A method for form-finding optimization of mesh antenna electrical performance weighting

Abstract

The application discloses a kind of mesh antenna electric performance weighting's form finding optimization method, comprising the following steps;Step (1): input the initial structure parameters of antenna and electric parameters in optimization model;Step (2): according to the initial force density input, solve mechanical model, obtain corresponding cable net node coordinates;Step (3): according to the aperture field distribution function of mesh reflector antenna, generate weighting function;Step (4): generate sensitivity matrix and vector;Step (5): find the optimal force density increment that meets the constraint condition;Step (6): when the solution accuracy of quadratic programming does not meet the requirement, one-dimensional line search is carried out, and the step length of next iteration is found;Step (7): update mechanical model, obtain next iteration value;Step (8): judge whether to meet convergence condition;Step (9): output force density design variable.The application improves calculation efficiency, effectively reduces antenna structure design and electric performance design iteration cycle time.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of antennas, and particularly relates to a form-finding optimization method for the electrical performance weighting of a mesh antenna. BACKGROUND

[0002] Form design is an important step for a mesh antenna to form a specified reflector surface shape. There are mainly two typical form design methods, one is single-discipline structure design with the root mean square value as the target, and the other is mechatronic integrated design directly with the electrical performance gain as the target.

[0003] Maddio et al. proposed a force density-based form-finding method in the document "An optimized form-finding method of an asymmetric large deployable reflector[J]. Engineering Structures, 2019, 181: 27-34", which firstly verifies the feasibility of the method by using the support truss rigidity verification algorithm, and then considers the truss deformation and verifies the effectiveness of the method by using the minimum root mean square error of the nodes.

[0004] Nie et al. proposed a form design method for cable network structures with flexible frames in the document "Form finding and design optimization of cable network structures with flexible frames[J]. Computers&Structures, 2019, 220: 81-91", which couples the cable net and the support truss and establishes the balance equation between the nodes by processing the support frame stiffness matrix, and constructs an integrated form design model for solving.

[0005] The above methods only start from the perspective of structure design and do not combine with the electrical performance gain, which has certain limitations only by structure design to meet the needs of electrical performance.

[0006] Zhang Shuxin proposed a method of taking the far-field electrical performance of the antenna as the optimization target and selecting the maximum directional coefficient of the antenna main axis as the objective function to establish an optimization model in the document "Key technology research on mechatronic integrated optimization design of reflector antenna[D]. Xi'an: Xi'an University of Electronic Science and Technology, 2015", and the form adjustment of the mesh reflector antenna based on mechatronic integrated optimization design is realized by solving the model. The mechatronic integrated optimization method has a complicated calculation process and a slow iteration process, which is not conducive to improving the efficiency of the optimization design. Especially when the structure size of the antenna increases and the cable net structure becomes more complex, the calculation difficulty will be nonlinearly increased, which limits the optimization design of the antenna. SUMMARY

[0007] In order to overcome the deficiencies of the prior art, the purpose of the present application is to provide a net antenna electric performance weighted form-finding optimization method, which uses sensitivity analysis method to link the net antenna net surface node displacement vector, force density increment and cable net tension, and introduces the electric performance into the optimization target through the aperture field weighting method for optimization. The calculation efficiency is improved, and the iteration cycle time of the antenna structure design and electric performance design is effectively reduced.

[0008] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0009] A net antenna electric performance weighted form-finding optimization method, comprising the following steps:

[0010] Step (1): input the initial structure parameters, electric parameters, upper and lower limits of cable net tension, initial force density and optimization iteration convergence conditions of the net antenna into the optimization model;

[0011] The optimization model is the entire program, and the parameter input of step one is equivalent to outputting the basic parameters without specific output, which is for the preparation of step two.

[0012] Step (2): solve the mechanical model according to the initial force density to obtain the corresponding cable net node coordinates;

[0013] Step (3): generate a weighting function according to the aperture field distribution function of the net antenna, and obtain the root mean square value after weighting;

[0014] Step (4): update the second-order Hessian matrix and the first-order sensitivity vector through sensitivity analysis to generate the sensitivity matrix and vector;

[0015] Step (5): establish a quadratic programming model through the coefficient matrix composed of the sensitivity matrix and vector, and solve the model to find the optimal force density increment that meets the constraint condition;

[0016] Step (6): when the quadratic programming solution accuracy does not meet the requirement, perform one-dimensional line search to find the step length for the next iteration;

[0017] Step (7): update the mechanical model according to the optimal solution obtained in the one-dimensional line search to obtain the next iteration value;

[0018] Step (8): judge whether the root mean square value obtained in step (3) meets the convergence condition;

[0019] Step (9): output the force density design variable.

