Mesh antenna node morphing and reconfiguration method and apparatus

Abstract

This invention discloses a method and device for reconstructing the deformation of mesh antenna nodes, belonging to the field of spaceborne mesh antennas. Based on the geometric position and topological connection relationship of the mesh antenna, a mapping model between node displacement and cable element strain is established. RBF radial basis interpolation is introduced, and the displacement information of a small number of control points is used to characterize the deformation field of the entire reflector surface, establishing an explicit relationship between cable element strain and control point deformation. Singular value decomposition is performed on this mapping matrix to extract the dominant strain characteristics; then, combined with column-pivot QR decomposition, the most linearly independent cable elements with the most significant response to the dominant strain are automatically identified as the placement positions for strain sensors. This invention achieves high-precision reconstruction of mesh antenna node displacements with a limited number of sensors, effectively reducing the number of sensors required while ensuring reconstruction accuracy, thus solving the problems of large sensor count and high system complexity in on-orbit deformation monitoring of spaceborne mesh antennas.

Description

Technical Field

[0001] This invention belongs to the field of spaceborne mesh antenna technology, specifically relating to a method and device for deforming and reconstructing mesh antenna nodes. Background Technology

[0002] As a key component for high-precision space signal transmission and reception, the stability of the reflector surface of a spaceborne mesh antenna directly affects its electrical performance during its on-orbit service. Due to long-term exposure to the complex thermal and mechanical environment of space, the antenna structure inevitably deforms. Therefore, real-time and accurate monitoring and reconstruction of the displacement of the reflector nodes are prerequisites for ensuring its operational performance and achieving active on-orbit adjustment.

[0003] Currently, the technical approaches for monitoring and reconstructing mesh antenna deformation can be mainly divided into two categories: non-contact measurement methods and methods based on structural response inversion. Non-contact methods mainly include photogrammetry and radio holography. Photogrammetry reconstructs the three-dimensional shape from multi-view images. Although widely used in ground testing, it is easily affected by temperature changes and reference drift caused by microgravity when used in orbit, making it difficult to maintain long-term stable high accuracy. Radio holography reconstructs the surface shape by inverting the phase of the electromagnetic field, but it relies on an external radio source, is susceptible to space electromagnetic interference, and has complex data processing and poor real-time performance, making it difficult to meet the needs of real-time monitoring.

[0004] Methods based on structural response inversion infer overall deformation by measuring internal physical quantities (such as cable tension or strain). Tension-based methods, in particular, rely on the cable-net force balance equation for inversion and are only applicable to given load conditions. For example, Liu, in his paper "A novel identification approach of mesh reflector based on cable tension sensing" (Acta Astronautica 2024, Vol.214: 277–295), established a least-norm 2 model of vertical cable tension error based on the cable-net tension balance equation by embedding tension sensors within the vertical adjustment cables. This enabled deformation reconstruction under uniform temperature and uniform stiffness degradation conditions on the reflector surface. However, this method may lead to significant reconstruction errors under non-uniformly varying conditions. Strain-based methods are a more promising approach, with the core being the establishment of a mapping relationship between strain and displacement. Existing research primarily employs inverse finite element method (iFEM), modal analysis, or Ko displacement theory. However, directly applying these methods to spaceborne mesh antennas faces significant challenges: First, mesh antennas are highly flexible, prestressed nonlinear structures prone to large displacements, while traditional modal analysis methods, based on the assumption of small deformations, have limited applicability. Second, accurate reconstruction methods, such as the inverse finite element method, typically require the number of strains measured to be no less than the number of degrees of freedom to be reconstructed. This means that sensors need to be deployed on hundreds or even thousands of cable elements, resulting in a large system size, high cost, reduced reliability, and poor engineering feasibility. Furthermore, most methods rely on the constitutive parameters of the material (such as the elastic modulus) when establishing the displacement-strain model, but these material parameters may degrade or become uncertain in orbit due to the space environment, which directly introduces reconstruction errors.

