Finite element model reverse reconstruction method and application based on ceiling nodes and keel

Abstract

This invention belongs to the field of building engineering information technology and 3D reconstruction technology. Addressing the problems of difficulty in accurately modeling complex ceiling nodes without drawings and the insufficient applicability of traditional reverse engineering models, it discloses a method and application for reverse reconstruction of finite element models based on ceiling nodes and keel structures. Specifically, multi-view images of the ceiling nodes are first acquired, and enhanced images are obtained through enhancement processing to achieve 3D reconstruction. Based on these enhanced images, a 3D point cloud of the ceiling node is reconstructed. A first triangular mesh model is generated through surface reconstruction, and then a second triangular mesh model is obtained through optimization. A quadrilateral mesh model is then generated through re-meshing. This quadrilateral mesh model is then solidified and parametrically processed to obtain the solid geometric model of the ceiling node. The solid geometric model of the ceiling node is coupled with a simplified keel model to establish a node-keel integrated finite element model. This invention realizes the transformation of complex ceiling nodes from images to engineering-usable finite element models, and has significant engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of building engineering information technology and three-dimensional reconstruction technology, specifically a method and application of reverse reconstruction of finite element models based on ceiling nodes and keel. Background Technology

[0002] In the field of building structure analysis and construction design, ceiling nodes, as the core components connecting ceiling panels and keel systems, have complex geometric shapes and diverse detailed structures, which directly affect the overall stability, load-bearing capacity and construction feasibility of the ceiling structure. They are a key link in the safety assessment of ceiling systems.

[0003] Traditional numerical simulation and analysis of suspended ceiling structures primarily rely on manual geometric modeling using complete design drawings. However, in real-world engineering scenarios, many existing suspended ceiling buildings are difficult to model accurately due to their age, poor preservation of drawings, or lack of design data, making it challenging to obtain the true geometric dimensions, connection methods, and detailed structural features of the nodes. To address this issue, existing technologies typically employ idealized simplification strategies, constructing numerical models by assuming node connection forms and ignoring complex structural details. This results in significant deviations between the model and the actual mechanical properties of the nodes, failing to accurately reflect the true stress state and deformation patterns of the suspended ceiling structure, thus posing significant risks to structural safety assessments.

[0004] With the development of 3D data acquisition and reverse modeling technologies, these technologies are increasingly being applied to modeling scenarios involving components without blueprints. Currently, the mainstream 3D data acquisition methods fall into two main categories: one is laser scanning technology, which can acquire high-precision 3D point cloud data of components and accurately reconstruct structural details. However, it suffers from drawbacks such as high equipment purchase and usage costs, complex operation procedures, and strict requirements for workspace, making it difficult to promote and apply on a large scale in ordinary construction projects. The other category is image-based 3D reconstruction technology, which relies on ordinary digital cameras to acquire data. It boasts advantages such as low cost, flexible operation, and strong adaptability, making it the preferred solution for low-cost reverse modeling.

[0005] However, for small-scale and structurally complex components such as ceiling nodes, existing image-based reverse modeling techniques still have significant shortcomings: First, the reconstructed 3D point cloud is prone to containing a large number of outliers and noise, leading to geometric distortion in the mesh model generated by subsequent surface reconstruction; Second, the initially reconstructed triangular mesh model has poor regularity and insufficient surface continuity, which can easily lead to low computational efficiency and distorted simulation results when directly used for finite element numerical simulation; Third, reverse reconstruction can only obtain the surface model of the component, lacking solid thickness and parametric features, making it difficult to meet the engineering requirements of finite element analysis for solid models.

[0006] Therefore, how to achieve accurate and efficient conversion of complex and detailed ceiling nodes from image data to engineering-usable finite element models, and solve the problem of balancing modeling accuracy and engineering applicability in existing technologies, remains a technical bottleneck that urgently needs to be overcome in the field of building engineering informatization. Summary of the Invention

[0007] To address the aforementioned problems of difficulty in accurately reproducing the true geometric shape and connection characteristics of complex ceiling nodes without drawings, distortion of mechanical response due to traditional idealized simplified modeling, and the insufficiency of noise in image-based reverse reconstruction models to meet the requirements of finite element analysis, this invention aims to provide a method for constructing a node-keel integrated finite element model that is consistent with the actual ceiling node structure, has good geometric continuity, and strong engineering applicability. This method uses multi-view images as the data foundation and combines image enhancement, point cloud optimization, multi-stage mesh reconstruction and smoothing, solid modeling, parametric surface fitting, and multi-fidelity coupled simulation. This method enables low-cost, high-precision, and efficient construction of a node-keel integrated finite element model that is consistent with the actual ceiling node structure, has good geometric continuity, and strong engineering applicability. Thus, it realizes a reverse reconstruction method based on finite element models of ceiling nodes and keels for the safety analysis of ceiling node structures without drawings.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: On the one hand, a method for reverse reconstruction of finite element models based on ceiling nodes and keel is proposed, including the following steps: Multi-view digital images were acquired around the ceiling nodes and enhanced to obtain a set of enhanced images for 3D reconstruction. The 3D point cloud of the ceiling node is reconstructed based on the enhanced image set, and a first triangular mesh model is generated by surface reconstruction. The first triangular mesh model is then optimized to obtain a second triangular mesh model. The second triangular mesh model is remeshed into a quadrilateral mesh model, and the quadrilateral mesh model is solidified and parameterized to obtain the solid geometric model of the ceiling node. A simplified keel model is established, and the solid geometric model of the ceiling node is coupled with the simplified keel model to construct an overall finite element model of the node-keel system.

