H-shaped steel beam size high-precision measurement method based on three-dimensional scanning

Abstract

The application discloses a high-precision size measurement method for H-shaped steel beams based on three-dimensional scanning and belongs to the technical field of three-dimensional measurement. The method comprises the following steps: obtaining three-dimensional point cloud data of an H-shaped steel beam; pre-processing the three-dimensional point cloud data to obtain initial point cloud; extracting a flange and a web area in the initial point cloud to generate a structure segmentation mask; performing adaptive non-uniform sampling on each area based on the structure segmentation mask to obtain a sparse feature point set; performing spatial topology reconstruction on the sparse feature point set to establish a local deformation field; performing deformation compensation on the initial point cloud based on the local deformation field to obtain compensated point cloud; and performing size parameter extraction on the compensated point cloud to obtain the geometric size of the H-shaped steel beam. The method effectively suppresses point cloud noise and deformation interference through a structure adaptive sampling strategy and a deformation field compensation mechanism, and high-precision size measurement is realized.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional measurement technology, specifically a high-precision measurement method for the dimensions of H-shaped steel beams based on three-dimensional scanning. Background Technology

[0002] In steel structure construction and bridge engineering, the geometric dimension inspection of H-beams is a crucial process to ensure the assembly accuracy and structural safety of components. Traditional measurement methods mainly rely on contact measuring tools such as steel tape measures and vernier calipers, which are inefficient and highly susceptible to human factors. Non-contact measurement technology based on 3D scanning can quickly acquire the complete surface morphology of components and has been gradually promoted in industrial inspection. Existing technical solutions for measuring the dimensions of H-beams using 3D scanning typically include steps such as point cloud acquisition, noise reduction, overall registration, and model fitting. The common practice is to uniformly downsample or randomly sample the point cloud and then calculate parameters such as flange width and web height through overall plane fitting. This type of solution faces a double defect in practical applications. On the one hand, the abrupt changes in geometric curvature in areas such as the flange edges and web connections of H-beams are critical locations that determine dimensional accuracy. Uniform sampling cannot represent the differences in these areas, resulting in blurred edge features. When fitting the plane, boundary deviations are easily introduced, leading to uncontrollable errors in the measurement of flange thickness and web height. On the other hand, H-beams often experience minor deformations due to the release of internal stress during manufacturing, transportation, or assembly. Furthermore, point cloud distortion caused by instrument vibration or environmental factors may be superimposed during scanning. Conventional methods directly extract dimensions from the original point cloud or a simply denoised point cloud, directly transferring the deformation to the calculation results. This makes the measurement accuracy insufficient for high-level assembly requirements. To address these issues, a high-precision measurement method is needed that can adaptively preserve edge features based on the structural characteristics of H-beams and effectively compensate for latent deformations, thereby improving the robustness and accuracy of dimension extraction. Summary of the Invention

[0003] This invention provides a high-precision measurement method for the dimensions of H-shaped steel beams based on three-dimensional scanning. It aims to solve the problems of edge feature degradation caused by uniform sampling and deformation interference that cannot be eliminated by direct point cloud measurement in the prior art by non-uniform feature sampling guided by structural segmentation and local deformation field compensation, thereby achieving high-precision extraction of the geometric dimensions of H-shaped steel beams.

[0004] To achieve the above objectives, the present invention provides the following technical solution: The present invention provides a high-precision measurement method for the dimensions of H-shaped steel beams based on three-dimensional scanning, the method comprising the following steps:

[0005] Acquire 3D point cloud data of the H-beam. Preferably, when acquiring 3D point cloud data, first use standard gauge blocks to calibrate the 3D scanner, establish the transformation relationship between the scanner coordinate system and the world coordinate system, and perform coordinate correction on the scanner based on this transformation relationship. Then, use the calibrated scanner to scan the H-beam to obtain the 3D point cloud data of the measured steel beam, thereby eliminating the coordinate deviation of the scanning system itself.

[0006] The acquired 3D point cloud data is preprocessed to obtain an initial point cloud. As a preferred method, this preprocessing procedure performs statistical filtering on the 3D point cloud data to remove outlier noise points, and then performs voxel downsampling on the denoised point cloud to obtain an initial point cloud with a uniform overall distribution. This effectively reduces data redundancy while preserving the overall structural morphology, providing a high-quality data foundation for subsequent region segmentation and feature extraction.

[0007] The flange and web regions are extracted from the initial point cloud to generate a structural segmentation mask. Specifically, principal component analysis is performed on the initial point cloud to determine the principal direction of the H-beam in space. Then, the point cloud is projected along this principal direction to generate a projection density distribution map. The flange region is determined based on the local peak positions in the projection density distribution map, while the local valley positions correspond to the web region. This automatically generates structural segmentation masks for the flange and web. This process utilizes the significant differences in projection density between the H-beam cross-sectional shape to accurately and quickly distinguish between the flange and web.

