Geometric access control and derivative backtracking-based rod bending measurement method and system

Abstract

The present application belongs to the technical field of spatial grid structure bending rod measurement, aiming at the problem of extraction failure caused by strong background interference in existing laser scanning detection and systematic under-fitting error existing in discrete slice method, a rod bending measurement method and system based on geometric access control and derivative backtracking are proposed. The present application firstly proposes a geometric access control random sampling consistency mechanism based on global radius adaptive locking, combined with connected domain topology analysis, to accurately extract the pure point cloud of the target rod; secondly, the skeleton points extracted from the pure point cloud are fitted with cubic B-spline, and the theoretical peak value is located by solving the derivative zero point of the bending vector height function in the continuous domain; further, the region of interest is resampled based on the theoretical peak value trigger, and the outlier skeleton points are removed by introducing a quadratic polynomial trend lock; finally, weighted fine fitting is performed. The present application eliminates the discretization sampling error from the mathematical principle, and realizes the measurement accuracy of sub-millimeter level.

Description

Technical Field

[0001] This invention belongs to the field of spatial grid structure bending member measurement technology, specifically involving a member bending measurement method and system based on geometric gate and derivative backtracking. Background Technology

[0002] Spatial steel structures mainly include space frame structures, space shell structures, and other spatial grid structures, as well as cable-stayed structures and tubular truss structures. Due to their strong spanning capacity, well-defined stress distribution, high overall stiffness, and ease of fabrication and installation, spatial steel structures are widely used in large public buildings, such as airport terminal roofs, large stadiums or performance venues, large light industrial plants, and coal and material yard canopies. The initial geometric bending of the members is a key sensitive factor inducing nonlinear buckling instability in the structure. According to the "Standard for Acceptance of Construction Quality of Steel Structures," the allowable deviation of the bending sag of the members is extremely small (usually L / 1000).

[0003] Existing technologies mainly suffer from the following two types of problems: Poor anti-interference ability: Traditional density-based denoising algorithms (such as DBSCAN and SOR) have difficulty distinguishing between high-density cables and poles due to structured objects such as suspended cables around the poles, causing the algorithms to fail.

[0004] Measurement accuracy is limited: Existing methods mostly use the slicing method. Due to the randomness of physical bending extremes, it is difficult for discrete slices to precisely capture the point of maximum bending, resulting in a systematic "underfitting error" that fails to meet acceptance requirements. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a method and system for measuring the bending of structural members based on geometric access control and derivative backtracking. First, this invention proposes a geometric access control random sampling consistency (RANSAC) mechanism based on global radius adaptive locking, combined with connected component topology analysis, to accurately extract the pure point cloud of the target structural member under strong cable interference. Second, a cubic B-spline curve is fitted to the initial skeleton points extracted from the pure point cloud, and the theoretical peak value is located by solving for the zero point of the derivative of the bending sag function in the continuous domain. Then, based on the theoretical peak value, backtracking and resampling of the region of interest (ROI) is triggered, and a quadratic polynomial trend lock is introduced to remove outlier skeleton points. Finally, a weighted fine fitting is performed.

[0006] The technical solution adopted in this invention is as follows: In a first aspect, the present invention protects a method for measuring the bending of a rod based on geometric gate control and derivative backtracking, the method comprising: Obtain the original point cloud set of the target member, and correct the original point cloud set to be oriented with the major axis of the target member as the reference point. Local coordinate system of the axis; Based on the original point cloud set in the local coordinate system, random multi-section sampling is performed along the long axis of the target rod. Unconstrained circle fitting is performed on each section, and the median of the unconstrained circle fitting radius is taken as the physical true radius of the target rod. Based on the physical true radius, a geometric access control constraint function is constructed. The radius of the randomly sampled circular model is identified, and the circular model that does not conform to the physical true radius is eliminated. The connected component is cleaned by DBSCAN clustering to obtain the pure point cloud of the target rod. The initial skeleton points are extracted by slicing the pure point cloud, a cubic B-spline curve is fitted, the bending sag function is defined, and the zero point of the derivative of the bending sag function is solved in the continuous parameter domain to obtain the theoretical maximum bending position of the target rod. The region of interest is set with the theoretical maximum bending position as the center. The original point cloud set is backsampled within the region of interest to obtain the skeleton points of the region of interest. The RANSAC algorithm is then used to fit a quadratic polynomial trend line to perform trend locking and cleaning of the skeleton points of the region of interest. Weights are assigned to the skeleton points of the cleaned region of interest, and a weighted fitting is performed to calculate the final bending sag of the target member.

[0007] Preferably, the original point cloud set of the target member is obtained, and the original point cloud set is corrected to a local coordinate system with the major axis of the target member as the coordinate axis, including: Obtain the original point cloud set of the target member, calculate the geometric center of the original point cloud set, and center the coordinates of each point in the original point cloud set relative to the geometric center so that the geometric center of the original point cloud set coincides with the origin of the local coordinate system. Construct the covariance matrix, perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues, and sort the eigenvalues ​​from largest to smallest; Take the eigenvector corresponding to the largest eigenvalue as the major axis direction of the target member, construct a rotation matrix, and map the original point cloud set to the local correction space of the local coordinate system. At this time, the major axis direction of the target member is completely aligned with the X-axis of the local coordinate system.