[0009] Furthermore, based on the enhanced image set, the 3D point cloud of the ceiling node is reconstructed, and a first triangular mesh model is generated through surface reconstruction. The first triangular mesh model is then optimized to obtain a second triangular mesh model, specifically including: Using an enhanced image set as input, the motion reconstruction method and multi-view stereo matching method are employed to output a dense 3D point cloud reconstruction. Using dense 3D point clouds as input, an outlier removal method based on local neighborhood statistical analysis is adopted to output an effective dense 3D point cloud. Using an effective dense 3D point cloud as input, an implicit function is constructed using a filtered Poisson surface reconstruction method, and isosurfaces are extracted to output the first triangular mesh model. Using the first triangular mesh model as input, an optimization method combining Laplace smoothing and history-constrained Laplace smoothing is adopted to output the optimized second triangular mesh model.

[0010] Furthermore, using the enhanced image set as input, a method combining motion reconstruction structure and multi-view stereo matching is employed to sequentially reconstruct sparse and dense 3D point clouds, specifically including: Using an enhanced image set as input, and based on the structure-of-motion method, through feature point matching, camera pose estimation, triangulation reconstruction and bundle adjustment optimization, the output is a sparse 3D point cloud and camera parameters from each viewpoint. Using sparse 3D point clouds and camera parameters from various perspectives as input, a multi-view stereo matching method is employed to perform pixel-by-pixel depth estimation and fusion, generating dense 3D point clouds.

[0011] Furthermore, the second triangular mesh model is re-meshed into a quadrilateral mesh model, and the quadrilateral mesh model is solidified and parametrically processed to obtain the solid geometric model of the ceiling node, specifically including: Using the second triangular mesh model as input, the triangular mesh is reconstructed into a quadrilateral mesh using the triangular patch merging method guided by the direction field, and simplified by combining geometric error control, and the simplified quadrilateral mesh model is output. Using a simplified quadrilateral mesh model as input, the inner and outer meshes are generated by offsetting along the vertex normal direction, and the lateral boundaries are connected to output a closed solid mesh with volume properties. Using a closed solid mesh as input, the system outputs a solid geometric model of the ceiling node through geometric partitioning, parametric processing, and fitting of a non-uniform rational B-spline surface.

[0012] Furthermore, the simplified keel model is a simplified model that retains the main load-bearing structure of the keel, removes non-critical details, and matches the connection interface size with the solid geometric model of the ceiling.

[0013] Furthermore, a simplified keel model is established, and the solid geometric model of the ceiling node is connected with the simplified keel model to construct an overall finite element model of the node-keel system, specifically including: In the connection area between the ceiling node and the keel, the mechanical transfer and geometric continuity between the simplified keel model and the solid geometric model of the ceiling node are realized through coupling constraints or binding contact, and the node-keel overall finite element model is constructed.

[0014] Furthermore, a finite element model reverse reconstruction system based on ceiling nodes and keel is proposed to realize the aforementioned finite element model reverse reconstruction method based on ceiling nodes and keel. The system includes: Image acquisition and enhancement module: used to acquire multi-view digital images around the ceiling nodes and perform enhancement processing to obtain an enhanced image set; Point cloud processing and triangular mesh optimization module: used to reconstruct the 3D point cloud of the ceiling node from the enhanced image set, generate the first triangular mesh model through surface reconstruction, and optimize the first triangular mesh model to obtain the second triangular mesh model; Quadrilateral Mesh and Solid Model Construction Module: Used to remesh the second triangular mesh model into a quadrilateral mesh model, and to solidify and parameterize the quadrilateral mesh model to obtain the solid geometric model of the ceiling node; Coupling module: Used to create a simplified keel model, coupling the solid geometric model of the ceiling node with the simplified keel model to construct an overall finite element model of the node-keel.

[0015] On the other hand, an electronic device is proposed, comprising: At least one processor; and The memory is communicatively connected to the processor; The memory stores instructions that are executed by the processor, which enable the processor to perform the aforementioned reverse reconstruction method of the finite element model based on ceiling nodes and keel.

[0016] The beneficial effects of this invention are: 1. This invention first enhances the acquired multi-view images using the Contrast-Limited Adaptive Histogram Equalization (CLAHE) algorithm; then, it reconstructs sparse 3D point clouds using the Structure for Motion Restoration (SfM) method, and performs global joint optimization using a bundle adjustment method to obtain sparse 3D point clouds and camera parameters for each viewpoint; based on the obtained camera parameters, it uses a PatchMatch-based multi-view stereo matching method to perform pixel-by-pixel depth estimation and multi-view depth map fusion to obtain dense 3D point clouds of ceiling nodes; finally, it eliminates outliers and suppresses reconstruction noise through local neighborhood statistical analysis. This process realizes the transformation from 2D images to high-quality dense 3D point clouds, significantly improving the point cloud density and accuracy of key details such as node connection interfaces and edges, solving the problems of high noise and missing details in traditional image-based point cloud reconstruction, and providing high-quality data support for subsequent surface reconstruction.

[0017] 2. This invention employs a screened Poisson surface reconstruction algorithm to perform implicit surface fitting on dense 3D point clouds. An adaptive octree partitioning method balances detail representation with computational efficiency, generating a continuous first triangular mesh model. Further optimization using a combination of Laplacian smoothing and history-constrained Laplacian smoothing (HC-Laplacian) reduces high-frequency noise introduced by point cloud reconstruction and suppresses overall shrinkage through history constraints, fully preserving key geometric features such as connection interfaces and edges of ceiling nodes. The final result is a smooth, distortion-free, and feature-complete second triangular mesh model, overcoming the technical shortcomings of traditional mesh smoothing methods, such as easy shrinkage and blurred details.

