Prefabricated bridge pier column installation quality automatic evaluation method based on three-dimensional laser point cloud

Abstract

The invention provides a prefabricated bridge pier column installation quality automatic evaluation method based on a three-dimensional laser point cloud. The prefabricated bridge pier column installation quality automatic evaluation method is used for measuring the perpendicularity of a high pier and the distance between pier columns. The method comprises the following steps: an unmanned aerial vehicle laser scanning system collects pier point cloud data according to an optimized flight path, and pre-processes the pier point cloud data to improve data quality; quickly segmenting the point cloud by using an improved adaptive octree and a machine learning algorithm, and extracting a pier point cloud; and based on the finely segmented point cloud, calculating the included angle between the center axis of the bridge pier and the plane normal of the capping beam and the coordinate of the center point of the top surface of the bridge pier to realize accurate evaluation of the perpendicularity of the bridge pier and the distance between adjacent bridge piers. The optimization of the flight path of the unmanned aerial vehicle is combined with the point cloud data preprocessing, so that the data quality can be effectively improved, and the data volume is reduced. Meanwhile, point cloud segmentation is performed by fusing an improved adaptive octree and a machine learning algorithm, so that piers, capping beams and backgrounds can be accurately distinguished, and geometric features of pier studs are completely extracted.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of bridge monitoring, and particularly relates to a prefabricated bridge pier installation quality automatic evaluation method based on three-dimensional laser point clouds. BACKGROUND

[0002] In the field of bridge construction, prefabricated structures are increasingly widely applied due to their quality control advantages, cost-effectiveness and fast construction speed. Among them, prefabricated pier installation is a key link, and its quality directly affects the subsequent construction efficiency and the overall structural performance of the bridge.

[0003] During the installation of the prefabricated pier, mortar needs to be uniformly laid on the surface of the cap beam to provide a stable and flat foundation, and then the pier column is installed through sleeve-reinforcement connection, and it is crucial to ensure that the sleeve and the embedded reinforcement are accurately aligned. During the assembly stage, a total station instrument is often used to monitor the positional deviation, and a jack is used to adjust the angle to ensure the perpendicularity and the central position; during the grouting stage, it is necessary to ensure that the grouting material fills the gap between the pier bottom and the cap beam to form a reliable bearing interface, and then high-strength grouting material is injected to realize fixed connection. The entire process is highly dependent on manual operation, and high technical and experience requirements are placed on the construction personnel.

[0004] Pier perpendicularity deviation is a key indicator for evaluating the installation quality and is affected by multiple factors. In terms of manual operation, uneven mortar laying and improper jack adjustment can easily lead to deviation; in terms of materials and construction technology, insufficient grouting and abnormal mortar hardening can also cause problems. Moreover, an increase in the height of the pier can amplify the influence of the perpendicularity deviation, change the stress state of the pier, increase the distance difference between adjacent piers, bring difficulties to the subsequent installation of prefabricated components, and even affect the service life and safety of the bridge. Therefore, it is necessary to accurately measure the pier perpendicularity and the relative distance and adjust the design and production of the prefabricated cap beam and segments accordingly.

[0005] At present, a total station instrument is commonly used to measure the angle and distance of the pier, but the thickness of the concrete protective layer is inconsistent, and multiple surfaces and multiple points of a single pier need to be measured, which is complex and low in efficiency. When multiple consecutive piers are detected, the measuring station needs to be frequently moved, and the overall measurement takes a long time, which seriously affects the progress of the project.

[0006] In addition to the total station instrument, three-dimensional reconstruction techniques for obtaining the geometric information of the bridge pier column mainly include image-based and laser-based techniques.

[0007] Image-based three-dimensional reconstruction uses a UAV tilt photography to obtain images and then reconstructs a point cloud model. Although the efficiency and accuracy are improved to a certain extent by optimizing the flight path, using an automatic aerial triangulation framework, and distributing task division, there are still many problems, such as the dependence on the resolution and shooting angle of the camera, the high requirements for the UAV and the photography equipment, the large amount of multi-angle image data, the high consumption of computing resources for model creation, and the long reconstruction time.

[0008] Based on laser three-dimensional reconstruction, three-dimensional information is obtained by measuring reflected light through emitting laser pulses. Ground laser scanning combined with digital twin method can reconstruct bridge pier model to evaluate perpendicularity. However, ground laser scanning has limited range, and large-scale scanning requires multiple deployment of measuring stations, which increases cost and reduces efficiency. Airborne laser scanning combined with specific algorithms can achieve point cloud segmentation and geometric information calculation of large-span bridges.

[0009] And after data acquisition, point cloud segmentation is also crucial when reconstructing three-dimensional point cloud model. Algorithm-based methods include bottom-up and top-down strategies. Bottom-up uses classic algorithms to segment point cloud and then classify, which relies on accurate surface segmentation. In actual scenarios, noise and occlusion will affect the segmentation effect, and manually defined rules have poor adaptability to complex structures. Top-down relies on semantic category knowledge and prior geometric features to simultaneously segment and classify, which relies on design information and clean point cloud. In actual engineering, design deviations, background noise, etc. will limit its application.

[0010] Learning-based methods are represented by deep learning algorithms such as PointNet, which directly process raw data and can automatically learn feature patterns for segmentation. However, actual applications face problems such as the need for a large amount of labeled data, high hardware performance requirements, and long inference time, limiting efficiency and on-site applicability.

