Adjustment Method for Active Reflector Panels of Large Radio Telescopes Based on Search Algorithms

Abstract

The present invention relates to a method for adjusting the shape of the active reflecting panel of a large radio telescope based on a search algorithm. When in the reference state, the active reflecting surface is a reference spherical surface, and the main cable nodes are adjusted radially to form a working parabolic surface in the working state. The working parabolic surface is made to approach the ideal parabolic surface as much as possible through the following steps: Step 1, establish a single-objective optimization model, with the main cable nodes falling on the ideal parabolic surface as a constraint, so that during the adjustment process, for all combinations of vertex and focus changes, find the maximum change amplitude of the distance between adjacent two main cable nodes in each combination case, and take the minimum of all the maximum change amplitudes as the optimization objective; Step 2, use a traversal search algorithm based on a variable step size strategy to solve the single-objective optimization model. The optimization idea of the present invention is unique, achieving a good optimization effect on the premise of reducing the algorithm complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of large radio telescopes, and particularly relates to a method for adjusting the active reflector panel of a large radio telescope based on a search algorithm. Background Art

[0002] The working principle of a large radio telescope is to reflect the signals emitted by celestial bodies to the feed cabin through the reflector panel, so as to observe the celestial body to be measured. Adjusting the reflecting surface to the working paraboloid is the key to the entire active reflection technology. In actual engineering, the working paraboloid is adjusted as close as possible to the ideal paraboloid in order to obtain the best reception effect. In the prior art, the algorithm complexity is high during the optimization process of adjusting the working paraboloid to the ideal paraboloid, and the optimization effect is not ideal. Summary of the Invention

[0003] In order to overcome the above-mentioned disadvantages of the prior art, the purpose of the present invention is to provide a method for adjusting the active reflector panel of a large radio telescope based on a search algorithm. Under various constraints of the reflector panel adjustment, an ideal paraboloid is determined, and then by adjusting the radial expansion and contraction amount of the actuator, the reflecting surface is adjusted to the working paraboloid, so that the working paraboloid is as close as possible to the ideal paraboloid. This method has the characteristics of low algorithm complexity, simple objective function and constraint conditions.

[0004] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0005] A method for adjusting the active reflector panel of a large radio telescope based on a search algorithm, wherein the active reflecting surface is a reference spherical surface in the reference state, and the main cable nodes are radially adjusted to form a working paraboloid in the working state. The following steps are used to make the working paraboloid as close as possible to the ideal paraboloid:

[0006] Step 1, taking min(maxλ η ) γ as the objective function, and establishing a single-objective optimization model with the following conditions as the constraint conditions:

[0007] min(maxλ η ) γ

[0008]

[0009] The objective function means that during the adjustment process, under all combinations of vertices and foci, the maximum change amplitude dete of the distance between adjacent two main cable nodes in each combination case is calculated, and the minimum value is taken among all the maximum change amplitudes dete;

[0010] The parameter definitions are as follows:

[0011] η: The number of times to traverse all corresponding working paraboloids with the maximum variation amplitude dete of the distance between adjacent main cable nodes as the target in all vertex and focus combinations;

[0012] γ: The number of times to traverse the obtained maximum variation amplitude dete;

[0013] Δr i : The distance from the main cable node on the reference sphere to the working paraboloid adjusted radially;

[0014] r 1i : In the spherical coordinate system, the polar radius of the main cable node on the reference sphere;

[0015] (x 1i ,y 1i ,z 1i ): In the rectangular coordinate system, the coordinates of the main cable node on the reference sphere;

[0016] r 2i : In the spherical coordinate system, the polar radius of the main cable node on the working paraboloid after the vertex changes;

[0017] (x 2i ,y 2i ,z 2i ): In the rectangular coordinate system, the coordinates of the main cable node on the working paraboloid after the vertex changes;

[0018] Q: The limit of the radial expansion and contraction of the main cable node;

[0019] Ψ: The maximum angle between the reflected light and the vertical direction under the variable limit position of the focus;

[0020] δ: The adjustable range of the focus;

[0021] r: In the spherical coordinate system, the polar radius of the main cable node on the working paraboloid before the vertex changes;

[0022] F 0 : The focal length of the working paraboloid before the vertex changes;

[0023] R: The radius of the reference sphere;

[0024] θ: The zenith angle between the line connecting the main cable node and the origin and the positive z-axis direction on the working paraboloid before the vertex changes;