[0005] In summary, existing methods, when applied to real-time on-orbit deformation monitoring of spaceborne mesh antennas, generally suffer from problems such as sensitivity to environmental interference, heavy computational burden, reliance on precise material parameters, or the need to deploy a large number of sensors to achieve the required accuracy, leading to an overly complex system. Summary of the Invention

[0006] The purpose of this invention is to provide a method and device for reconstructing deformable nodes of a mesh antenna, aiming to achieve high-precision and low-cost on-orbit deformation and reconstruction of mesh antennas.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for reconstructing deformable mesh antenna nodes includes the following steps: Based on the topological connection relationship and boundary node deformation of the mesh antenna, a mapping model between the displacement of free nodes of the cable mesh and the strain of the cable elements is established. By introducing RBF radial basis interpolation, some nodes are selected from all free nodes of the cable net as control points, and an interpolation function is established to characterize the deformation field of the entire reflecting surface using the deformation of the control points. Based on the mapping model and the interpolation function, a mapping matrix from the deformation of the control point to the strain of the cable element is established, and singular value decomposition is performed on the obtained mapping matrix to extract the dominant strain characteristics. Combining column-pivot QR decomposition, the most linearly independent cable element is selected from the dominant strain characteristics as the installation position of the strain sensor, and the mapping relationship between the strain of the selected cable element and the deformation of the control point is established. Using the strain data of the cable element actually measured at the installation location of the strain sensor, the deformation of the control point is calculated according to the mapping relationship, and then the deformation of the entire reflective surface structure is obtained using the interpolation function.

[0008] Furthermore, the establishment of the mapping model between the free node displacement of the cable net and the strain of the cable elements includes: The diagonal matrix is ​​formed by the coordinate differences of the nodes at both ends of the cable element in each direction, and combined with the topological matrix of the cable net; Under the assumption of small deformation, by taking the total differential of this geometric relationship, the linear relationship expression between the strain of the cable element and the displacement of the free node is derived, thereby obtaining the mapping matrix from the displacement of the free node to the strain of the cable element to describe the connection relationship of the cable net; Taking the total differential of the element length expression under small deformation conditions, we obtain the linear relationship between the element length change and the nodal displacement, and then derive the relationship matrix between the strain of the cable element and the free nodal displacement and the boundary nodal displacement. The mapping relationship between free nodal displacement, boundary nodal displacement, and cable element strain is obtained through mathematical transformation.

[0009] Furthermore, establishing a deformation field of the entire reflecting surface using the displacement of the control points includes: An interpolation function is constructed using a linear combination of radial basis functions and low-order polynomials. Based on the coordinates of the control points themselves, the weighting coefficients and polynomial coefficients are solved by using the condition that the interpolation function is exactly valid at the control points. For any free node, its coordinates are substituted into the interpolation function with predetermined coefficients to obtain the deformation of the node as a linear combination of the deformation of the control points, thus establishing a linear mapping matrix between the overall deformation and the deformation of the control points.

[0010] Furthermore, based on the mapping model and the interpolation function, a mapping matrix from the deformation of the control point to the strain of the cable element is established, and singular value decomposition is performed on the obtained mapping matrix to extract the dominant strain features, including: Based on the mapping matrix from free nodal displacement to cable element strain, and combined with the linear mapping matrix between full-field deformation and control point deformation, the mapping matrix from RBF control point deformation to cable element strain is derived. Perform singular value decomposition on the mapping matrix to obtain the left singular matrix, the singular value diagonal matrix, and the right singular matrix; Sort the singular values ​​from largest to smallest, and select the column vectors of the left singular matrix corresponding to the top Nc largest singular values ​​as the dominant strain features, where Nc equals the total number of control points.

[0011] Furthermore, the step of combining column-pivoting QR decomposition to select the most linearly independent cable element from the dominant strain characteristics as the installation location of the strain sensor includes: The first Nc columns of the extracted left singular matrix corresponding to the dominant strain characteristics are used to form a matrix and then transposed. The transposed matrix is ​​subjected to column pivoting QR decomposition to obtain the permutation vector. The row indices indicated by the first Nc elements in the permutation vector are determined as the cable element numbers that are most linearly independent and most sensitive to the dominant strain mode, and these numbers are used as the optimal placement locations for the strain sensors.