[0008] Based on the generated structural segmentation mask, adaptive non-uniform sampling is performed on each region belonging to the flange and web to obtain a sparse feature point set. During adaptive non-uniform sampling, the degree of curvature change in the local neighborhood of each point is calculated, and a corresponding sampling density threshold is set according to the local curvature change. This allows for the retention of denser sampling points in geometric edge regions with significant curvature changes, while only a small number of sampling points are retained in flat regions. As a result, the data size is significantly compressed in the sparse feature point set, while the geometric details that play a key role in dimensional measurement, such as flange edges and web boundaries, are fully preserved.

[0009] Spatial topology reconstruction is performed based on a sparse feature point set to establish a local deformation field covering the entire H-shaped steel beam. Preferably, points in the sparse feature point set are used as nodes to construct a Delaunay triangulation. For each triangle in the triangulation, the coordinates of its three vertices and their corresponding coordinates in an ideal, undeformed model are extracted. An affine transformation matrix is ​​calculated based on these two sets of coordinates and decomposed into a rotation matrix and a strain matrix. The strain matrix is ​​used as the deformation gradient tensor corresponding to the triangle. Interpolation is then performed on the deformation gradient tensor across the entire space to obtain a local deformation field that describes the local stretching, compression, and bending degrees of various regions of the point cloud. This local deformation field precisely characterizes the local distortion deviations caused by instrument vibration, environmental disturbances, and other factors during the scanning process.

[0010] Based on the established local deformation field, deformation compensation is performed on each point in the initial point cloud. The corresponding displacement vector is calculated according to the local deformation field at the location of the point, and this displacement vector is applied in reverse to the original coordinates, thereby eliminating the local deformation introduced during the scanning process and obtaining a compensated point cloud. The compensated point cloud is closer to the true geometry of the steel beam, ensuring the accurate extraction of dimensional parameters.

[0011] Dimensional parameters are extracted from the compensated point cloud to obtain high-precision geometric dimensions of the H-beam. As a preferred approach, a random sampling consensus algorithm is first used to robustly extract the flange point set and web point set from the compensated point cloud. Then, plane fitting is performed on the flange point set to obtain the flange plane equation, and plane fitting is performed on the web point set to obtain the web plane equation. Based on the fitted planes, the vertical distance between the two flange planes is calculated to obtain the flange width, and the length of the intersection line between the flange plane and the web plane is calculated to obtain the web height. Finally, the flange thickness and web thickness are obtained from the thickness direction spans of the flange point set and web point set, respectively. By using the deformed point cloud for plane fitting, the interference of local distortion on the fitting accuracy is eliminated, resulting in higher measurement accuracy and repeatability of the extracted geometric dimensions.

[0012] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0013] The initial point cloud is structurally segmented into flange and web regions, generating a structural segmentation mask. Based on this mask, local curvature changes are independently calculated for different regions, and a sampling density threshold is set accordingly. The sampling point density is increased in regions with drastic curvature changes, such as flange edges and web junctions, while the sampling point density is significantly reduced in regions with gentle curvature changes, such as the middle section of the flat plate, resulting in a sparse feature point set. This segmentation-driven adaptive non-uniform sampling strategy allows the point cloud to retain denser original morphological information in geometrically abrupt regions, avoiding the smoothing effect of uniform downsampling on edge features. This enables accurate positioning of the flange boundary and web junction line during subsequent plane fitting and thickness calculation, significantly improving the measurement accuracy of flange width and web height, while reducing the number of redundant points and lowering the computational load. A Delaunay triangulation is constructed using the sparse feature point set as nodes. The vertex coordinates of each triangle and their corresponding point coordinates in the ideal model are extracted. The affine transformation matrix is ​​calculated and decomposed into a rotation matrix and a strain matrix, with the strain matrix used as the deformation gradient tensor. Interpolating the deformation gradient tensor yields a local deformation field covering the entire initial point cloud. The displacement vector of each point in the initial point cloud is calculated based on this local deformation field, and this vector is applied to the corresponding point coordinates to eliminate point cloud distortion caused by manufacturing stress, temperature-induced deformation, or scanning disturbances, resulting in a compensated point cloud. This deformation compensation process does not rely on the overall rigid registration concept; instead, it uses the strain tensor field of the local mesh to finely characterize the non-uniform deformation distribution, making the compensated point cloud closer to the actual design geometry of the component. When fitting the flange plane and web plane from the compensated point cloud and extracting dimensional parameters, systematic errors introduced by deformation can be effectively eliminated, resulting in more accurate geometric dimensions. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0015] Figure 1 This is a flowchart of a high-precision measurement method for H-beam dimensions based on 3D scanning;

[0016] Figure 2 This is a flowchart of the point cloud structure segmentation mask generation process for H-shaped steel beams;

[0017] Figure 3 This is a distribution map of the average distance between points after statistical filtering to remove outliers;

[0018] Figure 4 This is a diagram showing the projected density distribution and local peak-valley values ​​of an H-beam cross-section.

