Geometric configuration optimization design method of ring column type mesh antenna for electrical performance

Abstract

The invention relates to a geometric configuration optimization design method of an annular column type mesh antenna for electrical performance. The method comprises the following steps of: 1, inputting structural parameters and electromagnetic calculation parameters of a ring column antenna, simulating external force influence received by an antenna cable net, and obtaining a standard deviation of cable unit length random error distribution; 2, inputting an initial value of a design variable; step 3, obtaining a balance matrix and cable tension thereof; 4, obtaining a sensitivity matrix of node errors and cable unit lengths; 5, obtaining a sensitivity matrix of the length of the cable unit and the standard deviation of the distribution of the cable unit; step 6, calculating a standard deviation of phase error random distribution; 7, calculating an average power directional diagram and a main shaft gain loss mean value according to the phase error random distribution standard deviation; 8, solving the optimization design model; step 9, judging whether a convergence condition is met or not; and step 10, outputting the design variable when the updated design variable meets the requirement. According to the invention, the structure optimization of the ring column type mesh antenna oriented to electrical performance can be realized.

Description

Technical Field

[0001] The present invention belongs to the field of antenna technology, and in particular relates to a geometric configuration optimization design method of a ring-column mesh antenna oriented towards electrical performance. Background Art

[0002] Ring-column mesh antennas are increasingly being used in space antenna design due to their light weight, compact size, and high aspect ratio. These antennas utilize a cable-net structure to support the parabolic shape, utilizing a laid wire mesh to transmit and receive electromagnetic waves. Designing the cable tension is crucial to antenna structure design, ensuring the antenna's reflective surface achieves the desired surface accuracy and electrical performance. Developing the cable tension and shape to meet structural stiffness requirements is a crucial step in mesh antenna design.

[0003] Liu Yang et al. published an optimization method for solving the front and rear mesh surfaces separately in the paper “A Design and Analysis Method for the Cable Net Structure of a Ring Column Antenna” (Journal of Xidian University, 2019, 46(04):43-48). This method first calculates the prestress of the front mesh surface and then calculates the prestress of the rear cable net through the equilibrium equation. Ding Yankang proposed a surface accuracy adjustment method based on an optimization model in the paper “Structural Analysis and Design of Large-Scale Space Ring Column Deployable Antenna” (Xidian University, 2022). With surface accuracy as the objective function, the optimization solution is performed through sequential quadratic programming.

[0004] The above literature all uses surface accuracy as a design objective or constraint function, striving to achieve high surface accuracy for the cable net system from a structural design perspective. However, without integrating this with electrical performance gains during the design phase, achieving optimal electrical performance is difficult. Summary of the Invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for optimizing the geometric configuration of a ring-column mesh antenna with an eye on electrical performance. This method introduces the electrical parameters of the ring-column antenna into the optimized design of the cable net geometric configuration, thereby realizing the optimization of the ring-column mesh antenna structure with an eye on electrical performance.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A geometric configuration optimization design method for a ring-shaped mesh antenna oriented towards electrical performance includes the following steps:

[0008] Step 1: Based on the ring-shaped antenna structural parameters and electromagnetic calculation parameters, simulate the external force effect on the antenna wire mesh and obtain the standard deviation of the random error distribution of the cable unit length;

[0009] Step 2: Obtain the initial values ​​of design variables;

[0010] Step 3: Perform structural mechanics analysis based on the input structural parameters to obtain the equilibrium matrix and its cable tension;

[0011] Step 4: Obtain the sensitivity matrix of node error and cable unit length based on the mechanical properties of the cable network;

[0012] Step 5: Calculate the sensitivity matrix of normal deviation to cable element length and the standard deviation of its distribution based on the sensitivity matrix of node error and cable element length;

[0013] Step 6: Calculate the standard deviation of the phase error random distribution based on the normal deviation and standard deviation;

[0014] Step 7: Calculate the average power pattern and the mean of the main axis gain loss based on the standard deviation of the phase error random distribution;

[0015] Step 8: Solve the optimization design model based on the initial values ​​of the design variables, cable tension, and equilibrium matrix;

[0016] Step 9: Determine whether the convergence conditions are met;

[0017] Step 10: When the updated design variables meet the requirements, output the design variables.

[0018] The step 1 is specifically as follows:

[0019] Antenna structure parameters include the user-provided ring-shaped mesh antenna diameter, focal length, cable unit cross-sectional area, Young's elastic modulus, and cable net tension;

[0020] The electromagnetic calculation parameters include cone pin parameters, aperture field shape parameters, and radiation electric field distribution under ideal conditions.