[0011] Overall, in the current construction of prefabricated bridges, there are deficiencies in bridge pier installation quality detection and bridge geometric information acquisition technology. Therefore, a new automated, efficient, and accurate quality evaluation method is urgently needed to meet engineering needs. SUMMARY

[0012] To solve the problems existing in the prior art, the present application provides a prefabricated bridge pier installation quality automatic evaluation method based on three-dimensional laser point cloud, comprising the following steps:

[0013] S1, using an unmanned aerial vehicle laser scanning system to collect point cloud data of the bridge pier according to a predetermined flight path;

[0014] S2, preprocessing the collected point cloud data, including using a pass-through filter to remove invalid points and outliers, and applying a voxel grid filter for downsampling;

[0015] S3, using an improved adaptive octree algorithm, a three-dimensional local descriptor for feature calculation, and a machine learning algorithm to quickly segment the preprocessed point cloud data and extract the point cloud of the bridge pier;

[0016] S4, based on the segmented bridge pier point cloud, evaluating the perpendicularity of the bridge pier by calculating the included angle between the pier center axis and the cap beam plane normal;

[0017] S5, based on the segmented bridge pier point cloud, the distance between the centers of the pier top surface is calculated to evaluate the distance between adjacent bridge piers.

[0018] The key reasonable selection feature points of the UAV flight path design. In view of the geometric complexity of the bridge pier in the construction scene, the height of the pier, the lateral spacing and the topographic change of the construction area need to be considered comprehensively. In order to ensure the comprehensive coverage of side scanning and the comprehensive coverage of the bridge pier from top to bottom, a layered Z-shaped flight path can be adopted. By scanning at different height levels, data blind spots can be avoided. For the side scanning path, the flight height h and the path deviation distance L need to be determined according to the height H pillar of the bridge pier and the vertical field of view angle of the laser radar. The flight height h can be expressed as:

[0019]

[0020] Where: h is the flight height, H pillar is the height of the bridge pier, θ vertical is the vertical field of view angle of the laser radar, and L is the path deviation distance.

[0021] In order to ensure the efficiency and accuracy of subsequent point cloud processing, the data is preprocessed. In view of the distribution of the bridge pier and the pile cap along the driving direction, the straight-through filter is first applied to quickly remove invalid points and outliers in the lateral and height range:

[0022] P filtered

[0023] ={(x,y,z)∈P∣x min ≤x i ≤x max ,y min ≤y i ≤y max ,z min ≤z i ≤z max}

[0024] In the formula, P is the original point cloud set, P filtered is the filtered point cloud set, P i is (x i , y i , z i ) is the coordinate of P i in the original point cloud set P, and the subscripts min and max represent the minimum and maximum values of all point coordinates on the corresponding axis respectively.

[0025] And through the voxel fusion (Voxel Grid Filter) to point cloud data dimensionality reduction and simplification, the continuous space is discretized into voxel grid, to ensure high precision, the voxel grid step is limited to not more than 3 mm, to retain the structure of the boundary information. Centroid sampling method is adopted, and the centroid is selected as the representative point in each voxel, which further reduces the data amount:

[0026]

[0027] In the formula, p centroid The centroid of the point cloud set is represented by n, and the number of points in the voxel.

[0028] Although the preprocessing has been carried out, the point cloud data still faces the challenges of large sample size, complex background and significant interference.

[0029] The normal vector characteristics of the pile cap are important basis for evaluating the displacement of the pier column. For the extraction of pile cap plane point cloud, this paper adopts the conventional method based on height filtering. Because the pile cap is low in height and rectangular plane in the point cloud field, combined with its geometric shape and position characteristics, the target point cloud is accurately screened by height limit, which provides a reliable basis for subsequent accurate analysis:

[0030] P GAP_filtered = {(x, y, z) e P | z min ≤ z ≤ z max}

[0031] P GAP_filtered is the point cloud set filtered as the pile cap. First, the Alpha Shape or Convex Hull method is used to extract the preliminary outline of the pile cap. Because the preliminary outline may have curves or irregular edges, the Minimum Bounding Rectangle (MBR) algorithm is used to calculate the bounding box and generate a standardized rectangular outline. The method removes redundant point clouds and completes the missing area of the pile cap.

[0032] In order to solve the problem of bridge pier point cloud segmentation disturbed by background and noise, this paper proposes a kind of bridge pier point cloud fast segmentation method combined with improved adaptive octree and machine learning, which realizes the automatic segmentation of continuous bridge pier.

[0033] An improved adaptive octree voxelization method is proposed to reduce the computational complexity of point cloud segmentation. Based on octree spatial decomposition, the method recursively subdivides the three-dimensional space to enclose the point cloud in the smallest cubic root node. Non-empty voxels continue to be subdivided until the stopping conditions such as the point number threshold or the minimum voxel size are met. The two-stage termination criterion dynamically adjusts the decomposition depth: the first stage determines whether to enter the second stage by comparing the node point number with the threshold α; the second stage calculates the feature values using local descriptors and compares the feature vector differences between adjacent voxels. If the difference exceeds the threshold β, it is considered that there is significant geometric change in the region, and further refinement is needed. Otherwise, the division is stopped. The adaptive octree dynamic adjustment mechanism significantly reduces the number of voxels in smooth regions. The chi-square distance is used to compare the feature vector differences f1 and f2 between adjacent voxels:

[0034]

[0035] where f 1,i and f 2,i are the i-th dimension of vectors f1 and f2, respectively, and ∈ is a small positive number to avoid division by zero.