[0019] Figure 5 It is the curve showing the positional variation of the local deformation gradient tensor components along the principal direction;

[0020] Figure 6 This is a frequency distribution diagram of the measured values ​​of the edge width of the compensation point cloud. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See Figure 1 This invention provides a high-precision measurement method for the dimensions of H-beams based on 3D scanning. The method acquires a point cloud of the steel beam surface through 3D scanning, followed by preprocessing, structural segmentation, adaptive sampling, deformation field construction and compensation, ultimately extracting high-precision geometric dimensions. Specifically, the 3D scanner is calibrated using standard gauge blocks to establish a transformation relationship between the scanner's coordinate system and the world coordinate system. Based on this transformation relationship, the scanner's coordinates are corrected. The corrected scanner is then used to scan the H-beam to acquire 3D point cloud data. This 3D point cloud data is preprocessed to obtain an initial point cloud. The flange and web regions are extracted from the initial point cloud to generate a structural segmentation mask. Based on the structural segmentation mask, adaptive non-uniform sampling is performed on each region to obtain a sparse feature point set. Spatial topology reconstruction is performed on the sparse feature point set to establish a local deformation field. Based on the local deformation field, deformation compensation is performed on the initial point cloud to obtain a compensated point cloud. Dimensional parameters are extracted from the compensated point cloud to obtain the geometric dimensions of the H-beam.

[0023] Example 1: In some embodiments, the process of preprocessing 3D point cloud data to obtain an initial point cloud includes two steps: statistical filtering to remove outliers and voxel downsampling.

[0024] In practical implementation, the 3D point cloud data of the H-shaped steel beam acquired by the 3D scanner contains outliers caused by environmental reflections, occlusion, or sensor noise. These outliers are far from the main point cloud and sparsely distributed. The statistical filtering method for removing outliers is as follows: traverse every point in the 3D point cloud data, calculate the average distance from each point to its K nearest neighbors, where K is a preset number of nearest neighbors. The value of K is set to 50, chosen to ensure the neighborhood is sufficient to cover local point density fluctuations while maintaining acceptable computational efficiency. Statistical analysis is then performed on the average distance values ​​of all points to calculate the mean of the average distances. and standard deviation According to the mean and standard deviation Set a distance threshold; the expression for the distance threshold is: ,in, The standard deviation factor. The value is set to 1.0. The criterion of 1.0 is to effectively filter out highly discrete outliers while preserving the integrity of the main point cloud. The average distance of each point is compared to a distance threshold. If the average distance of a point is greater than the threshold, the point is marked as an outlier and deleted; if the average distance of a point is less than or equal to the threshold, the point is retained. Through this statistical filtering process, the point cloud after removing outliers is obtained.

[0025] In practice, even after outlier removal, the point cloud still suffers from uneven point density. For example, the point density is higher on steel surfaces closer to the scanner and lower at more distant locations. Voxel downsampling is used to obtain a uniformly distributed initial point cloud. Voxel downsampling is implemented by creating a 3D voxel grid and enclosing the outlier-removed point cloud within it. The grid side length of the 3D voxel grid is... The value is set to 2 millimeters, and the grid side length is... The 2mm grid was chosen because the measurement of H-beam dimensions requires the point spacing to be less than one-tenth of the smallest dimension of the measured feature, and the 2mm grid preserves weld and edge details. For each non-empty cell in the 3D voxel grid, the centroid coordinates of all points within that cell are calculated. These centroid coordinates are obtained by taking the arithmetic mean of the coordinate components of each point within the cell. The calculated centroid points are used to represent all points within the non-empty cell, resulting in a uniformly distributed initial point cloud. After voxel downsampling, the spacing between adjacent points in the initial point cloud tends to be consistent, and the overall point cloud density decreases, reducing the amount of data required for subsequent processing.

[0026] See Figure 3 The figure shows a histogram of the average point distance distribution in the 3D point cloud data of Example 1 after statistical filtering to remove outliers. The horizontal axis represents the average point distance in millimeters, and the vertical axis represents the frequency of points within the corresponding interval. Blue bars represent points that were retained, and orange bars represent points identified as outliers. The red dashed line in the figure represents the distance threshold, the value of which corresponds to the mean. Add standard deviation factor Multiply by standard deviation ,Right now In this implementation Take 1.0.

[0027] As can be seen from the figure, the average distance of most points is concentrated in the range of approximately 2 mm to 7 mm, with the frequency peaking in the range of 4 mm to 6 mm. This indicates that the distance between the main point cloud points and their neighboring points is relatively concentrated and dense. The distance threshold line is located at approximately 7 mm. Points with an average distance greater than this threshold are identified as outliers. These points are significantly fewer in number, and their average distances are more dispersed, ranging from 7 mm to over 15 mm, showing that these points are far from their neighboring points, consistent with the characteristics of outliers.

[0028] Example 2: In some embodiments, see Figure 2 The process of extracting the flange and web regions from the initial point cloud and generating a structural segmentation mask includes three steps: principal component analysis to determine the principal direction, projection along the principal direction to generate a projection density distribution map, and region division based on local peaks and valleys.