[0012] Furthermore, based on the QR decomposition, the position of the strain sensor is installed. After obtaining the actual measurement data, the deformation of the RBF control point is calculated based on the relationship between the free node deformation of the reflector control point and the strain of the cable net. Then, the deformation of the entire reflector structure is obtained by using the RBF interpolation function, thus completing the reconstruction of the antenna reflector node deformation.

[0013] Furthermore, the mapping model is established solely based on node coordinates and topological connections.

[0014] In a second aspect, the present invention provides a mesh antenna node deformation and reconstruction system, comprising a first construction module, a second construction module, an extraction module, a selection module, and a reconstruction module, wherein: The first building module is used to establish a mapping model between the displacement of free nodes in the cable mesh and the strain of cable elements based on the topological connection relationship and the deformation of boundary nodes of the mesh antenna. The second building module is used to introduce RBF radial basis interpolation, select some nodes from all free nodes of the cable net as control points, and establish an interpolation function that uses the deformation of the control points to characterize the deformation field of the entire reflecting surface. Extraction module: used to establish a mapping matrix from the deformation of the control point to the strain of the cable element based on the mapping model and the interpolation function, and to perform singular value decomposition on the obtained mapping matrix to extract the dominant strain features; Selection module: Used to combine column principal component QR decomposition to select the most linearly independent cable element from the dominant strain characteristics as the installation position of the strain sensor, and establish the mapping relationship between the strain of the selected cable element and the deformation of the control point; Reconstruction module: Used to calculate the deformation of the control point by using the strain data of the cable element actually measured at the installation position of the strain sensor, and then use the interpolation function to obtain the deformation of the entire reflective surface structure.

[0015] Thirdly, a terminal device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0016] Fourthly, a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0017] Compared with the prior art, the present invention has the following beneficial technical effects: This invention discloses a method for reconstructing the deformation of mesh antenna nodes. Based on the geometric position and topological connections of the mesh antenna, a mapping model is established between node displacement and cable element strain. RBF radial basis interpolation is introduced, utilizing displacement information from a small number of control points to characterize the deformation field of the entire reflector surface, and an explicit relationship is established between cable element strain and control point deformation. Furthermore, singular value decomposition is performed on this mapping matrix to extract the dominant strain characteristics; then, combined with column principal component QR decomposition, the most linearly independent cable elements with the most significant response to the dominant strain are automatically identified as the placement locations for strain sensors. This invention enables high-precision reconstruction of mesh antenna node displacement using only a limited number of sensors. While ensuring reconstruction accuracy, it effectively reduces the number of sensors required, solving the problem of a large number of sensors and high system complexity in on-orbit deformation monitoring of spaceborne mesh antennas. The reconstruction method of this invention is based on a pure geometric mapping model, using RBF interpolation to characterize the entire field displacement with a small number of control points, and combining singular value decomposition and column principal component QR decomposition to automatically select the most sensitive and linearly independent cable elements with the most dominant strain characteristics as sensing locations, thereby achieving a significant reduction in the number of sensors while ensuring reconstruction accuracy.

[0018] This invention establishes a displacement-strain geometric mapping relationship independent of material parameters, thus avoiding the impact of parameter uncertainties on reconstruction. It utilizes RBF interpolation to achieve dimensionality reduction of the displacement field, then extracts the dominant strain mode using SVD, and optimizes sensor placement through QR decomposition, forming a complete sensor dimensionality reduction and reconstruction system. This method transforms the deformation reconstruction problem into a linear inversion problem based on key strain measurements, ensuring reconstruction accuracy while significantly reducing system complexity and on-orbit maintenance costs, demonstrating strong engineering applicability. Attached Figure Description