[0036] The voxel feature value is a key indicator for determining whether to continue voxel division. In the segmentation process of the pier column point cloud, the calculation of the local descriptor is crucial because its result will be used as the input of the machine learning model. Fast Point Feature Histogram (FPFH) is selected as the feature extraction tool for voxels because it is an efficient three-dimensional feature descriptor. It is an accelerated version of Point Feature Histogram (PFH) that quantifies the relationship between the point's own normal vector and the normal vectors of neighboring points to represent three-dimensional geometric features, providing a richer feature space for subsequent classification models and helping to more accurately distinguish target categories and background point clouds.

[0037] Point pair triplet features are the basic components of the descriptor. Before calculation, a local coordinate system needs to be defined, which will ensure the translation and rotation invariance of the local surface of the point cloud. Specifically, for each pair of points P s and P t and their corresponding normal vectors n s and n t , a local coordinate system with UVW axes is constructed with P s as the coordinate origin and P t as the target point. The triplet features α, φ, θ between the point pair P s and P t can be calculated through specific mathematical formulas. These angle features can describe the geometric relationship between the point pair:

[0038] α = arccos (v·n t )

[0039]

[0040] Where d is the distance between two points P t and P s The Euclidean distance between them, d = ||P t -P s ||2. α and φ are the dot products between normalized vectors, where α represents the normal vector n t The angle between it and the coordinate axis v, φ represents the vector P t -P s The angle between the coordinate axis u and θ is the vector n t The angle between u and w after projection onto the plane defined by u and w.

[0041] For the query point P q , a neighborhood sphere with a radius of r is established with it as the center of the sphere, and the neighborhood points in the sphere are searched. PFH calculates the four-tuple features (α, φ, θ, d) of each pair of points in the neighborhood, and places these statistical features in a histogram, thereby forming a relative relationship between all points, which is used to describe the surface features of the point cloud. FPFH is improved on the basis of PFH. First, the SPFH feature descriptor between the query point and the neighborhood point is calculated, ignoring the mutual connection between the neighborhood points. Then, the FPFH descriptor is obtained by calculating the statistical weighted average of the neighborhood point and its adjacent point pairs:

[0042]

[0043] Where, FPFH(p q ) is point p q The final fast point feature histogram feature vector of SPFH(p q ) is point p q Simplified point feature histogram of . Represents point p q The neighborhood point set of w qi is the weight, usually point p q and point p i The Euclidean distance between them.

[0044] After obtaining the feature vectors of each point, the voxel-level FPFH feature vector is calculated by averaging. A voxel contains multiple points, and the FPFH feature vector of this voxel is the average of the FPFH feature vectors of these points:

[0045]

[0046] Point cloud segmentation is performed using a lightweight gradient boosting decision tree machine learning model, LightGBM, which combines the efficiency of traditional methods with the flexibility of machine learning, processing voxels one by one with previously computed voxel-level features as input, high-dimensional feature vectors to distinguish target and background point clouds, balancing efficiency and accuracy in practical applications. LightGBM improves performance through a leaf node growth strategy (preferentially splitting the leaf node with the largest gain to enhance fitting ability and control complexity to prevent overfitting) and a histogram-based algorithm (quickly locating the optimal feature split point, reducing computational complexity and memory usage), based on the gradient boosting framework for iterative training, using a second-order Taylor expansion to approximate the objective function:

[0047]

[0048] where, is the prediction value of the tth iteration. f (t) is the new tree or learning model added through each iteration in the gradient boosting algorithm, used to optimize the objective function and improve the final prediction result; is the first-order derivative of the loss function; is the second-order derivative of the loss function. Because is a constant and has nothing to do with the optimization process, it can be removed from the equation.

[0049] Minimizing the loss by constructing a new decision tree involves node splitting and leaf node weight calculation:

[0050]

[0051] where w j is the weight of the jth leaf node, I j represents the sample set of the jth leaf node, and λ is the regularization parameter, which sets the maximum number of leaf nodes and the minimum number of samples to avoid overfitting.

[0052] LightGBM adopts an additive model form, generating the final prediction value by gradually accumulating the output of each decision tree:

[0053]

[0054] where, is the prediction value, f (t) is the output of the tth decision tree, and T represents the total number of iterations.

[0055] LightGBM model completed the rough segmentation of the bridge pier voxels, but there are scattered voxels or incomplete regions. To refine the segmentation results, the region refinement and fusion method is introduced. First, the initial identified voxels are divided into multiple segments by connected component analysis, and the integrity is evaluated according to the number of segment voxels. The segment with voxel number greater than or equal to the predefined threshold is considered as a complete region, which is directly fitted to the plane and included in the result set, otherwise the incomplete segment is expanded. Expansion is to search for adjacent voxels at the segment boundary, and whether to include them is determined according to whether the distance from the voxel midpoint to the fitted plane is less than the threshold. The iteration is completed for the incomplete region. Then the adjacent regions with similar fitted planes (the distance between planes is less than the predefined threshold) are merged into larger complete regions, and finally the accurate bridge pier set is formed, the steps are as follows:

[0056] S1, initialization: extract connected voxel group {R i} from V, initialize empty set P complete .

[0057] S2, for each voxel group {R i}: if |R i | ≥ predefined threshold, then fit the plane and add to P complete . Otherwise, expand: for each boundary voxel, if the distance to the fitted plane ≤ threshold d th , then add adjacent voxels. If |R i | ≥ threshold V min after expansion, then add to P complete .

[0058] S3, merge regions in P complete : for regions R i , R j , if similar and adjacent, then merge them.

