-tensioning column vector of the cable segment is shown, NUMC is the total number of cable network nodes, NUMU is the total number of cable network constraint nodes, and NUME is the total number of the cable segment.
The invention also aims to provide the framed antenna manufactured by the framed antenna cable net electromechanical integration manufacturing method.
The electromechanical integration manufacturing method of the framework type antenna cable net provided by the invention solves the problem of gaps among modules on the reflecting surface of the framework type antenna. The optimization method is based on the particle swarm algorithm, the fitness function is formed by the tension balance condition of the cable net structure and the upper limit and the lower limit of the cable section tension, the electrical performance of the antenna and the mechanical performance of the cable net are considered, the mechanical model of the cable net structure with geometric nonlinear characteristics is solved by the optimization algorithm, and the vertical span structural form at the cable net boundary of the module is searched, so that the influence of the reflecting surface gap on the electrical performance of the antenna is reduced to the greatest extent within the allowable range of the mechanical performance of the cable net.
The electromechanical integration design method of the framework type antenna cable net considering the gap influence meets the tension balance condition of the cable net structure and limits the upper limit and the lower limit of the tension of the cable section, takes the electrical property and the mechanical property of the cable net as the target function, and thus, the rigid requirement during antenna design can be met, and the design effect can be optimized; the objective function of the optimization model is a function of the node coordinate variables, while the cable node coordinates are related to the droop ratio, and thus the objective function is an implicit function of the droop ratio. For the highly nonlinear multi-target problem, the multi-target problem is solved by weighting the targets, and the constraint problem is converted into an unconstrained problem by constructing a proper fitness function, so that a PSO algorithm can be selected for solving. The invention can design the cable net mechanical structure of the antenna, ensure the mechanical property of the cable net to be within the allowable range and greatly reduce the influence of the reflecting surface gap on the electrical property of the antenna.
Drawings
Fig. 1 is a flowchart of a method for manufacturing a structural antenna cable network electromechanical integration according to an embodiment of the present invention.
Fig. 2 is a schematic view of stress balance of a cable network structure node provided in the embodiment of the present invention.
Fig. 3 is a finite element model diagram of a framed antenna according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of an objective function iteration process provided in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, the method for manufacturing a structural antenna cable network electromechanical integration according to an embodiment of the present invention includes the following steps:
s101: analyzing the electrical property of the framework type antenna, and mathematically describing the gain of the antenna;
s102: carrying out mechanical analysis on the cable net structure, and designing the balance tension of each cable section in the cable net;
s103: establishing an optimized mathematical model of the electromechanical integration design of the framework type antenna cable network through analysis;
s104: based on the tension balance condition and the fitness function of the upper and lower limits of the tension of the cable section, the electromechanical integration design method of the framework type antenna cable net based on Particle Swarm Optimization (PSO) algorithm and considering the gap influence is provided.
The application of the principles of the present invention will now be described in further detail with reference to specific embodiments.
The electromechanical integration manufacturing method of the framework type antenna cable net provided by the embodiment of the invention comprises the following steps:
1) the electromechanical integration design of the cable net is carried out on the basis of analyzing the electrical property of the antenna, and the electrical property characteristic of the framework type antenna is firstly determined; each module of the framework type expandable antenna is manufactured and assembled in parallel, and a metal wire mesh with good electric conductivity is paved on each module and almost totally reflects electromagnetic waves incident on the surface. For the border cable net part of each module, the triangular patch area at the border is damaged due to the existence of the vertical crossing ratio, so that gaps occur among the modules. The slot affects the electrical performance of the antenna, mainly by reducing the gain, and the effect of the slot on the gain of the reflecting surface can be considered from the area loss of the slot.
2) Another point of the electromechanical integration design of the cable net is the mechanical analysis of the cable net structure. The self nodes on the cable net all need to satisfy the tension balance condition to ensure the mechanical balance of the cable net structure, and the tension value T of the cable net part can be obtained by constructing the force balance equation of the cable net structureNUME×1. As the sag ratio is reduced, the stress of the boundary cable section becomes larger, and the tension distribution of the cable net is more uneven.
3) The size of the gap on the reflecting surface is mainly determined by the vertical span ratio of each module cable net, and the vertical span ratios of the modules are independent of each other due to the parallelism of the modules of the framework antenna, so the vertical span ratio of each module cable net is taken as a design variable and is recorded as:
Find ρ＝[ρ1，ρ2，…，ρNUMM]T(1)
where ρ is1The droop ratio of the 1 st module is indicated, and NUMM indicates the total number of modules.