[0018] 3. This invention reorganizes the second triangular mesh model into a quadrilateral mesh model by guiding the direction field, and simplifies the number of meshes based on geometric error control, thereby improving the efficiency of finite element calculation. Then, it generates inner and outer meshes by offsetting along the vertex normal direction, and forms a closed solid mesh with volume properties through lateral connection surfaces, thus endowing the model with volume properties. Furthermore, it constructs a continuous and smooth solid geometric model of the ceiling node through geometric partitioning, parametric mapping, and fitting of non-uniform rational B-spline surfaces, which solves the problems of large computational load and stress concentration distortion of triangular meshes, and meets the hard requirements of finite element numerical simulation for mesh regularity and closure. Attached Figure Description

[0019] Figure 1 This is a flowchart of the ceiling node image processing and 3D point cloud reconstruction optimization process of the present invention; Figure 2 This is a flowchart of the ceiling node surface reconstruction and quadrilateral mesh model thicknessing process of the present invention; Figure 3 This is a flowchart of the ceiling node surface reconstruction fitting and finite element model generation process of the present invention; Figure 4 This is an image enhancement effect diagram from Embodiment 1 of the present invention; Figure 5 This is a diagram illustrating the generation and processing effect of a dense point cloud model in Embodiment 1 of the present invention. Figure 6 This is a diagram showing the surface generation and smoothing effect in Embodiment 1 of the present invention; Figure 7 This is a diagram illustrating the reconstruction effect of a quadrilateral mesh in Embodiment 1 of the present invention. Figure 8 This is a diagram showing the thickness generation effect in Embodiment 1 of the present invention; Figure 9 The diagrams show the equivalent stress and strain distributions of the ceiling node in the multi-fidelity coupled finite element simulation of the present invention, as shown in Embodiment 1 of the present invention. Detailed Implementation

[0020] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0021] Example 1: See attached document Figures 1-9 The reverse reconstruction method based on the finite element model of the ceiling node and the keel, as shown, specifically includes the following steps: S1. Collect multi-view digital images around the ceiling nodes and perform enhancement processing to obtain a set of enhanced images for three-dimensional reconstruction; Specifically, S1 includes the following sub-steps: S101. Multi-view digital image acquisition: Pre-plan camera shooting positions around the physical entity of the ceiling node, acquiring digital images from multiple perspectives at different angles and heights. Ensure that the overlap ratio of the same ceiling node area in images from adjacent perspectives is no less than 50%. The shooting angle must completely cover the top surface, sides, connection interfaces, and other key structural parts of the ceiling node, with no blind spots. Maintain consistent camera parameters during shooting, keeping the focal length fixed and avoiding frequent adjustments to the shooting distance to ensure clear imaging of the ceiling node and reduce blurring, overexposure, or underexposure. Prioritize shooting in environments with sufficient and uniform natural light. When ambient light is insufficient, use dimmable LED supplementary lighting from the side, with the supplementary lighting angle at 30-45° to the node surface to enhance surface texture details and acquire multi-view digital images covering the entire structure of the ceiling node.

[0022] S102, Multi-view digital image enhancement processing; This sub-step takes the multi-view digital images acquired in S101 as input, uses the Contrast-Limited Adaptive Histogram Equalization (CLAHE) algorithm to enhance the images, and outputs an enhanced image set. .

[0023] The acquired multi-view digital images are converted into grayscale or luminance component images to eliminate interference from color channels in subsequent feature extraction. The processed image is divided into several equally sized local sub-regions, and grayscale distribution histograms are calculated independently for each sub-region. A contrast-limited adaptive histogram equalization (CLAHE) algorithm is then used to calculate the grayscale distribution histogram for each local sub-region.

[0024] Specifically, the gray-level frequency distribution is statistically analyzed within each local sub-region, and the pixel frequency corresponding to gray level z is denoted as n. z To construct a grayscale histogram, the expression is: (1); Where z is the current gray level index, z∈[0,L-1]; Let n be the pixel frequency distribution function for gray level z.z This represents the number of pixels with a grayscale value equal to z.

[0025] Set a contrast limit threshold, with a limit factor of clipLimit=3.0, and an actual cropping threshold T. c Determine using the following formula: (2); Where A is the total number of pixels in the local sub-region, and L is the total number of gray levels (for 8-bit grayscale images, L is usually taken as 256).

[0026] Crop histogram peaks that exceed the actual cropping threshold: When the gray-level histogram function corresponds to the pixel frequency n at the current gray level z... z Exceeding the actual cropping threshold When overflowing, the excess portion is cropped to prevent noise areas from being excessively amplified. The cropped cumulative overflow value is then evenly redistributed to each gray level to avoid excessive amplification of noise areas.

[0027] Calculate the cumulative distribution function for the clipped and redistributed histogram: (3); in, For grayscale index variables, This is a local grayscale mapping function.

[0028] Based on this, a local grayscale mapping function is constructed: (4); in, CDF is the enhanced grayscale value after grayscale z-mapping. min This is the first non-zero cumulative value (i.e., the smallest non-zero cumulative distribution value).

[0029] Specifically, the adaptive pruning threshold determined by equation (2) The cumulative distribution function calculated by equation (3) is used to control the contrast enhancement magnitude of each local sub-region. Equation (4) is used to map the original gray level z to a uniform distribution space. It uses the cumulative distribution function to map the original gray level z to the enhanced gray value. This achieves local contrast stretching.

[0030] Bilinear interpolation is used to fuse the grayscale mapping results of adjacent sub-regions, eliminating abrupt brightness changes at region boundaries and outputting an enhanced image with uniform brightness and clear structural edges and texture features. After processing all input multi-view digital images, an enhanced image set is obtained. .in, Let R be the r-th enhanced image, where r is the image index variable and R is the total number of images.