[0059] S4, return P complete .

[0060] After obtaining the three-dimensional reconstruction model, the axis fitting of the pier column is needed:

[0061] Merge the point cloud data of the four vertical surfaces of the pier column into one point cloud set where N is the total number of point clouds of the four surfaces, and the centroid of all points is calculated Decenter the coordinates of all points to obtain q i , and construct the covariance matrix:

[0062]

[0063] where, is the outer product of the decentralized vector of points. Perform eigenvalue decomposition on the covariance matrix C to obtain eigenvalues and corresponding eigenvectors. The eigenvector corresponding to the largest eigenvalue v max is the principal direction of the point cloud distribution, that is, the direction of the pier axis. Therefore, the axis equation can be expressed as:

[0064]

[0065] Where v max is the axis direction, and t is a scalar parameter. The normal vector of the deck plane is the reference for the vertical evaluation of the pier column. The normal vector n cap of the fitted deck plane a·x+b·y+c·z+d=0 is (a, b, c).

[0066] In the step of evaluating the verticality of the bridge pier column, the included angle θ I between the center axis of the pier column and the normal of the bent cap plane is calculated, and the calculation formula is:

[0067]

[0068] Where v axis is the direction vector of the bridge pier center axis. n cap is the normal vector of the bent cap plane.

[0069] The distance between adjacent bridge piers is calculated by calculating the Euclidean distance d between the center points of the pier top surfaces, and the calculation formula is:

[0070]

[0071] Where P 1,top and P 2,top represent the coordinates of the center points of the top surfaces of the two adjacent piers, respectively.

[0072] Beneficial effects: The present application proposes a prefabricated bridge installation quality automatic evaluation system based on 3D laser point cloud. The system can efficiently collect pier point cloud data with the help of an optimized UAV flight path, and effectively improve data quality and reduce data volume through a series of preprocessing operations, laying a solid foundation for subsequent accurate analysis. At the same time, the improved adaptive octree and machine learning algorithm are innovatively combined for point cloud segmentation, which can accurately distinguish between piers, bent caps and backgrounds, and completely extract their geometric features. In addition, according to the point cloud processing flow, the 3D spatial relationship of the pier center axis, the top surface center point and the bent cap plane normal is used to accurately calculate the pier verticality and the adjacent distance, and the quantitative evaluation of the installation quality is realized.

[0073] The application is mainly applied to the quality detection scene of prefabricated bridge construction. It can realize high-precision quality evaluation, greatly reduce detection error, and significantly improve detection efficiency. A single person can quickly complete the quality detection of all piers in the construction section. The entire evaluation process has high automation degree and fast data processing speed, has significant advantages in improving the quality control level of prefabricated bridge construction and speeding up the engineering progress, and strongly promotes the intelligent development of the bridge construction industry. BRIEF DESCRIPTION OF DRAWINGS

[0074] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of these drawings.

[0075] Figure 1 is a schematic diagram of the workflow of the present application;

[0076] Figure 2 is a schematic diagram of flight path planning in the implementation of the present application;

[0077] Figure 3 is a schematic diagram of point cloud data processing flow in the implementation of the present application;

[0078] Figure 4 is a schematic diagram of improved adaptive octree point cloud segmentation in the implementation of the present application;

[0079] Figure 5 is a schematic diagram of three-dimensional local descriptor in the implementation of the present application;

[0080] Figure 6 is a schematic diagram of pier verticality and spacing calculation in the implementation of the present application;

[0081] Figure 7 is a schematic diagram of measurement error in the implementation of the present application. DETAILED DESCRIPTION

[0082] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0083] Embodiment:

[0084] I. System construction and preparation

[0085] See Figures 1-7Before implementing the method, a corresponding software and hardware system needs to be built:

[0086] The UAV-LS in hardware: a UAV with high-performance LiDAR is selected, such as the DJI M350 Pro UAV with Riegl miniVUX-1UAV LiDAR scanner in actual engineering. This combination ensures stable flight performance and longer endurance, meeting the needs of large-area bridge pier point cloud data collection. Its automatic return and obstacle avoidance functions also improve the safety of the data collection process. The data processing device is equipped with a computer with 16 GB of memory, an Intel Core i7-10870H@2.20 GHz processor, and an Nvidia GeForce RTX 3070 Laptop GPU, running Windows 10 64-bit operating system, providing strong computing support for point cloud data processing and analysis.

[0087] In the software environment, point cloud data collection software is equipped for flight path planning, data collection parameter setting, etc. This software supports controlling UAV flight according to the predetermined optimized flight path, and monitors the working state of the LiDAR and the data collection in real time. Professional point cloud processing software such as CloudCompare and PolyWorks needs to be installed to have rich functions of point cloud preprocessing, segmentation, fitting, etc. for subsequent processing and analysis of collected point cloud data. Machine learning algorithm platforms such as Python's Scikit-learn and LightGBM library are selected to implement improved adaptive octree algorithm, three-dimensional local descriptor calculation, and LightGBM machine learning algorithm on the platform to complete the tasks of fast segmentation and classification of point clouds.

[0088] As shown in Figure 2 , the flight height, speed, path deviation distance, etc. of the UAV need to be set according to the actual height, distribution range of the bridge pier, and the performance parameters of the LiDAR. The flight height calculation formula is:

[0089]

[0090] The appropriate flight height is determined in combination with the vertical field angle of the Riegl miniVUX-1UAV LiDAR scanner. The path deviation distance is also adjusted according to the actual situation to ensure comprehensive coverage of the bridge pier area. Before data collection, the LiDAR is calibrated, including distance calibration, angle calibration, etc. to ensure the accuracy of the collected point cloud data. At the same time, appropriate laser emission frequency, scanning angle, etc. parameters are set to improve the density and quality of point cloud data.