[0020] The step (1) is specifically:

[0021] The structural parameters of the mesh antenna include an antenna aperture, a focal length, and a bias height, and the electrical parameters include a working frequency, and upper and lower limits of cable tension, an initial force density, and an optimization iteration convergence condition.

[0022] The step (2) is specifically:

[0023] Solving the following mechanical model:

[0024] find q = [q1, q2, …, q m ] T

[0025]

[0026] wherein q represents a force density vector, q m m represents the mth component in the force density vector, ε r ′ ms represents a weighted root mean square, and ε represents a node deformation column vector on a reflecting surface, Q = [Q1, Q2, …, Q n ] T represents a weight function column vector composed of all node aperture field amplitude distribution functions, diag(Q) represents a diagonal matrix with Q as diagonal elements, n represents the number of nodes, F represents cable force, F, represents upper and lower limits of cable force;

[0027] A set of force density values is obtained by solving the mechanical model, and the corresponding cable net node coordinates are obtained from the relationship between the node deformation and the force density increment and the force density. The node coordinates of the jth iteration and the j-1th iteration are related to each other, and the relationship between the node deformation column vector, the cable net tension vector column vector, and the force density increment is obtained.

[0028]

[0029] F (j) = diag(L (j) )q (j) .

[0030] wherein Δr (j) represents a node deformation column vector, represents a cable net force density column vector, Δq (j) represents a force density increment, F (j) represents a jth iteration cable net tension vector, L (j) represents a jth iteration cable segment length vector, and diag(L (j) ) represents a matrix with L (j) as the main diagonal elements.

[0031] The step (3) is specifically:

[0032] The weighting function is generated according to the aperture field distribution function of the mesh reflector antenna:

[0033]

[0034] wherein Q(x P ,y P ) is the aperture field distribution function, x P ,y P represent the coordinate vectors of the points on the aperture, d is the projected aperture of the offset reflector, h is the offset height of the offset reflector, represents the distance from the center point of the projected aperture to the coordinate origin, B is the aperture field amplitude control parameter, B = 10 ET / 20 , ET is the edge taper, and represents the amplitude ratio from the center of the projected aperture to the edge of the aperture.

[0035] The target is to generate the weighting function, wherein Q(x P ,y P ) is still the aperture field distribution function, and the aperture field distribution function is taken as the weighting function, which means that the aperture field function is changed into Qi, which is the aperture field amplitude distribution function value below.

[0036] The weighted root mean square value is as follows:

[0037]

[0038] wherein Qi represents the aperture field amplitude distribution function value corresponding to the node i, and ε i represents the node deformation column vector, and n represents the number of nodes. Qi is the specific value obtained by inputting the specific coordinate value into the distribution function.

[0039] The step (4) is specifically:

[0040] The weighted sensitivity is calculated according to the following formula:

[0041]

[0042] wherein K r (j) represents the sensitivity matrix of the node deformation relative to the node coordinates in three directions, I represents the unit matrix with diagonal elements being 1, f represents the focal length of the mesh antenna, diag(x (j) ) represents the diagonal matrix with x (j) as the diagonal elements, and x (j) ,y (j)) represent the coordinate components of the x-axis and y-axis.

[0043]

[0044] where H, G represent the second order Hessian matrix and the first order sensitivity column vector of the objective function to the force density, respectively, K q (j) represents the Jacobi matrix of the reflecting surface node position vector to the cable net force density vector obtained by sensitivity analysis in the jth iteration, K r (j) represents the sensitivity matrix of the node deformation to the three direction node coordinates, and ε represents the node deformation column vector on the reflecting surface, and diag(Q) represents the diagonal matrix with Q as the diagonal elements.

[0045] The step (5) is specifically:

[0046] According to the obtained sensitivity matrix and vector, a coefficient matrix is formed, denoted as:

[0047] The coefficient matrix is two matrices of G and H in step 4;

[0048] A quadratic programming model is established, denoted as:

[0049] findΔq (j)

[0050]

[0051] where Δq (j) is the force density increment, and obj (j) represents the optimization objective function.

[0052] The step (6) is specifically:

[0053] findμ (j)

[0054] min obj (j)

[0055]

[0056] where μ is the search interval (0, 1), F, is the upper and lower limit of the cable force, and a one-dimensional line search is performed by using the bisection method, and according to the lower and upper limit values of the cable tension constraint, the next iteration step is determined.

