Method for automatically evaluating installation quality of prefabricated bridge pier column based on three-dimensional laser point cloud

Abstract

The application provides a prefabricated bridge pier column installation quality automatic evaluation method based on three-dimensional laser point cloud, which is used for measuring the verticality of high piers and the pier column spacing. The method comprises the following steps: an unmanned aerial vehicle laser scanning system collects bridge pier point cloud data according to an optimized flight path, and pre-processes to improve the data quality; the point cloud is quickly segmented by using an improved adaptive octree and a machine learning algorithm, and the bridge pier point cloud is extracted; based on the finely segmented point cloud, the verticality of the bridge pier and the spacing between adjacent bridge piers are accurately evaluated by calculating the included angle between the bridge pier center axis and the cap beam plane normal and the coordinates of the center point of the bridge pier top surface. The optimized unmanned aerial vehicle flight path of the application is combined with point cloud data preprocessing, which can effectively improve the data quality and reduce the data volume. At the same time, the improved adaptive octree and machine learning algorithm are combined for point cloud segmentation, which can accurately distinguish the bridge pier, cap beam and background, and completely extract the pier column geometric features.

Description

Technical Field

[0001] This invention relates to the field of bridge monitoring technology, specifically an automatic evaluation method for the installation quality of prefabricated bridge piers based on three-dimensional laser point clouds. Background Technology

[0002] In the field of bridge construction, precast structures are increasingly widely used due to their advantages in quality control, cost-effectiveness, and rapid construction. Among these, the installation of precast piers is a critical step, and its quality directly affects the efficiency of subsequent construction and the overall structural performance of the bridge.

[0003] During the installation of precast bridge piers, mortar must be evenly laid on the surface of the cap beam to provide a stable and flat foundation. The pier column is then installed using a sleeve-reinforcing bar connection, ensuring precise alignment between the sleeve and the embedded reinforcing bar. During the assembly phase, a total station is often used to monitor positional deviations, and jacks are used to adjust the angle to ensure verticality and centering. In the grouting phase, it is crucial to ensure that the grout fills the gap between the bottom of the pier and the cap beam, forming a reliable load-bearing interface. High-strength grout is then injected to achieve a fixed connection. The entire process is highly manual, requiring a high level of skill and experience from the construction personnel.

[0004] The verticality deviation of bridge piers is a key indicator for evaluating installation quality and is affected by multiple factors. In terms of manual operation, uneven mortar application and improper jack adjustment can easily lead to deviations. Regarding materials and construction techniques, insufficient grouting and abnormal mortar hardening can also cause problems. Furthermore, increasing the height of the piers amplifies the impact of verticality deviation, altering the stress state of the piers, increasing the difference in spacing between adjacent piers, creating difficulties for subsequent precast component installation, and even affecting the bridge's service life and safety. Therefore, accurately measuring the verticality and relative distance of the piers, and adjusting the design and production of precast cap beams and segments accordingly, is essential.

[0005] Currently, total stations are commonly used in engineering projects to measure the angles and distances of bridge piers. However, due to the inconsistent thickness of the concrete protective layer, measurements need to be taken on multiple surfaces and at multiple points for a single pier, which is complex and inefficient. When inspecting multiple consecutive piers, frequent movement of the measuring station and comprehensive measurements are time-consuming, seriously affecting the project schedule.

[0006] Besides total stations, there are two main 3D reconstruction technologies for obtaining geometric information of bridge piers: image-based and laser-based.

[0007] Image-based 3D reconstruction utilizes UAV oblique photography to acquire images and then reconstruct point cloud models. While techniques such as optimizing flight paths, employing automatic aerial triangulation frameworks, and distributed task partitioning have improved efficiency and accuracy to some extent, several problems remain, including reliance on camera resolution and shooting angle, high requirements for UAVs and photographic equipment, large amounts of multi-angle image data acquisition, high computational resource consumption for model creation, and long reconstruction time.

[0008] Laser-based 3D reconstruction acquires 3D information by emitting laser pulses and measuring reflected light. Ground-based laser scanning combined with digital twin methods can reconstruct bridge pier models to assess verticality; however, ground-based laser scanning has a limited range, and large-scale scanning requires multiple deployments of stations, increasing costs and reducing efficiency. Airborne laser scanning, combined with specific algorithms, can achieve point cloud segmentation and geometric information calculation for long-span bridges.

[0009] Furthermore, point cloud segmentation is crucial during 3D point cloud model reconstruction after data acquisition. Algorithm-based methods can be categorized into bottom-up and top-down strategies. Bottom-up approaches use classic algorithms to segment and classify point clouds, relying on accurate surface segmentation. In real-world scenarios, noise and occlusion can affect segmentation results, and manually defined rules are poorly adaptable to complex structures. Top-down approaches perform segmentation and classification simultaneously based on semantic category knowledge and prior geometric features, relying on design information and clean point clouds. However, in practical engineering, design deviations and background noise can limit their application.