[0031] S2. Reconstruct the 3D point cloud based on the enhanced image set, generate the first triangular mesh model through surface reconstruction, optimize the first triangular mesh model to obtain the second triangular mesh model; Specifically, S2 includes the following sub-steps: S201, to enhance the image set Using the Structure for Motion (SfM) method and multi-view stereo matching method as input, the output is a dense 3D point cloud reconstruction, specifically including: S2011, This sub-step enhances the image set. Using the Structure from Motion (SfM) method as input, the algorithm performs feature point matching, camera pose estimation, triangulation reconstruction, and bundle adjustment optimization to output a sparse 3D point cloud. and camera parameters from various perspectives.

[0032] First, the input grayscale image data Constructing a Gaussian-scale space: (5); The Gaussian kernel function is expressed as follows: (6); Where x is the pixel coordinate of the image in the horizontal direction, y is the pixel coordinate of the image in the vertical direction, σ is the scale parameter, and * represents the convolution operation. This is the Gaussian kernel function.

[0033] By constructing a scale-space difference function Local extrema are detected in a three-dimensional scale space to obtain scale-invariant feature points, where k is the scale scaling factor. The scale parameter σ is amplified to the adjacent scale parameter kσ to construct the Gaussian difference.

[0034] Matching feature points in images from different viewpoints and Where u and v represent the horizontal and vertical pixel coordinates of the matched feature point in the first view, respectively. , Let l and l represent the horizontal and vertical pixel coordinates of the corresponding matching feature point in the second view, respectively. Let T represent the translation vectors of the corresponding matching feature points in the first and second views, respectively, where T is the transpose sign; and and The geometric relationships satisfy the epipolar constraints: , where F is the basic matrix, describing the polar geometric relationship between the two shooting perspectives.

[0035] If the camera intrinsic parameter matrix is ​​Kq Then the essential matrix E can be derived from the fundamental matrix F: The camera rotation matrix R is recovered by performing singular value decomposition on the essential matrix E. q With translation vector This allows us to determine the external attitude parameters of each shooting angle relative to the spatial coordinate system of the ceiling node.

[0036] For the matched feature point pairs and their corresponding camera parameters, the spatial point coordinates are recovered using triangulation. Let the spatial point be... , where X m Y m Z m These are the coordinate components of the m-th spatial feature point in the X, Y, and Z directions of the three-dimensional coordinate system.

[0037] spatial point The projection process onto the camera's imaging plane satisfies the perspective projection relation: (7); in, Let R be the projected pixel coordinates of the m-th spatial feature point on the image plane at the q-th shooting viewpoint. q l q Let be the camera rotation matrix and translation vector corresponding to the q-th shooting viewpoint, respectively. This is the perspective division projection function.

[0038] To improve overall geometric consistency, a bundle adjustment method is used to globally and jointly optimize all camera pose parameters and 3D point coordinates. The objective function is to minimize the sum of squared reprojection errors. (8); in, These are the coordinates of the feature points actually observed.

[0039] The intrinsic parameter matrices of each camera viewpoint are obtained through nonlinear least squares optimization, and these matrices are K. q Rotation matrix R q Translation vector l q With spatial point Coordinates are used to generate an optimized sparse 3D point cloud. .

[0040] S2012, This sub-step uses sparse 3D point clouds and camera parameters from each viewpoint (intrinsic parameter matrix is ​​K) q Rotation matrix R q Translation vector l q Using as input, a multi-view stereo matching method is employed for pixel-by-pixel depth estimation and fusion to generate a dense 3D point cloud. .

[0041] First, using the camera intrinsic parameter matrix K output by S2011 q The pixel coordinates are corrected based on the camera radial distortion model to eliminate the impact of camera lens distortion on subsequent depth estimation. The camera radial distortion model is expressed as follows: (9); in, The corrected normalized horizontal coordinates of the imaging plane. The corrected normalized vertical coordinates of the imaging plane. To normalize the horizontal coordinates of the imaging plane before correction, To normalize the vertical coordinates of the imaging plane before correction, r is the radial distance from the current image point to the origin of the normalized imaging plane, and satisfies... , , This is the radial distortion coefficient. The correction process relies on the camera intrinsic parameter K provided by S2011. q This is used to convert pixel coordinates into normalized coordinates.

[0042] After obtaining the distortion-free image sequence, a multi-view stereo matching method based on PatchMatch is used for pixel-by-pixel depth estimation. For a pixel s in the reference view, let its depth be d, then the spatial point can be represented as: (10); in, Let K be the homogeneous pixel coordinates, a be the horizontal coordinate component of the pixel in the reference view on the image plane, b be the vertical coordinate component of the pixel in the reference view on the image plane, and K be the vertical coordinate component of the pixel in the reference view on the image plane. s R s l s These are the camera intrinsic parameter matrix, rotation matrix, and translation vector corresponding to the reference view, respectively. Let be the coordinates of the spatial point obtained by backprojecting the pixel s and its assumed depth d.

[0043] The reprojected coordinates of this spatial point in the adjacent view are: (11); in, This is the intrinsic parameter matrix of the camera corresponding to the adjacent view. This is the rotation matrix of the camera corresponding to the adjacent view. Let be the translation vector of the camera corresponding to the adjacent view. The coordinates of the reprojected pixels of the spatial point on the adjacent view image plane.

[0044] Estimating the optimal depth by minimizing the photometric uniformity energy function: (12); in, Let I1 be the grayscale value of the reference view, I2 be the grayscale value of the adjacent view, and N(η) be the local neighborhood window centered on the reference pixel η. Let c be the reprojection mapping function based on the assumed depth d, where c is the pixel index within the neighborhood window. Let c be the coordinates of the c-th pixel within the local neighborhood window N(η).

[0045] To improve matching reliability, the normalized cross-correlation coefficient (NCC) is used to evaluate matching confidence: (13); in, , This represents the average grayscale value of a local window.