[0008] More preferably, a geometric gate constraint function is constructed based on the physical true radius. Radius identification is performed on the randomly sampled circular models, eliminating those that do not conform to the physical true radius. Connectivity cleaning is then performed using DBSCAN clustering to obtain a clean point cloud of the target member, including: Take any section along the major axis of the target member as the cross-section of the slice, and randomly select 3 points from the point cloud of the cross-section of the slice. As the minimum sample set; Calculate 3 points Determined center of circle and radius , generate Center of the circle A circular model with radius . If radius If the absolute value of the difference between the circle model and the actual physical radius is greater than the preset geometric tolerance, the circle model is determined to be a pseudo model generated by noise, and is directly discarded and the subsequent calculation is skipped. If radius If the absolute value of the difference between the actual radius and the physical radius is less than or equal to the preset geometric tolerance, then calculate the distance from all points in the cross section of the slice to the center of the circle model. Points whose absolute value of the difference between the distance and the actual radius is less than or equal to the preset geometric tolerance are taken as interior points, and the number of interior points is counted. Repeat the above random sampling consensus iteration process, retain the circle model parameter with the most interior points as the final fitting result of the cross-section of the slice, and obtain the center coordinates of the cross-section of the slice. ; After completing random sampling consistency iteration on the cross-sections of all slices of the target member, DBSCAN clustering is performed on the interior points, retaining the cluster with the most interior points and removing spatially isolated misjudged points.

[0009] More preferably, the expression for the geometric gate function is as follows: ; in, For the current circle model For the preset geometric tolerance, when When =0, the current circle model is discarded directly. Represents the physical true radius. This indicates otherwise.

[0010] More preferably, after completing the random sampling consensus iteration on the cross-sections of all slices of the target member, DBSCAN clustering is performed on the interior points, retaining the cluster with the most interior points and removing spatially isolated misclassified points, including: Define the Euclidean distance threshold between the centers of the cross sections of adjacent slices. The fitting results of the cross-sectional profiles of the slices distributed along the long axis of the target member are as follows: , ( , () represents the coordinates of the center of the cross section of the slice in the previous iteration; If we calculate the distance between the center of the cross-section of the current slice and the center of the cross-section of the previous valid slice... The fitting center is shifted to the outside of the target member, the current abnormal center is discarded, and the center of the cross section of the effective slice in the previous iteration is used or interpolated to replace it, thereby eliminating isolated misjudged points in space.

[0011] More preferably, the initial skeleton points are extracted by slicing the pure point cloud, a cubic B-spline curve is fitted, a bending sag function is defined, and the zero point of the derivative of the bending sag function is solved in the continuous parameter domain to obtain the theoretical maximum bending position of the target member, including: For the center coordinates of the extracted effective slice's cross-sectional profile, the cross-sectional coordinates in the local coordinate system are: ,Right now For the initial skeleton points of the cross section of this effective slice in the local coordinate system, transform the initial skeleton points in the local coordinate system back to the initial skeleton points in the world coordinate system. ; Define the vector connecting the first and last endpoints of the fitted B-spline curve as... Any point on the B-spline curve arrive The vertical distance is According to the extreme value condition The theoretical extreme parameters are obtained by solving. Thus, the theoretical maximum bending position in the local coordinate system is obtained. Axis coordinates ,in, The curve is a cubic B-spline fitted curve, with subscripts... Representing the local coordinate system Axial components, This indicates the optimal parameters of the cubic B-spline fitted curve at the theoretical extreme value. The point at that location in the local coordinate system Axis coordinate values.

[0012] More preferably, a region of interest is defined centered on the theoretical maximum curvature position. Within this region, the original point cloud set is backsampled to obtain the skeleton points of the region of interest. Then, the RANSAC algorithm is used to fit a quadratic polynomial trend line to perform trend locking and cleaning of the skeleton points, including: At the theoretical maximum bending position Set the window as the center. For the region of interest, where Using a preset distance threshold, we backtrack to the original point cloud set and perform slice fitting with a preset density to obtain the skeleton point set of the region of interest; Project the skeleton point set of the region of interest onto... and Planes, respectively fitted with quadratic curves using RANSAC. As a trend line, in , , and , , These are the coefficients of the corresponding quadratic polynomial fitting curve in the plane. Indicates the independent variable. , Let each be a dependent variable of the quadratic polynomial fitting curve in the corresponding plane, and calculate the skeleton point set of the region of interest. The residuals from each skeleton point to the trend line are used to eliminate those with residuals greater than a set threshold. Outliers.

[0013] A more preferred objective function for weighted fitting is: ; in, The cleaned region of interest skeleton point set The first in Each skeleton point has a weight. Set as global weight times ( ), As a smoothing factor, skeleton points The corresponding curve parameters, To finely fit the curve in parameters The coordinates of the fitted point at that location, To finely fit the curve with respect to the curve parameters The second derivative, skeleton points The corresponding curve parameters.