[0025] F: The focal length of the working paraboloid after the vertex changes;

[0026] θ i : The zenith angle between the line connecting the main cable node and the origin and the positive z-axis direction on the working paraboloid after the vertex changes

[0027] ξ: The distance that the vertex of the working paraboloid moves radially;

[0028] θ 1i : The angle between the main cable node on the spherical surface and the positive z-axis direction;

[0029] The angle between the projection of the polar radius of the main cable node on the spherical surface on the xoy plane and the positive x direction;

[0030] |G i G i+1 |: The distance between adjacent main cable nodes before adjusting the main cable nodes;

[0031] |G′ i G′ i+1 |: The distance between adjacent main cable nodes after adjusting the main cable nodes;

[0032] λ i : The change range of the distance between adjacent main cable nodes before and after radially adjusting the main cable nodes;

[0033] Step 2, use a traversal search algorithm based on a variable step size strategy to solve the single-objective optimization model, and the steps are as follows:

[0034] Step1: Use the search algorithm to traverse and solve

[0035] Set R, set the z coordinate change amount ddF of the focus and the z coordinate change amount dF of the vertex of the working paraboloid, traverse and optimize ddF and dF, and set the distance f from the vertex of the working paraboloid to the focus as f = 0.466×R + ddF + dF;

[0036] Step2: Find the points within the set aperture range

[0037] Judge whether the main cable node is within the set aperture range, and convert the main cable node within the set aperture range from the three-dimensional coordinate system x, y, z to the spherical coordinate system r, θ, Calculate the polar radius of the point corresponding to the main cable node on the working paraboloid, which is And calculate the radial adjustment amount and the adjusted three-dimensional coordinates of the main cable node therefrom. The maximum radial adjustment amount of the main cable node is W, a = (sin(θ)) 2 , b = -4×f×cos(θ), c = -4×f×(R + dF);

[0038] Step3: Calculate the change range of the distance between adjacent main cable nodes before and after adjustment

[0039] Determine whether each main cable node corresponding to the reflection panel is within the set aperture range. If it is, return the digital form of the main cable node number at this time; if it is not within the range, return 0 and record it in matrix A. Matrix A is a multi-row and three-column matrix, and the three elements of each row represent the situation of the main cable nodes corresponding to the three vertices of a triangular reflection panel within the set aperture range, which is obtained by subtracting the adjusted polar radius from the polar radius of the main cable node before adjustment. If the element is greater than 0, it means that the main cable node corresponding to this vertex is within the set aperture range; if the three elements of each row in matrix A are all greater than zero, it means that the triangle corresponding to these three elements is entirely within the set aperture range. Calculate the change amplitude between adjacent main cable nodes after the main cable node changes from the basic position to the ideal position, and the maximum change amplitude is dete.

[0040] Step4: Use the change amplitude and the maximum radial adjustment amount as constraint conditions

[0041] Optimize the maximum change amplitude dete. When the maximum change amplitude dete satisfies being less than the set value m, determine whether the maximum radial adjustment amount W satisfies being less than the set value n, and record the vertex position, focus position of the working paraboloid that meet the conditions, the maximum radial adjustment amount W of the main cable node, and the maximum change amplitude dete.

[0042] Step5: Return to step1 for variable-step traversal optimization

[0043] Adjust the step size, substitute the vertex position and focus position of the working paraboloid that meet the conditions obtained in Step4 into step1, and set a small step size (the smaller the step size, the higher the accuracy) to obtain a more accurate maximum radial adjustment amount W and maximum change amplitude dete of the main cable node.

[0044] In the embodiment, the judgment method of Step2:

[0045] Project the main cable node onto the xoy plane, and judge the distance from the main cable node to the origin o on the xoy plane. If it is less than 1 / 2 of the set aperture, then this main cable node is within the set aperture range, and store these points in matrix B for subsequent calls. Each element in matrix B represents the digital number of the point within the set aperture range.

[0046] In the embodiment, the calculation method of the radial adjustment amount of the main cable node in Step2:

[0047] r 1i Obtained from the provided three-dimensional coordinates; after the vertex and focus of the working paraboloid are determined, the equation of the working paraboloid is expressed in spherical coordinate form, and then r is obtained by a quadratic equation of one variable 2i , the difference Δr between the polar radii of the main cable node before and after adjustment i is the radial adjustment amount of the main cable node, and the adjusted three-dimensional coordinates are obtained by the formula Calculated

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] When constructing the reflection panel adjustment model of the present invention, it innovatively takes the main cable nodes falling on the ideal paraboloid as a constraint, and takes the minimum maximum deformation of the main cable as the optimization goal. Under the premise of reducing the algorithm complexity, good optimization effects are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic structural diagram of a large radio telescope.