[0091] II. Point cloud data acquisition (S1)

[0092] The point cloud data of the bridge pier is collected according to a predetermined optimized flight path using a UAV laser scanning system.

[0093] The design model of the bridge pier is analyzed, and key feature points such as the center point of the top of the pier and the edge point of the bottom are extracted as waypoints. These feature waypoints will serve as an important basis for flight path planning, ensuring that the UAV can scan the bridge pier from different angles. According to the feature waypoints, an optimized flight path is generated. In actual engineering, a layered Z-shaped flight mode is adopted to comprehensively scan the bridge pier at different height layers. The spacing of each layer of flight path is set to between 5-10 meters according to the scanning range of the laser radar and the accuracy requirements of the point cloud data. At the same time, a surrounding flight path is added around the pier to obtain detailed point cloud data of the side of the pier.

[0094] Before the UAV takes off, check whether the power, device connection state, flight parameter settings, etc. of the UAV are normal. Ensure that the laser radar device has been correctly turned on and preheated, ready for data collection. The UAV flies according to the predetermined flight path, while the laser radar continuously emits laser pulses and receives reflected signals to collect point cloud data of the bridge pier. During the flight, the flight status and data collection progress of the UAV are monitored in real time to ensure the integrity and accuracy of the data collection. The collected point cloud data is directly stored in the UAV or external storage device. In order to facilitate subsequent data processing and management, the data is named and stored according to the number of the bridge pier, the collection time, etc.

[0095] III. Point cloud data preprocessing (S2)

[0096] After data collection, the data is processed as shown in Figure 3 .

[0097] First, the collected point cloud data is preprocessed to improve data quality, reduce noise and redundant data, and provide a good data foundation for subsequent point cloud segmentation and analysis.

[0098] According to the actual size and position of the bridge pier, the filtering range of the point cloud data is defined. For example, by setting the value range of the point cloud on the X, Y, Z three coordinate axes, the invalid points and outliers outside the bridge pier area are removed. In actual application, the filtering range is accurately set in combination with the design size and actual position of the bridge pier.

[0099] The pass-through filter function in the point cloud processing software is used to filter the collected raw point cloud data. The points in the point cloud data that are not within the defined range are removed to obtain the filtered point cloud data. The formula for calculating the filtered point cloud set is:

[0100] P filtered

[0101] = {(x, y, z) e P | x min ≤ x i ≤ x max , y min ≤ y i ≤ y max , z min ≤ z i ≤ z max}

[0102] In the formula, P is the original point cloud set, P filtered is the filtered point cloud set, P i is (x i , y i , z i ) is the coordinate of P i in the original point cloud set P, and the subscripts min and max represent the minimum and maximum values of all point coordinates on the corresponding axis, respectively.

[0103] According to the density of point cloud data and the accuracy requirement of subsequent processing, the size of the voxel grid is set. Generally, the voxel size is between 0.01-0.1 meters, and for the area with high point cloud density, the voxel size can be appropriately increased to reduce the data amount. In engineering, according to the specific situation of the collected point cloud data, the voxel size is set to 0.05 meters, which effectively reduces the data amount. The point cloud data is divided into a voxel grid using the voxel grid filter function in the point cloud processing software. For each voxel grid, the centroid of all points in it is calculated as the representative point of the voxel, thereby realizing the down-sampling of point cloud data. The down-sampled point cloud data not only retains the geometric features of the original point cloud, but also reduces the data amount and improves the efficiency of subsequent processing.

[0104] For the point cloud data down-sampled by the voxel grid filter, the centroid is calculated, and the calculation formula is:

[0105]

[0106] In the formula, P centroid represents the centroid of the point cloud set, and n is the number of points in the voxel.

[0107] Further sampling is performed on the down-sampled point cloud data according to a certain sampling radius and sampling density with the centroid as the center. The points far away from the centroid or distributed too sparsely are removed, and the points important for describing the geometric features of the bridge pier column are retained, thereby further optimizing the point cloud data.

[0108] Four, fast segmentation of point cloud (S3)

[0109] The normal vector characteristics of the bearing platform are important basis for evaluating the deviation of the pier column. For the extraction of bearing platform point cloud, this paper adopts the conventional method based on height filtering. Due to the low height and rectangular plane of the bearing platform in the point cloud field, combined with its geometric shape and position characteristics, the target point cloud is accurately screened through height restriction, providing a reliable basis for subsequent accurate analysis:

[0110] P GAP_filtered = {(x, y, z)∈P∣z min ≤z≤z max}

[0111] P GAP_filtered is the point cloud set filtered as the bearing platform. First, the Alpha Shape or Convex Hull method is used to extract the preliminary outline of the bearing platform. Since the preliminary outline may have curves or irregular edges, the Minimum Bounding Rectangle (MBR) algorithm is then used to calculate the bounding box and generate a standardized rectangular outline. The method removes redundant point clouds and completes the missing areas of the bearing platform.

[0112] As shown in Figure 4 , the improved adaptive octree algorithm, three-dimensional local descriptor for feature calculation, and machine learning algorithm are used to quickly segment the preprocessed point cloud data and extract the point cloud of the bridge pier column.