[0029] In practice, principal component analysis is performed on the initial point cloud to determine the principal directions of the H-beam. Assume the initial point cloud contains... There are 3 points, each represented as a three-dimensional coordinate vector. ,in, Calculate the centroid coordinate vector of the initial point cloud. , The expression is:

[0030]

[0031] in, This represents the total number of points in the initial point cloud. Indicates the first point in the initial point cloud The three-dimensional coordinate vector of a point This represents the centroid coordinate vector of the calculated initial point cloud. Based on the centroid coordinate vector... Constructing the covariance matrix covariance matrix The expression is:

[0032]

[0033] in, This represents a covariance matrix of dimension 3×3. (The sentence is incomplete and requires further context.) Eigenvalue decomposition yields three eigenvalues. , , and the corresponding feature vectors , , The eigenvalues ​​satisfy Largest eigenvalue Corresponding feature vector This refers to the principal direction of the H-beam, which corresponds to the length extension direction of the steel section. Eigenvector and A set of orthogonal bases forming a plane perpendicular to the principal direction.

[0034] In practice, the point cloud is projected along the main direction to generate a projection density distribution map. For each point in the initial point cloud... Calculate the projected coordinates of the point on the plane perpendicular to the principal direction. Projected coordinates The calculation method is as follows:

[0035]

[0036] in, Indicates the first The point is at Projected coordinates in the direction, Indicates the first The point is at Projected coordinate values ​​in the direction. The projection plane is divided into... The grid, the number of grid rows Set to 200, number of grid columns Set to 200. and The value of 200 is chosen to match the cross-sectional dimensions of the H-beam, ensuring that the side length of each grid cell corresponds to approximately 1 to 2 millimeters of the actual size, thus guaranteeing sufficient resolution of cross-sectional details in the density distribution map. For each grid cell, the number of projection points falling into it is counted, and this count is used as the density value of that grid cell. After traversing each grid cell, a 3D point cloud projection density distribution map is formed in the main direction.

[0037] In practical implementation, based on the local peaks and valleys of the projected density distribution map, the flange and web regions are divided, generating a structural segmentation mask. In the projected density distribution map, the two flanges and the middle web of the H-beam each appear as three high-density strip regions, with the low-density regions between the strips corresponding to the intervals between the flanges and the web. The structure is segmented along the projected density distribution map. Axial direction or Using an axial scanning method, density curves are extracted for each row or column of the projected density distribution map. Local peaks and valleys are detected on these curves. Local peaks are defined as points whose density values ​​are greater than those of their adjacent positions, and local valleys are defined as points whose density values ​​are less than those of their adjacent positions. These detected valleys serve as boundaries to divide the projected density distribution map into several connected regions. These connected regions are then labeled based on their geometry and relative position: elongated regions located on the sides are labeled as flange regions, and elongated regions located in the middle are labeled as web regions. The labeling results are mapped back to each point in the initial point cloud, assigning each point a region category label to form a structural segmentation mask. In the structural segmentation mask, points belonging to the flange region are labeled with a first value, and points belonging to the web region are labeled with a second value; these two values ​​differ to distinguish between the two structural types.

[0038] See Figure 4 The figure illustrates the key process of structural segmentation based on the projection density distribution map in Example 2. The horizontal axis represents the projection coordinate u, in millimeters, ranging from -150mm to 150mm. The vertical axis represents the projection point density, reflecting the number of projection points of the initial point cloud on the vertical principal direction plane. The blue scatter points represent the actual projection density distribution data, and the orange curve is a smoothed fitting curve of the density, used to more accurately identify the density change trend. The curve clearly shows three main peaks, located at approximately -90mm, 0mm, and 90mm, with peak projection densities reaching approximately 115, 95, and 120, respectively, representing the two flange regions and the middle web region of the H-beam. There are obvious valleys between the three peaks, with projection densities of approximately 10 at the valley points, located at approximately -30mm and 30mm. The local peak points marked by green triangles in the figure correspond to the center positions of the three high-density regions, and the local valley points marked by red squares serve as the dividing boundaries between the flanges and the web. Based on the local peak and valley characteristics of the density curve, two flange regions and one web region are clearly defined, forming a structural segmentation mask.

[0039] Example 3: In some embodiments, the process of performing adaptive non-uniform sampling on each region to obtain a sparse feature point set includes three steps: calculating local curvature changes, setting a sampling density threshold, and adjusting the sampling density according to the curvature changes.

[0040] In practical implementation, the structural segmentation mask divides the initial point cloud into flange and web regions. Adaptive non-uniform sampling is then performed independently on each of the flange and web regions. For a target region, the local curvature change at each point within that region is calculated. Let the target region contain... Let any point in the target region be denoted as . ,in, , This represents the total number of points in the target area. Indicates the first in the target region The three-dimensional coordinate vector of a point. Search point of The nearest neighbor points form a neighborhood point set. The value is set to 30. The value of 30 is chosen to ensure that the neighborhood range can cover the local geometric fluctuations on the steel surface, while avoiding an excessively large neighborhood that would cause a smooth transition in curvature estimation. The covariance matrix of the neighborhood point set is then calculated. covariance matrix The expression is:

[0041]