[0051] Figure 2 It is a schematic local structure diagram (axonometric drawing) of a large radio telescope.

[0052] Figure 3 It is a schematic local structure diagram (front view) of a large radio telescope.

[0053] Figure 4 It is a schematic local structure diagram (top view) of a large radio telescope.

[0054] Figure 5 It is a schematic sectional view of a large radio telescope during observation.

[0055] Figure 6 It is the spherical coordinate system established by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The following describes the embodiments of the present invention in detail with reference to the drawings and embodiments.

[0057] Referring to Figure 1 、 Figure 2 、 Figure 3 and Figure 4 , the large radio telescope is composed of an active reflector system, a signal receiving system (feed cabin), and related control, measurement, and support systems. Among them, the active reflector system is an adjustable spherical surface composed of main cable nets 1, reflection panels 2, lower cables 3, actuators 4, and peripheral support structures 5 and other main components. The main cable net 1 is composed of flexible main cables 6 in the form of a geodesic triangle grid, and is used to support the reflection panel 2 and its back frame structure 7. One reflection panel 2 and its back frame structure 7 are installed on each triangular grid, and the entire cable net is fixed on the peripheral support structure 5. The connection points of the main cables 6 are the main cable nodes 8, and each main cable node 8 is connected to a lower cable 3. The lower end of the lower cable 3 is connected to the actuator 4 fixed on the ground to realize the shape control of the main cable net 1. There are certain gaps between adjacent reflection panels 2, which can ensure that the reflection panels 2 will not be deformed by extrusion or pulling during displacement.

[0058] Referring to Figure 5, the active reflector can be divided into two states: the reference state and the working state. In the reference state, the reflector is a spherical surface with a radius of R, i.e., the reference spherical surface; in the working state, the shape of the reflector is adjusted to an approximately rotating paraboloid with an aperture of D, i.e., the working paraboloid. The center of the reference spherical surface is C, and the center of the receiving plane of the feed cabin can only move on a spherical surface (i.e., the focal plane) concentric with the reference spherical surface. The radius difference between the two concentric spherical surfaces is F = 0.466R (where R is the radius of the reference spherical surface, and F / R is called the focal ratio). The effective area for the feed cabin to receive signals is a central disk. When the large radio telescope observes a celestial target S in a certain direction, the center of the receiving plane of the feed cabin is moved to the intersection point P of the straight line SC and the focal plane, and a part of the reflecting panels 2 on the reference spherical surface is adjusted to form an approximately rotating paraboloid with the straight line SC as the axis of symmetry and P as the focus, so as to reflect and converge the parallel electromagnetic waves from the celestial target S to the effective area of the feed cabin.

[0059] Adjusting the reflector to the working paraboloid is the key to the active reflector technology, and this process is completed by the cooperation of the lower cables 3 and the actuators 4. The length of the lower cable 3 is fixed. The actuators 4 are installed radially along the reference spherical surface, with their bottom ends fixed on the ground and their top ends capable of radially expanding and contracting along the reference spherical surface to complete the adjustment of the lower cable 3, thereby adjusting the position of the reflecting panel 2 and finally forming the working paraboloid.

[0060] Under the adjustment constraint of the reflecting panel 2, an ideal paraboloid is determined, and then by adjusting the radial expansion and contraction amount of the actuator 4, the reflector is adjusted to the working paraboloid. The optimization goal of the present invention is to make the working paraboloid as close as possible to the ideal paraboloid to obtain the best reception effect after the celestial electromagnetic waves are reflected by the reflector.