[0046] During the depth estimation process, the S2011 outputs a sparse point cloud. This can serve as a priori constraint for the depth search range: For each pixel, the hypothetical depth d candidate value that minimizes the photometric consistency energy value error is obtained through Equation (12), and reliable depth estimates with NCC higher than the threshold (e.g., 0.85) and reprojection error satisfying the constraint are selected using Equation (13). Only depth estimates that satisfy the NCC threshold and reprojection error constraint are retained.

[0047] For multi-view depth points that pass the consistency screening, a weighted fusion method is used to generate unified 3D coordinates: (14); in, The coordinates of the spatial point obtained by backprojection from the h-th viewpoint, with weights The matching confidence weights for corresponding viewpoints can be either NCC values ​​or normalized backlighting errors. Through multi-view spatial consistency verification and weighted accumulation, a high-density, low-noise dense 3D point cloud of ceiling nodes is generated. .

[0048] S202, using dense three-dimensional point clouds As input, an outlier removal method based on local neighborhood statistical analysis is used to output an effective dense 3D point cloud. .

[0049] Specifically, this sub-step uses the dense 3D point cloud obtained in S2012. As input, a kd-tree-based nearest neighbor search structure is used to construct a spatial index for the dense 3D point cloud. Let the reconstructed dense 3D point cloud be... ,in, Let θ be the coordinates of the θ-th spatial point on the surface of the ceiling node. , , These represent the coordinate components of the point in the three directions of the three-dimensional coordinate system, and M is the total number of points in the dense three-dimensional point cloud. A kd-tree structure is established by recursively partitioning the spatial coordinate axes, allowing any point... The set of nearest neighbors can be represented as: ,in, The number of nearest neighbors. For point The Nearest neighbor points.

[0050] For each target point Calculate the Euclidean distance between it and its nearest neighbors: ,in, For target point Its first Neighboring points Calculate the Euclidean distance between the points and the average neighborhood distance of that point. .

[0051] Calculate the mean and standard deviation of the average neighborhood distance of all points across the entire point cloud: (15); in, This represents the average local point spacing of the entire ceiling node point cloud. The degree of dispersion of the point spacing distribution.

[0052] Assuming that the neighborhood distance follows an approximately normal distribution, according to statistics... In principle, the anomaly detection threshold is set as follows: ,in, For abnormal probability control coefficients, when When = 3, it corresponds to approximately the 99.7% confidence interval of a normal distribution. If a point satisfies: If the point deviates significantly from its local neighborhood distribution, it is considered an outlier and removed.

[0053] The above statistical outlier removal process can remove outliers and unstable points caused by mismatches, depth estimation errors, or occlusion during 3D reconstruction, while retaining a stable and spatially consistent effective dense 3D point cloud. .

[0054] S203, with effective dense 3D point cloud As input, an implicit function is constructed and isosurfaces are extracted using a filtered Poisson surface reconstruction method, and the first triangular mesh model is output. ; Specifically, this sub-step is based on the effective dense 3D point cloud data output by S202. ,in, Let e ​​be the three-dimensional coordinates of the e-th sampling point on the surface of the ceiling node. Let G be the corresponding unit normal vector and G be the total number of samples. A continuous implicit function model is constructed using an adaptive octree-based screening method for Poisson surface reconstruction.

[0055] First, based on the point cloud spatial bounding box size L bbox and expected minimum resolution Determine the maximum reconstruction depth: (16); Among them, L bbox The longest side length of the point cloud bounding box. The minimum geometric detail scale that is allowed to be expressed.

[0056] During the octree partitioning process, the number of sampling points N contained in each node is counted. cell When the following conditions are met: Continue subdividing if necessary, otherwise stop subdividing; among which, An empirically stable value between 8 and 15 is selected to ensure the reliability of local normal estimation and gradient constraints.

[0057] Adaptive octree construction is achieved using the above conditions, controlling the computational scale while preserving the structural details of the ceiling nodes. A vector field is constructed based on the sampled point normal vectors. (17); in, For the Dirac distribution function, It is a spatial location variable.

[0058] The core objective of Poisson reconstruction is to solve for the implicit function. This allows its gradient to approximate the vector field, i.e., satisfy: .

[0059] Based on the variational principle, a screening Poisson energy function can be constructed: (18); The first term is the gradient divergence constraint term, used to constrain the implicit function to be solved. gradient field With the vector field constructed from the unit normal vectors of the sampling points As consistent as possible The first term is the solution domain; the second term is the screening term, which constrains the implicit function at the sampling point location. The function value at that point should be as close to zero as possible. is a weighting parameter used to balance gradient consistency and data fit.

[0060] Taking the Euler-Lagrange equation for this energy functional, we obtain the sieved Poisson equation: (19); in, For vector fields The divergence; And it is represented as a sparse linear system of equations in the discrete octree basis function space: (20); in, This represents the implicit function coefficient vector at the octree node. Let be a sparse symmetric positive definite matrix formed by discretization using the Laplace operator. It is the right-hand term vector formed by the divergence constraint and the sampling point constraint.

[0061] The Gauss–Seidel relaxation combined with a multigrid V-cycle iterative method is used to solve the linear system on an octree multilayer structure to obtain the implicit function. Numerical solution. Set the isosurface threshold: This involves taking the average of the implicit function values ​​at the sampling points as the level of the isosurface to eliminate the overall offset caused by discrete errors. This is achieved by extracting values ​​that satisfy: The isosurfaces are used to generate a triangular mesh model representing the geometry of the ceiling nodes, denoted as the first triangular mesh model. .