[0014] Secondly, this invention protects a spatial structural member bending measurement system based on geometric gate noise reduction and derivative-guided backtracking, the measurement system comprising: The data acquisition and preprocessing module is used to acquire the original point cloud set of the target member and correct the original point cloud set to be oriented with the major axis of the target member as the reference point. Local coordinate system of the axis; The physical radius locking module is used to randomly sample multiple sections along the long axis of the target rod based on the original point cloud set in the local coordinate system, perform unconstrained circle fitting on each section, and use the median of the unconstrained circle fitting radius as the physical true radius of the target rod. The geometric access control denoising module is used to construct geometric access control constraint functions based on the physical true radius, identify the radius of randomly sampled circular models, remove circular models that do not conform to the physical true radius, and clean the connected components through DBSCAN clustering to obtain the clean point cloud of the target rod. The derivative optimization module is used to slice the pure point cloud to extract the initial skeleton points, fit a cubic B-spline curve, define the bending sag function, solve for the zero point of the derivative of the bending sag function in the continuous parameter domain, and obtain the theoretical maximum bending position of the target rod. The backtracking resampling module is used to set the region of interest with the theoretical maximum bending position as the center, backtracking resampling the original point cloud set within the region of interest to obtain the skeleton points of the region of interest, and using the RANSAC algorithm to fit a quadratic polynomial trend line to perform trend locking and cleaning of the skeleton points of the region of interest. The weighted fitting module is used to assign weights to the skeleton points of the cleaned region of interest, perform weighted fitting, and calculate the final bending sag of the target member.

[0015] Preferably, the geometric access control noise reduction module includes: The extraction module is used to take any cross-section along the long axis of the target member as a cross-sectional area for a slice, and randomly extract 3 points from the point cloud of the cross-sectional area. As the minimum sample set; The circle model fitting module is used to calculate three points. Determined center of circle and radius , generate Center of the circle A circular model with radius . The judgment module is used to calculate the radius. If the absolute value of the difference between the actual radius and the physical radius is greater than the preset geometric tolerance, the circle model is determined to be a pseudo model generated by noise, and is directly discarded and skipped from subsequent calculations; if the absolute value is less than or equal to the preset geometric tolerance, the distance from all points in the cross section of the slice to the center of the circle model is calculated, and points whose absolute value of the difference between the distance and the actual radius is less than or equal to the preset geometric tolerance are taken as interior points, and the number of interior points is counted. The iteration module repeats the processes of the extraction module, the circle model fitting module, and the judgment module. It retains the circle model parameter with the most interior points as the final fitting result of the cross-section of the slice, and obtains the center coordinates of the cross-section of the slice. ; The DBSCAN clustering and cleaning module is used to perform DBSCAN clustering on the interior points after random sampling consistency iteration is completed on the cross-sections of all slices of the target member. It retains the cluster with the most interior points and removes spatially isolated misjudged points.

[0016] Beneficial effects: (1) This invention utilizes the rigidity characteristic of the constant cross-sectional radius of the rod to propose the geometric access control random sampling consistency (RANSAC) mechanism. Unlike the traditional post-processing screening, this method directly rejects pseudo-models that do not conform to the physical radius during the RANSAC fitting process, thus fundamentally solving the problem of cable entanglement interference.

[0017] (2) This invention adopts a mathematical model to guide physical sampling, proposes a coarse-to-fine closed-loop feedback mechanism, utilizes the continuous differentiability of B-spline curves, predicts the extreme value position by solving the zero point of the derivative of the bending sag function in the continuous domain, and guides the backtracking resampling of ROI skeleton points.

[0018] (3) In the skeleton point resampling stage, the present invention introduces RANSAC parabolic trend lock and local median filtering to effectively remove residual high-weight noise in the ROI region and prevent non-physical oscillations in the fitted curve.

[0019] (4) This invention significantly suppresses the systematic underfitting error caused by the traditional uniform slicing method from a mathematical perspective. Theoretically, it can reduce the upper bound of the approximation error to one percent of the traditional method, greatly improving the measurement accuracy of curve fitting. It is suitable for construction quality acceptance and safety assessment of large spatial grid structures. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 It is the original point cloud of a noisy, curved rod.

[0022] Figure 2 It is the pure point cloud of the rod after the geometric access control noise reduction.

[0023] Figure 3 It is the skeleton points (local) of the extracted rod point cloud.

[0024] Figure 4 It involves fitting B-spline curves (locally) to the skeleton points.

[0025] Figure 5 The maximum bending position is obtained by finding the derivative.

[0026] Figure 6 It is a curved rod for suspending cables.

[0027] Figure 7 The bending value is measured manually.

[0028] Figure 8 The results of coarse fitting and derivative optimization are shown in the figure; (a) is the bending sag function. (a) Schematic diagram of theoretical peak location; (b) is the bending sagitta function. The result of the first derivative is shown in the figure.

[0029] Figure 9 The results of ROI backtracking and trend cleaning are shown in the figure; (a) is the high-density resampling of ROI region backtracking (step size 5mm, including discrete skeleton points); (b) is the RANSAC trend lock cleaning result (2 outliers were removed and 39 valid ROI skeleton points were retained).

[0030] Figure 10 It is the result of weighted fine fitting and the final calculation result of bending sagitta. Detailed Implementation

[0031] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention. It should be understood that the terminology used in this invention is merely for describing particular embodiments and is not intended to limit the present invention.