The design of the cable net needs to comprehensively consider the quality of electrical performance and mechanical performance, the main evaluation index of the electrical performance is antenna gain, the quality of the mechanical performance depends on the maximum-minimum tension ratio of the cable net, and the satellite-borne cable net deployable antenna can be influenced by a complex space environment in space and mainly shows a thermal load effect with constantly changing space, and the stability of the antenna cable net can be directly influenced by the uniform tension distribution of the cable net. In the model, the goal of maximizing the gain can be equivalent to the minimum loss gain, and the other optimization goal is the minimum maximum-minimum tension ratio of the cable net, then the optimization goals are as follows:
Figure BDA0001176804010000051
wherein f is1Gain loss between the ideal reflecting surface and the actual reflecting surface, f2The ratio of the maximum tension to the minimum tension of the upper cable net, the lower cable net and the vertical cables is arithmetically averaged.
Because the dimension and the magnitude of the two target values are different, the target functions are considered to be respectively subjected to normalization processing, each target function is multiplied by corresponding weight by adopting a weighting coefficient method, and multiple targets are integrated into a single target to be solved, so that the final target function is optimized as follows:
Figure BDA0001176804010000061
in the formula, α1、α2The weights are respectively corresponding to the two objective functions.
The constraints in this problem are three: firstly, the pretension of the cable nets at the symmetrical positions in the cable nets is equal, namely the constraint condition of a linear equation; secondly, the pretension value of the cable section in the cable net is changed within the range of the design requirement, and the pretension value is a linear inequality constraint; and thirdly, upper and lower limit constraints of the design variable value. The mathematical expression of the constraint is therefore:
S.T.g(ρ)＝AT＝0
Figure BDA0001176804010000062
Figure BDA0001176804010000063
wherein A is a topological matrix of the structure,Tand
Figure BDA0001176804010000064
the upper and lower limit values of the cable net tension,ρand
Figure BDA0001176804010000065
the vertical span ratio is an upper limit value and a lower limit value.
4) Because the particle swarm optimization cannot directly solve the constrained optimization problem, the constrained problem needs to be converted into an unconstrained problem to be solved in the solving process. The equality constraint is converted into the form of inequality constraint:
hi(ρ)＝|gi(ρ)|-δ≤0,i＝1,...,NUMC (5)
where ε is an allowable tolerance (a very small positive value) and NUMC is the number of cord elements. When | gi(ρ) | - δ ≦ 0, the solution ρ is considered feasible.
The tension constraint can be written as:
Figure BDA0001176804010000066
hi(ρ)＝-Ti(ρ)+T≤0,i＝1,…,NUMC (7)
constructing a fitness function as:
Figure BDA0001176804010000067
wherein f ismaxIs the fitness value of the worst feasible individual in the population;
Figure BDA0001176804010000071
therefore, the optimized mathematical model of the electromechanical integration design method of the framework type antenna cable network is as follows:
Findρ＝[ρ1，ρ2，…，ρNUMM]T
Figure BDA0001176804010000072
ρj∈[ρjl,ρju],j＝1,…,NUMM
in the embodiment of the invention:
the determination of the gain of the reflecting surface in the step 1) comprises the following steps:
the calculation formula for calculating the far-zone radiation electric field of the reflector antenna by using the surface current method is as follows:
Figure BDA0001176804010000073
wherein the content of the first and second substances,
Figure BDA0001176804010000074
k 2 pi/lambda is the free space wavenumber, lambda is the wavelength, η 120 pi is the free space wave impedance, r represents the distance of the far field observation point to the coordinate center,
Figure BDA0001176804010000075
is taken as a unit of a dyadic vector,
Figure BDA0001176804010000076
is a unit dyadic vector
Figure BDA0001176804010000077
Sigma is the projection of the reflecting surface on the aperture surface,
Figure BDA0001176804010000078
represents a position vector of a point on the reflecting surface, and
Figure BDA0001176804010000079
is a function of N and p,
Figure BDA00011768040100000710
is the unit out-of-normal vector for that point,
Figure BDA00011768040100000711
is the incident magnetic field vector.
And (3) after the integral calculation is carried out on each patch on the reflecting surface by using the above formula to obtain the far-zone radiation electric field of each unit, all the patches are superposed in a far field to obtain the far-zone radiation electric field of the whole antenna.