[0062] S204, using the first triangular mesh model As input, an optimization method combining Laplacian smoothing and history-constrained Laplacian smoothing (HC-Laplacian) is used to output the optimized second triangular mesh model. ; Specifically, this sub-step targets the first triangular mesh model. For each vertex in the point cloud, a set of its first-order neighboring vertices is established, and a discrete Laplacian operator is constructed based on the topological connectivity. The Laplacian displacement vector of the vertex is calculated, and the vertex is updated along the weighted average direction of its neighboring vertices to complete the Laplacian smoothing iteration, thereby reducing the high-frequency noise introduced by the point cloud reconstruction.

[0063] Subsequently, the history-constrained Laplacian smoothing (HC-Laplacian) algorithm is introduced, using the original position of the vertex as a history constraint term. The Laplacian smoothing term and the history constraint term are then combined to iteratively optimize the vertex position. Specifically, in the t-th iteration, the new vertex position... From the current smoothing term and historical position By employing common constraints, the geometric shrinkage effect is suppressed while smoothing the mesh surface, and key geometric features such as the connection interfaces and edges of the ceiling nodes are fully preserved. After iteration, a smooth and structurally continuous optimized triangular mesh model is obtained, denoted as the second triangular mesh model. .

[0064] S3. Remesh the second triangular mesh model into a quadrilateral mesh model, and perform solidification and parameterization on the quadrilateral mesh model to obtain the solid geometric model of the ceiling node. Specifically, S3 includes the following sub-steps: S301, using the second triangular mesh model As input, a triangular mesh is reconstructed into a quadrilateral mesh using a direction field-guided triangular patch merging method, and simplified by combining geometric error control. The output is a simplified quadrilateral mesh model. ; Specifically, this sub-step is based on the second triangular mesh model. The vertex coordinates and face normal information are used to perform geometric analysis on the model surface. A direction field is constructed through normal consistency constraints to provide directional guidance for mesh reconstruction.

[0065] Under the constraint of the orientation field, the triangular mesh model is reparameterized. Following the principle of edge orientation consistency, two topologically adjacent triangular faces with consistent geometric orientations are combined into a quadrilateral element, generating a mesh structure dominated by quadrilaterals. Specifically, by analyzing the normal angle and common edge direction between triangular faces, two adjacent triangular faces that meet the normal consistency threshold and have consistent common edge directions are merged and reconstructed into a quadrilateral element. Irregular nodes such as T-shaped nodes and degenerate quadrilaterals generated during mesh reconstruction are topologically adjusted and constraint-optimized to ensure that the quadrilateral mesh meets the requirements of connectivity, angular continuity, and face regularity.

[0066] A simplified algorithm based on geometric error control is adopted, which iteratively merges facets or removes redundant vertices, and sets an error threshold: (twenty one); in, The proportionality coefficient has a value range of 0.5-1.0; γ=0.002.

[0067] During the simplification process, the geometric deviation between the current mesh and the original mesh is calculated after each operation. If the deviation is less than the error threshold... If the simplification operation is accepted, the iteration stops; otherwise, iteration stops. Through the above processing, the number of meshes is reduced while ensuring that the geometric error of the model does not exceed a preset threshold, resulting in a simplified quadrilateral mesh model. .

[0068] S302, using a simplified quadrilateral mesh model As input, offset along the vertex normal direction to generate inner and outer meshes and connect lateral boundaries, outputting a closed solid mesh with volume properties. .

[0069] Specifically, this sub-step is based on a simplified quadrilateral mesh model. The vertex coordinates and patch normal information are used to move the vertex along its normal direction according to the preset thickness parameters. Each vertex is offset by its normal vector to generate an outer mesh with the same topology as the original quadrilateral mesh. The thickness parameter... According to the thickness of the single-layer aluminum plate of the keel node As its thickness, the simplified quadrilateral mesh is used as the inner structure, and the offset mesh is used as the outer structure. Triangular patches are used to connect the boundary vertices of the inner and outer meshes to generate lateral connection surfaces, forming a closed three-dimensional mesh topology, resulting in a closed solid mesh with volume properties. .

[0070] S303, with closed solid mesh As input, through geometric partitioning, parametric mapping, and non-uniform rational B-spline (NURBS) surface fitting, the output is a solid geometric model of the ceiling node. .

[0071] Specifically, this sub-step applies to closed solid mesh models. Geometric partitioning is performed. Based on the model's topology and curvature variations, the overall mesh is divided into several surface patches with continuous geometric features to avoid surface fitting crossing obvious geometric abrupt changes. For each surface patch, a set of mesh vertices is established. ,in, For the first The 3D vertex coordinates of each grid vertex. , , The first The coordinate components of each grid vertex in the first, second, and third coordinate directions. This represents the total number of mesh vertices within the current surface patch region. Parametric mapping is performed on this region to construct two-dimensional parameter pairs (...). , ),in, For the first The parameter values ​​of each grid vertex in the first parameter direction. For the first The parameter values ​​of each mesh vertex in the second parameter direction are used to establish the vertex. With parameter domain points ( , A one-to-one correspondence between them.

[0072] A surface fitting method based on non-uniform rational B-splines (NURBS) is used within the parameter domain, and its standard expression is: (twenty two); in, As control points, For the corresponding weights, , Let p and o be the B-spline basis functions, i be the control point number in the first parameter direction, p be the order of the basis function in the first parameter direction, j be the control point number in the second parameter direction, o be the order of the basis function in the second parameter direction, n be the total number of control points in the first parameter direction minus one, and m be the total number of control points in the second parameter direction minus one.

[0073] The basis functions satisfy the Cox–de Boor recurrence relation: (twenty three); in, Let be the value of the i-th node in the B-spline node vector, where i is the index number of the basis function / node. , These are the interval nodes of the corresponding order in the node vector.

[0074] To make the NURBS surface S(u,z) approximate the original mesh vertices Using the distance error from the mesh vertices to the surface as the objective function, a least-squares optimization model is constructed: (twenty four); in, For the NURBS surface points corresponding to the parameter positions, This represents the total squared error.