[0019] Figure 1This is a flowchart of a mesh antenna node deformation and reconstruction method according to an embodiment of the present invention; Figure 2 A finite element model diagram of a mesh antenna provided in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the actual deformation of the mesh antenna provided in an embodiment of the present invention; Figure 4 This is a deformation cloud map of the reflector node obtained under the 0.5mm reconstruction accuracy requirement of an embodiment of the present invention; Figure 5 This is a deformation cloud map of the reflective surface node obtained under the 1mm reconstruction accuracy requirement of an embodiment of the present invention; Figure 6 A schematic diagram of sensor distribution at a reconstruction accuracy of 0.47mm provided in this embodiment of the invention; Figure 7 A schematic diagram of sensor distribution when the reconstruction accuracy is 0.92mm, provided in an embodiment of the present invention. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0021] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0022] It should be noted that the terms "first" and "second" in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0023] The present invention will now be described in further detail with reference to the accompanying drawings: like Figure 1As shown, a method for reconstructing deformable mesh antenna nodes includes the following steps: Step 1: Based on the topological connection relationship and boundary node deformation of the mesh antenna, establish a mapping model between the displacement of free nodes in the cable mesh and the strain of the cable elements; The process of establishing a mapping model includes: The diagonal matrix is ​​formed by the coordinate differences of the nodes at both ends of the cable element in each direction, and combined with the topological matrix of the cable net; Under the assumption of small deformation, by taking the total differential of this geometric relationship, the linear relationship expression between the strain of the cable element and the displacement of the free node is derived, thereby obtaining the mapping matrix from the displacement of the free node to the strain of the cable element to describe the connection relationship of the cable net; Taking the total differential of the element length expression under small deformation conditions, we obtain the linear relationship between the element length change and the nodal displacement, and then derive the relationship matrix between the strain of the cable element and the free nodal displacement and the boundary nodal displacement. The mapping relationship between free nodal displacement, boundary nodal displacement, and cable element strain is obtained through mathematical transformation.

[0024] In detail, for a given mesh antenna, based on the provided mesh antenna topology and boundary node deformation, a mapping model is established between the displacement of free nodes in the cable mesh and the strain of the cable elements.

[0025] The specific process for establishing the mapping relationship between the deformation of free nodes in a cable net and the strain of cable elements is as follows: For the cable mesh structure of a mesh antenna, the length of its cable mesh element is... L diagonal array L d It can be generated by the nodes at both ends of the cable element. x , y , z Composition of directional coordinate difference: ; in U d , V d , W d Indicates that the nodes at both ends of the cable element in equilibrium state are x , y , z The diagonal matrix formed by the differences in direction coordinates can be represented as:

[0026]

[0027]

[0028] In the above formula This represents the coordinate matrix of the free nodes of the cable net. This represents the coordinate matrix of the cable net boundary nodes (which are also truss nodes); Represents the topology matrix of the free nodes of the cable net. Represents the topology matrix of the boundary nodes. and Together they form the cable net topology matrix C , Ruosuo k Connecting nodes i and nodes j ,but C The k Line 1 i and the j Each element is set to 1 and... 1, as shown below:

[0029] The change in element length of the cable net structure under small deformation (large deformation can be obtained through Newton-Raphson iteration) By taking the total differential of equation (1), we can obtain: ; in , , For cable unit x , y , z From the direction coordinate difference vector, we can obtain:

[0030] Cable net strain ε The relationship between the nodal displacements and the nodal displacements can be expressed as:

[0031] make K t This represents the displacement-strain relationship matrix of free nodes. K g The boundary node displacement-strain relationship matrix is ​​shown below:

[0032]

[0033] Based on the least squares principle, after measuring the strain of the cable elements and the deformation of the known boundary nodes, the deformation of the free nodes of the cable net can be expressed as:

[0034] in , .

[0035] Step 2: Introduce RBF radial basis interpolation, select some nodes from all free nodes of the cable net as control points, and establish an interpolation function that uses the deformation of the control points to characterize the deformation field of the entire reflecting surface. Establishing a deformation field characterizing the entire reflecting surface using the deformation of the control points includes: An interpolation function is constructed using a linear combination of radial basis functions and low-order polynomials. Based on the coordinates of the control points themselves, the weighting coefficients and polynomial coefficients are solved by using the condition that the interpolation function is exactly valid at the control points. For any free node, its coordinates are substituted into the interpolation function with predetermined coefficients to obtain the deformation of the node as a linear combination of the deformation of the control points, thus establishing a linear mapping matrix between the overall deformation and the deformation of the control points.