[0021] The step 2 is specifically as follows:

[0022] Enter the initial value of the design variable ΔX

[0023] ΔX=[Δx1,Δx2,Δx i ,...,Δx n ,Δz1,Δz2,Δz i ,...,Δz n ] T

[0024] Among them, ΔX represents the column vector composed of the displacement of the rear cable network nodes, Δx i , Δz i They represent the node displacement of the i-th back cable net node in the x and z directions respectively, and n represents the total number of back cable net nodes in the geometric configuration optimization.

[0025] The step 3 is specifically as follows:

[0026] According to the node coordinates and connection information of the cable net structure, the force balance matrix and cable tension F of the cable net structure are generated.

[0027] AF=0

[0028] Among them, A is the tension balance matrix of the cable net system, and its dimension is 2N f ×M; F is the cable tension column vector, dimension is M×1; where N f represents the number of unconstrained free nodes in the cable net system, and M is the number of cable segments between free nodes.

[0029] The step 4 is specifically as follows:

[0030] The sensitivity matrix K of node error and cable unit length is obtained according to the mechanical characteristics of the cable net L ;

[0031] K L =[-sin(ξ / 2),cos(ξ / 2)]

[0032] Where ξ represents the angle between the line connecting any point on the reflecting surface and the focal axis.

[0033] The step 5 is specifically as follows:

[0034] Calculate the sensitivity matrix K of the normal deviation to the cable element length and its standard deviation σ ε ;

[0035] According to the following formula, the relationship between the normal deviation and the cable element length error is obtained:

[0036] K=K r K L

[0037] Where K represents the sensitivity matrix between the normal deviation and the cable element length error, K r K r Represents the transformation matrix composed of the angle function relationship of each node, K L The sensitivity matrix representing the cable net node position error and cable unit length.

[0038] The standard deviation σ of the normal deviation to the cable element length is obtained as follows ε

[0039] σ ε =sqrt(diag(K T K))

[0040] Where K represents the sensitivity matrix between the normal deviation and the cable element length error, sqrt represents the square root operation, diag(K T K) represents K T K is a diagonal matrix with diagonal elements.

[0041] The step 6 is specifically as follows:

[0042] The standard deviation σ of the random distribution of phase error is obtained according to the following formula n

[0043]

[0044] Among them, σ n represents the standard deviation of the random distribution of phase error, σ ε It represents the standard deviation of the normal deviation of points on the reflecting surface, and ξ represents the angle between the line connecting any point on the reflecting surface and the focal axis.

[0045] The step 7 is specifically as follows:

[0046] Calculate the average power pattern and the mean of the main axis gain loss;

[0047] The average power pattern can be obtained according to the following formula

[0048]

[0049] Among them, μ(EE * ) represents the average power pattern, a is the radius of the aperture surface, N represents the total number of rings in the aperture surface, E n,n-1 represents the radiation electric field between the nth ring and the n-1th ring in an ideal state, σ n , σ m Represents the standard deviation of the random distribution of the phase error of the nth and mth loops.

[0050] The step 8 is specifically as follows:

[0051] Solving the optimization design model

[0052] findΔX

[0053] min f(ΔX)=-μ(ΔG(0,0))

[0054]

[0055] Where ΔX represents the initial value of the design variable, f(ΔX) represents the main axis gain loss mean objective function, F is the cable tension, A is the equilibrium matrix generated by the cable net structure node information and the tension cable structure connection information, m t Indicates the number of vertical cables, and the vertical cable tension is set to an average value F t,avg , ΔX up , ΔX low Represent the upper and lower limit column vectors of the design variable ΔX, F up 、F low are the upper and lower limits of the cable force respectively.

[0056] The step 9 is specifically as follows:

[0057] Determine whether the convergence conditions are met. If not, return to step 2 to adjust the design variables.

[0058] ΔX (i) =ΔX (i-1) +μ (j)

[0059] where ΔX (i) represents the design variable of the i-th iteration, μ (j) represents the j-th iteration step.