[0113] The space where the preprocessed point cloud data is located is divided into a root node, and then the node is recursively decomposed according to the number of points in the node and the feature vector difference of adjacent voxels. If the number of points in the node is greater than the minimum point threshold and the feature vector difference of adjacent voxels is greater than the threshold, the node is decomposed into eight sub-nodes. The node decomposition process continues until the stop condition is met, such as the number of points in the node being less than the minimum point threshold or the feature vector difference being less than the threshold. In practical applications, the values of and are set reasonably according to the characteristics of the point cloud data and the subsequent segmentation requirements, effectively decomposing the space into an octree.

[0114] The chi-square distance is used to compare the feature vector difference of adjacent voxels, and the calculation formula is:

[0115]

[0116] In the formula, f 1,i and f 2,i are the i-th dimension of vectors f1 and f2, respectively, and ∈ is a small positive number used to avoid division by zero.

[0117] As shown in Figure 5 , for each pair of points P s and P t and their corresponding estimated normal vectors ns and n t , P s is the coordinate origin, P t is the target, and a local coordinate system with u, v, w as three axes is constructed. The three-direction features a, f, q between points P s and P t can be expressed as:

[0118] a = arccos (v · n t )

[0119]

[0120] In the formula, d is the Euclidean distance between two points P t and P s , d = ||P t -P s ||2. a and f are the dot products between the normalized vectors, where a represents the angle between the normal vector n t and the coordinate axis v, f represents the angle between the vector P t -P s and the coordinate axis u, and q is the angle between the vector n t after projection on the plane defined by u and w and u.

[0121] For the query point p q , a spherical neighborhood is established with the query point as the center and a radius of r, and the neighborhood points in the sphere are searched. First, the simplified point feature histogram (SPFH) feature descriptor between the query point and its neighborhood points is calculated, and the pairwise connections between the neighborhood points are ignored. Then, the point pairs formed by each neighborhood point and the adjacent points within the neighborhood radius r are counted and weighted and averaged to derive the FPFH descriptor:

[0122]

[0123] In the formula, FPFH(p q ) is the final fast point feature histogram (FPFH) feature vector of point p q . SPFH(p q ) is the simplified point feature histogram (SPFH) of point p q . represents the neighborhood point set of point p q . w qi is the weight, which is usually the Euclidean distance between point p q and point p i .

[0124] Computing voxel-level FPFH feature vectors: Based on the point-based feature vectors, the voxel-level FPFH feature vectors are calculated by averaging the feature vectors of all points within the voxel. If a voxel contains multiple points m, the FPFH feature vector of the voxel can be represented as:

[0125]

[0126] The calculated voxel-level FPFH feature vectors are used as input features, and the known voxel categories (such as bridge pier voxel, background voxel) are used as labels to construct a training data set. The training data set is divided into training set and validation set, generally according to the ratio of 80%:20%, for model training and verification. In actual engineering, a sufficient number of samples are prepared to ensure the accuracy of model training.

[0127] On the LightGBM algorithm platform, the hyperparameters of the model are set, such as learning rate, iteration number, maximum number of leaf nodes, minimum number of samples per leaf node, etc. Then the model is trained using the training set, a new decision tree is generated by optimizing the objective function, and finally the predictions of all decision trees are accumulated. The objective function is composed of the loss function L and the regularization term R, and the goal of the model in the tth iteration is to minimize the objective function by constructing a new decision tree:

[0128]

[0129] In order to improve the optimization efficiency, LightGBM uses second-order Taylor expansion to approximate the objective function:

[0130]

[0131] In the formula, is the prediction value of the tth iteration. f (t) In the gradient boosting algorithm, new trees or learning models are added by each iteration to optimize the objective function and improve the final prediction results; is the first-order derivative of the loss function; is the second-order derivative of the loss function. Because is a constant and has nothing to do with the optimization process, it can be removed from the equation.

[0132] Minimizing the loss by constructing a new decision tree involves node splitting and leaf node weight calculation:

[0133]

[0134] In the formula, w j is the weight of the jth leaf node, I jis the sample set represented by the jth leaf node, and λ is the regularization parameter. The maximum number of leaf nodes and the minimum number of samples are set to avoid overfitting.

[0135] LightGBM adopts the form of additive model, and generates the final prediction value by gradually accumulating the output of each decision tree:

[0136]

[0137] wherein, is the prediction value, f (t) is the output of the tth decision tree, and T represents the total number of iterations.

[0138] In actual training, after adjusting the hyperparameters for many times, a model with good performance on the validation set is obtained.

[0139] The LightGBM model completes the rough segmentation of the bridge pier voxels, but there are scattered voxels or incomplete regions. In order to refine the segmentation result, the region refinement and fusion method is introduced. First, the initial identified voxels are divided into multiple segments by connected component analysis, and the integrity is evaluated according to the number of segment voxels. The segment whose voxel number is greater than or equal to the pre-defined threshold is considered as a complete region, which is directly fitted to a plane and included in the result set, otherwise the incomplete segment is expanded. The expansion is to search for adjacent voxels at the boundary of the segment, and decide whether to include them according to whether the distance from the voxel center to the fitted plane is less than the threshold. The iteration is completed for the incomplete region. Then, adjacent regions with similar fitted planes (the distance between planes is less than a pre-defined threshold) are merged into larger complete regions, and finally an accurate bridge pier set is formed, with the following steps:

[0140] From the voxel set V predicted by the model belonging to the bridge pier region, extract the connected voxel group {R i}, initialize an empty set P complete .