[0057] The step (7) is specifically:

[0058] According to the optimal solution obtained in the one-dimensional line search, it can be superimposed into the j-1th model to update the model, and gradually iterate until convergence;

[0059] q (j) =q (j-1) +μ (j) Δq (j)*

[0060] wherein q (j) represents a column vector composed of segment force density, and Δq (j)* represents an optimal solution obtained by using a quadratic programming algorithm, and μ (j) is the jth iteration step.

[0061] The step (8) is specifically:

[0062] It is judged whether the root mean square value obtained in the step (3) satisfies a convergence condition, and if yes, the step (9) is performed, otherwise, a new force density variable after one-dimensional search is used as an input variable, and the step (4) is performed.

[0063] The convergence condition is that the weighted root mean square value is less than 10 -5 mm.

[0064] The step (9) is specifically:

[0065] When the updated force density design variable satisfies a requirement, the force density design variable is outputted.

[0066] In the design of the optimization objective function, the error distribution of the antenna surface is considered, and the electrical performance requirement of the antenna structure is also considered, the aperture field distribution function of electromagnetics is introduced into the objective function for weighted optimization, so that the central region of the antenna, which has a great influence on the overall electrical performance, has a larger proportion in the optimization objective, and the structural optimization design beneficial to the performance requirement of the antenna is realized.

[0067] The traditional shape optimization method cannot clearly show the specific distribution of the electrical performance for the structural optimization design of the mesh antenna, and the same numerical error may lead to different electrical performance results in the traditional method. The error is reasonably distributed according to the characteristics of electromagnetics of the mesh antenna, the precision of the central region which has a great influence on the overall electrical performance of the antenna is higher, and the precision of the peripheral region which has a small influence can be appropriately reduced, so that the same error can achieve better electrical performance effect compared with the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 The flowchart of the electrical performance weighted optimization shape finding method of the mesh antenna provided by the embodiment of the present application. DETAILED DESCRIPTION

[0069] The present application will be further described in detail below with reference to the accompanying drawings.

[0070] Please refer to Figure 1 , Figure 1 The flowchart of the electrical performance weighted optimization shape finding method of the mesh antenna provided by the embodiment of the present application, which includes:

[0071] Step 1, input initial structural parameters and electrical parameters of the antenna

[0072] Input the mesh structure parameters, electrical parameters, upper and lower limits of cable tension, initial force density, optimization iteration convergence conditions, etc.

[0073] Step 2, solve the mechanical model according to the input force density, and solve the stress and deformation state of each cable segment of the antenna under the current force density design variable.

[0074] Solve the mechanical model, obtain the corresponding cable net node coordinates, and relate the node deformation coordinates of the jth iteration and the (j-1)th iteration to obtain the relationship between the node deformation column vector, the cable net tension vector column vector and the force density increment.

[0075] Step 3, generate a weighted function to divide the contributions of different regions of the antenna profile to the overall electrical performance with corresponding weights.

[0076] According to the aperture field distribution function of the mesh antenna, the weighted function is generated according to the following formula:

[0077]

[0078] Where Q(x P ,y P ) is the aperture field distribution function, x P ,y P represent the coordinate vectors of the points on the aperture surface, d is the projection aperture of the offset reflector, h is the offset height of the offset reflector, represents the distance from the center point of the projection aperture surface to the coordinate origin, B is the aperture field amplitude control parameter, B = 10ET / 20, ET is the edge taper, and represents the amplitude ratio from the center of the projection aperture surface to the edge of the aperture.

[0079] The weighted root mean square value is as follows:

[0080]

[0081] Where Q represents the aperture field function, ε i represents the node deformation column vector, and n represents the number of nodes.

[0082] Step 4, perform sensitivity analysis to obtain the sensitivity matrix of the corresponding weight function, and relate the cable net force density increment to the reflector node deformation.

[0083] The weighted sensitivity is calculated according to the following formula:

[0084]

[0085] Where K r (j)sensitivity matrix of node deformation with respect to three direction node coordinates, I represents unit matrix with diagonal elements of 1, f represents focal length of mesh antenna, diag(x (j) ) represents diagonal matrix with x (j) as diagonal elements, x (j) , y (j)) represent coordinate components of x-axis and y-axis.

[0086]

[0087] wherein H, G represent second order Hessian matrix and first order sensitivity column vector of objective function with respect to force density respectively, K q (j) represents Jacobi matrix of node position vector of reflecting surface with respect to force density vector of cable net obtained through sensitivity analysis in jth iteration, K r (j) represents sensitivity matrix of node deformation with respect to three direction node coordinates, ε represents column vector of node deformation on reflecting surface, diag(Q) represents diagonal matrix with Q as diagonal elements.