[0032] Example 1: A Method for Measuring Rod Bending Based on Geometric Gating and Derivative Backtracking This embodiment provides a method for measuring the bending of a rod based on geometric access control and derivative backtracking, including: S1. Data Acquisition and Preprocessing: Obtain the original point cloud set of the target member, calculate the eigenvectors of the covariance matrix of the original point cloud set using Principal Component Analysis (PCA), and correct the original point cloud set to be aligned with the major axis of the target member. Local coordinate system of the axis; S2. Adaptive Physical Radius Locking: Based on the original point cloud set in the local coordinate system, random multi-section sampling is performed along the long axis of the target member. Unconstrained circle fitting is performed on each section, and the median of the unconstrained circle fitting radius is used as the true physical radius. ; S3, Geometric Access Control Noise Reduction: Based on Physical Real Radius Constructing geometric gate constraint functions The radius of the randomly sampled circle model is identified, and those that do not conform to the physical reality are eliminated. The circular model was obtained, and the connected components were cleaned by DBSCAN clustering to obtain the pure point cloud of the target rod. S4. Coarse Fitting and Derivative Optimization: Extract initial skeleton points by slicing the pure point cloud. Fit a cubic B-spline curve and define the bending sagitta function. Solving in the continuous parameter domain To obtain the theoretical maximum bending position of the target member. ; S5, ROI Retrospection and Trend Cleansing: Based on the theoretical maximum bending position A region of interest (ROI) is set at the center. The original point cloud set is backtracked to perform high-density resampling of ROI skeleton points. The RANSAC algorithm is used to fit a quadratic polynomial trend line to perform trend locking and cleaning of the resampled ROI skeleton points. S6. Weighted fine fitting: Assign weights to the skeleton points of the cleaned region of interest, perform weighted fitting, and calculate the final bending sag of the target member.

[0033] Specifically, S1 uses data pose normalization to obtain the original point cloud set of the target member. This set is typically located in the world coordinate system, and the covariance matrix is ​​constructed. The eigenvalues ​​of the target member are decomposed, and the eigenvector corresponding to the largest eigenvalue is the major axis direction of the member. A rotation matrix is ​​then constructed based on this. Correct the target member to the alignment along The local coordinate system is axially distributed, where N represents the total number of points in the original point cloud set; T represents the transpose sign.

[0034] Construct rotation matrix Correct the target member to the alignment along The specific operations for establishing a local coordinate system with axial distribution are as follows: A1. Centralized processing: First, calculate the original point cloud set. geometric center The coordinates of each point in the original point cloud set are centered relative to the geometric center: This makes the geometric center of the original point cloud set coincide with the origin of the local coordinate system, where This represents the original point cloud after decentralization.

[0035] A2. Constructing the covariance matrix: Construct a 3x3 covariance matrix. : ; A3. Eigenvalue decomposition: For the covariance matrix... Perform eigenvalue decomposition to obtain eigenvalues ​​λ1≥λ2≥λ3 and their corresponding unit eigenvectors. , , .

[0036] A4. Constructing the rotation matrix and transformation: Take the unit eigenvector v1 corresponding to the largest eigenvalue λ1 as the major axis direction of the target member (i.e., the X-axis of the local coordinate system), and construct the rotation matrix. assemble the original point cloud Local correction space mapped to the local coordinate system Its expression is At this point, the major axis of the target member is perfectly aligned with the X-axis of the coordinate system.

[0037] In S3, geometric gate noise reduction is the core anti-interference operation in this embodiment, specifically including random sampling over the entire length range. slices (e.g.) An unconstrained fitted circle is used, and the median radius is taken as the physical true radius. .

[0038] Access control discrimination: In the Random Sample Consensus (RANSAC) iteration, for the circular model generated by random sampling... ,like If the value is 10mm, it is considered an interference model (electrical wire or walkway) and is directly removed. Connectivity cleaning: DBSCAN clustering is performed on the internal points, retaining the cluster with the most points and removing spatially isolated misclassified points.

[0039] The geometric gate function in the above steps Defined as: ; in, The radius of the circle model generated by the current RANSAC iteration. For the preset geometric tolerance, Represents the physical true radius. Indicates otherwise; when When this happens, the current model is discarded directly without performing interior point statistics.

[0040] The specific process for S3 is as follows: B1. Minimal Set Sampling: For a single rod point cloud, take any cross section of the rod as the cross section of a slice, and randomly select 3 points. As the minimum sample set.

[0041] B2. Using the geometric principle that three points determine a circle, analytically calculate the center of the circle determined by these three points. and radius .

[0042] B3. If the calculated radius If the model (a circle defined by three points) is determined to be a "pseudo-model" generated by noise (such as wires), it will be discarded and subsequent calculations will be skipped.

[0043] B4, if Then calculate the distance from all points within the slice to the center of the circle. Statistical satisfaction The number of points.

[0044] B5. Repeat the RANSAC iteration process described above, retaining the circle model parameter with the most interior points as the final fitting result for the section, and obtain the center coordinates of the circle of the section profile. .

[0045] B6. After completing circle fitting for all slices, perform connected component cleaning. Define a threshold for the Euclidean distance between the centers of adjacent slices. .

[0046] Fitting results for slices distributed along the axial direction of the member: ; If the calculated distance between the center of the current slice and the center of the previous valid slice... If the abnormal center is found to be outside the member due to noise interference from wires or other sources, it will be determined that the fitting center has shifted to the outside of the member. The current abnormal center will be forcibly discarded, and the center of the cross section of the effective slice in the previous iteration will be used or interpolated to replace it, thereby eliminating isolated misjudged points in space and ensuring the continuity of the skeleton.