[0061] For this reason, the method adopted by the present invention is as follows:

[0062] Step 1, initialization of the mathematical model for optimizing the adjustment of the ideal paraboloid

[0063] The optimization goal of the present invention is transformed into that the main cable nodes of the active reflector in the working state are on the ideal paraboloid obtained by solving. That is, by taking the main cable nodes falling on the ideal paraboloid as a constraint, and taking the minimum value of the maximum change amplitude dete between adjacent two main cable nodes as the optimization goal, a single-objective optimization model is established. Taking the center of the reference spherical surface as the origin, a spherical coordinate system is established. Refer to Figure 6 , r represents the polar radius of the main cable node on the working paraboloid before the vertex changes, represents the angle rotated counterclockwise from the positive direction of the x-axis to the direction. Let the point p(x 1i , y 1i , z 1i ) be located on the reference spherical surface, then there is:

[0064]

[0065] In the formula, r 1i represents the polar radius of the main cable node on the reference sphere, and (x 1i , y 1i , z 1i ) represents the coordinates of the main cable node on the reference sphere in the rectangular coordinate system; i = 1, 2... N, and N represents the number of main cable nodes included on the reference sphere. To represent a definite point in the spherical coordinate system, two more angles are needed.

[0066]

[0067] In the formula, θ 1i represents the angle between the main cable node on the sphere and the positive direction of the z-axis, that is, the angle between the direction in the figure and the positive direction of the z-axis.

[0068]

[0069] In the formula, represents the angle between the projection of the polar radius of the main cable node on the sphere on the xoy plane and the positive direction of the x-axis, that is, the angle between the direction in the figure and the positive direction of the x-axis.

[0070] In summary, the position of the main cable node on the reference sphere is represented in spherical coordinates as

[0071] Furthermore, considering the special case where the celestial target S is located directly above the reference sphere, such that the intersection point K of the straight line connecting the celestial target S and the feed cabin and the reference sphere is the vertex of the working paraboloid, the equation of the working paraboloid in this state (based on the three-dimensional Cartesian coordinate system) is:

[0072] x 2 + y 2 = 4F 0 (z + R) 4)

[0073] In the formula, F 0 represents the focal length of the working paraboloid before the vertex changes, that is, the focal length of the ideal paraboloid. By way of example, F 0 = 0.466R, where R represents the radius of the reference sphere. Transforming Equation 4) into the spherical coordinate system gives:

[0074] r 2 sin 2 θ - 4F 0 r cosθ - 4F 0 R = 0 5)

[0075] From Equation 5), it can be deduced that:

[0076]

[0077] The above formula can be derived from the quadratic formula for a quadratic equation of one variable.

[0078] Consider the radial displacement of the main cable node:

[0079] Since the adjustment factor of the reflecting panel needs to be considered, that is, the pulling of the lower cable will cause the displacement change of the main cable node, which will in turn affect the adjustment of the reflecting panel. Assume that the vertex K of the ideal parabola moves down by ξ meters, and the equation of the parabolic surface after movement is

[0080] x 2 +y 2 =4F(z + R + ξ) 7)

[0081] In the formula, F is the focal length of the working parabolic surface after the vertex changes, F = F 0 + ξ, and ξ is the distance that the vertex of the working parabolic surface moves along the radial direction. Then, for any main cable node corresponding to the working parabolic surface after the vertex changes, the polar radius

[0082]

[0083] Then, the distance from the main cable node on the reference sphere to the working parabolic surface adjusted along the radial direction is

[0084] Δr i =|r 1i -r 2i | 9)

[0085] Consider the slight change in the distance between adjacent nodes:

[0086] After the reference sphere is adjusted by the lower cable, the working parabolic surface is obtained. The purpose of the present invention is to make the working parabolic surface as close as possible to the ideal parabolic surface, so that the main cable node is located on the ideal parabolic surface, that is, the corresponding main cable node on the working parabolic surface is also on the obtained ideal parabolic surface, and the polar radius is r 2i . Since the actuator drives the main cable node to adjust in the radial direction, the angle θ i 、 of the corresponding main cable node on the working parabolic surface remains unchanged. Let the spatial coordinates of the main cable node corresponding to the working parabolic surface be G i ′(x 2i , y 2i , z 2i ), where

[0087]

[0088] (x 2i , y 2i , Z 2i) represents the coordinates of the main cable nodes on the working parabolic surface after the vertex changes in the rectangular coordinate system.

[0089] Furthermore, the coordinates of the main cable nodes on the reference spherical surface are G i (x 1i , y 1i , z 1i ). Then the distance between adjacent main cable nodes before adjustment of the main cable nodes is

[0090]

[0091] The distance between adjacent main cable nodes after adjustment of the main cable nodes is

[0092]

[0093] In summary, the change range of the distance between adjacent nodes before and after adjustment of the main cable nodes is

[0094]

[0095] Step 2, establish a single-objective optimization model

[0096] Based on placing the main cable nodes on the desired ideal parabolic surface, the obtained ideal parabola is difficult to meet the limit conditions of the change range of the distance between the main cable nodes. Therefore, the optimal solution is taken to make the change range of the main cable nodes as small as possible, and the following single-objective optimization model based on the variable step size search algorithm is established.