The directional coefficients of the reflector antenna are:
Figure BDA00011768040100000712
wherein the content of the first and second substances,
Figure BDA00011768040100000713
representing the radiation power of the feed.
And (3) after the integral calculation is carried out on each patch on the reflecting surface by using the above formula to obtain the far-zone radiation electric field of each unit, all the patches are superposed in a far field to obtain the far-zone radiation electric field of the whole antenna.
Will D1Substituting the gain formula of the antenna:
G＝D1η (12)
the effect of the slot on the antenna gain can be analyzed.
The mechanical analysis of the cable net structure in the step 2) comprises the following steps:
the tension distribution of the cable section is obtained by solving a static equilibrium equation of the antenna, and then the influence of the vertical-span ratio on the mechanical property of the antenna is evaluated. For a certain node i on the spatial cable network structure balance configuration shown in fig. 2, the force balance equation in the x, y and z directions is as follows:
Figure BDA0001176804010000081
wherein, tijIs cable force,. lijIs the length of the rope segment unit ij，xi,yi,zi,xj,yj,zjIs a node coordinate value, fix,fiy,fizThe external force applied to the node i in the x, y and z directions.
Integrating each unconstrained node equation in the cable network into a matrix form, the cable network balance equation can be obtained as follows:
A3(NUMC-NUMU)×NUMETNUME×1＝03(NUMC-NUMU)×1(14)
in the formula, A3(NUMC-NUMU)×NUMEAs a balanced matrix of nets, TNUME×1The pre-tensioning column vector of the cable segment is shown, NUMC is the total number of cable network nodes, NUMU is the total number of cable network constraint nodes, and NUME is the total number of the cable segment.
The application effect of the present invention will be described in detail with reference to the simulation example.
the optical aperture of a certain framework type antenna is 7.2m, the focal length of an upper net surface is 7.2195m, the focal length of a lower net surface is 14.439m, the wavelength is 150mm, the frequency of the antenna is 2GHz, the number of module layers is 2 layers, the number of module cable net sections is 4, the number of nodes of the upper net surface of the antenna is 427, the total number of cable sections is 2569, the number of adjusting cables is 385, the weight factor alpha is a weight factor1＝0.6，α20.4. The finite element model is shown in FIG. 3.
when the method of the invention is adopted to carry out the electromechanical integration design of the framework type antenna cable net considering the influence of gaps, an objective function iteration curve is shown in figure 4, it can be seen from the figure that the objective function value is continuously reduced along with the increase of the optimization iteration times, the objective function value is reduced to 0.2356 after 20 iterations, the gain loss is reduced to 0.9352dB from 1.7923dB, the tension ratio is changed from 5.9555 to 8.9757, table 1 lists various parameter values before and after optimization, the requirements of different emission tasks on the gain and the mechanical property of the antenna are considered to be different, therefore, the two properties can be balanced in the initial design stage of the antenna, a decision maker can adjust the weight factor α1and alpha2Can set proper parameters for PSO algorithm, such as seed number and c1、c2Or increase the number of terminations to obtain the best possible optimum value.
TABLE 1 comparison of parameters before and after optimization
Figure BDA0001176804010000091
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (6)

1. A method for mechanically and electrically integrating and manufacturing a framework type antenna cable net is characterized in that the method for mechanically and electrically integrating and manufacturing the framework type antenna cable net is based on a particle swarm algorithm, and a fitness function is formed by using a tension balance condition of a cable net structure and upper and lower limits of cable section tension; solving a cable network structure mechanical model with geometric nonlinear characteristics by using a particle swarm optimization algorithm, and searching a vertical span structure at a cable network boundary of a module; and (3) designing to obtain an optimized vertical span structure at the boundary of the module cable net by taking the electrical property and the mechanical property of the cable net as target functions.