[0060] Beneficial effects of the present invention:

[0061] This invention incorporates electrical performance parameters into the geometric optimization design of a ring-shaped, cylindrical mesh antenna, achieving electrical performance-focused structural optimization of the antenna. In terms of structural optimization, the node displacements of the rear cable mesh are used as variables. By establishing a sensitivity matrix between node errors and cable unit lengths, the standard deviation of the random distribution of phase errors is further derived, which is used to calculate the main axis gain loss. By solving the optimization model, not only is the force distribution of the vertical cable mesh averaged, but the antenna's electrical performance under random errors is also effectively improved. This method can effectively improve the electrical performance of the mesh antenna, particularly with respect to radiation efficiency, gain, and directivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Flowchart of the present invention.

[0063] Figure 2 is the initial geometric configuration of the radial monolithic sheet in the initial state.

[0064] Figure 3 is the initial geometric configuration of the radial monolithic sheet in the optimal state. DETAILED DESCRIPTION

[0065] The present invention will be described in further detail below with reference to the accompanying drawings.

[0066] See Figure 1 , Figure 1 The flowchart of the method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance provided for the implementation of the present invention includes:

[0067] Step 1: Input the ring-shaped antenna structure and electromagnetic calculation parameters, as well as the standard deviation of the random error distribution of the cable unit length;

[0068] The input structural parameters provided by the user include the aperture, focal length, cross-sectional area of ​​the cable unit, Young's elastic modulus, and cable net tension of the ring-shaped mesh antenna; the electrical parameters include the cone pin parameters, aperture field shape parameters, and the radiation electric field distribution under ideal conditions. The standard deviation of the random error distribution of the cable unit length is assumed to follow a Gaussian distribution with a mean of 0 and a variance of σ.

[0069] Step 2: Input the initial values ​​of the design variables;

[0070] Enter the initial value of the design variable ΔX

[0071] ΔX=[Δx1,Δx2,Δx i ,...,Δx n ,Δz1,Δz2,Δz i ,...,Δz n ] T

[0072] Among them, ΔX represents the column vector composed of the displacement of the rear cable network nodes, Δx i , Δz i They represent the node displacement of the i-th back cable net node in the x and z directions respectively, and n represents the total number of back cable net nodes in the geometric configuration optimization.

[0073] Step 3: Carry out structural mechanics analysis and obtain the equilibrium equation and its tension according to the input antenna structure parameters; generate the force balance matrix and tension F of the cable net structure according to the node coordinates and connection information of the cable net structure.

[0074] AF=0

[0075] Among them, A is the tension balance matrix of the cable net system, and its dimension is 2N f ×M; F is the cable tension column vector, dimension is M×1; where N f represents the number of unconstrained free nodes in the cable net system, and M is the number of cable segments between free nodes.

[0076] A point i in the structure is connected to a node jkm through a unit abc. The equilibrium equation of point i is:

[0077]

[0078] Where: X i 、Y i , Z i represents the node coordinates, L a , L b , L c Indicates the length of the cable segment, T a 、T b 、T c Represents the tension of the cable segment. Writing the above formula in matrix form yields AF=0.

[0079] Step 4: Obtain the sensitivity matrix of node error and cable unit length based on the mechanical properties of the cable network;

[0080] The sensitivity matrix K of node error and cable unit length is obtained according to the mechanical characteristics of the cable net L ;

[0081] K L =[-sin(ξ / 2),cos(ξ / 2)]

[0082] Where ξ represents the angle between the line connecting any point on the reflecting surface and the focal axis.

[0083] Step 5: Calculate the sensitivity matrix of normal deviation to cable element length and the standard deviation of its distribution;

[0084] Calculate the sensitivity matrix K of the normal deviation to the cable element length and its standard deviation σ ε ;

[0085] According to the following formula, the relationship between the normal deviation and the cable element length error is obtained:

[0086] K=K r K L

[0087] Where K represents the sensitivity matrix between the normal deviation and the cable element length error, K r K r Represents the transformation matrix composed of the angle function relationship of each node, K L The sensitivity matrix representing the cable net node position error and cable unit length.

[0088] The standard deviation σ of the normal deviation to the cable element length is obtained as follows ε

[0089] σ ε =sqrt(diag(K T K))

[0090] Where K represents the sensitivity matrix between the normal deviation and the cable element length error, sqrt represents the square root operation, diag(K T K) represents K T K is a diagonal matrix with diagonal elements.

[0091] Step 6: Calculate the standard deviation of the phase error random distribution based on the standard deviation of the normal deviation;

[0092] The standard deviation σ of the random distribution of phase error is obtained according to the following formula n

[0093]

[0094] Among them, σ n represents the standard deviation of the random distribution of phase error, σ ε It represents the standard deviation of the normal deviation of points on the reflecting surface, and ξ represents the angle between the line connecting any point on the reflecting surface and the focal axis.