[0097] Objective function: During the adjustment process, in all combinations of vertices and foci, find the maximum change range dete of the distance between adjacent two main cable nodes in each combination case, and take the minimum value among all the maximum change ranges dete, expressed as min(maxλ η ) γ , where ηγ represents the ordinal number of traversing the ideal parabolic surface in the model. Specifically, η represents the number of times of traversing all the corresponding working parabolic surfaces with the maximum change range dete of the distance between adjacent two main cable nodes as the objective in all combinations of vertices and foci; γ represents the number of times of traversing the obtained maximum change range dete.

[0098] Constraint conditions:

[0099] a) The radial expansion and contraction amount of the main cable nodes is between -0.6 m and +0.6 m, that is

[0100] Δr i =|r 1i -r 2i |≤0.6 14)

[0101] b) The change value of the focus of the ideal parabolic surface in the model conforms to the derived range

[0102]

[0103] c) In the reference state, all main cable nodes are located on the reference spherical surface

[0104]

[0105] d) The polar radius of any point on the working paraboloid with the vertex at point K

[0106]

[0107] e) Other geometric relationships

[0108] In summary, a single-objective optimization model is established.

[0109] min(maxλ η ) γ

[0110]

[0111] Where Q represents the limit of the radial expansion and contraction of the main cable nodes, which is taken as 0.6 m in this embodiment; Ψ represents the maximum angle between the reflected light and the vertical direction under the variable limit position of the focus; δ represents the adjustable range of the focus; θ represents the zenith angle between the connection line between the main cable node and the origin and the positive z-axis direction on the working paraboloid before the vertex changes; θ i represents the zenith angle between the connection line between the main cable node and the origin and the positive z-axis direction on the working paraboloid after the vertex changes; λ i represents the change amplitude of the distance between adjacent main cable nodes before and after radially adjusting the main cable nodes.

[0112] Step 3: Design a traversal search algorithm based on a variable step size strategy for solution, and the steps are as follows:

[0113] Step1: Data preprocessing

[0114] Convert the numbers of the main cable nodes, mainly converting non-numeric numbers into numeric numbers. For example, the numbers A, B, C, D, E can be converted into 1, 2, 3, 4, 5 respectively. Another example is that the number "A0" can be converted into "10".

[0115] Step2: Use the search algorithm to traverse and solve

[0116] Set R. For example, R = 300.4 m can be taken, and set the change amount ddF of the z coordinate of the focus and the change amount df of the z coordinate of the vertex of the working paraboloid. dF = -0.6:0.01:0.6. Traverse and optimize ddF and dF. Set the distance f from the vertex of the working paraboloid to the focus as f = 0.466×R + ddF + dF.

[0117] Step3: Find points within the set aperture range

[0118] Determine whether the main cable nodes are within the set aperture range. The main cable nodes within the set aperture range are transformed from the three-dimensional coordinate system x, y, z to the spherical coordinate system r, θ, Calculate the polar radius of the point corresponding to the main cable node on the ideal paraboloid, which is And thereby calculate the radial adjustment amount of the main cable node and the adjusted three-dimensional coordinates. The maximum radial adjustment amount of the main cable node is W. a = (sin(θ)) 2 , b = -4×f×cos(θ), c = -4×f×(R + dF).

[0119] Exemplarily, in this step, the judgment method is as follows:

[0120] Project the main cable node onto the xoy plane, and judge the distance from the main cable node to the origin o on the xoy plane. If it is less than 1 / 2 of the set aperture, then this main cable node is within the set aperture range, and these points are stored in matrix B for subsequent call. Each element in matrix B represents the digital number of the point within the set aperture range.

[0121] Exemplarily, in this step, the calculation method of the radial adjustment amount of the main cable node is as follows:

[0122] r 1i Obtained from the provided three-dimensional coordinates; after the vertex and focus of the working paraboloid are determined, the equation of the working paraboloid is expressed in spherical coordinate form, and then r is obtained from the quadratic equation of one variable 2i , the difference Δr in the polar radius of the main cable node before and after adjustment i Namely, it is the radial adjustment amount of the main cable node, and the adjusted three-dimensional coordinates are calculated by the formula Calculated.