[0047] S4 uses continuous-domain derivative optimization to extract initial skeleton points from the denoised clean point cloud. A cubic B-spline curve is fitted, and the peak value is determined using derivative optimization. Specifically, derivative optimization involves defining the vector connecting the first and last endpoints of the fitted curve as... Any point on the B-spline curve arrive The vertical distance is By solving nonlinear programming problems By identifying the extreme values ​​and using numerical optimization algorithms to approximate the zero point of the first derivative, the peak value can be located in the continuous parameter domain, thus avoiding missed measurements caused by discrete slicing.

[0048] The expression is: , The coordinates of the first endpoint of the cubic B-spline fitted curve are given.

[0049] To find the maximum curvature, i.e., to solve... According to Fermat's lemma, the derivative at the extreme point is zero: ; Solving this equation yields the theoretical extremum parameters. Thus, the theoretical maximum bending position in the local coordinate system is obtained. Axis coordinates ,in, The curve is a cubic B-spline fitted curve, with subscripts... Representing the local coordinate system Axial components, This indicates that the cubic B-spline fitted curve is in the parameter The point at that location in the local coordinate system Axis coordinate values. This step breaks through the limitations of discrete slicing and locks the peak value in the continuous domain.

[0050] Initial skeleton points in the above process The extraction process is as follows: The center coordinates of the valid slice extracted for Random Sampling Consistency (RANSAC) The cross-sectional coordinates in the local coordinate system are ,Right now For the initial skeleton points of the cross section of this effective slice in the local coordinate system, transform the initial skeleton points in the local coordinate system back to the initial skeleton points in the world coordinate system. According to the inverse transformation principle of principal component analysis, the coordinate transformation satisfies the following transformation relationship: ; in, Representing the rotation matrix Transpose.

[0051] In obtaining discrete skeleton points Then, each initial skeleton point can be used. Fitting a cubic B-spline curve is similar to linear fitting or curve fitting of planar points. Further details will not be elaborated here.

[0052] The specific operation of S5 is as follows: Set the window as the center. (Region of Interest), return to the original point cloud set, and perform high-density (e.g., 5mm spacing) slicing fitting to obtain the ROI skeleton point set. Trend Lock: This technique addresses persistent noise points close to the surface of the rod within the ROI region by using the RANSAC algorithm to fit a quadratic curve. ,in The coefficient of the quadratic term, The coefficient of the linear term, This is a constant term. Outliers that are more than 15mm away from the trend line are removed. This step ensures the stability of subsequent high-weighted fitting.

[0053] Based on the trend lock principle described above, the specific operation of trend lock cleaning in this embodiment is as follows: project all skeleton points to... and Plane; fit quadratic polynomial trend lines using the RANSAC algorithm respectively. As a trend line, in , , and , , These are the coefficients of the corresponding quadratic polynomial fitting curve in the plane. Indicates the independent variable. , Let each be a dependent variable of the quadratic polynomial fitting curve in the corresponding plane, and calculate the skeleton point set of the region of interest. The residuals from each skeleton point to the trend line are used to eliminate those with residuals greater than a set threshold. Outlier points (e.g., 15mm) are used to prevent non-physical oscillations.

[0054] The objective function for weighted fine fitting in S6 is: ; in, The cleaned region of interest skeleton point set The first in Each skeleton point has a weight. Set as global weight times ( ), As a smoothing factor, To finely fit the curve in parameters The coordinates of the fitted point at that location, To finely fit the curve with respect to parameters The second derivative, skeleton points The corresponding curve parameters.

[0055] Subsequently, a fine-fit curve was obtained. The two ends and And define the vector connecting the two endpoints. Therefore, refine the fitted curve Any skeleton point perpendicular distance to the connecting vector V for: = ; Furthermore, the obtained The maximum value is the final bending sagitta.

[0056] Weights are assigned to skeleton points within the region of interest. =10, proof of convergence of the error in calculating the final high-precision bending sagitta: Let the actual bending curve of the rod be... The maximum bending occurs at Axis coordinates In the traditional uniform slicing method, the slice spacing is assumed to be... ,Leave The nearest sampling point Axis coordinates are According to Taylor's expansion formula, in Nearby error for: ; in For the member at its theoretical maximum bending position The true bending sagitta value at the location; For the rod at discrete sampling points The true bending sagitta value at that location. For true curved curves At the position of maximum bending The first derivative, The second derivative represents the local curvature at that location.

[0057] because It is an extreme point. ,and Then the upper bound of the error is: ; As can be seen from the above formula, the systematic error of the traditional method is related to the slice step size. square Proportional.

