A method for generating a fitted catenary from point cloud data

Abstract

The application discloses a method for generating a catenary fitting curve from point cloud data, which is used for the design or maintenance of target power facilities. The method comprises the following steps: collecting point cloud data of the target power facilities by a sensing device; preprocessing the collected data, including denoising, segmentation and coordinate conversion, to extract key point data related to the catenary; based on the preprocessed key point data, establishing a catenary mathematical model containing gravity, tension and catenary length parameters; using an optimization algorithm to solve the parameters of the mathematical model, minimizing the deviation between the model and the key point data; finally, generating the geometric shape and parameterized description of the catenary according to the fitting calculation results. The application combines point cloud data processing and catenary modeling technology, realizes efficient and accurate fitting of the catenary characteristics in power facilities, and is suitable for catenary form analysis and engineering needs in the design and maintenance of power facilities.

Description

Technical Field

[0001] This invention relates to the field of power data processing technology, and in particular to a method for generating a fitted catenary from point cloud data. Background Technology

[0002] In existing technologies, the analysis and modeling of catenary morphology in power facilities is a crucial aspect of power engineering design and maintenance. Traditional methods typically rely on manual measurement or simple geometric models, which have limitations in data acquisition and processing efficiency. In recent years, with the development of point cloud data acquisition technology, high-precision lidar and 3D scanning equipment have been widely applied to acquire geometric information of power facilities, and catenary fitting using point cloud data has gradually become a research hotspot. In related technologies, the combination of point cloud data and physical models makes the analysis of the geometric morphology and parametric characteristics of catenaries more scientific.

[0003] However, existing technologies suffer from significant problems in point cloud data processing, key point extraction, and catenary fitting. First, noise and background data interference lead to inaccurate point cloud preprocessing results. Second, fitting methods based on simplified models struggle to fully reflect the actual physical characteristics of the catenary. Third, the limitations of optimization algorithms can easily cause the model to get trapped in local optima, compromising fitting accuracy. These issues restrict the widespread application of point cloud data in catenary fitting and also, to some extent, affect the efficiency and reliability of power facility design and maintenance.

[0004] To address the aforementioned problems, this invention proposes a novel method for generating fitted catenary curves from point cloud data. Summary of the Invention

[0005] This application provides a method for generating a fitted catenary from point cloud data to improve the efficiency and accuracy of catenary fitting.

[0006] This application provides a method for generating a fitted catenary from point cloud data, including:

[0007] Point cloud data used to describe the target power facility is collected through sensing devices;

[0008] The collected point cloud data is preprocessed to extract key point data related to the catenary; wherein, the preprocessing includes denoising, segmentation and coordinate transformation;

[0009] Based on the preprocessed key point data, a catenary mathematical model is established, which includes parameters such as gravity, tension, and catenary length.

[0010] The parameters of the catenary mathematical model are solved using an optimization algorithm to minimize the deviation between the model and the key point data.

[0011] Based on the results of the fitting calculation, the geometry and parametric description of the catenary are generated for use in the design or maintenance of the target power facility.

[0012] Furthermore, the acquisition of point cloud data for describing the target power facility via sensing devices includes:

[0013] Based on the location and type of the target power facility, determine the spatial range in which point cloud data needs to be collected. The range includes the starting point, ending point and path area of ​​the catenary. At the same time, consider the impact of the surrounding environment on data collection. The surrounding environment includes the presence of obstacles or interference.

[0014] Based on the scope of the target area and the specific characteristics of the power facilities, select sensing devices, including lidar, 3D scanners or other high-precision measuring devices, and set the operating parameters of the devices, including scanning angle, resolution, sampling frequency and measurement distance.

[0015] The sensing device is placed at multiple viewpoints in the target area and scanned sequentially to collect point cloud data of the target power facilities, ensuring that the details of the key parts of the catenary and its connection points are fully recorded, while avoiding the occurrence of data blind spots.