[0010] Learning-based methods, represented by deep learning algorithms such as PointNet, directly process raw data and can automatically learn feature patterns to achieve segmentation. However, practical applications face challenges such as the need for large amounts of labeled data, high hardware performance requirements, and long inference times, limiting their efficiency and field applicability.

[0011] Overall, current technologies for inspecting the quality of pier installation and acquiring bridge geometry information are inadequate in precast bridge construction. Therefore, there is an urgent need for a new, automated, efficient, and accurate quality assessment method to meet engineering requirements. Summary of the Invention

[0012] To address the problems existing in the prior art, this invention provides an automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds, comprising the following steps:

[0013] S1. Use a drone laser scanning system to collect point cloud data of bridge piers according to a predetermined flight path;

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

[0015] S3. The improved adaptive octree algorithm, the 3D local descriptor for feature calculation and the machine learning algorithm are used to quickly segment the preprocessed point cloud data and extract the point cloud of the bridge pier.

[0016] S4. Based on the segmented point cloud of the bridge pier, the verticality of the bridge pier is evaluated by calculating the angle between the central axis of the pier and the normal line of the cap beam plane.

[0017] S5. Based on the segmented point cloud of the bridge piers, the spacing between adjacent bridge piers is evaluated by calculating the Euclidean distance between the center points of the top surfaces of the piers.

[0018] The key to UAV flight path design lies in the rational selection of feature points. Given the complex geometric features of bridge piers in construction scenarios, it is necessary to comprehensively consider the pier height, lateral spacing, and terrain variations of the construction area. To ensure comprehensive coverage of the side scan and the bridge piers from top to bottom, a layered Z-shaped flight path can be adopted. By scanning at different altitude levels, data blind spots can be avoided. For the side scan path, the flight altitude h and path deviation distance L need to be determined based on the bridge pier height H. pillar The flight altitude h is determined by the vertical field of view of the lidar.

[0019]

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

[0021] To ensure the efficiency and accuracy of subsequent point cloud processing, the data is preprocessed. Given that the bridge piers and abutments are distributed along the traffic direction and have limited lateral and vertical ranges, a pass-through filter is first applied to quickly remove invalid and outlier points:

[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, P filtered It is the filtered point cloud, P i For (x) i ,y i ,z i P is the original point cloud set P. i The coordinates are given by the subscripts min and max, which represent the minimum and maximum values ​​of the coordinates of all points on the corresponding axes, respectively.

[0025] Furthermore, the point cloud data is dimensionality reduced and simplified using voxel grid filtering, discretizing the continuous space into a voxel grid. To ensure high accuracy, the voxel grid step size is limited to no more than 3 mm to preserve the boundary information of the structure. A centroid sampling method is employed, selecting the centroid as a representative point in each voxel to further reduce the data volume.

[0026]

[0027] In the formula, p centroid Let n denote the centroid of the point cloud, where n is the number of points within the voxel.

[0028] Despite preprocessing, point cloud data still faces challenges such as large sample size, complex background, and significant interference.

[0029] The normal vector characteristics of the pier cap are an important basis for evaluating pier offset. For point cloud extraction of the pier cap, this paper adopts a conventional method based on height filtering. Since the pier cap has a relatively low height and is a rectangular plane in the point cloud field, by combining its geometric shape and positional characteristics, the target point cloud is accurately filtered by height restriction, providing a reliable foundation for subsequent accurate analysis.

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

[0031] P GAP_filtered The set of point clouds selected as the foundation is shown. First, the initial contour of the foundation is extracted using the Alpha Shape or Convex Hull method. Since the initial contour may contain curves or irregular edges, the Minimum Bounding Rectangle (MBR) algorithm is then used to calculate the bounding box, generating a standardized rectangular contour. This method removes redundant point clouds and fills in missing areas of the foundation.

[0032] To address the issue of background and noise interference in bridge pier point cloud segmentation, this paper proposes a fast bridge pier point cloud segmentation method that combines an improved adaptive octree and machine learning to achieve automatic segmentation of continuous bridge piers.

[0033] An improved adaptive octree voxel partitioning method is used to reduce the computational complexity of point cloud segmentation. This method is based on octree spatial decomposition, recursively subdividing the 3D space to enclose the point cloud within the root node of the smallest cube. Non-empty voxels are further subdivided until a stopping condition such as a point count threshold or minimum voxel size is met. Its two-stage termination criterion dynamically adjusts the decomposition depth: the first stage determines whether to proceed to the second stage based on whether the number of nodes exceeds a threshold α; the second stage uses local descriptors to calculate feature values ​​and compares the differences in feature vectors of adjacent voxels. If the difference exceeds a threshold β, the region is considered to have significant geometric changes, and further subdivision is required; otherwise, the segmentation stops. The dynamic adjustment mechanism of the adaptive octree significantly reduces the number of voxels in smooth regions. The chi-square distance is used to compare the feature vector differences f1 and f2 of adjacent voxels.