2. The method of claim 1, wherein the method comprises the steps of:
1) determining the electrical performance characteristics of the frame antenna; each module of the framework type expandable antenna is manufactured and assembled in parallel, and a metal wire mesh with good electric conductivity is paved on each module to almost totally reflect electromagnetic waves incident on the surface; for the boundary cable net part of each module, considering the influence of the gap on the gain of the reflecting surface from the area loss of the gap;
2) the mechanical analysis of the cable net structure, the force balance equation of the cable net structure is constructed to obtain the tension value T of the cable net partNUME×1；TNUME×1The pre-tension column vector of the cable segment is shown, and NUME is the total number of the cable segment;
3) the size of the slot on the reflector antenna is determined by the vertical span ratio of each module cable net, and the vertical span ratio of each module cable net is taken as a design variable and recorded as:
Find ρ＝[ρ1，ρ2，…，ρNUMM]T；
where ρ is1A droop ratio value representing the 1 st module, and NUMM representing the total number of modules;
in the model, the gain maximization target is equivalent to the loss gain minimum, another optimization target is the maximum-minimum tension ratio of the cable net, and then the optimization targets are as follows:
Figure FDA0002405226430000011
wherein f is1Gain loss between the ideal reflecting surface and the actual reflecting surface, f2The arithmetic mean of the ratio of the maximum tension to the minimum tension of the upper cable net, the lower cable net and the vertical cable;
and multiplying each objective function by corresponding weight by adopting a weighting coefficient method, integrating multiple objectives into a single objective and solving, wherein the optimized final objective function is as follows:
Figure FDA0002405226430000021
in the formula, α1、α2Weights corresponding to the two objective functions respectively;
the constraints in this problem are three: firstly, the pretension of the cable nets at the symmetrical positions in the cable nets is equal, namely the constraint condition of a linear equation; secondly, the pretension value of the cable section in the cable net is changed within the range of the design requirement, and the pretension value is a linear inequality constraint; thirdly, upper and lower limit constraints of the design variable value, so the mathematical expression of the constraint conditions is as follows:
S.T. g(ρ)＝AT＝0
Figure FDA0002405226430000022
Figure FDA0002405226430000023
wherein A is a topological matrix of the structure,Tand
Figure FDA0002405226430000024
the upper and lower limit values of the cable net tension,ρand
Figure FDA0002405226430000025
the vertical span ratio is the upper limit value and the lower limit value of the vertical span ratio;
4) because the particle swarm optimization cannot directly solve the constrained optimization problem, the constrained problem needs to be converted into an unconstrained problem to be solved in the solving process; the equality constraint is converted into the form of inequality constraint:
hi(ρ)＝|gi(ρ)|-δ≤0,i＝1,...,NUMC；
wherein, delta is an allowable tolerance, and NUMC is the number of cable units; when | gi(ρ) | - δ ≦ 0, the solution ρ is considered feasible.
3. The method of claim 2, wherein the directional coefficients of the reflector antenna are:
Figure FDA0002405226430000026
wherein the content of the first and second substances,
Figure FDA0002405226430000027
representing the radiation power of the feed source;
after performing integral calculation on each patch on the reflecting surface to obtain a far-zone radiation electric field of each unit, overlapping all patches in a far field to obtain a far-zone radiation electric field of the whole antenna;
will D1Substituting the gain formula of the antenna:
G＝D1η。
4. a method for manufacturing a structural antenna cable net in an electromechanical integration manner as claimed in claim 2, wherein the force balance equation of a certain node i in the cable net structure balance configuration in the x, y and z directions is:
Figure FDA0002405226430000031
Figure FDA0002405226430000032
Figure FDA0002405226430000033
wherein, tijIs cable force,. lijIs the length, x, of the cord segment unit iji,yi,zi,xj,yj,zjIs a node coordinate value, fix,fiy,fizThe external force applied to the node i in the x, y and z directions.
5. The method of claim 4, wherein each unconstrained node equation in the cable network is integrated into a matrix form, resulting in a cable network equilibrium equation as follows,
A3(NUMC-NUMU)×NUMETNUME×1＝03(NUMC-NUMU)×1；
in the formula, A3(NUMC-NUMU)×NUMEAs a balanced matrix of nets, TNUME×1The pre-tensioning column vector of the cable segment is shown, NUMC is the total number of cable network nodes, NUMU is the total number of cable network constraint nodes, and NUME is the total number of the cable segment.
6. The method for manufacturing a structural antenna cable net in an electromechanical integration manner according to claim 4, wherein the method in 4) further comprises:
the tension constraint is written as:
Figure FDA0002405226430000034
hi(ρ)＝-Ti(ρ)+T≤0,i＝1,…,NUMC；
constructing a fitness function as:
Figure FDA0002405226430000035
wherein f ismaxIs the fitness value of the worst feasible individual in the population;
Figure FDA0002405226430000036
the optimized mathematical model of the electromechanical integration design method of the framework type antenna cable network is as follows:
Find ρ＝[ρ1，ρ2，…，ρNUMM]T
Figure FDA0002405226430000041
ρj∈[ρjl,ρju],j＝1,…,NUMM。
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