[0123] Step4: Calculate the change amplitude of the distance between adjacent main cable nodes before and after adjustment

[0124] Determine whether each main cable node corresponding to the reflection panel is within the aperture range. If it is, return the digital form number of the main cable node being judged at this time; if it is not within the range, return 0 and record it in matrix A. Matrix A is a matrix with multiple rows and three columns. The three elements in each row represent the situation of the main cable nodes corresponding to the three vertices of a triangular reflection panel within the set aperture range, which is obtained by subtracting the adjusted polar radius from the polar radius of the main cable node before adjustment. If the element is greater than 0, it means that the main cable node corresponding to this vertex is within the set aperture range. If all three elements in each row of matrix A are greater than zero, it means that the triangle corresponding to these three elements is entirely within the set aperture range. Calculate the change amplitude between adjacent main cable nodes after the main cable nodes change from the base position to the ideal position, and the maximum change amplitude is dete.

[0125] Step5: Use the change amplitude and the maximum radial adjustment amount as constraints

[0126] Optimize the maximum change amplitude dete. When the maximum change amplitude dete satisfies being less than the set value m, judge whether the maximum radial adjustment amount W satisfies being less than the set value n, and record the vertex position, focus position, maximum radial adjustment amount W of the main cable node, and the maximum change amplitude dete of the working paraboloid that meet the conditions. For example, m is taken as 0.07% and n is taken as 0.6. For example, the maximum value of all calculated radial adjustment amounts of the main cable nodes can be compared using the max function in matlab.

[0127] Step6: Return to step2 for variable-step traversal optimization

[0128] Adjust the step size, substitute the vertex position and focus position of the working paraboloid that meet the conditions obtained in Step5 into step2, and set a small step size to obtain a more accurate maximum radial adjustment amount W and maximum change amplitude dete of the main cable node.

[0129] When constructing the reflection panel adjustment model of the present invention, taking the main cable node falling on the ideal paraboloid as a constraint, through the traversal search of all combination situations of the vertex and the focus, within the variable range of the vertex and the focus, a combination situation of the vertex and the focus is searched, so that the maximum change amplitude between adjacent main cable nodes on the corresponding working paraboloid is the smallest, that is, the working paraboloid is the optimized ideal paraboloid. The optimized paraboloid has the advantages of high reception ratio of celestial signals and low algorithm complexity.