[0034]

[0035] In the formula, f 1,i and f 2,i ∈ are the i-th dimensions of vectors f1 and f2, respectively, and ∈ is a small positive number used to avoid zero denominators.

[0036] Voxel eigenvalues ​​are a key indicator for determining whether to continue voxel segmentation. In the segmentation of pier point clouds, the computation of local descriptors is crucial because their results serve as input to machine learning models. Fast Point Feature Histogram (FPFH), an efficient 3D feature descriptor, was chosen as a voxel feature extraction tool. It is an accelerated version of Point Feature Histogram (PFH), representing 3D geometric features by quantifying the relationship between a point's own normal vector and the normal vectors of its neighboring points. This provides a richer feature space for subsequent classification models, helping to more accurately distinguish between target categories and background point clouds.

[0037] Point-pair triplet features are the basic building blocks of a descriptor. Before computation, a local coordinate system needs to be defined, which ensures 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 its corresponding normal vector n s and n t , with P s Let P be the origin of the coordinate system. t For the target point, construct a local coordinate system with UVW axes. Point pair P s and P t The triplet features α, φ, θ between points can be calculated using specific mathematical formulas. These angular features can describe the geometric relationship between point pairs.

[0038] α=arccos(v·n t )

[0039]

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

[0041] For query point P q A neighborhood sphere with radius r is established with the queried point as its center, and neighborhood points within the sphere are searched. PFH calculates the quadruple features (α, φ, θ, d) for each pair of points in the neighborhood and places these statistical features in a histogram to form the relative relationships between all points, used to describe the surface features of the point cloud. FPFH improves upon PFH by first calculating the SPFH feature descriptor between the query point and its neighboring points, ignoring the interconnections between neighboring points. Then, by calculating the statistically weighted average of the neighboring point and its adjacent point pairs, the FPFH descriptor is obtained.

[0042]

[0043] In the formula, FPFH(p q () is point p q The final fast point feature histogram feature vector. SPFH(p) q () is point p q The simplified point feature histogram. Point p q The set of neighborhood points. qi It is the weight, usually for 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] LightGBM, a lightweight gradient boosting decision tree machine learning model, is used for point cloud segmentation. It combines the efficiency of traditional methods with the flexibility of machine learning, processing previously computed voxel-level features as input voxel-by-voxel. The high-dimensional feature vectors facilitate the differentiation of target and background point clouds, balancing efficiency and accuracy in practical applications. LightGBM improves performance through a leaf node growth strategy (prioritizing the splitting of leaf nodes with the largest gain to enhance fitting ability and control complexity to prevent overfitting) and a histogram-based algorithm (quickly locating the optimal feature splitting point, reducing computational complexity and memory usage). It iterative training is based on a gradient boosting framework, using a second-order Taylor expansion to approximate the objective function.

[0047]

[0048] In the formula, f is the predicted value for the t-th iteration. (t) In the gradient boosting algorithm, new trees or learning models are continuously added in each iteration to optimize the objective function and improve the final prediction results. The first derivative of the loss function; This is the second derivative of the loss function. Because It is a constant and is independent of the optimization process, so 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] In the formula, w j It is the weight of the j-th leaf node, I j Let represent the sample set of the j-th leaf node, and λ be the regularization parameter. By setting the maximum and minimum number of leaf nodes, overfitting can be avoided.

[0052] LightGBM uses an additive model, progressively accumulating the outputs of each decision tree to generate the final prediction:

[0053]

[0054] In the formula, It is the predicted value, f (t) It is the output of the t-th decision tree, where T represents the total number of iterations.

[0055] The LightGBM model achieved a coarse segmentation of bridge pier voxels, but scattered voxels or incomplete regions existed. To refine the segmentation results, a region refinement and fusion method was introduced. First, connected component analysis was used to divide the initially identified voxels into multiple segments. The completeness of each segment was assessed based on the number of voxels. Segments with a voxel count greater than or equal to a predefined threshold were considered complete regions, directly fitted to a plane, and included in the result set. Otherwise, incomplete segments were expanded. Expansion involved searching for neighboring voxels at the segment boundaries, and inclusion was determined by whether the distance from the voxel's midpoint to the fitted plane was below a threshold. This process iteratively completed the segmentation of incomplete regions. Then, adjacent regions with similar fitted planes (plane spacing below a predefined threshold) were merged into larger complete regions, ultimately forming a precise set of bridge piers. The steps are as follows:

[0056] S1. Initialization: Extract connected element sets {R} from V. i}, initialize the empty set P complete .

[0057] S2, for each voxel group {R i}: If |R i If |≥ a predefined threshold, then fit the plane and add it to P. complete Otherwise, extend the algorithm: for each boundary voxel, if the distance to the fitted plane is ≤ threshold d... th If |R| is added, then adjacent voxels are added. i |≥threshold V min Then add to P complete .