[0042] in, Indicated by point The covariance matrix of the neighborhood points centered at the center has a dimension of 3×3; Indicates the number of points in the neighborhood set; Point The neighborhood point set of the first Three-dimensional coordinate vectors of points; The centroid coordinate vector of the neighborhood point set is obtained by taking the arithmetic mean of the coordinate components of all points in the neighborhood point set. For the covariance matrix... Eigenvalue decomposition yields three eigenvalues, which are arranged in descending order of value. , , ,in, Point The corresponding largest eigenvalue, Point The corresponding second largest eigenvalue, Point The corresponding minimum eigenvalue. Calculation point. Local curvature variation coefficient Local curvature variation coefficient The expression is:

[0043]

[0044] in, Point The local curvature variation coefficient ranges from 0 to 1 / 3. A value closer to 0 indicates a flatter local surface, while a larger value indicates a higher degree of curvature. The local curvature variation coefficient is calculated for each point within the target region, resulting in a set of curvature variation coefficients for all points.

[0045] In practice, a sampling density threshold is set based on local curvature changes. The distribution of local curvature change coefficients at all points within the target area is statistically analyzed, and the mean value of the local curvature change coefficients is calculated. and the maximum value of the local curvature variation coefficient Set the sampling density threshold parameter. , The value is set to 0.3 multiplied by the total number of points within the target area. That is, the number of retained points is approximately 30% of the original number of points. The local curvature variation coefficient... Transformed into points via linear mapping sampling weights Sampling weights The expression is:

[0046]

[0047] in, Point The sampling weights; This represents the minimum value of the local curvature variation coefficient within the target region; This represents the maximum value of the local curvature variation coefficient within the target region, i.e. ; This represents the preset upper limit of the sampling weight. The value is set to 1.0; This represents the preset lower limit value of the sampling weight. The value is set to 0.1. The 0.1 value is chosen to ensure that a small number of points are retained in flat areas to maintain the integrity of the region's outline. This is based on sampling weights. Determine the sampling probability for each point Sampling probability The expression is:

[0048]

[0049] in, Point The sampling probability of being selected into the sparse feature point set; This represents the sampling density threshold parameter.

[0050] In practice, the sampling point density is increased in areas with large curvature changes and decreased in areas with small curvature changes. This is based on the sampling probability of each point. Randomly sample points within the target area, each point With probability Retained, by probability Points are discarded. After traversing all points within the target region, the remaining points constitute the sampling point set of the target region. The sampling point set obtained from adaptive non-uniform sampling of the flange region and the sampling point set obtained from adaptive non-uniform sampling of the web region are merged to form a sparse feature point set. Due to the local curvature variation coefficient... At locations of geometric abrupt changes, such as flange edges, welds, and web connections, the values ​​are larger, and the sampling probability of the corresponding points is higher. Therefore, areas with large curvature changes retain a high density of sampling points. In flat locations, such as the middle of the flange plane and the middle of the web plane, the local curvature change coefficient values ​​are smaller, and the sampling probability of the corresponding points is lower. Therefore, areas with small curvature changes retain a low density of sampling points.

[0051] Example 4: In practice, the process of spatial topology reconstruction of sparse feature point sets and establishment of local deformation fields includes three steps: constructing a Delaunay triangulation, calculating the deformation gradient tensor corresponding to each triangle, and interpolating the deformation gradient tensor to generate a local deformation field covering the entire initial point cloud.

[0052] In the specific implementation, a Delaunay triangulation is constructed using a sparse feature point set as nodes. The sparse feature point set, obtained in the previous steps, contains 3D points retained after adaptive non-uniform sampling from the flange and web regions. Each point in the sparse feature point set is treated as a node, and all nodes generate a Delaunay triangulation in 3D space. The Delaunay triangulation satisfies that the circumcircle of any triangle does not contain any nodes other than the three vertices of that triangle, achieved through point-by-point insertion or edge-flipping algorithms. The completed Delaunay triangulation consists of a series of tetrahedral elements forming a 3D volume structure, or, for a sparse feature point set approximately located on the same surface, it can degenerate into a 2D manifold mesh composed of a series of triangular facets. The index information and topological adjacency relationships of each triangle vertex in the Delaunay triangulation are stored.

[0053] In practice, the deformation gradient tensor is calculated for each triangle in the Delaunay triangulation. Any triangle in the Delaunay triangulation is denoted as triangle 'triangle'. ,in, Number the triangle index. , This represents the total number of triangles in the Delaunay triangulation. Extracting triangles. The coordinates of the three vertices in the initial point cloud coordinate system are as follows: , , Each coordinate is a three-dimensional column vector. Triangles are also obtained simultaneously. The coordinates of the three vertices in the ideal model of the H-beam are as follows: , , The ideal model of an H-beam is a standard 3D model constructed according to the dimensions of the H-beam design drawings, or a reference point cloud obtained after global rigid registration of the initial point cloud. The corresponding point in the ideal model for each point in the sparse feature point set is determined as follows: the entire sparse feature point set is iteratively registered with the ideal model using nearest-point registration; based on the transformation relationship after registration, the nearest point in the ideal model for each sparse feature point is found as its corresponding point. The affine transformation matrix is ​​calculated based on the coordinates of the three vertices in the initial point cloud coordinate system and the coordinates of their corresponding points in the ideal model. The affine transformation matrix is ​​then used. Adding a translation vector to a 3×3 matrix can map the coordinates of the three vertices from the ideal model space to the initial point cloud space, satisfying the following relationship:

[0054]

[0055] in, Represents a triangle The corresponding 3×3 affine transformation matrix, Represents a triangle The corresponding translation vector, Represents a triangle No. The coordinates of each vertex in the initial point cloud coordinate system Represents a triangle No. The coordinates of the corresponding points of each vertex in the ideal model. To solve for the affine transformation matrix... The coordinates are centroided. The centroids of the three vertices in the initial point cloud coordinate system are calculated. The centroid of the three corresponding points in the ideal model The expressions are respectively and Construct a centroid-free matrix. and , The Listed as , The Listed as Affine transformation matrix By solving We obtained, among which, Representation matrix The pseudo-inverse matrix. Translation vector. Depend on calculate.

[0056] In practical implementation, the affine transformation matrix will be... Decompose into rotation matrices and strain matrix , strain matrix As a triangle The corresponding deformation gradient tensor. For the affine transformation matrix... Perform polar decomposition; the expression for polar decomposition is:

[0057]

[0058] in, Let 3×3 be an orthogonal matrix that satisfies And the determinant is +1, which is the rotation matrix obtained from the extreme decomposition; This represents a 3×3 symmetric positive definite matrix, which is the strain matrix obtained from the extreme decomposition. Directly as a triangle The corresponding deformation gradient tensor. Polar decomposition is calculated by... Eigenvalue decomposition implementation: for matrix Eigenvalue decomposition yields the eigenvalue matrix. and eigenvector matrix ,satisfy Then the strain matrix Rotation matrix Deformation gradient tensor Reflects the triangle The local stretching and compression deformation experienced from the ideal model state to the scanned state. The above calculation is repeated for each triangle in the Delaunay triangulation to obtain the deformation gradient tensor for each triangle.

[0059] In practice, the deformation gradient tensor is interpolated to obtain a local deformation field covering the entire initial point cloud. Any point in the initial point cloud is denoted as point A. According to the point The spatial location determines the triangle within the Delaunay triangulation to which it belongs, or, for a tetrahedral subdivision, the tetrahedron to which it belongs. In the case of a triangular mesh, find the containing point. Projected triangle ,in Containing point The triangle index. Calculate the point. In triangle The barycentric coordinates on The centroid coordinates satisfy and The deformation gradient tensor is interpolated using a weighted summation of barycentric coordinates. Local deformation field tensor at point The expression is:

[0060]

[0061] in, Point The local deformation field tensor obtained by interpolation is a 3×3 matrix; Represents a triangle The deformation gradient tensor corresponding to the triangle containing the first vertex. Represents a triangle The deformation gradient tensor corresponding to the triangle containing the second vertex. Represents a triangle The deformation gradient tensor corresponding to the triangle containing the third vertex is taken as the average of the deformation gradient tensors of all triangles sharing that vertex. Point In triangle The centroid coordinate coefficients corresponding to the first vertex. Point In triangle The centroid coordinate coefficients corresponding to the second vertex. Point In triangle The centroid coordinate coefficients corresponding to the third vertex. , , Through point With triangle The ratio of the areas of the sub-triangles formed by the three vertices is used to calculate the interpolation. If a tetrahedral partition is used, the interpolation is extended to a weighted sum of the voxel coordinates based on the four vertices within the tetrahedron. For each point in the initial point cloud, the local deformation field tensor at each point is calculated using the above interpolation method. The local deformation field tensors of all points together constitute the local deformation field covering the entire initial point cloud. The local deformation field records the material deformation state at each location in the initial point cloud space, which is used for subsequent deformation compensation of the initial point cloud.

[0062] See Figure 5 The figure shows the positional variation trends of the three components U11, U22, and U33 of the deformation gradient tensor in the local deformation field corresponding to the Delaunay triangulation constructed based on the sparse feature point set in Example 4, along the main direction of the H-beam. The horizontal axis represents the position along the main direction in millimeters, ranging from 0 to 6000 mm, covering the entire length range of the H-beam; the vertical axis represents the component values ​​of the deformation gradient tensor, with values ​​concentrated between 0.993 and 1.022, indicating a small degree of deformation and a gradual change.

[0063] Specifically, the blue solid line represents component U11, whose numerical curve exhibits periodic fluctuations. The peak is concentrated around 2000 mm, reaching a maximum value of 1.022, while the trough appears around 2800 mm, with an overall fluctuation amplitude of approximately 0.03, indicating significant local deformation in this main direction. The orange dashed line represents component U22, whose trend differs from U11. The peak appears around 3500 mm, with a maximum value of approximately 1.014, and the lowest trough is approximately 0.995. Its fluctuation amplitude is slightly smaller than U11, indicating moderate local deformation. The green dotted line represents component U33, whose fluctuation amplitude falls between U11 and U22. The peak appears near 1500 mm, with a peak value of approximately 1.012, and the lowest trough is approximately 0.996, exhibiting slight deformation.