[0141] For each voxel group {R i}, if |R i | (the number of voxels in the voxel group {R i}) is greater than or equal to the pre-defined threshold, fit the plane of {R i} and add it to P complete . Otherwise, expand: for each boundary voxel, if the distance to the fitted plane is less than or equal to the threshold, add the adjacent voxel. If |R i | is greater than or equal to the threshold after expansion, add it to P complete . In actual operation, according to the density of point cloud and the actual situation of bridge pier, the pre-defined threshold and distance threshold are reasonably set, and the voxel group is effectively processed.

[0142] Merge P completeRegion in R i ,R j If they are similar and adjacent, merge them. The condition of judging the similarity of regions can be that the distance between planes is lower than a predefined threshold, etc.

[0143] Return the regions P complete after refinement and fusion, i.e., the point cloud of the extracted bridge pier.

[0144] Five, evaluation of the verticality of the pier (S4)

[0145] As shown in the scenario, the verticality and spacing of the pier are evaluated. Figure 6

[0146] Based on the bridge pier point cloud obtained by segmentation, the verticality of the bridge pier is evaluated by calculating the included angle between the pier center axis and the cap beam plane normal.

[0147] From the segmented pier point cloud, a number of feature points at the top and bottom of the pier are selected. In engineering examples, from the segmented pier point cloud, clustering algorithms are used in combination with manual screening to select points that can accurately represent the center positions of the top and bottom of the pier. For example, for a typical circular pier, the most concentrated areas of the top and bottom point clouds are found by clustering, and the most representative points are then selected as feature points. Then, the least square method is used to fit a straight line to these carefully selected feature points, thereby obtaining the direction vector v axis of the pier center axis. The equation of the fitted straight line is:

[0148]

[0149] where L is the position vector of a point on the straight line, is the position vector of a known point on the straight line, and t is the parameter.

[0150] When calculating the cap beam plane normal vector, the cap beam point cloud data is first accurately extracted from the segmented point cloud according to the height and geometric characteristics of the cap beam. For cap beams with regular shapes, such as rectangular cap beams, the point cloud range can be circled according to the height range and the approximate plane contour. Then, a plane fitting algorithm is used, specifically the least square method, to fit the cap beam point cloud to obtain the equation of the cap beam plane:

[0151] a·x+b·y+c·z+d=0

[0152] where a, b, and c are the components of the normal vector n cap of the plane. In this example, the fitted cap beam plane normal vector accurately reflects the spatial orientation of the cap beam plane. The verticality included angle is calculated to obtain the direction vector v axis ​and the normal vector n of the cap beam plane cap Then, the angle θ between them is calculated by the vector dot product formula I The calculation formula is:

[0153]

[0154] The inverse cosine function can then be used to obtain the angle between the central axis of the pier and the normal of the cap beam plane. This angle is the key indicator for evaluating the verticality of the pier.

[0155] VI. Assessment of the distance between adjacent bridge piers (S5)

[0156] Based on the segmented bridge pier point cloud, the spacing between adjacent bridge piers is evaluated by calculating the Euclidean distance between the center points of the pier top surfaces.

[0157] Based on the geometric features and height information of the bridge pier, the top surface point cloud data is accurately extracted from the pier point cloud. For example, for a cylindrical bridge pier, the top surface point cloud is extracted by setting a height threshold and identifying the relatively flat top point cloud area.

[0158] Use the centroid calculation formula to calculate the centroid of the top surface point cloud. This centroid is the center point of the top surface of the pier. The centroid calculation formula is:

[0159]

[0160] Calculate the spacing between adjacent bridge piers by calculating the Euclidean distance d between the center points of the pier top surfaces. The calculation formula is:

[0161]

[0162] Where, P 1,top and P 2,top Respectively represent the coordinates of the center points of the top surfaces of two adjacent piers.

[0163] like Figure 7 The error shown is an engineering example.

[0164] The above embodiments are merely exemplary descriptions of the present invention and do not limit its scope of protection. Those skilled in the art may also make partial changes thereto. Any equivalent replacement that complies with the spirit of the invention falls within the scope of protection of the present invention.

Claims

1. A method for automatically evaluating the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds, characterized in that: The following steps are involved: S1. Use the UAV laser scanning system to collect point cloud data of bridge piers according to the predetermined flight path; S2, preprocessing the collected point cloud data, including removing invalid points and outliers using a pass filter, and applying a voxel grid filter for downsampling; S3. Using the improved adaptive octree algorithm, 3D local descriptors for feature calculation, and machine learning algorithms, the pre-processed point cloud data is quickly segmented to extract the point cloud of the bridge pier. S4. Based on the segmented bridge pier point cloud, the verticality of the bridge pier is evaluated by calculating the angle between the pier center axis and the normal line of the cap beam plane; S5. Based on the segmented bridge pier point cloud, the spacing between adjacent bridge piers is evaluated by calculating the Euclidean distance between the center points of the pier top surfaces.

2. The method for automatically assessing the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds according to claim 1 is characterized in that: The calculation formula for the drone’s flight height h and path deviation distance L is: Where h is the flight altitude, H pillar is the bridge pier height, θ vertical is the vertical field of view angle of the lidar, and L is the path deviation distance.