[0058] In this method, the ROI is located using derivatives, and the sampling step size is locally increased. The new upper bound of the error then becomes: ; Example 2: Rod Bending Measurement System Based on Geometric Access Control and Derivative Backtracking This embodiment provides a rod bending measurement system based on geometric access control and derivative backtracking. The measurement system includes: The data acquisition and preprocessing module is used to acquire the original point cloud set of the target member and correct the original point cloud set to be oriented with the major axis of the target member as the reference point. Local coordinate system of the axis; The physical radius locking module is used to randomly sample multiple sections along the long axis of the target rod based on the original point cloud set in the local coordinate system, perform unconstrained circle fitting on each section, and use the median of the unconstrained circle fitting radius as the physical true radius of the target rod. The geometric access control denoising module is used to construct geometric access control constraint functions based on the physical true radius, identify the radius of randomly sampled circular models, remove circular models that do not conform to the physical true radius, and clean the connected components through DBSCAN clustering to obtain the clean point cloud of the target rod. The derivative optimization module is used to slice the pure point cloud to extract the initial skeleton points, fit a cubic B-spline curve, define the bending sag function, solve for the zero point of the derivative of the bending sag function in the continuous parameter domain, and obtain the theoretical maximum bending position of the target rod. The backtracking resampling module is used to set the region of interest with the theoretical maximum bending position as the center, backtracking resampling the original point cloud set within the region of interest to obtain the skeleton points of the region of interest, and using the RANSAC algorithm to fit a quadratic polynomial trend line to perform trend locking and cleaning of the skeleton points of the region of interest. The weighted fitting module is used to assign weights to the skeleton points of the cleaned region of interest, perform weighted fitting, and calculate the final bending sag of the target member.

[0059] The geometric access control noise reduction module includes: The extraction module is used to take any cross-section along the long axis of the target member as a cross-sectional area for a slice, and randomly extract 3 points from the point cloud of the cross-sectional area. As the minimum sample set; The circle model fitting module is used to calculate three points. Determined center of circle and radius , generate Center of the circle A circular model with radius . The judgment module is used to calculate the radius. If the absolute value of the difference between the actual radius and the physical radius is greater than the preset geometric tolerance, the circle model is determined to be a pseudo model generated by noise, and is directly discarded and skipped from subsequent calculations; if the absolute value is less than or equal to the preset geometric tolerance, the distance from all points in the cross section of the slice to the center of the circle model is calculated, and points whose absolute value of the difference between the distance and the actual radius is less than or equal to the preset geometric tolerance are taken as interior points, and the number of interior points is counted. The iteration module repeats the processes of the extraction module, the circle model fitting module, and the judgment module. It retains the circle model parameter with the most interior points as the final fitting result of the cross-section of the slice, and obtains the center coordinates of the cross-section of the slice. ; The DBSCAN clustering and cleaning module is used to perform DBSCAN clustering on the interior points after random sampling consistency iteration is completed on the cross-sections of all slices of the target member. It retains the cluster with the most interior points and removes spatially isolated misjudged points.

[0060] Application example: For bent poles with suspended cables, such as... Figure 6 As shown, during 3D scanning, a raw point cloud set containing the target pole and suspension cables (noise) is obtained, such as... Figure 1 As shown. The specific processing and recognition application flow is as follows: First, the data pose is normalized. Principal component analysis (PCA) is used to calculate the eigenvectors of the covariance matrix of the original point cloud set, correcting the irregularly oriented rod point cloud to the local coordinate system so that its principal axis (major axis) is perfectly aligned with the X-axis. Then, random multi-section sampling is performed along the entire length of the rod, and unconstrained circle fitting is performed. The median of the fitted radius is adaptively extracted as the physical true radius of the rod. .

[0061] Next, geometric gating denoising is performed. A geometric gating function is introduced into the RANSAC circle fitting iteration. The local point cloud geometry curvature caused by the suspended cable differs from the actual physical radius of the rod. The differences are significant, and the access control mechanism will directly identify and eliminate these interference points caused by cables; at the same time, it will combine DBSCAN clustering to eliminate spatially isolated false points, thereby completely removing cable noise and obtaining clean point cloud data (such as...). Figure 2 (As shown).

[0062] After obtaining the clean point cloud, extract the initial skeleton points using the standard step size (e.g., ...). Figure 3 As shown), and perform a coarse fit on it using a cubic B-spline curve (as shown). Figure 4 As shown), the peak value is determined by derivative optimization (e.g. Figure 5 As shown), the derivative optimization specifically involves defining the vector connecting the first and last endpoints of the fitted curve as... Any point on the B-spline curve arrive The vertical distance is ,like Figure 8 As shown in (a). To avoid the problem of the discrete slices missing the actual maximum bending point, the property of the continuous differentiability of the B-spline curve is utilized to solve the bending sagitta function. The zero of the first derivative is used to precisely locate the theoretical maximum bending position in the continuous domain. ,like Figure 8 As shown in (b), the theoretical extreme parameter The maximum bending position is 0.52. It is 520mm.

[0063] Subsequently, this measurement system triggered a derivative-guided backtracking mechanism, using the theoretical peak value... Define a region of interest (ROI) centered on the point cloud, then backtrack to the original point cloud set and perform high-density resampling of this local region to extract a high-density ROI skeleton point set (e.g., ...). Figure 9 As shown in (a)). To prevent interference from persistent noise points close to the surface of the rod, a quadratic polynomial trend line is fitted using RANSAC. Outliers exceeding a set threshold from the trend line are removed. In this embodiment, two discrete points are removed, leaving 39 valid ROI skeleton points, thus completing trend locking and cleaning (as shown in (a)). Figure 9 (as shown in (b)).