[0064] Example 5: In practice, the process of compensating for deformation in the initial point cloud based on the local deformation field to obtain the compensated point cloud is as follows: For each point in the initial point cloud, the displacement vector corresponding to that point is calculated according to the local deformation field, and then the displacement vector is applied to the coordinates of that point. The local deformation field has been established in the previous steps and covers all spatial positions of the initial point cloud. For the initial point cloud with coordinates... The point, among which Given a 3D column vector, find the local deformation field tensor at the location of this point. Local deformation field tensor It is a 3×3 symmetric positive definite matrix, representing the strain tensor from the ideal model state of the H-beam to the scanned state. Displacement vector. The calculation formula is:

[0065]

[0066] in, Indicates the initial point cloud coordinates as The displacement vector corresponding to the point is a three-dimensional column vector. Represents a 3×3 identity matrix. Point The local deformation field tensor at that location. This represents the three-dimensional coordinate vector of the point in the initial point cloud. (Displacement vector) The direction is determined by the strain tensor The difference from the identity matrix determines that its size is related to the distance from the point to the origin and the degree of local deformation. The displacement vector is calculated. Afterwards, the coordinates of the compensation point pass The process involves iterating through all points in the initial point cloud and calculating the coordinates of each compensation point. All compensation points constitute the compensation point cloud. After deformation compensation, the geometry of the compensation point cloud approximates the true shape of the H-beam under stress-free conditions, eliminating the influence of local deformation caused by gravity, welding, or residual stress.

[0067] In practice, the process of extracting dimensional parameters from the compensation point cloud to obtain the geometric dimensions of the H-beam is as follows: fit the flange plane and the web plane from the compensation point cloud respectively; calculate the distance between the flange planes to obtain the flange width; calculate the intersection of the flange plane and the web plane to obtain the web height; and calculate the thickness of the flange and the web.

[0068] In practical implementation, the flange plane and web plane are fitted separately from the compensation point cloud. A random sample-consensus algorithm is used to extract the flange point set and web point set from the compensation point cloud. Plane fitting is performed on the flange point set to obtain the flange plane equation; similarly, plane fitting is performed on the web point set to obtain the web plane equation. The process of extracting the flange point set using the random sample-consensus algorithm is as follows: A distance threshold parameter is set. , The value is set to 0.5 mm. The 0.5 mm threshold is chosen because the surface flatness processing error of H-beams typically ranges from 0.3 mm to 0.8 mm, and 0.5 mm accurately distinguishes between in-plane points and edge points. Three points are randomly selected from the compensation point cloud subset marked as the flange region in the structural segmentation mask. The candidate plane equation determined by these three points is calculated. The vertical distance from all points in the flange region of the compensation point cloud to the candidate plane equation is calculated, and points with vertical distances less than a distance threshold parameter are considered. Points within the candidate plane are marked, and the number of points within the candidate plane is recorded. The random sampling process is repeated, with 200 iterations. The candidate plane containing the most points is selected as the flange reference plane, and the points within this candidate plane constitute the flange point set. The same random sampling consensus algorithm is performed on the web region compensation point cloud subset to extract the web point set. When fitting the flange point set to the plane, the least squares method is used. An overdetermined linear equation system is constructed from the coordinates of all points in the flange point set, and the normal vector and constant term of the flange plane equation are solved. The least squares method is also used to fit the web point set to obtain the web plane equation.

[0069] In practical implementation, the flange width is obtained by calculating the distance between the flange planes. The H-beam has two flanges, and the equations for the first and second flange planes are obtained by fitting these equations. Since the two flange planes are theoretically parallel, the normal vectors of the first and second flange plane equations are calculated, and the average direction of the two normal vectors is taken as the common flange normal vector. A point is randomly selected within the flange region of the compensated point cloud and projected onto the two flange planes along the direction of the common flange normal vector; the distance between the two projected points is the flange width. To improve robustness, multiple measurement points are selected within the flange region to calculate the distance between them, and the average value is taken as the final flange width value.

[0070] In practice, the web height is obtained by calculating the intersection line between the flange plane and the web plane. The equations of the first flange plane and the web plane are solved simultaneously to obtain the equation of the first intersection line; the equations of the second flange plane and the web plane are then solved simultaneously to obtain the equation of the second intersection line. Since the first and second intersection lines are parallel, the perpendicular distance from a point on the first intersection line to the second intersection line is calculated; this distance is the web height. This calculation is repeated at multiple locations along the intersection line within the web region, and the average value is taken as the web height.

[0071] In practice, the flange thickness and web thickness are calculated. For the flange thickness, the points in the flange point set are projected along the direction of the common flange normal vector, the distribution range of the projected values ​​is statistically analyzed, and the difference between the maximum and minimum projected values ​​is taken as the flange thickness. For the web thickness, the perpendicular distances from all points in the web point set to the web plane equation are calculated, the distribution range of the distance values ​​is statistically analyzed, and the difference between the maximum and minimum distances is taken as the web thickness.