[0088] Step 5, according to sensitivity matrix and aperture field amplitude distribution function, a quadratic programming model is established to find optimal force density increment meeting constraint condition.

[0089] findΔq (j)

[0090]

[0091] Step 6, one-dimensional line search is used to find step length of next iteration.

[0092] findμ (j)

[0093] min obj (j)

[0094]

[0095] One-dimensional line search is carried out by using dichotomy method, according to F , as lower limit and upper limit value of cable tension, the step length of next iteration is determined.

[0096] Step 7, mechanical model is updated, and value of force density increment is iteratively updated, if current force density cannot meet convergence requirement, one-dimensional search is carried out for iteration.

[0097] According to optimal solution obtained by solving, the model can be updated in j-1th model, and the model is iteratively updated until convergence.

[0098] q(j) = q (j-1) + μ (j) Δq (j)*

[0099] wherein q represents a column vector of cable segment force density composition, Δq (j)* represents an optimal solution obtained by using a quadratic programming algorithm, μ (j) is the jth iteration step.

[0100] Step 8, judge whether the convergence condition is met.

[0101] Judge whether the convergence condition is met, if met, go to step 9, otherwise go to step 4;

[0102] Step 9, output the force density design variable.

[0103] When the updated force density design variable meets the requirement, output the force density design variable.

[0104] The present application introduces the electrical performance into the structure root mean square value calculation in the form of a weighted function, and proposes a mesh antenna cable net structure form design method of electrical performance weighted root mean square value with the weighted root mean square value as the target. The method considers the electrical performance through the weighted function, and realizes high iteration efficiency through the structure root mean square value.

[0105] The advantages of the present application can be further illustrated by the following simulation experiment:

[0106] Simulation conditions:

[0107] The antenna aperture is d=9.23m, the focal length is f=6m, the offset height is h=5m, the feed inclination angle is ψ0=41.64°, the working frequency is 2GHz. The cable net elastic modulus is 20Gpa, the density is 1685kg / m 3 , and the Poisson's ratio is 0.3. The truss elastic modulus is 150Gpa, the density is 1600kg / m 3 , and the Poisson's ratio is 0.3.

[0108] Simulation results:

[0109] The mesh antenna electrical performance weighted form-finding optimization method of the present application is adopted. The results are shown in Table 1. As can be seen from Table 1, the optimization results of the electrical performance weighted method and the mechatronic integrated optimization method are similar, and the difference in electrical performance gain loss is not large, and the optimal gain difference of the two methods is only 0.2dB, but the iteration number of the electrical performance weighted method is significantly reduced, the iteration optimization time is reduced by 69.6%, and the memory occupation is reduced by 51.7%. Compared with the single-discipline optimization, the electrical performance weighted method has little difference in iteration time, memory and iteration number, and the gain loss of the electrical performance weighted method is less.

[0110] Table 1

[0111]

[0112] The parts not described in detail in the present embodiment belong to the commonly used means known in the art, which are not described here. The above examples are only illustrative of the present application and do not constitute a limitation on the protection scope of the present application. Any design identical to or similar to the present application falls within the protection scope of the present application.

[0113] The above examples are only illustrative of the present application and do not constitute a limitation on the protection scope of the present application. Any design identical to or similar to the present application falls within the protection scope of the present application.

Claims

1. A method for form-finding optimization of a mesh antenna electrical performance weighting, characterized in that, The method comprises the following steps; Step (1): inputting initial structure parameters, electrical parameters, upper and lower limits of cable net tension, initial force density and optimization iteration convergence conditions of the mesh antenna into an optimization model; Step (2): solving a mechanical model according to the initial force density to obtain corresponding cable net node coordinates; Step (3): generating a weighting function according to an aperture field distribution function of the mesh antenna, and obtaining a root mean square value after weighting; Step (4): updating a second-order Hessian matrix and a first-order sensitivity vector through sensitivity analysis to generate a sensitivity matrix and a vector; Step (5): establishing a quadratic programming model through a coefficient matrix formed by the sensitivity matrix and the vector, and solving the model to find an optimal force density increment meeting the constraint conditions; Step (6): when the quadratic programming solving precision does not meet the requirement, performing one-dimensional line search to find a step length for next iteration; Step (7): updating the mechanical model according to the optimal solution obtained in the one-dimensional line search to obtain an iteration value in the next step; Step (8): judging whether the root mean square value obtained in step (3) meets the convergence condition; Step (9): outputting the force density design variable; The step (3) is specifically as follows: a weighting function is generated according to an aperture field distribution function of the mesh reflector antenna: Where Q(x) P ,y P ) is the aperture field distribution function, x P ,y P Let represent the coordinate vectors of a point on the aperture surface, d be the projected aperture of the offset reflector, h be the offset height of the offset reflector, h represent the distance from the center point of the projected aperture surface to the origin, and B be the aperture field amplitude control parameter, B = 10. ET / 20 ET is the edge taper, representing the amplitude ratio from the center of the projected aperture plane to the edge of the aperture. a weighted root mean square value is as follows: where Qi represents the value of the aperture field amplitude distribution function corresponding to node i, ε i represents the node deformation column vector, and n represents the number of nodes.

