Surface deformation parameter calculation method, storage medium and electronic device

Abstract

The application discloses a curved surface deformation parameter calculation method, a storage medium and electronic equipment, and relates to the technical field of measurement. The method comprises the following steps: obtaining initial target grid data and reference grid data, wherein the initial target grid data is obtained through finite element calculation; calculating the curvature change weight of nodes based on the initial target grid data and the reference grid data; in each iteration cycle, calculating the node distance and distance weight of the nodes based on the target grid data and the reference grid data; registering the target grid data and the reference grid data based on the curvature change weight and the distance weight, and calculating a target function based on the node distance and the distance weight; if the target function converges or the current iteration number reaches a preset iteration number, outputting the grid data obtained through the current registration, otherwise taking the grid data as the target grid data of the next iteration cycle. Thus, the rigid body displacement parameters of the curved surface structure in the finite element calculation result can be separated, so that the curved surface deformation parameters are obtained.

Description

Technical Field

[0001] This invention relates to the field of measurement technology, and in particular to a method for calculating surface deformation parameters, a storage medium, and an electronic device. Background Technology

[0002] Vacuum or pressure vessels are widely used in fusion facilities. For example, the main body of a tokamak device includes an external vacuum dewar and a vacuum chamber, which are large-curvature, thin-walled vessels. Because these devices typically have large spatial dimensions, they cannot be integrally molded. Instead, a modular molding and welding technique is used, dividing the vessel into several uniform pieces, casting them separately, and then assembling them. The vessel has many windows connecting to other components, and the complex load conditions experienced by fusion devices necessitate high precision for these windows, which in turn places high demands on the large-curvature surface molding of the vessel. During the surface molding process, from the manufacturing and welding of individual components to the assembly of multiple components, elastic-plastic deformation of the surface can occur, affecting the final product's appearance. Due to the high cost, long construction period, and high technical difficulty of these vessels, traditional design theories cannot effectively predict or control each stage of the manufacturing process. Therefore, iterative optimization design and production processes guided by finite element analysis are necessary. However, the finite element analysis results can only provide displacement contour maps of the nodes, which include rigid body displacement parameters and deformation parameters, but not surface deformation parameters, which brings great inconvenience to the manufacturing and design optimization of the container.

[0003] Furthermore, finite element method (FEM) computation is a discrete numerical computation method. The simplest and most common approach is to discretize a continuum into smaller elements using a mesh, and then solve for the result. The mesh can be viewed as point cloud data with a topological structure. Registration of point cloud data P1 and P2 involves calculating rotation and translation transformation matrices, aiming to register P2 to P1 as closely as possible. The Kabsch algorithm is a common registration algorithm; it solves for the optimal rotation matrix and translation vector in the least squares sense. It uses the mesh before and after the finite element calculation as initial parameters for analytical deformation and rigid body displacement, similar to point cloud registration. Therefore, for cases with deformation, this transformation only aims to register P2 to P1 as closely as possible, while the deformed portion is retained as a residual. However, if the mesh undergoes significant deformation or has high deformation requirements, the least squares method becomes affected by large deformation points, impacting the registration accuracy and consequently the evaluation of deformation parameters. Summary of the Invention

[0004] The purpose of this invention is to propose a method, storage medium, and electronic device for calculating surface deformation parameters, so as to separate the rigid body displacement parameters of the surface structure in the finite element calculation results, thereby obtaining the surface deformation parameters.

[0005] In a first aspect, embodiments of the present invention propose a method for calculating surface deformation parameters, comprising: acquiring initial target mesh data and reference mesh data, wherein the initial target mesh data is obtained based on the finite element calculation results corresponding to the surface structure, and the reference mesh data is the actual mesh data of the surface structure; calculating the curvature change weight of nodes based on the initial target mesh data and the reference mesh data; calculating the node distance and distance weight of nodes based on the target mesh data and the reference mesh data in each iteration cycle; registering the target mesh data and the reference mesh data based on the curvature change weight and the distance weight, and calculating an objective function based on the node distance and the distance weight; if the objective function converges or the current iteration number reaches a preset iteration number, then using the mesh data registered in the current iteration cycle as the deformation parameter of the surface structure; otherwise, using the mesh data registered in the current iteration cycle as the target mesh data for the next iteration cycle.