[0036] By using RBF radial basis interpolation, some nodes are selected from all free nodes of the cable net as control points, and an interpolation function is established to characterize the deformation field of the entire reflecting surface using the deformation of the control points.

[0037] The deformation field of the entire reflecting surface is characterized by the deformation of control points. The specific process is as follows: By selecting a subset of control points, RBF interpolation represents the deformation of the entire reflecting surface through a linear combination of radially symmetric basis functions. Its basic form can be expressed as:

[0038] in Represents a node X The displacement vector at that point, This indicates the selected cable net control node. N c Indicates the total number of control points; ω i These are the weighting coefficients. It is an RBF function that depends only on the point. With control points European distance r = ; p ( X ) represents a low-order polynomial term used to enhance global smoothness, and can be expressed as .

[0039] make The set of control point deformations can be determined by solving a system of linear equations. x Directional weight coefficient vector ω x and polynomial coefficient vector

[0040]

[0041] in This represents the interpolation matrix, whose elements are... is a symmetric matrix; P It is a matrix formed by polynomials at control points, which can be represented as 1 indicates that the dimension is N c A column vector of type ×1, where all elements are 1; Control point x Directional deformation. The inverse of the matrix on the left side of the above equation is represented by a matrix... A This means, that is: ; matrix A By dividing the matrix into blocks, we can decompose it into 2×2 matrices. x Directional weight coefficient vector ω x and polynomial coefficient vector c x This can be further expressed as:

[0042]

[0043] Similarly, y , z The interpolation of direction also conforms to the above relationship, which can be simplified to:

[0044]

[0045] After obtaining the weight coefficient vector and the polynomial coefficient vector, the coordinates of the free nodes of the reflecting surface are substituted into the RBF interpolation formula to obtain the corresponding interpolation matrix. Therefore, the deformation of the free nodes on the reflecting surface can be expressed as a function controlling the node deformation, i.e.:

[0046]

[0047] Step 3: Based on the mapping model and the interpolation function, establish a mapping matrix from the deformation of the control point to the strain of the cable element, and perform singular value decomposition on the obtained mapping matrix to extract the dominant strain features; The extraction process of dominant strain characteristics includes: Based on the mapping matrix from free nodal displacement to cable element strain, and combined with the linear mapping matrix between full-field deformation and control point deformation, the mapping matrix from RBF control point deformation to cable element strain is derived. Perform singular value decomposition on the mapping matrix to obtain the left singular matrix, the singular value diagonal matrix, and the right singular matrix; Sort the singular values ​​from largest to smallest, and select the column vectors of the left singular matrix corresponding to the top Nc largest singular values ​​as the dominant strain features, where Nc equals the total number of control points.

[0048] Based on the mapping model in step one and the RBF interpolation function in step two, a mapping matrix from the deformation of the RBF control points to the strain of the cable elements is established, and singular value decomposition is performed on the obtained mapping matrix to extract the dominant strain characteristics.

[0049] A mapping matrix from RBF control point deformation to cable element strain is established, and the dominant strain characteristics are extracted. The specific establishment process is as follows: The control point coordinates contain known boundary node deformations; the matrix... K c If we divide it into two parts, one part being the free node control and the other part being the boundary node, then the following holds:

[0050] This leads to the relationship between the strain of the cable net and the control points of the reflecting surface:

[0051]

[0052]

[0053] After processing, the relationship between the free node deformation of the reflector control point and the strain of the cable net can be obtained as follows:

[0054] Introducing Singular Value Decomposition (SVD) to the mapping matrix Perform key characteristic strain analysis on the mapping matrix. Perform SVD decomposition:

[0055] in U s It is a left singular matrix, and its column vectors form an orthogonal basis for the strain space; It is a diagonal matrix, and the diagonal elements are singular values, representing the importance of the corresponding basis vectors; V s It is a right singular matrix, and its column vectors form an orthogonal basis for the displacement space.