2. The method of claim 1, wherein, The step (1) is specifically as follows: structure parameters of the mesh antenna include an antenna aperture, a focal length and a bias height, electrical parameters include a working frequency, and upper and lower limits of cable net tension, an initial force density and optimization iteration convergence conditions.

3. The method of claim 1, wherein the method further comprises: The step (2) is specifically as follows: the following mechanical model is solved: find q = [q1, q2,..., q m ] T where q represents the force density vector, q m represents the mth component of the force density vector, ε′ rms represents the weighted root mean square, ε represents the column vector of nodal deformation on the reflecting surface, Q = [Q1, Q2,..., Q n ] T represents the column vector of weight functions consisting of all nodal far-field amplitude distribution functions, diag(Q) represents the diagonal matrix with Q as the diagonal elements, n represents the number of nodes, F represents the cable force, F , the upper and lower limits of the cable force; a set of force density values are obtained by solving the mechanical model, corresponding cable net node coordinates are obtained from the relationship between node deformation and force density increment and force density, the relationship between the node deformation column vector, the cable net tension vector column vector and the force density increment is obtained by connecting node coordinates in the jth iteration and the (j-1)th iteration; F (j) = diag(L (j) )q (j) where Δr (j) is the nodal deformation column vector, is the cable net force density column vector, Δq (j) is the force density increment, F (j) is the jth iteration cable net tension vector, L (j) is the jth iteration cable segment length vector, diag(L (j) ) is the matrix with L (j) as the main diagonal elements.

4. The method of claim 3, wherein the method further comprises: The step (4) is specifically as follows: the weighted sensitivity is calculated according to the following formula: wherein K r (j) denotes the sensitivity matrix of the node deformation with respect to the three-direction node coordinates, I denotes a unit matrix with diagonal elements being 1, f denotes the focal length of the mesh antenna, diag(x (j) ) denotes a diagonal matrix with x (j) as diagonal elements, x (j) , y (j)) denote the coordinate components of the x-axis and y-axis; where H, G represent the second order Hessian matrix and the first order sensitivity column vector of the objective function with respect to the force density, K q (j) denotes the Jacobian matrix of the position vector of the reflective surface nodes with respect to the force density vector of the cable net at the jth iteration, K r (j) denotes the sensitivity matrix of the node deformation with respect to the three direction node coordinates, ε denotes the column vector of the node deformation on the reflective surface, and diag(Q) denotes the diagonal matrix with Q as the diagonal elements.

5. The method of claim 4, wherein, The step (5) is specifically as follows: a quadratic programming model is established according to the obtained sensitivity matrix H and G; find delta q (j) wherein Δq is the force density increment, and obj represents an optimization objective function.

6. The method of claim 3, wherein the method further comprises: The step (6) is specifically as follows: findμ (j) min obj (j) where μ is the search interval (0, 1), F , are the lower and upper limits of the cable force, and a one-dimensional line search is performed using the bisection method to determine the step size for the next iteration based on the lower and upper limits of the cable force constraint.

7. The method of claim 6, wherein the method further comprises: The step (7) is specifically as follows: the optimal solution obtained in the one-dimensional line search can be superimposed into the (j-1)th model to update the model, and the iteration is gradually performed until convergence; q (j) = q (j-1) + μ (j) Δq (j)* where q represents a column vector of cable segment force density components, Δq (j)* represents the optimal solution obtained using a quadratic programming algorithm, μ (j) is the jth iteration step size.

8. The method of claim 7, wherein, The step (8) is specifically as follows: whether the root mean square value obtained in step (3) meets the convergence condition is judged, if the requirement is met, the step (9) is performed, otherwise, a new force density variable after the one-dimensional search is used as an input variable, and the step (4) is performed; Convergence condition: Weighted RMS value less than 10 -5 mm.

9. The method of claim 1, wherein, The step (9) is specifically as follows: when the updated force density design variable meets the requirement, the force density design variable is output.

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