[0006] In some embodiments, obtaining the initial target mesh data includes: performing finite element calculations on the target device based on the geometric model, operating conditions, and boundary conditions of the target device, wherein the target device includes the curved surface structure; and extracting the portion corresponding to the curved surface structure from the finite element calculation results of the target device as the initial target mesh data.

[0007] In some embodiments, the curvature change weight is obtained by the following formula:

[0008]

[0009]

[0010]

[0011] in, Let $\frac{k}{i}$ represent the curvature of the $i$-th node corresponding to $k$, where $k \in {P, Q}$, $P$ represents the reference mesh data, and $Q$ represents the target mesh data. This represents the sum of the angles of all triangles surrounding the i-th node corresponding to k. Let represent the Voronoi area or mixed area of ​​the i-th node corresponding to k. This represents the change in curvature at the i-th node. This represents the curvature change weight of the i-th node. express The variance of , e represents the natural coefficient, i is an integer greater than or equal to 1 and less than or equal to n, and n is the total number of nodes in the grid data.

[0012] In some embodiments, the distance weight is represented by the following formula:

[0013]

[0014]

[0015] in, This represents the node distance of the i-th node. This represents the position coordinates of the i-th node corresponding to the reference grid data P. This represents the position coordinates of the i-th node corresponding to the target mesh data Q. This represents the distance weight of the i-th node. express The variance of , e represents the natural coefficient, i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

[0016] In some embodiments, registering the target mesh data and the reference mesh data based on the curvature change weight and the distance weight includes: obtaining a combined weight based on the curvature change weight and the distance weight, and calculating a first centroid of the target mesh data and a second centroid of the reference mesh data based on the combined weight; decentralizing the target mesh data based on the first centroid and decentralizing the reference mesh data based on the second centroid; calculating a weighted covariance matrix based on the combined weight and the two decentralization results; performing singular value decomposition on the weighted covariance matrix to obtain a rotation vector, and obtaining a translation vector based on the first centroid, the second centroid, and the weighted covariance matrix; and obtaining registered mesh data based on the rotation vector, the translation vector, and the decentralized target mesh data.

[0017] In some embodiments, the combined weights are obtained by the following formula:

[0018]

[0019] in, This represents the combined weight of the i-th node. , This represents the weight adjustment coefficient, and , This represents the curvature change weight of the i-th node. This represents the distance weight of the i-th node, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

[0020] In some embodiments, the objective function is obtained by the following formula:

[0021]

[0022] in, Denotes the objective function, This represents the node distance of the i-th node. This represents the distance weight of the i-th node, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

[0023] In some embodiments, before performing iterations, the method further includes: performing initial registration of the initial target grid data and the reference grid data using the Kabsch algorithm.

[0024] Secondly, embodiments of the present invention provide a computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, it implements the surface deformation parameter calculation method described in the first aspect.

[0025] Thirdly, embodiments of the present invention provide an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein when the computer program is executed by the processor, it implements the surface deformation parameter calculation method described in the first aspect.

[0026] The surface deformation parameter calculation method, storage medium, and electronic device of this invention first acquire initial target mesh data and reference mesh data, with the initial target mesh data obtained through finite element method (FEM) calculation. Then, based on the initial target mesh data and reference mesh data, the curvature change weights of the nodes are calculated. Subsequently, in each iteration cycle, the curvature change weights, node distances, and distance weights of the nodes are calculated based on the target mesh data and reference mesh data. The target mesh data and reference mesh data are registered based on the curvature change weights and distance weights, and an objective function is calculated based on the node distances and distance weights. If the objective function converges or the current iteration number reaches a preset iteration number, the currently registered mesh data is used as the deformation parameters of the surface structure; otherwise, the currently registered mesh data is used as the target mesh data for the next iteration cycle. Thus, the rigid body displacement parameters of the surface structure in the finite element method calculation results can be separated, thereby obtaining the surface deformation parameters. Attached Figure Description