3. The method for automatically evaluating the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds according to claim 1 is characterized in that: Step S2 includes: S21, spatial range filtering: Use a straight-through filter to remove invalid points and outliers to obtain a filtered point cloud set: P filtered ={(x,y,z)∈P∣x min ≤x i ≤x max ,y min ≤y i ≤y max ,z min ≤z i ≤z max } S22. Calculation of body centroid: Perform voxel grid downsampling on the filtered point cloud and calculate the centroid of each voxel: S23. Cap point cloud extraction: Filter the cap point cloud based on the height range: P GAP_filtered ={(x,y,z)∈P∣z min ≤z≤z max } Where P is the original point cloud set, P filtered is the filtered point cloud set, P i is (x i ,y i ,z i ) is the original point cloud set P i The subscripts min and max represent the minimum and maximum values ​​of the coordinates of all points on the corresponding axis, respectively. centroid Represents the centroid of the point cloud, n is the number of points in the voxel P GAP_filtered It is the point cloud collection that is filtered as the cap.

4. The method for automatically evaluating the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds according to claim 1 is characterized in that: The first stage of the fast point cloud segmentation method described in step S3 is to use the improved adaptive octree algorithm to evaluate the number of points in the node: Use the chi-squared distance d to compare the differences in the eigenvectors of adjacent voxels: Where, f 1,i and f 2,i are the i-th dimension of vectors f1 and f2, ∈ is a positive number used to avoid the denominator being zero, and d is the number of points P t and P s The Euclidean distance between them, d = ||P t -P s ||2; 3D local descriptors for feature computation: α=arccos(v n t ) Where α and φ are the dot products between normalized vectors, and α represents the normal vector n t The angle between it and the coordinate axis v, φ represents the vector P t -P s The angle between the coordinate axis u and θ is the vector n t The angle between u and w after projection on the plane defined by u and w; The FPFH feature descriptor used for feature calculation is calculated as follows: FPFH(p q ) is point p q The final fast histogram feature vector, SPFH(p q ) is point p q The simplified point feature histogram of Represents point p q Neighborhood point set, w qi is the weight, for point p q and point p i The Euclidean distance between Based on the calculated point feature vector, the voxel-level FPFH feature vector is calculated by averaging. A voxel contains multiple points p1, p2, ..., p m , the FPFH feature vector of this voxel is expressed as:

5. The method for automatically assessing the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that: The machine learning method based on the gradient boosting framework in step S3 includes: A leaf-node-based growth strategy is adopted to prioritize splitting leaf nodes with the largest gain, thereby improving fitting ability and controlling complexity to avoid overfitting. A histogram algorithm is used to quickly locate the optimal splitting point of features, reducing computational complexity and memory usage.

6. The machine learning method based on the gradient boosting framework according to claim 5, wherein the objective function O (t) It mainly consists of the loss function L and the regularization term R. The goal of the model at the tth iteration is to build a new decision tree f (t) (x) to minimize the objective function, and approximate the objective function through the second-order Taylor expansion: Where, is the predicted value of the tth iteration, f (t) In the gradient boosting algorithm, new trees or learning models are added in each iteration to optimize the objective function and improve the final prediction results. is the first-order derivative of the loss function; is the second-order derivative of the loss function; in, The weight of each leaf node is calculated by minimizing the objective function, and LightGBM adopts the form of an additive model. By gradually accumulating the output of each decision tree, the weight calculation formula and the final prediction value are: Where w j is the weight of the jth leaf node, I j represents the sample set of the jth leaf node, λ is the regularization parameter, which avoids overfitting by setting the maximum number of leaf nodes and the minimum number of samples. is the predicted value, f (t) is the output of the t-th decision tree, and T represents the total number of iterations.

7. The method for automatically evaluating the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds according to claim 1 is characterized in that: The machine learning algorithm in step S3, wherein the refined region refinement and fusion method includes: S31, Initialization: Extract connected voxel groups {R i }, initialize the empty set P complete ; S32, for each voxel group {R i }: If | R i |≥predefined threshold, then R i Fitting plane and add to P complete ; Otherwise, expand R i : For each boundary voxel v j , if the fitting plane The distance ≤ threshold d th , then add the adjacent voxel v k ; If after expansion | R i |≥Threshold V min , then add to P complete ; S33, Merge P complete Region in: For region R i ,R j ,if If they are similar and adjacent, merge them; S34, return to P complete .

8. According to the method for automatically assessing the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds as claimed in claim 1, the pier axis is fitted by: Merge the point cloud data of the four facades of the pier into one point cloud collection Where N is the total number of four surface point clouds, and the centroid of all points is calculated Decentralize the coordinates of all points to get q i , and construct the covariance matrix: in, It is the outer product of the decentralized vector of the point. The covariance matrix C is decomposed into eigenvalues ​​to obtain the eigenvalues ​​and corresponding eigenvectors. The eigenvector v corresponding to the maximum eigenvalue is max is the main direction of point cloud distribution, that is, the direction of the pier axis, so the axis equation is expressed as: where v max is the axis direction, t is a scalar parameter, the normal vector of the cap plane is the reference for the vertical evaluation of the pier column, and the normal vector n of the cap plane after fitting a·x+b·y+c·z+d=0 cap =(a,b,c).

9. The method for automatically evaluating the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that: The evaluation of the verticality and spacing of the bridge piers in step S4 includes calculating the angle θ between the central axis of the pier and the normal line of the cap beam plane. I The Euclidean distance d between the center point of the top surface of the pier is calculated, where θ I The calculation formulas for d and d are: Where p 1,top and P 2,top Respectively represent the coordinates of the center points of the top surfaces of two adjacent piers, v axis is the direction vector of the central axis of the pier, n cap is the normal vector to the cap beam plane.

Images