[0064] Finally, a weighted fine-fit is performed. The cleaned, high-density ROI skeleton points are assigned extremely high weights; in this embodiment, the ROI skeleton point weights are... =10, substitute into the objective function to perform weighted fine fitting. Extract the two endpoints of the fine-fit curve to construct the baseline connection vector V, and calculate the perpendicular distance from the ROI skeleton point to this connection vector. The final calculated maximum vertical distance is the high-precision bending sag of the rod with the suspension cable (e.g., Figure 10 (As shown). In this case, the actual bending target value is 100mm, as... Figure 7 As shown, the outline of the rod was scanned by a handheld high-precision scanner and the bending value was measured manually. The bending value obtained was 99.3 mm. The maximum bending value calculated by the above measurement algorithm of the present invention was 98.75 mm, with an error of 0.55 mm.

[0065] The above-described embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited thereto. Any simple changes or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the scope of the technology disclosed in the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for measuring rod bending based on geometric access control and derivative backtracking, characterized in that, The measurement method includes: Obtain the original point cloud set of the target member, and correct the original point cloud set to be oriented with the major axis of the target member as the reference point. Local coordinate system of the axis; Based on the original point cloud set in the local coordinate system, random multi-section sampling is performed along the long axis of the target rod. Unconstrained circle fitting is performed on each section, and the median of the unconstrained circle fitting radius is taken as the physical true radius of the target rod. Based on the physical true radius, a geometric access control constraint function is constructed. The radius of the randomly sampled circular model is identified, and the circular model that does not conform to the physical true radius is eliminated. The connected component is cleaned by DBSCAN clustering to obtain the pure point cloud of the target rod. The initial skeleton points are extracted by slicing the pure point cloud, a cubic B-spline curve is fitted, the bending sag function is defined, and the zero point of the derivative of the bending sag function is solved in the continuous parameter domain to obtain the theoretical maximum bending position of the target rod. The region of interest is set with the theoretical maximum bending position as the center. The original point cloud set is backsampled within the region of interest to obtain the skeleton points of the region of interest. The RANSAC algorithm is then used to fit a quadratic polynomial trend line to perform trend locking and cleaning of the skeleton points of the region of interest. Weights are assigned to the skeleton points of the cleaned region of interest, and a weighted fitting is performed to calculate the final bending sag of the target member. A geometric gate constraint function is constructed based on the physical true radius. Radius identification is performed on randomly sampled circular models, eliminating those that do not conform to the physical true radius. Connectivity cleansing is then performed using DBSCAN clustering to obtain a clean point cloud of the target member, including: Take any section along the major axis of the target member as the current slice's cross-section, and randomly select 3 points from the point cloud of this cross-section. As the minimum sample set; Calculate 3 points Determined center of circle and radius , generate Center of the circle A circular model with radius . If radius If the absolute value of the difference between the circle model and the actual physical radius is greater than the preset geometric tolerance, the circle model is determined to be a pseudo model generated by noise, and is directly discarded and the subsequent calculation is skipped. If radius If the absolute value of the difference between the actual radius and the physical radius is less than or equal to the preset geometric tolerance, then calculate the distance from all points in the cross section of the slice to the center of the circle model. Points whose absolute value of the difference between the distance and the actual radius is less than or equal to the preset geometric tolerance are taken as interior points, and the number of interior points is counted. Repeat the above random sampling consensus iteration process, retain the circle model parameter with the most interior points as the final fitting result of the cross-section of the slice, and obtain the center coordinates of the cross-section of the slice. ; After completing the random sampling consistency iteration on the cross-section of all slices of the target member, DBSCAN clustering is performed on the interior points, retaining the cluster with the most interior points and removing spatially isolated misjudged points. The expression for the geometric gate function is as follows: ； in, For the preset geometric tolerance, when When =0, the current circle model is discarded directly. Represents the physical true radius. This indicates otherwise.

2. The measurement method according to claim 1, characterized in that, Obtain the original point cloud set of the target member, and correct the original point cloud set to be oriented with the major axis of the target member as the reference point. The local coordinate system of the axes includes: Obtain the original point cloud set of the target member, calculate the geometric center of the original point cloud set, and center the coordinates of each point in the original point cloud set relative to the geometric center so that the geometric center of the original point cloud set coincides with the origin of the local coordinate system. Construct the covariance matrix, perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues, and sort the eigenvalues ​​from largest to smallest; Take the eigenvector corresponding to the largest eigenvalue as the major axis direction of the target member, construct a rotation matrix, and map the original point cloud set to the local correction space of the local coordinate system. At this time, the major axis direction of the target member is completely aligned with the X-axis of the local coordinate system.

3. The measurement method according to claim 1, characterized in that, After completing the random sampling consensus iteration on the cross-sections of all slices of the target member, DBSCAN clustering is performed on the interior points. The cluster with the most interior points is retained, and spatially isolated misclassified points are removed, including: Define the Euclidean distance threshold between the centers of the cross sections of adjacent slices. The fitting results of the cross-sectional profiles of the slices distributed along the long axis of the target member are as follows: , ( , () represents the coordinates of the center of the cross section of the slice in the previous iteration; If we calculate the distance between the center of the cross-section of the current slice and the center of the cross-section of the previous valid slice... The fitting center is shifted to the outside of the target member, the current abnormal center is discarded, and the center of the cross section of the effective slice in the previous iteration is used or interpolated to replace it, thereby eliminating isolated misjudged points in space.