[0027] Figure 1 This is a flowchart of a method for calculating surface deformation parameters according to an embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of a Dewar cold shield structure using a tokamak device, as an example of the present invention;

[0029] Figure 3 This is a flowchart of a method for calculating surface deformation parameters according to a specific embodiment of the present invention;

[0030] Figure 4This is an example diagram of the Dewar cold screen structure after removing rigid body displacement, as an example of the present invention;

[0031] Figure 5 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0032] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0033] The following description, with reference to the accompanying drawings, describes the surface deformation parameter calculation method, storage medium, and electronic device according to embodiments of the present invention.

[0034] Figure 1 This is a flowchart of a method for calculating surface deformation parameters according to an embodiment of the present invention.

[0035] like Figure 1 As shown, the methods for calculating surface deformation parameters include:

[0036] S11, obtain initial target mesh data and reference mesh data, wherein the initial target mesh data is obtained based on the finite element calculation results corresponding to the curved surface structure, and the reference mesh data is the actual mesh data of the curved surface structure.

[0037] As one implementation method, obtaining initial target mesh data includes: performing finite element calculations on the target device based on its geometric model, operating conditions, and boundary conditions, wherein the target device includes a curved surface structure; and extracting the corresponding curved surface structure portion from the finite element calculation results of the target device as the initial target mesh data.

[0038] For example, the target device may include a curved vacuum container or pressure vessel, such as a tokamak device, whose curved structure includes a Dewar cold shield structure, etc.

[0039] Specifically, commercial finite element software such as ANSYS and ABAQUS can be used to perform finite element calculations based on the geometric model, operating conditions, and boundary conditions of the target equipment, and the mesh data before and after the calculation can be exported. For example, based on Workbench, after static analysis, the outer surface of the container can be selected from the displacement contour plot to export STL format mesh data. STL format mesh data includes the nodal coordinates of the mesh and the topological relationships between nodes. Figure 2 As shown, the STL format mesh data of the Dewar cold shield structure of the tokamak device before and after deformation are exported, including the initial target mesh data Q and the reference mesh data P.

[0040] according to Figure 2 The data shown, taking a triangular mesh as an example, is the mesh data (i.e., reference mesh data) before the finite element calculation. The grid data after calculation (i.e., the initial target grid data) is The data structures for P and Q include: grid node coordinate information. and topology information Let the total number of nodes be n, and let the node coordinates be in a rectangular coordinate system. Taking the coordinate values ​​of the axis as an example, it is represented as follows:

[0041] ,

[0042] in, It is an integer greater than or equal to 1 and less than or equal to n. This represents the i-th node in the reference grid data. express Pointed Axis position coordinates, This represents the i-th node in the initial target grid data. Point of Axis position coordinates.

[0043] It should be noted that, in addition to triangular meshes, the mesh data can also be 4-node quadrilateral meshes, 4-node tetrahedral meshes, 8-node hexahedral meshes, etc., and the specific type can be selected according to the needs.

[0044] S12 calculates the curvature change weights of nodes based on the initial target mesh data and the reference mesh data.

[0045] As one implementation method, the curvature change weight is obtained by the following formula:

[0046]

[0047]

[0048]

[0049] in, Let represent the curvature of the i-th node corresponding to k, where k∈{P,Q}, Q represents the target mesh data, and P represents the reference mesh data. This represents the sum of the angles of all triangles surrounding the i-th node corresponding to k. Let represent the Voronoi area or mixed area of ​​the i-th node corresponding to k. This represents the change in curvature at the i-th node. This represents the curvature change weight of the i-th node. express The variance of , e represents the natural coefficient, i is an integer greater than or equal to 1 and less than or equal to n, and n is the total number of nodes in the grid data.