[0075] More specifically, the goal of equation (24) is to find a set of control points. This makes all mesh vertices Its corresponding surface points The sum of squared Euclidean distances between them is minimized.

[0076] In practical solutions, to maintain the linearity of the problem, the weights are usually fixed. Then the surface degenerates into a B-spline surface, and the objective function with respect to the control points... It is a linear quadratic form, which can be written in standard linear least squares form: (25); Where Y is the value of the basis function , The coefficient matrix consists of H, which is the vector of the control points to be determined, and X, which is the vector of the sample points. Through the normal equation: Solve for the control point positions to achieve surface fitting in the least squares sense.

[0077] Smoothing is performed on each of the fitted NURBS surfaces, and continuity constraints are applied to adjacent surfaces to ensure positional or tangential continuity between them. All surface patches are then combined to form a closed, continuous, and smooth solid geometric model of the ceiling node. .

[0078] S4. Establish a simplified keel model, connect the solid geometric model of the ceiling node with the simplified keel model, and construct an overall finite element model of the node-keel; Specifically, S4 includes the following sub-steps: S401. Simplified Keel Model Establishment: Using Rhino 3D modeling software, a simplified geometric model of the keel is established based on the actual structural characteristics of the ceiling system. The main load-bearing structure of the main and secondary keels is retained, while non-critical details that do not affect the mechanical transmission, such as surface decorative textures and non-load-bearing holes, are removed. This ensures that the simplified keel model matches the solid geometric model of the ceiling nodes. The connection interface size and position are perfectly matched, and the simplified keel model is denoted as... .

[0079] S402, Construction of the overall finite element model of the node-keel; The above-obtained solid geometric model of the ceiling node... With simplified keel model Importing the Abaqus finite element analysis software, in the connection area between the node and the keel, mechanical transfer and geometric continuity between them are achieved through shared nodes, coupling constraints, or bonded contact, thus constructing an integral node-keel finite element model. .

[0080] In this embodiment, to verify the engineering applicability of the node-keel integral finite element model constructed in this invention, the following simulation analysis is performed. First, the node-keel integral finite element model... Assign actual material properties to the engineering structure (such as elastic modulus, Poisson's ratio, density, etc.). For the overall finite element model of the node-keel system... The mesh was re-generated, with a high-precision fine mesh used for the ceiling node area and a suitable conventional mesh used for the keel area, ensuring a balance between computational accuracy and efficiency. Boundary conditions and loading conditions were set for the overall model in the finite element software. A fixed constraint was applied to one end of the keel to restrict its displacement in all spatial directions, while an axial tensile loading condition controlled by displacement or force was applied to the other end.

[0081] Then, the static structural solver of the finite element software is used to perform axial tensile numerical simulation on the completed overall finite element model. After the calculation is completed, the equivalent stress distribution diagram and strain distribution diagram of the connection area between the ceiling node and the keel are output. See appendix. Figure 9 Data such as deformation, peak stress, and strain distribution at the node connections are extracted to obtain the complete mechanical response of the node connections within the overall keel system.

[0082] Example 2: The finite element model reverse reconstruction system based on ceiling nodes and keel disclosed in this embodiment is implemented based on the finite element model reverse reconstruction method based on ceiling nodes and keel in Embodiment 1, specifically including: Image acquisition and enhancement module: used to acquire multi-view digital images around the ceiling nodes and perform enhancement processing to obtain an enhanced image set; Point cloud processing and triangular mesh optimization module: used to reconstruct a 3D point cloud from an enhanced image set, generate a first triangular mesh model through surface reconstruction, and optimize the first triangular mesh model to obtain a second triangular mesh model; Quadrilateral Mesh and Solid Model Construction Module: Used to remesh the second triangular mesh model into a quadrilateral mesh model, and to solidify and parameterize the quadrilateral mesh model to obtain the solid geometric model of the ceiling node; Coupling module: Used to create a simplified keel model, connect the solid geometric model of the ceiling node with the simplified keel model, and construct an overall finite element model of the node-keel.

[0083] Example 3: This embodiment provides an electronic device that can be used to execute the reverse reconstruction method of the finite element model based on ceiling nodes and keel as described in Embodiment 1 above, realizing fully automated processing of the ceiling node from image acquisition to finite element model construction. The electronic device includes: At least one processor, which may be a central processing unit (CPU), graphics processing unit (GPU), digital signal processor (DSP), application-specific integrated circuit (ASIC), field-programmable gate array (FPGA) or other programmable logic device, is used to perform arithmetic logic operations and data processing; The memory, which is communicatively connected to the processor, may be volatile memory (such as RAM) and / or non-volatile memory (such as ROM, flash memory, hard disk, etc.) for storing computer-executable instructions and intermediate data (such as images, point clouds, mesh models, etc.) generated during the execution of the method. Communication interface, used for exchanging data with external devices (such as cameras, sensors, displays, cloud servers, etc.); Input / output interfaces are used to connect interactive devices such as keyboards, mice, touch screens, and displays.

[0084] The memory stores computer programs (instructions) that can be executed by the processor. When the processor executes the instructions, it is able to perform the following operations: (1) Control the external or built-in camera to acquire multi-view digital images of the ceiling node, and perform contrast-limited adaptive histogram equalization (CLAHE) enhancement processing on the image; (2) Based on the enhanced image, sparse 3D point cloud and dense 3D point cloud are reconstructed using structure of motion restoration (SfM) and multi-view stereo matching technology. The first triangular mesh model is generated by surface reconstruction. Then, the optimized second triangular mesh model is obtained by combining Laplacian smoothing and history-constrained Laplacian smoothing (HC-Laplacian). (3) The second triangular mesh model is re-meshed into a quadrilateral mesh model, and the inner and outer meshes are generated by offsetting along the vertex normal direction. A closed solid mesh is formed by connecting the lateral boundaries, and then a continuous and smooth ceiling node solid geometric model is constructed by fitting the non-uniform rational B-spline (NURBS) surface. (4) Establish a simplified keel model, and connect the keel model with the node entity model through coupling constraints or binding contact to construct a node-keel overall finite element model.