[0095] Step 7: Calculate the average power pattern and the mean of the main axis gain loss based on the standard deviation of the phase error random distribution;

[0096] The average power pattern μ(EE * )

[0097]

[0098] Among them, μ(EE * ) represents the average power pattern, a is the radius of the aperture surface, N represents the total number of rings in the aperture surface, E n,n-1 represents the radiation electric field between the nth ring and the n-1th ring in an ideal state, σ n , σ m represents the standard deviation of the random distribution of the phase error of the nth and mth loops,

[0099] Step 8: Solve the optimization design model;

[0100] Solving the optimization design model

[0101] findΔX

[0102] min f(ΔX)=-μ(ΔG(0,0))

[0103]

[0104] Where ΔX represents the design variable, f(ΔX) represents the main axis gain loss mean objective function, F is the cable tension, A is the equilibrium matrix generated by the cable net structure node information and the tension cable structure connection information, m t Indicates the number of vertical cables, and the vertical cable tension is set to an average value F t,avg , ΔX up , ΔX low Represent the upper and lower limit column vectors of the design variable ΔX, F up 、F low are the upper and lower limits of the cable force respectively.

[0105] Step 9: Determine whether the convergence conditions are met;

[0106] ΔX (i) =ΔX (i-1) +μ (j)

[0107] where ΔX(i) represents the design variable of the i-th iteration, μ (j) Indicates the j-th iteration step. (The process of loop iteration).

[0108] Determine whether the convergence conditions are met. If not, return to step 2 to adjust the design variables.

[0109] Step 10: Output the optimal solution.

[0110] When the updated design variables meet the requirements, the design variables are output;

[0111] The advantages of the present invention can be further illustrated by the following simulation experiments:

[0112] 1. Simulation conditions:

[0113] The ring-shaped antenna has a maximum projected aperture of 100m, a focal length of 60m, and a central inner diameter of 5m. It operates at a frequency of 0.3GHz, a taper parameter of -12dB, and an aperture field shape parameter of 1. The aperture plane is divided radially into 48 sectors and circumferentially into 27 rings.

[0114] 2. Simulation results:

[0115] The geometric configuration of the monolithic chip before optimization is as follows Figure 2 As shown, the optimal monolithic geometric configuration obtained by the method of the present invention is as follows Figure 3 shown.

[0116] By comparison Figure 2 and Figure 3 It can be seen that the vertical cables in the optimized geometric configuration have tilted to varying degrees, and the reversed-curved part of the lower cable net is closer to the upper cable net.

[0117] Random error Initial state gain loss (dB) Optimal state gain loss (dB) 6.3mm -1.58 -0.21

[0118] It can be clearly seen from Table 1 that the optimized cable net structure increases the gain from -1.58dB to -0.21dB at the same random error, which is a significant improvement.

[0119] Aiming at the electrical performance design requirements of mesh antennas, the present invention proposes an electrical performance-oriented geometric configuration optimization design method for ring-column mesh antennas, thereby achieving structural optimization and improvement of electrical performance.

[0120] Adding the influence of electrical performance into the optimization target is more conducive to maximizing electrical performance.

[0121] The parts not described in detail in this embodiment are commonly known in the industry and are not described here one by one. The above examples are merely illustrative of the present invention and do not constitute a limitation on the scope of protection of the present invention. All designs that are the same or similar to the present invention fall within the scope of protection of the present invention.

Claims

1. A geometric configuration optimization design method for a ring-shaped mesh antenna oriented towards electrical performance, characterized in that: The following steps are included: Step 1: Based on the ring-shaped antenna structural parameters and electromagnetic calculation parameters, simulate the external force effect on the antenna wire network and obtain the standard deviation of the random error distribution of the cable unit length; Step 2: Obtain the initial values ​​of design variables; Step 3: Perform structural mechanics analysis based on the input structural parameters to obtain the force balance matrix and its cable tension; Step 4: Obtain the sensitivity matrix of node error and cable unit length based on the mechanical properties of the cable network; Step 5: Calculate the sensitivity matrix of normal deviation to cable element length and the standard deviation of its distribution based on the sensitivity matrix of node error and cable element length; Step 6: Calculate the standard deviation of the phase error random distribution based on the normal deviation and standard deviation; Step 7: Calculate the average power pattern and the mean of the main axis gain loss based on the standard deviation of the phase error random distribution; Step 8: Solve the optimization design model based on the initial values ​​of the design variables, cable tension, and equilibrium matrix; Step 9: Determine whether the convergence conditions are met; Step 10: When the updated design variables meet the requirements, output the design variables.

2. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 1, wherein: The step 1 is specifically as follows: Antenna structure parameters include the user-provided ring-shaped mesh antenna diameter, focal length, cable unit cross-sectional area, Young's elastic modulus, and cable net tension; The electromagnetic calculation parameters include cone pin parameters, aperture field shape parameters, and radiation electric field distribution under ideal conditions.

3. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 2, wherein: The step 2 is specifically as follows: Enter the initial value of the design variable ΔX ΔX=[Δx1,Δx2,Δx i ,...,Δx n ,Δz1,Δz2,Δz i ,...,Δz n ] T Among them, ΔX represents the column vector composed of the displacement of the rear cable network nodes, Δx i , Δz i They represent the node displacement of the i-th back cable net node in the x and z directions respectively, and n represents the total number of back cable net nodes in the geometric configuration optimization.

4. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 3, wherein: The step 3 is specifically as follows: According to the node coordinates and connection information of the cable net structure, the force balance matrix and cable tension F of the cable net structure are generated. AF=0 Among them, A is the tension balance matrix of the cable net system, and its dimension is 2N f ×M; F is the cable tension column vector, dimension is M×1; where N f represents the number of unconstrained free nodes in the cable net system, and M is the number of cable segments between free nodes.

5. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 4, wherein: The step 4 is specifically as follows: The sensitivity matrix K of node error and cable unit length is obtained according to the mechanical characteristics of the cable net L ; K L =[-sin(ξ / 2),cos(ξ / 2)] Where ξ represents the angle between the line connecting any point on the reflecting surface and the focal axis.

6. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 5, wherein: The step 5 is specifically as follows: Calculate the sensitivity matrix K of the normal deviation to the cable element length and its standard deviation σ ε ; According to the following formula, the relationship between the normal deviation and the cable element length error is obtained: K=K r K L Where K represents the sensitivity matrix between the normal deviation and the cable element length error, K r K r Represents the transformation matrix composed of the angle function relationship of each node, K L The sensitivity matrix representing the position error of the cable net nodes and the length of the cable unit; The standard deviation σ of the normal deviation to the cable element length is obtained as follows ε σ ε =sqrt(diag(K T K)) Where K represents the sensitivity matrix between the normal deviation and the cable element length error, sqrt represents the square root operation, diag(K T K) represents K T K is a diagonal matrix with diagonal elements.

7. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 6, wherein: The step 6 is specifically as follows: The standard deviation σ of the random distribution of phase error is obtained according to the following formula n Among them, σ n represents the standard deviation of the random distribution of phase error, σ ε It represents the standard deviation of the normal deviation of points on the reflecting surface, and ξ represents the angle between the line connecting any point on the reflecting surface and the focal axis.

8. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 7, wherein: The step 7 is specifically as follows: Calculate the average power pattern and the mean of the main axis gain loss; The average power pattern can be obtained according to the following formula Among them, μ(EE * ) represents the average power pattern, a is the radius of the aperture surface, N represents the total number of rings in the aperture surface, E n,n-1 represents the radiation electric field between the nth ring and the n-1th ring in an ideal state, σ n , σ m Represents the standard deviation of the random distribution of the phase error of the nth and mth loops.

9. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 8, wherein: The step 8 is specifically as follows: Solving the optimization design model findΔX min f(ΔX)=-μ(ΔG(0,0)) Where ΔX represents the initial value of the design variable, f(ΔX) represents the main axis gain loss mean objective function, F is the cable tension, A is the tension balance matrix of the cable net system generated by the cable net structure node information and the tension cable structure connection information, m t Indicates the number of vertical cables, and the vertical cable tension is set to an average value F t,avg , ΔX up , ΔX low Represent the upper and lower limit column vectors of the design variable ΔX, F up 、F low are the upper and lower limits of the cable force respectively.

10. The method for optimizing the geometric configuration of a ring-shaped mesh antenna for electrical performance according to claim 9, wherein: The step 9 is specifically as follows: Determine whether the convergence conditions are met. If not, return to step 2 to adjust the design variables. ΔX (i) =ΔX (i-1) +m (j) where ΔX (i) represents the design variable of the i-th iteration, μ (j) represents the j-th iteration step.

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