[0058] S3, merge P complete Region in: For region R i ,R j ,if If they are similar and adjacent, then merge them.

[0059] S4, Return to P complete .

[0060] After obtaining the 3D reconstruction model, the axis of the pier needs to be fitted:

[0061] The point cloud data of the four facades of the pier are merged into a single point cloud set. In the formula, N is the total number of points in the four facets, 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] in, It is the outer product of the centered vectors of a point. Eigenvalue decomposition is performed on the covariance matrix C to obtain eigenvalues ​​and their corresponding eigenvectors. The eigenvector v corresponding to the largest eigenvalue... max This is the main direction of the point cloud distribution, i.e., the direction of the pier axis. Therefore, the axis equation can be expressed as:

[0064]

[0065] Where v max Here, 't' represents the axial direction, and 't' is a scalar parameter. The normal vector of the pier cap plane serves as a reference for evaluating the verticality of the pier column. The normal vector 'n' of the fitted pier cap plane a·x+b·y+c·z+d=0 is... cap = (a, b, c).

[0066] In the step of assessing the verticality of bridge piers, the angle θ between the central axis of the pier and the normal to the cap beam plane is calculated. I The calculation formula is:

[0067]

[0068] In the formula, v axis It is the direction vector of the central axis of the bridge pier. cap It is the normal vector of the cap beam plane.

[0069] The distance between adjacent bridge piers is calculated by calculating the Euclidean distance d between the center points of the top surfaces of the piers. The formula is as follows:

[0070]

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

[0072] Beneficial Effects: This invention proposes an automatic evaluation system for the installation quality of precast bridges based on 3D laser point clouds. This system can efficiently collect point cloud data of bridge piers using optimized UAV flight paths, and through a series of preprocessing operations, effectively improve data quality and reduce data volume, laying a solid foundation for subsequent accurate analysis. Simultaneously, it innovatively integrates an improved adaptive octree with machine learning algorithms for point cloud segmentation, accurately distinguishing bridge piers, cap beams, and the background, and completely extracting their geometric features. Furthermore, based on the point cloud processing flow, it utilizes the 3D spatial relationship between the bridge pier's central axis, the center point of its top surface, and the plane normal of the cap beam to accurately calculate the verticality of the bridge piers and the spacing between adjacent piers, achieving a quantitative evaluation of installation quality.

[0073] This invention is primarily applied to quality inspection in precast bridge construction. It enables high-precision quality assessment, significantly reduces inspection errors, and dramatically improves inspection efficiency, allowing a single person to quickly complete the quality inspection of all piers in a construction section. The entire assessment process is highly automated and features fast data processing, offering significant advantages in improving quality control and accelerating project progress in precast bridge construction, thus powerfully promoting the intelligent development of the bridge construction industry. Attached Figure Description

[0074] 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.

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

[0076] Figure 2 This is a schematic diagram of flight path planning in the implementation of this invention;

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

[0078] Figure 4 This is a schematic diagram of the improved adaptive octree point cloud segmentation in an embodiment of the present invention;

[0079] Figure 5 This is a schematic diagram of a three-dimensional local descriptor in an embodiment of the present invention;

[0080] Figure 6 This is a schematic diagram illustrating the calculation of the verticality and spacing of the pier columns in the implementation of this invention;

[0081] Figure 7 This is a schematic diagram of the measurement error in the implementation of this invention. Detailed Implementation

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

[0083] Example:

[0084] I. System Construction and Preparation

[0085] Please see Figure 1-7Before implementing this automatic evaluation method for the installation quality of precast bridge piers based on 3D laser point clouds, it is necessary to construct the corresponding hardware and software system:

[0086] The hardware includes a UAV-LS (Unmanned Aerial Vehicle-Laser System): UAVs equipped with high-performance LiDAR are selected, such as the DJI M350 Pro UAV equipped with the Riegl miniVUX-1 UAV LiDAR scanner used in the actual project. This combination ensures stable flight performance and long endurance, meeting the needs for large-area bridge pier point cloud data collection. Its automatic return-to-home and obstacle avoidance functions also improve the safety of the data collection process. Furthermore, the data processing equipment is equipped with a high-performance computer with 16GB of RAM, an Intel Core i7-10870H@2.20GHz processor, and an Nvidia GeForce RTX 3070 Laptop GPU, running a Windows 10 64-bit operating system, providing powerful computing support for point cloud data processing and analysis.

[0087] The software environment includes point cloud data acquisition software for flight path planning and data acquisition parameter settings. This software supports controlling the UAV to fly according to a predetermined optimized flight path and monitors the LiDAR's operating status and data acquisition in real time. Professional point cloud processing software such as CloudCompare and PolyWorks needs to be installed to provide rich point cloud preprocessing, segmentation, and fitting functions for subsequent processing and analysis of the acquired point cloud data. Furthermore, machine learning algorithm platforms such as Python's Scikit-learn and LightGBM libraries are selected to implement improved adaptive octree algorithms, 3D local descriptor calculations, and LightGBM machine learning algorithms on these platforms to achieve rapid point cloud segmentation and classification tasks.