[0056] Step four: Combining column-pivot QR decomposition, select the most linearly independent cable element from the dominant strain characteristics as the installation location for the strain sensor, and establish the mapping relationship between the strain of the selected cable element and the deformation of the control point: The process for determining the installation location of the strain sensor is as follows: The first Nc columns of the extracted left singular matrix corresponding to the dominant strain characteristics are used to form a matrix and then transposed. The transposed matrix is ​​subjected to column pivoting QR decomposition to obtain the permutation vector. The row indices indicated by the first Nc elements in the permutation vector are determined as the cable element numbers that are most linearly independent and most sensitive to the dominant strain mode, and these numbers are used as the optimal placement locations for the strain sensors.

[0057] In detail, column pivoting QR decomposition is used to select the most linearly independent cable element as the installation position of the strain sensor, and the mapping relationship between the strain of the selected cable element and the deformation of the control point is established.

[0058] The most linearly independent cable element is selected as the installation location for the strain sensor using column pivoting QR decomposition. The specific establishment process is as follows: In actual numerical calculations, to avoid the influence of numerical noise, the energy accumulation criterion is used to select the front... N c The combination of basis vectors that contributes the most. Meanwhile, to select the fewest number of most representative sensors, [the following is considered]: U s T The former N c Perform column pivoting QR decomposition on the column:

[0059] in Q It is an orthogonal matrix. R It is an upper triangular matrix, a permutation matrix. E The position of element "1" indicates the selected row index, which corresponds to the most linearly independent cable element that is most sensitive to the dominant strain mode, and is the optimal sensor placement position.

[0060] Step 5: Using the strain data of the cable element actually measured at the installation location of the strain sensor, calculate the deformation of the control point according to the mapping relationship, and then use the interpolation function to obtain the deformation of the entire reflective surface structure: The deformation of the RBF control points is calculated based on the measured strain of the cable elements, and the deformation of the entire reflector structure is obtained using the RBF interpolation function.

[0061] The deformation of the entire antenna reflector surface is obtained based on the measured strain of the cable element. The specific process is as follows: Based on the QR decomposition, the position of the strain sensor is installed. After obtaining the actual measurement data, the deformation of the RBF control point is calculated based on the relationship between the free node deformation of the reflector control point and the strain of the cable net. Then, the deformation of the entire reflector structure is obtained by using the RBF interpolation function, thus completing the reconstruction of the antenna reflector node deformation.

[0062] The application effects of this invention will be described in detail below with reference to simulation examples.

[0063] A prime-feed antenna has an aperture of 16m, a front and rear cable net focal length of 10m, and a height of 3.4m. The reflector surface is divided into 5 segments from the center of the net to the edge truss, and the edge annular truss is divided into 30 sides of equal length. The number of nodes in the front and rear cable nets is 61×2, and the total number of elements is 481. The cable net material is Kevlar fiber with an elastic modulus of 20GPa and a diameter of 1.4mm; its finite element model is as follows. Figure 2 As shown.

[0064] The aforementioned mesh antenna first employs an equal-tension method for initial configuration design, setting the tension values ​​of the front and rear cable nets to 25N to establish a baseline equilibrium state for the structure. Subsequently, a 3N vertically downward nodal force is applied to the free nodes of the front cable net to simulate the influence of environmental loads on the mesh antenna. The three-dimensional displacement field of the cable net nodes under this load is then used as the object of reconstruction analysis by the method proposed in this invention. Figure 3 As shown.