Claims

1. An active reflector panel adjustment method for a large radio telescope based on a search algorithm. When in the reference state, the active reflector surface is a reference spherical surface. The main cable nodes are adjusted radially to form a working parabolic surface in the working state. The following steps are used to make the working parabolic surface as close as possible to the ideal parabolic surface: Step 1, taking min(maxλ η ) γ as the objective function and the following conditions as the constraint conditions to establish a single-objective optimization model: min(maxλ η ) γ The objective function means that during the adjustment process, for all combinations of vertices and foci, the maximum change amplitude dete of the distance between adjacent main cable nodes in each combination case is calculated, and the minimum value is taken among all the maximum change amplitudes dete. The parameter definitions are as follows: η: The number of times of traversing all the corresponding working parabolic surfaces with the maximum change amplitude dete of the distance between adjacent main cable nodes as the objective for all combinations of vertices and foci. γ: The number of times of traversing the obtained maximum change amplitude dete. Δr i : The distance that the main cable node on the reference sphere is adjusted radially to the working paraboloid; r 1i : Polar radius of the main cable node on the reference spherical surface in the spherical coordinate system; (x 1i , y 1i , z 1i ): Coordinates of the main cable node on the reference sphere in the rectangular coordinate system; r 2i : Polar radius of the main cable node on the working paraboloid after the vertex changes in the spherical coordinate system; (x 2i , y 2i , z 2i ): In the rectangular coordinate system, the coordinates of the main cable nodes on the working parabolic surface after the vertex changes; Q: The limit of the radial expansion and contraction amount of the main cable nodes. Ψ: The maximum angle between the reflected light ray and the vertical direction under the variable limit position of the focus. δ: The adjustable range of the focus. r: In the spherical coordinate system, the polar radius of the main cable node on the working parabolic surface before the vertex changes. F 0 : The focal length of the working paraboloid before the vertex movement; R: The radius of the reference spherical surface. θ: The zenith angle between the line connecting the main cable node and the origin and the positive z-axis on the working parabolic surface before the vertex changes. F: The focal length of the working parabolic surface after the vertex changes. θ i : The zenith angle between the line connecting the main cable node and the origin and the positive z-axis direction on the working parabolic surface after the vertex movement ξ: The distance that the vertex of the working parabolic surface moves radially. θ 1i : The included angle between the main cable node on the spherical surface and the positive direction of the z-axis; The included angle between the projection of the polar radius of the main cable node on the spherical surface in the xoy plane and the positive x direction; |G i G i+1 |:Adjust the distance between adjacent main cable nodes before the main cable node with radial adjustment; |G′ i G′ i+1 |: the distance between adjacent main cable nodes after radially adjusting the main cable nodes λ i : The variation range of the distance between adjacent main cable nodes before and after radially adjusting the main cable nodes; Step 2: Solve the single-objective optimization model using a search algorithm based on a variable step size strategy. The steps are as follows: Step1: Use the search algorithm to traverse and solve. Set R, set the z-coordinate change amount ddF of the focus and the z-coordinate change amount dF of the vertex of the working parabolic surface, traverse and optimize ddF and dF, and set the distance f from the vertex of the working parabolic surface to the focus as f = 0.466×R + ddF + dF. Step2: Find points within the set aperture range. Determine whether the main cable node is within the set caliber range, and convert the main cable nodes within the set caliber range from the three-dimensional coordinate system x, y, z to the spherical coordinate system r, θ Calculate the polar radius of the point corresponding to the main cable node on the working paraboloid, which is And calculate the radial adjustment amount and the adjusted three-dimensional coordinates of the main cable node therefrom. The maximum radial adjustment amount of the main cable node is W, a = (sin(θ)) 2 , b = -4 × f × cos(θ), c = -4 × f × (R + dF); Step3: Calculate the change amplitude of the distance between adjacent main cable nodes before and after adjustment. Judge whether each main cable node corresponding to the reflector panel is within the set aperture range. If it is, return the digital form of the main cable node number at this time; if it is not within the range, return 0 and record it in matrix A. Matrix A is a multi-row and three-column matrix. The three elements in each row represent the situation of the main cable nodes corresponding to the three vertices of a triangular reflector panel within the set aperture range, which is obtained by subtracting the adjusted polar radius of the main cable node from the unadjusted one. If the element is greater than 0, it means that the main cable node corresponding to this vertex is within the set aperture range; if all three elements in each row of matrix A are greater than zero, it means that the triangle corresponding to these three elements is entirely within the set aperture range. Calculate the change amplitude between adjacent main cable nodes after the main cable node changes from the basic position to the ideal position. The maximum change amplitude is dete. Step4: Use the change amplitude and the maximum radial adjustment amount as constraint conditions. Optimize the maximum change amplitude dete. When the maximum change amplitude dete satisfies being less than the set value m, judge whether the maximum radial adjustment amount W satisfies being less than the set value n, and record the positions of the vertex and focus of the working parabolic surface that meet the conditions, the maximum radial adjustment amount W of the main cable node, and the maximum change amplitude dete. Step5: Return to step1 and traverse for optimization with variable step size Substitute the positions of the vertex and focus of the working paraboloid obtained in Step4 that meet the conditions into step1, and reduce the step size to obtain a more accurate maximum radial adjustment amount W and maximum variation amplitude dete of the main cable nodes.

2. The method for adjusting the active reflecting panel of a large radio telescope based on a search algorithm according to claim 1,[[]] wherein,[[]] the determination method of Step2:[[]] Project the main cable nodes onto the xoy plane, and judge the distance from the main cable nodes to the origin o on the xoy plane. If it is less than 1 / 2 of the set aperture, then the main cable nodes are within the set aperture range, and these points are stored in matrix B for subsequent calls. Each element in matrix B represents the digital number of the points within the set aperture range.

3. The method for adjusting the active reflecting panel of a large radio telescope based on a search algorithm according to claim 1,[[]] wherein,[[]] the calculation method of the radial adjustment amount of the main cable nodes in Step2:[[]] r 1i Obtained from the provided three-dimensional coordinates; after determining the vertex and focus of the working paraboloid, the equation of the working paraboloid is expressed in spherical coordinate form, and then r is obtained by solving a quadratic equation of one variable 2i , adjust the difference Δr in the polar radius of the front and rear main cable nodes i That is, the radial adjustment amount of the main cable node. The adjusted three-dimensional coordinates are calculated by the formula Calculated

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