[0088] like Figure 2 As shown, the drone's flight altitude, speed, and path deviation distance need to be set based on the actual height and distribution range of the bridge piers, as well as the performance parameters of the lidar. The flight altitude calculation formula is as follows:

[0089]

[0090] The appropriate flight altitude was determined by combining the vertical field of view of the Riegl miniVUX-1UAV LiDAR scanner. The path deviation distance was also adjusted according to the actual situation to ensure comprehensive coverage of the bridge pier area. Before data acquisition, the LiDAR was calibrated, including distance and angle calibration, to ensure the accuracy of the acquired point cloud data. Simultaneously, appropriate parameters such as laser emission frequency and scanning angle were set to improve the density and quality of the point cloud data.

[0091] II. Point Cloud Data Acquisition (S1)

[0092] The drone laser scanning system collects point cloud data of bridge piers according to a predetermined optimized flight path.

[0093] The design model of the bridge piers is analyzed to extract key feature points as waypoints, such as the center point of the pier top and the edge point of the bottom. These feature waypoints serve as an important basis for flight path planning, ensuring that the UAV can scan the bridge piers from different angles. Based on the feature waypoints, an optimized flight path is generated. In actual engineering, a layered Z-shaped flight method is adopted to comprehensively scan the bridge piers at different altitudes. The spacing between each flight path is set to 5-10 meters based on the scanning range of the LiDAR and the accuracy requirements of the point cloud data. Simultaneously, a surrounding flight path is added around the piers to obtain detailed point cloud data of the pier sides.

[0094] Before takeoff, check that the drone's battery level, device connectivity, and flight parameter settings are normal. Ensure the lidar equipment is correctly powered on and warmed up, ready for data acquisition. The drone flies along the predetermined flight path, while the lidar continuously emits laser pulses and receives reflected signals to collect point cloud data of the bridge piers. During flight, monitor the drone's flight status and data acquisition progress in real time to ensure the completeness and accuracy of the data. The collected point cloud data is stored directly on the drone or an external storage device. To facilitate subsequent data processing and management, the data is named and categorized according to the bridge pier number, acquisition time, and other information.

[0095] III. Point Cloud Data Preprocessing (S2)

[0096] After data collection, such as Figure 3 The process is as shown.

[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] The filtering range of point cloud data is defined based on the actual dimensions and location of the bridge piers. For example, by setting the value range of the point cloud on the X, Y, and Z coordinate axes, invalid points and outliers located outside the bridge pier area are removed. In practical applications, the filtering range is accurately set by combining the design dimensions and actual location of the bridge piers.

[0099] The raw point cloud data is filtered using the pass-through filter function in the point cloud processing software. Points outside the defined range are removed, resulting in filtered point cloud data. The formula for calculating the filtered point cloud set is:

[0100] P filtered

[0101] ={(x,y,z)∈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, P filtered It is the filtered point cloud, P i For (x) i ,y i ,z i P is the original point cloud set P. i The coordinates are given by the subscripts min and max, which represent the minimum and maximum values ​​of the coordinates of all points on the corresponding axes, respectively.

[0103] The voxel grid size is set according to the density of the point cloud data and the accuracy requirements of subsequent processing. Generally, the voxel size is between 0.01 and 0.1 meters. For areas with high point cloud density, the voxel size can be appropriately increased to reduce the data volume. In engineering practice, based on the specific conditions of the collected point cloud data, the voxel size is set to 0.05 meters, effectively reducing the data volume. The voxel grid filter function in the point cloud processing software is used to divide the point cloud data into voxel grids. For each voxel grid, the centroid of all points within it is calculated as the representative point of that voxel, thereby achieving downsampling of the point cloud data. The downsampled point cloud data retains the geometric features of the original point cloud while reducing the data volume, improving the efficiency of subsequent processing.

[0104] For point cloud data downsampled by a voxel grid filter, its centroid is calculated using the following formula:

[0105]

[0106] In the formula, P centroid Let n denote the centroid of the point cloud, where n is the number of points within the voxel.

[0107] Using the centroid as the center, and based on a certain sampling radius and sampling density, the downsampled point cloud data is further sampled. Points that are far from the centroid or too sparsely distributed are removed, while points that are more important for describing the geometric features of the bridge piers are retained, thereby further optimizing the point cloud data.

[0108] IV. Fast Point Cloud Segmentation (S3)

[0109] The normal vector characteristics of the pier cap are an important basis for evaluating pier offset. For point cloud extraction of the pier cap, this paper adopts a conventional method based on height filtering. Since the pier cap has a relatively low height and is a rectangular plane in the point cloud field, by combining its geometric shape and positional characteristics, the target point cloud is accurately filtered by height restriction, providing a reliable foundation for subsequent accurate analysis.