[0050] Optionally, It can also be obtained through discrete Laplace-Beltrami operators, surface fitting, and other methods.

[0051] In the above formula Gaussian weights are used, which allows nodes with smaller movements to contribute more to the fitting, while nodes with larger movements have smaller weights. This allows for better alignment of the static core region and highlights areas with large deformations. Optionally, Uniform weighting, triangular weighting, etc. can also be used.

[0052] S13, in each iteration cycle, calculate the curvature change weight of the nodes, the node distance, and the distance weight based on the target grid data and the reference grid data.

[0053] As one implementation method, the distance weight is represented by the following formula:

[0054]

[0055]

[0056] in, This represents the node distance of the i-th node (if there is no deformation, then...). =0, if deformation occurs, then ≠0), This represents the position coordinates of the i-th node corresponding to the reference grid data P. This represents the position coordinates of the i-th node corresponding to the target mesh data Q. This represents the distance weight of the i-th node. express The variance of , e represents the natural coefficient, i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

[0057] Optionally, Manhattan distance, Chebyshev distance, Mahalanobis distance, Hamming distance, etc. can also be used. Uniform weighting, triangular weighting, etc. can also be used.

[0058] It should be noted that during iteration, such as Figure 3 As shown, the initial value of the iteration number variable can be preset: The iteration termination conditions are set: the objective function termination condition ε and the maximum number of iterations termination condition. Furthermore, the curvature change weight serves as a static, prior guide when establishing the correspondence between points, and is not updated during iteration. This facilitates the rapid calculation of rigid body displacement parameters.

[0059] S14: Register the target grid data and the reference grid data based on curvature change weight and distance weight, and calculate the objective function based on node distance and distance weight.

[0060] In some examples, registration of target and reference grid data is performed based on curvature change weights and distance weights, including: obtaining a combined weight based on the curvature change weights and distance weights, and calculating the first centroid of the target grid data and the second centroid of the reference grid data based on the combined weights; decentering the target grid data based on the first centroid and the reference grid data based on the second centroid; calculating a weighted covariance matrix based on the combined weights and the two decentering results; performing singular value decomposition on the weighted covariance matrix to obtain a rotation vector, and obtaining a translation vector based on the first centroid, the second centroid, and the weighted covariance matrix; and obtaining the registered grid data based on the rotation vector, the translation vector, and the decentered target grid data.

[0061] As one implementation method, the combined weights are obtained by the following formula:

[0062]

[0063] in, This represents the combined weight of the i-th node. , This represents the weight adjustment coefficient, and , This represents the curvature change weight of the i-th node. This represents the distance weight of the i-th node, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

[0064] As another implementation method, the combined weights are obtained by the following formula:

[0065]

[0066] In the two embodiments described above, the weighting coefficient In practice, the weighting coefficients can be adjusted based on deformation characteristics and the specific structural form of the curved surface. For example, if there is significant local distance deformation, the distance weight can be increased, and a value of [missing value] can be taken. If there is a significant change in curvature, the curvature weight can be increased, and a value can be taken as... If the deformation is relatively uniform, a balanced weight can be used, and a weight can be selected. .

[0067] Specifically, see Figure 3 After obtaining the combined weights, the weighted centroids, namely the first centroid and the second centroid, are calculated using the following formula:

[0068] ,

[0069] in, Indicates the second mass. Indicates the first mass. This represents the i-th node in the reference grid data. This represents the i-th node in the target grid data.

[0070] Afterwards, based on , Decentralization, which involves moving the centroids of the reference grid data P and the target grid data Q to the origin, can be achieved using the following formula:

[0071] ,

[0072] in, , Let P be the set of points before and after it is centered. , Let Q represent the set of points before and after decentering.

[0073] Based on the two decentralization results and combined with the weights, the weighted covariance matrix is ​​calculated using the following formula:

[0074]

[0075] Where H represents the weighted covariance matrix, and T represents the transpose. , representing the combined weight vector.