[0065] Figure 4 The diagram shows the deformation contour map of the reflector node obtained using the method of this invention under a reconstruction accuracy requirement of 0.5 mm, corresponding to an actual reconstruction accuracy of 0.47 mm. Figure 5 The paper presents the deformation cloud map of the reflector node obtained using the method of this invention under a reconstruction accuracy requirement of 1 mm, corresponding to an actual reconstruction accuracy of 0.92 mm. It can be seen that, under both accuracy conditions, the deformation distribution obtained from the reconstruction generally matches the simulation results well, verifying the effectiveness and feasibility of the method of this invention. Figure 6 and Figure 7 The strain sensor arrangement is further presented for the two accuracy levels mentioned above. The results show that 50 sensors are required to achieve a reconstruction accuracy of 0.47 mm, while only 42 sensors are needed for 0.92 mm accuracy. This invention significantly reduces the number of sensors while ensuring reconstruction accuracy, achieving an effective balance between accuracy, cost, and system complexity, and possesses good engineering applicability.

[0066] In another embodiment of the present invention, a mesh antenna node deformation reconstruction system is provided, comprising a first construction module, a second construction module, an extraction module, a selection module, and a reconstruction module, wherein: The first building module is used to establish a mapping model between the displacement of free nodes in the cable mesh and the strain of cable elements based on the topological connection relationship and the deformation of boundary nodes of the mesh antenna. The second building module is used to introduce RBF radial basis interpolation, select some nodes from all free nodes of the cable net as control points, and establish an interpolation function that uses the deformation of the control points to characterize the deformation field of the entire reflecting surface. Extraction module: used to establish a mapping matrix from the deformation of the control point to the strain of the cable element based on the mapping model and the interpolation function, and to perform singular value decomposition on the obtained mapping matrix to extract the dominant strain features; Selection module: Used to combine column principal component QR decomposition to select the most linearly independent cable element from the dominant strain characteristics as the installation position of the strain sensor, and establish the mapping relationship between the strain of the selected cable element and the deformation of the control point; Reconstruction module: Used to calculate the deformation of the control point by using the strain data of the cable element actually measured at the installation position of the strain sensor, and then use the interpolation function to obtain the deformation of the entire reflective surface structure.

[0067] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can be implemented in one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs) containing computer-usable program code. The form of a computer program product implemented on ROM (optical memory, etc.).

[0068] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0069] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0070] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or substitutions to the specific implementation of the invention, but these changes, modifications or substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A method for reconstructing deformable mesh antenna nodes, characterized in that, Includes the following steps: Based on the topological connection relationship and boundary node deformation of the mesh antenna, a mapping model between the displacement of free nodes of the cable mesh and the strain of the cable elements is established. By introducing RBF radial basis interpolation, some nodes are selected from all free nodes of the cable net as control points, and an interpolation function is established to characterize the deformation field of the entire reflecting surface using the deformation of the control points. Based on the mapping model and the interpolation function, a mapping matrix from the deformation of the control point to the strain of the cable element is established, and singular value decomposition is performed on the obtained mapping matrix to extract the dominant strain characteristics. Combining column-pivot QR decomposition, the most linearly independent cable element is selected from the dominant strain characteristics as the installation position of the strain sensor, and the mapping relationship between the strain of the selected cable element and the deformation of the control point is established. Using the strain data of the cable element actually measured at the installation location of the strain sensor, the deformation of the control point is calculated according to the mapping relationship, and then the deformation of the entire reflective surface structure is obtained using the interpolation function.

2. The method for reconstructing deformable mesh antenna nodes according to claim 1, characterized in that, The establishment of the mapping model between the free node displacement of the cable net and the strain of the cable elements includes: The diagonal matrix is ​​formed by the coordinate differences of the nodes at both ends of the cable element in each direction, and combined with the topological matrix of the cable net; Under the assumption of small deformation, by taking the total differential of this geometric relationship, the linear relationship expression between the strain of the cable element and the displacement of the free node is derived, thereby obtaining the mapping matrix from the displacement of the free node to the strain of the cable element to describe the connection relationship of the cable net; Taking the total differential of the element length expression under small deformation conditions, we obtain the linear relationship between the element length change and the nodal displacement, and then derive the relationship matrix between the strain of the cable element and the free nodal displacement and the boundary nodal displacement. The mapping relationship between free nodal displacement, boundary nodal displacement, and cable element strain is obtained through mathematical transformation.