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

[0111] P GAP_filtered The set of point clouds selected as the foundation is shown. First, the initial contour of the foundation is extracted using the Alpha Shape or Convex Hull method. Since the initial contour may contain curves or irregular edges, the Minimum Bounding Rectangle (MBR) algorithm is then used to calculate the bounding box, generating a standardized rectangular contour. This method removes redundant point clouds and fills in missing areas of the foundation.

[0112] like Figure 4 As shown, an improved adaptive octree algorithm, a 3D local descriptor for feature calculation, and a machine learning algorithm are used to quickly segment the preprocessed point cloud data and extract the point cloud of the bridge piers.

[0113] The space containing the preprocessed point cloud data is divided into a root node. Then, based on the number of points within the node and the difference in feature vectors between adjacent voxels, the node is recursively decomposed. If the number of points within a node is greater than a minimum point threshold and the difference in feature vectors between adjacent voxels is greater than a threshold, the node is decomposed into eight child nodes. The node decomposition process continues until a stopping condition is met, such as the number of points within a node being less than the minimum point threshold or the difference in feature vectors being less than the threshold. In practical applications, based on the characteristics of the point cloud data and subsequent segmentation requirements, the values ​​of and were appropriately set, effectively performing octree decomposition of the space.

[0114] The chi-square distance is used to compare the difference in feature vectors between adjacent voxels. The calculation formula is as follows:

[0115]

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

[0117] like Figure 5 As shown, for each pair of points P s and P t and its corresponding estimated normal vector ns and n t , with P s Let P be the coordinate source point. t To achieve the objective, construct a local coordinate system with u, v, and w as the three axes. Point P s and P t The three-dimensional characteristics α, φ, θ between them can be expressed as:

[0118] α=arccos(v·n t )

[0119]

[0120] In the formula, d represents the two points P. t and P s The Euclidean distance between them, d = ||P t -P s 2. α and φ are the dot product of normalized vectors, where α represents the normal vector n. t The angle φ between vector P and the coordinate axis v represents the vector P. t -P s The angle θ between the vector n and the coordinate axis u is the vector n. t The angle between the projection onto the plane defined by u and w and u.

[0121] For query point p q A spherical neighborhood is established with the query point as the center and a radius of r. Neighboring points within the sphere are searched. First, the Simplified Point Feature Histogram (SPFH) feature descriptor between the query point and its neighbors is calculated, ignoring pairwise connections between neighbors. Then, for each neighboring point, the pairs formed with its neighbors within the neighborhood radius r are statistically analyzed, weighted, and averaged to derive the FPFH descriptor.

[0122]

[0123] In the formula, FPFH(p q () is point p q The final Fast Point Feature Histogram (FPFH) feature vector. SPFH(p q () is point p q Simplified Point Feature Histogram (SPFH). Point p q The set of neighborhood points. qi It is the weight, usually for point p. q and point p i The Euclidean distance between them.

[0124] Calculating voxel-level FPFH eigenvectors: Based on the eigenvectors of the calculated points, voxel-level FPFH eigenvectors are calculated by averaging the eigenvectors of all points within the voxel. If a voxel contains multiple points m, the voxel's FPFH eigenvector can be expressed as:

[0125]

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

[0127] On the LightGBM algorithm platform, the model's hyperparameters are set, such as learning rate, number of iterations, maximum number of leaf nodes, and minimum number of samples per leaf node. The model is then trained using the training set, generating new decision trees by optimizing the objective function, and finally accumulating the predictions from all decision trees. The objective function consists of a loss function L and a regularization term R. The model's goal in the t-th iteration is to minimize the objective function by constructing new decision trees.

[0128]

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

[0130]

[0131] In the formula, f is the predicted value for the t-th iteration. (t) In the gradient boosting algorithm, new trees or learning models are continuously added in each iteration to optimize the objective function and improve the final prediction results. The first derivative of the loss function; This is the second derivative of the loss function. Because It is a constant and is independent of the optimization process, so 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 It is the weight of the j-th leaf node, I jLet represent the sample set of the j-th leaf node, and λ be the regularization parameter. By setting the maximum and minimum number of leaf nodes, overfitting can be avoided.

[0135] LightGBM uses an additive model, progressively accumulating the outputs of each decision tree to generate the final prediction:

[0136]

[0137] In the formula, It is the predicted value, f (t) It is the output of the t-th decision tree, where T represents the total number of iterations.

[0138] In actual training, after multiple adjustments to the hyperparameters, a model that performed well on the validation set was obtained.