[0076] After obtaining H, SVD (Singular Value Decomposition) is performed on H to obtain the rotation vector. The process includes: first solving... eigenvalues ​​and eigenvectors And sorted in descending order of eigenvalues; The normalized product is denoted as a matrix. ;matrix and Used to calculate the rotation matrix : .

[0077] Then, the translation vector t is calculated using the following formula: .

[0078] Finally, a transformation is applied, that is, the rotation matrix U is applied to the decentralized point set. : .

[0079] S15. If the objective function converges or the current iteration number reaches the preset iteration number, the mesh data registered in the current iteration period is used as the deformation parameter of the surface structure; otherwise, the mesh data registered in the current iteration period is used as the target mesh data for the next iteration period.

[0080] For example, the objective function is obtained by the following formula:

[0081]

[0082] in, Describe the objective function. This represents the node distance of the i-th node. This represents the distance weight of the i-th node, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

[0083] Specifically, see Figure 3 Determine the objective function Is it less than the termination condition? ,or, ,judge Has the predetermined maximum number of iterations been reached? If so, terminate the iteration and output the result. Otherwise, update the target grid data. Then, proceed with the next iteration.

[0084] After the iterative calculation is completed, the current value obtained is... Mesh data to eliminate rigid body displacement.

[0085] In some embodiments of the present invention, such as Figure 3 As shown, before the iteration, the method also includes: using the Kabsch algorithm to perform initial registration of the target grid data and the reference grid data.

[0086] To illustrate the effectiveness of the surface deformation parameter calculation method in this embodiment of the invention, an experiment was conducted using a Dewar cold shield structure as an example. The experimental results are as follows: Figure 4 As shown. See also Figure 4 A comparison of the mesh data before and after registration shows that after eliminating rigid body displacement using the method of this invention, the actual deformation of the structure itself is separated and highlighted, making the contour deformation of the Dewar cold screen clearly discernible, which provides a direct and reliable basis for its structural optimization design.

[0087] The present invention also proposes a computer-readable storage medium.

[0088] In this embodiment, a computer program is stored on a computer-readable storage medium. When the computer program is executed by a processor, it implements the surface deformation parameter calculation method of the above embodiment.

[0089] In summary, the surface deformation parameter calculation method of this invention can solve the problem that existing methods cannot be applied to the evaluation of deformation parameters of large-surface vacuum containers or pressure vessels in finite element simulation analysis results. Specifically, the method of this invention can quickly and accurately separate rigid body displacement parameters from the finite element calculation results of vacuum containers or pressure vessels, thereby obtaining results containing only deformation parameters. These results can be used for iterative optimization of container design or surface profile detection of finite element calculation results under various working conditions, providing an important, effective, and economical basis for the design and optimization of vacuum containers or pressure vessels.

[0090] Figure 5 This is a structural block diagram of an electronic device according to an embodiment of the present invention.

[0091] like Figure 5 As shown, the electronic device 500 includes a processor 501 and a memory 503. The processor 501 and the memory 503 are connected, for example, via a bus 502. Optionally, the electronic device 500 may also include a transceiver 504. It should be noted that in practical applications, the transceiver 504 is not limited to one type, and the structure of this electronic device 500 does not constitute a limitation on the embodiments of the present invention.

[0092] Processor 501 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. Processor 501 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0093] Bus 502 may include a pathway for transmitting information between the aforementioned components. Bus 502 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 502 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 5 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0094] The memory 503 stores a computer program corresponding to the asynchronous serial communication method of the above embodiments of the present invention. This computer program is executed under the control of the processor 501. The processor 501 executes the computer program stored in the memory 503 to implement the content shown in the foregoing method embodiments.