3. The method for reconstructing deformable mesh antenna nodes according to claim 1, characterized in that, Establishing a deformation field characterizing the entire reflecting surface using the deformation of the control points includes: An interpolation function is constructed using a linear combination of radial basis functions and low-order polynomials. Based on the coordinates of the control points themselves, the weighting coefficients and polynomial coefficients are solved by using the condition that the interpolation function is exactly valid at the control points. For any free node, its coordinates are substituted into the interpolation function with predetermined coefficients to obtain the deformation of the node as a linear combination of the deformation of the control points, thus establishing a linear mapping matrix between the overall deformation and the deformation of the control points.

4. The method for reconstructing deformable mesh antenna nodes according to claim 1, characterized in that, Based on the mapping model and the interpolation function, a mapping matrix from the deformation of the control points to the strain of the cable elements is established, and singular value decomposition is performed on the obtained mapping matrix to extract the dominant strain features, including: Based on the mapping matrix from free nodal displacement to cable element strain, and combined with the linear mapping matrix between full-field deformation and control point deformation, the mapping matrix from RBF control point deformation to cable element strain is derived. Perform singular value decomposition on the mapping matrix to obtain the left singular matrix, the singular value diagonal matrix, and the right singular matrix; Sort the singular values ​​from largest to smallest, and select the column vectors of the left singular matrix corresponding to the top Nc largest singular values ​​as the dominant strain features, where Nc equals the total number of control points.

5. The method for reconstructing deformable mesh antenna nodes according to claim 1, characterized in that, The combined column-major QR decomposition selects the most linearly independent cable element from the dominant strain characteristics as the installation location of the strain sensor, including: The first Nc columns of the extracted left singular matrix corresponding to the dominant strain characteristics are used to form a matrix and then transposed. The transposed matrix is ​​subjected to column pivoting QR decomposition to obtain the permutation vector. The row indices indicated by the first Nc elements in the permutation vector are determined as the cable element numbers that are most linearly independent and most sensitive to the dominant strain mode, and these numbers are used as the optimal placement locations for the strain sensors.

6. The method for reconstructing deformable mesh antenna nodes according to claim 1, characterized in that, Using the strain data of the cable element actually measured at the installation location of the strain sensor, the deformation of the control point is calculated according to the mapping relationship, and then the deformation of the entire reflective surface structure is obtained using the interpolation function, including: Based on the QR decomposition, the position of the strain sensor is installed. After obtaining the actual measurement data, the deformation of the RBF control point is calculated based on the relationship between the free node deformation of the reflector control point and the strain of the cable net. Then, the deformation of the entire reflector structure is obtained by using the RBF interpolation function, thus completing the reconstruction of the antenna reflector node deformation.

7. The method for reconstructing deformable mesh antenna nodes according to claim 1, characterized in that, The mapping model is established based solely on node coordinates and topological connections.

8. A mesh antenna node deformation and reconfiguration system, characterized in that, It includes a first building module, a second building module, an extraction module, a selection module, and a refactoring module, wherein: The first building module is used to establish a mapping model between the displacement of free nodes in the cable mesh and the strain of cable elements based on the topological connection relationship and the deformation of boundary nodes of the mesh antenna. The second building module is used to introduce RBF radial basis interpolation, select some nodes from all free nodes of the cable net as control points, and establish an interpolation function that uses the deformation of the control points to characterize the deformation field of the entire reflecting surface. Extraction module: used to establish a mapping matrix from the deformation of the control point to the strain of the cable element based on the mapping model and the interpolation function, and to perform singular value decomposition on the obtained mapping matrix to extract the dominant strain features; Selection module: Used to combine column principal component QR decomposition to select the most linearly independent cable element from the dominant strain characteristics as the installation position of the strain sensor, and establish the mapping relationship between the strain of the selected cable element and the deformation of the control point; Reconstruction module: Used to calculate the deformation of the control point by using the strain data of the cable element actually measured at the installation position of the strain sensor, and then use the interpolation function to obtain the deformation of the entire reflective surface structure.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements as claimed in claim 1.

7. The steps of any of the methods described.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements as described in claim 1.

7. The steps of any of the methods described.

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