[0139] The LightGBM model achieved a coarse segmentation of bridge pier voxels, but scattered voxels or incomplete regions existed. To refine the segmentation results, a region refinement and fusion method was introduced. First, connected component analysis was used to divide the initially identified voxels into multiple segments. The completeness of each segment was assessed based on the number of voxels. Segments with a voxel count greater than or equal to a predefined threshold were considered complete regions, directly fitted to a plane, and included in the result set. Otherwise, incomplete segments were expanded. Expansion involved searching for neighboring voxels at the segment boundaries, and inclusion was determined by whether the distance from the voxel's midpoint to the fitted plane was below a threshold. This process iteratively completed the segmentation of incomplete regions. Then, adjacent regions with similar fitted planes (plane spacing below a predefined threshold) were merged into larger complete regions, ultimately forming a precise set of bridge piers. The steps are as follows:

[0140] Extract connected voxel sets {R} from the voxel set V belonging to the pier region predicted by the model. i}, initialize the empty set P complete .

[0141] For each voxel group {R i If |R i |(voxel group{R) i If the number of voxels in {R} is greater than or equal to a predefined threshold, then the fitted {R} is... i} plane and add to P complete Otherwise, expand: for each boundary voxel, if the distance to the fitted plane is less than or equal to a threshold, add neighboring voxels. If after expansion |R i If the value is greater than or equal to the threshold, add it to P. complete In practice, based on the density of the point cloud and the actual condition of the bridge piers, predefined thresholds and distance thresholds were reasonably set, and the voxel groups were effectively processed.

[0142] Merge P completeIn the region, for region R i ,R j ,if If regions are similar and adjacent, they are merged. Criteria for determining region similarity can include a planar distance below a predefined threshold.

[0143] Return to the refined and merged region P complete This refers to the point cloud extracted from the bridge piers.

[0144] V. Assessment of Pier Verticality (S4)

[0145] like Figure 6 In the scenario shown, the verticality and spacing of the pier columns are evaluated.

[0146] Based on the segmented point cloud of the bridge pier, the verticality of the bridge pier is evaluated by calculating the angle between the central axis of the pier and the normal line of the cap beam plane.

[0147] From the segmented point cloud of the bridge piers, several feature points at the top and bottom of the piers are selected. In the engineering example, a clustering algorithm combined with manual selection is used to select points that accurately represent the center positions of the top and bottom of the piers. For example, for a typical circular pier, clustering is used to find the regions where the top and bottom point clouds are most concentrated, and then the most representative points are selected as feature points. Then, the least squares method is used to fit a straight line to these carefully selected feature points to obtain the direction vector v of the pier's central axis. axis The equation of the fitted line is:

[0148]

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

[0150] When calculating the plane normal vector of the cap beam, the point cloud data of the cap beam is first accurately extracted from the segmented point cloud based on its height and geometric features. For cap beams with regular shapes, such as rectangular cap beams, the point cloud range can be delineated based on its height range and approximate planar outline. Next, a plane fitting algorithm is used, specifically the least squares method, to perform plane fitting on the cap beam point cloud, obtaining the equation of the cap beam plane:

[0151] a·x+b·y+c·z+d=0

[0152] Where a, b, and c are the normal vectors of the plane n. cap The components. In this example, the fitted normal vector of the cap beam plane accurately reflects the spatial orientation of the cap beam plane. The direction vector v of the pier center axis is obtained by calculating the verticality angle. axisand the normal vector n of the cap beam plane cap Then, the angle θ between them is calculated using the vector dot product formula. I The calculation formula is:

[0153]

[0154] The angle between the central axis of the pier and the normal line of the cap beam can be obtained by using the inverse cosine function. 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 point cloud of bridge piers, the spacing between adjacent bridge piers is evaluated by calculating the Euclidean distance between the center points of the top surfaces of the piers.

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

[0158] The centroid of the point cloud on the top surface is calculated using the centroid calculation formula. This centroid is the center point of the top surface of the bridge pier. The centroid calculation formula is as follows:

[0159]

[0160] The distance between adjacent bridge piers is calculated by calculating the Euclidean distance d between the center points of the top surfaces of the piers. The formula is as follows:

[0161]

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

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

[0164] The above embodiments are merely illustrative examples of the present invention and do not limit its scope of protection. Those skilled in the art can make partial changes to them, and any equivalent substitutions that conform to the spirit of the invention fall within the scope of protection of the present invention.