[0085] Optionally, the processor may also perform the following operations: apply axial tensile boundary conditions to the node-keel integral finite element model to perform numerical simulation, and obtain mechanical response data of the node connection area to verify the effectiveness of the model.

[0086] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for reverse reconstruction of finite element models based on ceiling nodes and keel, characterized in that, Includes the following steps: Multi-view digital images were acquired around the ceiling nodes and enhanced to obtain a set of enhanced images for 3D reconstruction. The 3D point cloud of the ceiling node is reconstructed based on the enhanced image set, and a first triangular mesh model is generated by surface reconstruction. The first triangular mesh model is then optimized to obtain a second triangular mesh model. The second triangular mesh model is remeshed into a quadrilateral mesh model, and the quadrilateral mesh model is solidified and parameterized to obtain the solid geometric model of the ceiling node. A simplified keel model is established, and the solid geometric model of the ceiling node is coupled with the simplified keel model to construct an overall finite element model of the node-keel system.

2. The method for reverse reconstruction of a finite element model based on ceiling nodes and keel as described in claim 1, characterized in that, The 3D point cloud of the ceiling nodes is reconstructed based on the enhanced image set. A first triangular mesh model is generated through surface reconstruction. The first triangular mesh model is then optimized to obtain a second triangular mesh model, which specifically includes: Using an enhanced image set as input, the motion reconstruction method and multi-view stereo matching method are employed to output a dense 3D point cloud reconstruction. Using dense 3D point clouds as input, an outlier removal method based on local neighborhood statistical analysis is adopted to output an effective dense 3D point cloud. Using an effective dense 3D point cloud as input, an implicit function is constructed using a filtered Poisson surface reconstruction method, and isosurfaces are extracted to output the first triangular mesh model. Using the first triangular mesh model as input, an optimization method combining Laplace smoothing and history-constrained Laplace smoothing is adopted to output the optimized second triangular mesh model.

3. The method for reverse reconstruction of a finite element model based on ceiling nodes and keel as described in claim 2, characterized in that, Using an enhanced image set as input, a method combining motion reconstruction structure and multi-view stereo matching is employed to sequentially reconstruct sparse and dense 3D point clouds, specifically including: Using an enhanced image set as input, and based on the structure-of-motion method, through feature point matching, camera pose estimation, triangulation reconstruction and bundle adjustment optimization, the output is a sparse 3D point cloud and camera parameters from each viewpoint. Using sparse 3D point clouds and camera parameters from various perspectives as input, a multi-view stereo matching method is employed to perform pixel-by-pixel depth estimation and fusion, generating dense 3D point clouds.

4. The method for reverse reconstruction of a finite element model based on ceiling nodes and keel as described in claim 3, characterized in that, The second triangular mesh model is remeshed into a quadrilateral mesh model, and the quadrilateral mesh model is then solidified and parametrically processed to obtain the solid geometric model of the ceiling node, specifically including: Using the second triangular mesh model as input, the triangular mesh is reconstructed into a quadrilateral mesh using the triangular patch merging method guided by the direction field, and simplified by combining geometric error control, and the simplified quadrilateral mesh model is output. Using a simplified quadrilateral mesh model as input, the inner and outer meshes are generated by offsetting along the vertex normal direction, and the lateral boundaries are connected to output a closed solid mesh with volume properties. Using a closed solid mesh as input, the system outputs a solid geometric model of the ceiling node through geometric partitioning, parametric processing, and fitting of a non-uniform rational B-spline surface.

5. The method for reverse reconstruction of a finite element model based on ceiling nodes and keel as described in claim 4, characterized in that, The simplified keel model is a simplified model that retains the main load-bearing structure of the keel, removes non-critical details, and matches the interface size with the solid geometric model of the ceiling.

6. The method for reverse reconstruction of a finite element model based on ceiling nodes and keel as described in claim 5, characterized in that, A simplified keel model is established, and the solid geometric model of the ceiling node is connected with the simplified keel model to construct an overall finite element model of the node-keel system, specifically including: In the connection area between the ceiling node and the keel, the mechanical transfer and geometric continuity between the simplified keel model and the solid geometric model of the ceiling node are realized through coupling constraints or binding contact, and the node-keel overall finite element model is constructed.

7. A finite element model reverse reconstruction system based on ceiling nodes and keel, used to implement the method described in any one of claims 1 to 6, characterized in that, The system includes: Image acquisition and enhancement module: used to acquire multi-view digital images around the ceiling nodes and perform enhancement processing to obtain an enhanced image set; Point cloud processing and triangular mesh optimization module: used to reconstruct the 3D point cloud of the ceiling node from the enhanced image set, generate the first triangular mesh model through surface reconstruction, and optimize the first triangular mesh model to obtain the second triangular mesh model; Quadrilateral Mesh and Solid Model Construction Module: This module is used to remesh the second triangular mesh model into a quadrilateral mesh model, and to solidify and parameterize the quadrilateral mesh model to obtain the solid geometric model of the ceiling node. Coupling module: Used to create a simplified keel model, coupling the solid geometric model of the ceiling node with the simplified keel model to construct an overall finite element model of the node-keel.

8. An electronic device, characterized in that, include: At least one processor; as well as The memory is communicatively connected to the processor; The memory stores instructions that are executed by the processor, which enable the processor to perform the reverse reconstruction method of the finite element model based on ceiling nodes and keel as described in any one of claims 1 to 6.

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