4. The measurement method according to claim 3, characterized in that, The initial skeleton points are extracted by slicing the pure point cloud, a cubic B-spline curve is fitted, a bending sag function is defined, and the zero point of the derivative of the bending sag function is solved in the continuous parameter domain to obtain the theoretical maximum bending position of the target member, including: For the center coordinates of the extracted effective slice's cross-sectional profile, the cross-sectional coordinates in the local coordinate system are: ,Right now For the initial skeleton points of the cross section of this effective slice in the local coordinate system, transform the initial skeleton points in the local coordinate system back to the initial skeleton points in the world coordinate system. ; Define the vector connecting the first and last endpoints of the fitted B-spline curve as... Any point on the B-spline curve arrive The vertical distance is According to the extreme value condition The theoretical extreme parameters are obtained by solving. Thus, the theoretical maximum bending position in the local coordinate system is obtained. Axis coordinates ,in, The curve is a cubic B-spline fitted curve, with subscripts... Representing the local coordinate system Axial components, This indicates the optimal parameters of the cubic B-spline fitted curve at the theoretical extreme value. The point at that location in the local coordinate system Axis coordinate values.

5. The measurement method according to claim 4, characterized in that, A region of interest (ROI) is defined centered on the theoretical maximum curvature position. Within this ROI, the original point cloud dataset is backsampled to obtain the ROI skeleton points. The RANSAC algorithm is then used to fit a quadratic polynomial trend line to perform trend locking and cleaning of the ROI skeleton points, including: At the theoretical maximum bending position Set the window as the center. For the region of interest, where Using a preset distance threshold, we backtrack to the original point cloud set and perform slice fitting with a preset density to obtain the skeleton point set of the region of interest; Project the skeleton point set of the region of interest onto... and Planes, respectively fitted with quadratic curves using RANSAC. and As a trend line, where... , , and , , These are the coefficients of the corresponding quadratic polynomial fitting curve in the plane. Indicates the independent variable. , Let each of these be the dependent variables of the quadratic polynomial fitting curve in the corresponding plane. Calculate the residual from each skeleton point in the skeleton point set of the region of interest to the trend line, and discard those with residuals greater than a set threshold. Outliers.

6. The measurement method according to claim 5, characterized in that, The objective function for weighted fitting is: ； in, The cleaned region of interest skeleton point set The first in One skeleton point, weight Set as global weight times, As a smoothing factor, skeleton points The corresponding curve parameters, To finely fit the curve, in the curve parameters The coordinates of the fitted point at that location, To finely fit the curve with respect to parameters The second derivative of .

7. A rod bending measurement system based on geometric access control and derivative backtracking, used to implement the measurement method described in any one of claims 1-6, characterized in that, The measurement system includes: The data acquisition and preprocessing module is used to acquire the original point cloud set of the target member and correct the original point cloud set to be oriented with the major axis of the target member as the reference point. Local coordinate system of the axis; The physical radius locking module is used to randomly sample multiple sections along the long axis of the target rod based on the original point cloud set in the local coordinate system, perform unconstrained circle fitting on each section, and use the median of the unconstrained circle fitting radius as the physical true radius of the target rod. The geometric access control denoising module is used to construct geometric access control constraint functions based on the physical true radius, identify the radius of randomly sampled circular models, remove circular models that do not conform to the physical true radius, and clean the connected components through DBSCAN clustering to obtain the clean point cloud of the target rod. The derivative optimization module is used to slice the pure point cloud to extract the initial skeleton points, fit a cubic B-spline curve, define the bending sag function, solve for the zero point of the derivative of the bending sag function in the continuous parameter domain, and obtain the theoretical maximum bending position of the target rod. The backtracking resampling module is used to set the region of interest with the theoretical maximum bending position as the center, backtracking resampling the original point cloud set within the region of interest to obtain the skeleton points of the region of interest, and using the RANSAC algorithm to fit a quadratic polynomial trend line to perform trend locking and cleaning of the skeleton points of the region of interest. The weighted fitting module is used to assign weights to the skeleton points of the cleaned region of interest, perform weighted fitting, and calculate the final bending sag of the target member.

8. The measurement system according to claim 7, characterized in that, The geometric access control noise reduction module includes: The extraction module is used to take any cross-section along the long axis of the target member as a cross-sectional area for a slice, and randomly extract 3 points from the point cloud of the cross-sectional area. As the minimum sample set; The circle model fitting module is used to calculate three points. Determined center of circle and radius , generate Center of the circle A circular model with radius . The judgment module is used to calculate the radius. If the absolute value of the difference between the actual radius and the physical radius is greater than the preset geometric tolerance, the circle model is determined to be a pseudo model generated by noise, and is directly discarded and skipped from subsequent calculations; if the absolute value is less than or equal to the preset geometric tolerance, the distance from all points in the cross section of the slice to the center of the circle model is calculated, and points whose absolute value of the difference between the distance and the actual radius is less than or equal to the preset geometric tolerance are taken as interior points, and the number of interior points is counted. The iteration module repeats the processes of the extraction module, the circle model fitting module, and the judgment module. It retains the circle model parameter with the most interior points as the final fitting result of the cross-section of the slice, and obtains the center coordinates of the cross-section of the slice. ; The DBSCAN clustering and cleaning module is used to perform DBSCAN clustering on the interior points after random sampling consistency iteration is completed on the cross-sections of all slices of the target member. It retains the cluster with the most interior points and removes spatially isolated misjudged points.

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