Claims

1. An automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds, characterized in that, Includes the following steps: S1. Use a drone laser scanning system to collect point cloud data of bridge piers according to a predetermined flight path; S2. Preprocess the collected point cloud data, including using a pass-through filter to remove invalid and outlier points, and applying a voxel grid filter for downsampling. S3. The improved adaptive octree algorithm, the 3D local descriptor for feature calculation and the machine learning algorithm based on the gradient boosting framework are used to quickly segment the preprocessed point cloud data and extract the point cloud of the bridge pier. S4. Based on the segmented point cloud of the bridge pier, the verticality of the bridge pier is evaluated by calculating the angle between the central axis of the pier 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 top surfaces of the piers. The first stage of the fast point cloud segmentation method described in step S3 is to use an improved adaptive octree algorithm to evaluate the number of points within a node: Use the chi-square distance d to compare the differences in the eigenvectors of adjacent voxels: ； In the formula, and They are vectors and In the i-th dimension, , is a positive number used to avoid a denominator of zero. There are two points. and The Euclidean distance between them ; 3D local descriptors for feature computation: ； In the formula, and It is the dot product between standardized vectors, where Normal vector with coordinate axes The angle between them Representing vectors with coordinate axes The angle between them, 𝜃 is a vector In the and After projection onto the defined plane, and The angle between them; The FPFH feature descriptors used for feature computation are calculated using the following formulas: ； It is a point The final fast histogram feature vector, It is a point Simplified point feature histogram, Point The neighborhood point set, It is the weight, for points. and points The Euclidean distance between them; Based on the calculated feature vectors of the points, voxel-level FPFH feature vectors are calculated by averaging. A voxel contains multiple points. The FPFH eigenvector of this voxel is represented as: ； The machine learning method based on the gradient boosting framework in step S3 includes: A leaf node-based growth strategy is adopted, which prioritizes splitting the leaf nodes with the largest gains to improve fitting ability and control complexity, thereby avoiding overfitting. The histogram algorithm is used to quickly locate the optimal split point of a feature, reducing computational complexity and memory usage.

2. The automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that, Drone flight altitude and path deviation distance The calculation formula is: ； ； In the formula, It is the flight altitude. It is the height of the bridge pier. It refers to the vertical field of view of the lidar. It is the path deviation distance.

3. The automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that, Step S2 includes: S21. Spatial Range Filtering: A pass-through filter is used to remove invalid and outlier points, resulting in a filtered point cloud. ； S22. Cenozoic Centroid Calculation: The filtered point cloud is downsampled using a voxel mesh, and the centroid of each point within a voxel is calculated. ； S23. Pier Point Cloud Extraction: Filtering Pier Point Cloud Based on Height Range: ; In the formula, It is a gathering of original points. It is a filtered point cloud. for For the origin point cloud collection middle The coordinates are given by the subscripts min and max, which represent the minimum and maximum values ​​of the coordinates of all points on the corresponding axes, respectively. This represents the centroid of the point cloud. The number of points within a voxel The set of point clouds selected as the support platform.

4. The machine learning method based on the gradient boosting framework according to claim 1, characterized in that, Where the objective function The model consists of a loss function L and a regularization term R. The goal of the model in the t-th iteration is to construct a new decision tree. To minimize the objective function, and then approximate the objective function using a second-order Taylor expansion: ； ； In the formula, Let be the predicted value for the t-th iteration. In the gradient boosting algorithm, new trees or learning models are continuously added in each iteration to optimize the objective function and improve the final prediction results. The first derivative of the loss function; This is the second derivative of the loss function; The weight of each leaf node is calculated by minimizing the objective function. LightGBM uses an additive model, progressively accumulating the outputs of each decision tree. The formulas for calculating the weights and generating the final predicted values ​​are as follows: ； ； In the formula, It is the first The weights of the leaf nodes Indicates the first A sample set of leaf nodes, These are regularization parameters; by setting the maximum and minimum number of leaf nodes, overfitting is avoided. It is a predicted value. It is the first The output of a decision tree, This represents the total number of iterations.

5. The automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that, The machine learning algorithm based on the gradient boosting framework in step S3 includes the following refined region refinement and fusion methods: S31. Initialization: Extract connected element groups from V. Initialize the empty set ; S32, For each voxel group :if If ≥ a predefined threshold, then Fitting plane and add to Otherwise, expand For each boundary voxel If to the fitted plane Distance ≤ threshold Then add adjacent voxels v k If after expansion ≥threshold Then add to ; S33, Merging Region in: For region , ,if If they are similar and adjacent, merge them; S34, Return .

6. The automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that, The fitting method for the pier column axis is as follows: The point cloud data of the four facades of the pier are merged into a single point cloud set. In the formula, N is the total number of points in the four facets, and the centroid of all points is calculated. Decenter the coordinates of all points to obtain And construct the covariance matrix: ； in, It is the outer product of the decentralized vectors of the points, over the covariance matrix. Eigenvalue decomposition yields eigenvalues ​​and their corresponding eigenvectors, with the eigenvector corresponding to the largest eigenvalue being... This is the main direction of the point cloud distribution, i.e., the direction of the pier axis, thus the axis equation is expressed as: ； in It is the direction of the axis. These are scalar parameters. The normal vector of the pier cap plane serves as a reference for evaluating the verticality of the pier column. The fitted pier cap plane... normal vector .

7. The automatic evaluation method for the installation quality of precast bridge piers based on three-dimensional laser point clouds according to claim 1, characterized in that, Step S4, which assesses the verticality and spacing of bridge piers, includes calculating the angle between the central axis of the pier and the normal to the cap beam plane. The Euclidean distance between the center point of the top surface of the pier is calculated. ,in and The calculation formula is: ； ； In the formula, and These represent the coordinates of the center points of the top surfaces of two adjacent piers. It is the direction vector of the central axis of the bridge pier. It is the normal vector of the cap beam plane.

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