[0072] See Figure 6 This figure shows the statistical frequency distribution of the flange width measurement results based on the compensated point cloud in Example 5. The horizontal axis represents the flange width (unit: mm), ranging from approximately 249.6 mm to 250.5 mm, and the vertical axis represents the frequency, with the highest frequency approaching 70. The blue bar chart shows the distribution of flange width data obtained from multiple measurements in the compensated point cloud. The red dashed line in the figure is the reference line for the flange width design value of 250 mm.

[0073] As shown in the figure, the measured values ​​exhibit a relatively concentrated and symmetrical distribution, with the frequency peaking around 250 mm in flange width, specifically at a peak frequency of approximately 66 times. This indicates that the compensated point cloud measurement method has high measurement accuracy and repeatability. The flange width measurements are mainly distributed between 249.8 mm and 250.2 mm, occupying the majority of the overall data range. Furthermore, the data are evenly distributed on both sides of the design value, without significant shifts or systematic errors.

[0074] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A high-precision measurement method for the dimensions of H-beams based on three-dimensional scanning, characterized in that, include: Obtain the 3D point cloud data of the H-beam; The three-dimensional point cloud data is preprocessed to obtain an initial point cloud; Extract the flange and web regions from the initial point cloud to generate a structural segmentation mask; Based on the structural segmentation mask, adaptive non-uniform sampling is performed on each region to obtain a sparse feature point set; Spatial topology reconstruction is performed on the sparse feature point set to establish a local deformation field; Based on the local deformation field, deformation compensation is performed on the initial point cloud to obtain a compensated point cloud; The dimensional parameters of the compensated point cloud are extracted to obtain the geometric dimensions of the H-beam.

2. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The preprocessing of the three-dimensional point cloud data to obtain an initial point cloud includes: Statistical filtering is performed on the three-dimensional point cloud data to remove outliers; Voxel downsampling is performed on the point cloud after outlier removal to obtain a uniformly distributed initial point cloud.

3. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The step of extracting the flange and web regions from the initial point cloud and generating a structural segmentation mask includes: Principal component analysis was performed on the initial point cloud to determine the principal direction of the H-beam. Project the point cloud along the main direction to generate a projection density distribution map; Based on the local peaks and valleys of the projected density distribution map, the flange and web regions are divided to generate a structural segmentation mask.

4. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The step of performing adaptive non-uniform sampling on each region to obtain a sparse feature point set includes: Calculate the local curvature change within each region; Based on the local curvature change, a sampling density threshold is set; Increase the sampling point density in regions with large curvature changes and decrease the sampling point density in regions with small curvature changes to obtain a sparse feature point set.

5. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The step of performing spatial topological reconstruction on the sparse feature point set and establishing a local deformation field includes: Using the sparse feature point set as nodes, construct a Delaunay triangulation; For each triangle in the Delaunay triangulation, calculate its deformation gradient tensor; Interpolating the deformation gradient tensor yields a local deformation field covering the entire initial point cloud.

6. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 5, characterized in that, The calculation of the deformation gradient tensor for each triangle in the Delaunay triangulation includes: Extract the coordinates of the three vertices of each triangle and their corresponding coordinates in the ideal model; Calculate the affine transformation matrix based on the vertex coordinates and the corresponding point coordinates; The affine transformation matrix is ​​decomposed into a rotation matrix and a strain matrix, and the strain matrix is ​​used as the deformation gradient tensor.

7. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The deformation compensation of the initial point cloud based on the local deformation field to obtain the compensated point cloud includes: For each point in the initial point cloud, calculate the displacement vector of that point based on the local deformation field; The displacement vector is applied to the coordinates of the point to eliminate the deformation effect and obtain the compensated point cloud.

8. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The step of extracting dimensional parameters from the compensated point cloud to obtain the geometric dimensions of the H-beam includes: Fit the flange plane and the web plane from the compensated point cloud, respectively; The flange width is obtained by calculating the spacing between the flange planes. The web height is obtained by calculating the intersection of the flange plane and the web plane; Calculate the thickness of the flange and web.

9. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 8, characterized in that, The step of fitting the flange plane and the web plane from the compensated point cloud includes: The random sampling consensus algorithm is used to extract the flange point set and the web point set from the compensation point cloud; By performing a plane fitting on the set of flange points, the flange plane equation is obtained; The web point set is fitted to a plane to obtain the web plane equation.

10. The high-precision measurement method for H-shaped steel beam dimensions based on three-dimensional scanning as described in claim 1, characterized in that, The acquisition of the three-dimensional point cloud data of the H-beam includes: The 3D scanner is calibrated using standard gauge blocks to establish the transformation relationship between the scanner coordinate system and the world coordinate system; Based on the transformation relationship, the scanner's coordinates are corrected; The H-beam was scanned using a calibrated scanner to obtain three-dimensional point cloud data.

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