[0095] Among them, electronic devices 500 include, but are not limited to: laptops, desktop computers, etc. Figure 5 The electronic device 500 shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0096] It should be noted that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0097] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0098] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0099] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0100] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0101] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0102] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0103] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for calculating surface deformation parameters, characterized in that, include: Acquire initial target mesh data and reference mesh data, wherein the initial target mesh data is obtained based on the finite element calculation results corresponding to the curved surface structure, and the reference mesh data is the actual mesh data of the curved surface structure; The curvature change weights of the nodes are calculated based on the initial target mesh data and the reference mesh data; In each iteration cycle, the node distance and distance weight are calculated based on the target grid data and the reference grid data; The target mesh data and the reference mesh data are registered based on the curvature change weight and the distance weight, and the objective function is calculated based on the node distance and the distance weight. If the objective function converges or the current iteration number reaches the preset iteration number, the mesh data registered in the current iteration period is used as the deformation parameter of the surface structure; otherwise, the mesh data registered in the current iteration period is used as the target mesh data for the next iteration period. The registration of the target grid data and the reference grid data based on the curvature change weight and the distance weight includes: A combined weight is obtained based on the curvature change weight and the distance weight, and the first centroid of the target mesh data and the second centroid of the reference mesh data are calculated based on the combined weight, as follows: ， in, Indicates the second centroid. Indicates the first centroid. This represents the combined weight of the i-th node. This represents the i-th node in the reference grid data. This represents the i-th node in the target grid data, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data; The target grid data is decentralized based on the first centroid, and the reference grid data is decentralized based on the second centroid. The weighted covariance matrix is ​​calculated based on the combined weights and the two decentralized results; The weighted covariance matrix is ​​subjected to singular value decomposition to obtain a rotation vector, and a translation vector is obtained based on the first centroid, the second centroid, and the weighted covariance matrix. Based on the rotation vector, the translation vector, and the decentralized target mesh data, the registered mesh data is obtained.

2. The method for calculating surface deformation parameters according to claim 1, characterized in that, Obtaining the initial target grid data includes: Finite element analysis is performed on the target equipment based on its geometric model, operating conditions, and boundary conditions, wherein the target equipment includes the curved surface structure. The portion corresponding to the curved surface structure is extracted from the finite element calculation results of the target device and used as the initial target mesh data.

3. The method for calculating surface deformation parameters according to claim 1, characterized in that, The curvature change weight is obtained by the following formula: in, Let $\frac{k}{i}$ represent the curvature of the $i$-th node corresponding to $k$, where $k \in {P, Q}$, $P$ represents the reference mesh data, and $Q$ represents the target mesh data. This represents the sum of the angles of all triangles surrounding the i-th node corresponding to k. Let represent the Voronoi area or mixed area of ​​the i-th node corresponding to k. This represents the change in curvature at the i-th node. This represents the curvature change weight of the i-th node. express The variance of , e represents the natural coefficient, i is an integer greater than or equal to 1 and less than or equal to n, and n is the total number of nodes in the grid data.

4. The method for calculating surface deformation parameters according to claim 1, characterized in that, The distance weight is expressed by the following formula: in, This represents the node distance of the i-th node. This represents the position coordinates of the i-th node corresponding to the reference grid data P. This represents the position coordinates of the i-th node corresponding to the target mesh data Q. This represents the distance weight of the i-th node. express The variance of , e represents the natural coefficient, i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

5. The method for calculating surface deformation parameters according to claim 1, characterized in that, The combined weights are obtained by the following formula: in, This represents the combined weight of the i-th node. , This represents the weight adjustment coefficient, and , This represents the curvature change weight of the i-th node. This represents the distance weight of the i-th node, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

6. The method for calculating surface deformation parameters according to claim 1, characterized in that, The objective function is obtained by the following formula: in, Denotes the objective function, This represents the node distance of the i-th node. This represents the distance weight of the i-th node, where i is an integer greater than or equal to 1 and less than or equal to n, and n represents the total number of nodes in the grid data.

7. The method for calculating surface deformation parameters according to any one of claims 1-6, characterized in that, Before performing iterations, the method further includes: The Kabsch algorithm is used to perform initial registration of the initial target grid data and the reference grid data.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating surface deformation parameters as described in any one of claims 1-7.

9. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory, wherein when the computer program is executed by the processor, it implements the surface deformation parameter calculation method as described in any one of claims 1-7.

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