[0016] Furthermore, the preprocessing of the collected point cloud data to extract key point data related to the catenary includes:

[0017] The collected point cloud data is preliminarily processed to remove discrete noise points caused by sensor errors or environmental interference, and spatial density filtering is used to smooth the point cloud data, retaining high-quality point data related to the target power facilities.

[0018] Based on the geometric shape and spatial location of the target power facility, a segmentation algorithm based on region growth or boundary features is used to separate the catenary-related region in the point cloud data from the background data, while excluding equipment or environmental information unrelated to the catenary.

[0019] Within the region of interest, a set of candidate points that may belong to the catenary is identified by curvature analysis, point density distribution, and vertical height variation characteristics. Point data that do not conform to the geometric characteristics of the catenary are then eliminated based on the continuity and connectivity of the candidate points.

[0020] Extract key points of the catenary from the candidate point set. Key points include the starting point, ending point and extreme points or turning points on the path of the catenary. Determine the specific location of the key points by comprehensively analyzing the spatial distribution and physical characteristics of the points.

[0021] The extracted catenary key points are subjected to coordinate transformation to be unified into a standardized coordinate system centered on the target power facility, and the spatial position of the key points is normalized.

[0022] Furthermore, the establishment of a catenary mathematical model based on the preprocessed key point data includes:

[0023] Geometric and physical property analysis is performed on the preprocessed and extracted catenary key point data, including the horizontal distribution of key points, vertical height variation and distance characteristics between key points, to obtain the initial conditions and constraint parameters for catenary modeling;

[0024] Based on the basic physical properties of the catenary, a parametric mathematical model of the catenary is constructed, taking the positions of the starting point, ending point and key points in the path of the catenary as the basis. The model includes the gravity factor, tension factor and length of the catenary as parameter inputs.

[0025] Based on the distribution characteristics of key points, the initial parameter values ​​of the catenary mathematical model are estimated using statistical and analytical methods, including the coordinates of the start and end points, the position of the lowest point of the catenary, and the initial values ​​of the tension and curvature of the model, so as to provide initial input for subsequent fitting calculations.

[0026] Physical constraints are embedded in the catenary mathematical model, including the tension balance relationship of the catenary, the ratio of gravity to tension, and the dependence of the catenary length on the distance between key points, to ensure that the mathematical model conforms to the actual physical characteristics of power facilities.

[0027] Based on the initially constructed catenary mathematical model, a framework for model optimization is defined, including parameter optimization objectives, error evaluation criteria, and optimization iteration process, laying the model foundation for fitting calculations.

[0028] Furthermore, the step of using an optimization algorithm to solve for the parameters of the catenary mathematical model to minimize the deviation between the model and the key point data includes:

[0029] By analyzing the geometric center, distance distribution, and curvature of the key point lines in the point cloud data, the initial values ​​of the catenary model parameters are determined. These initial values ​​include the gravity factor, tension factor, and catenary length, and are used as inputs for optimization iteration.

[0030] Based on the matching relationship between the catenary physical model and the point cloud data, an error function is constructed. The error function includes the vertical distance error from the key point to the catenary fitting curve and the deviation of the tension and gravity constraints. The tension and gravity constraints are determined by the vertical distribution trend of the key points in the point cloud.

[0031] Based on the matching degree between the distribution density of key points in the point cloud and the catenary morphology, dynamic weights are adaptively assigned to each error term in the error function to enhance the fitting accuracy in low-density key point regions, while ensuring that physical constraints play a dominant role in the optimization process.

[0032] During the optimization process, the parameter values ​​are updated by gradually and slightly perturbing the current parameter combination and combining the feedback of the error function. The perturbation range is adaptively shrunk based on the local characteristics of the key point data, thereby gradually approaching the global optimal solution.

[0033] Simultaneously, multiple sets of initial parameters are used to perform optimization calculations in parallel, and the fitting results of different paths are compared and interacted with each other. The path result with the smallest error is used to guide the parameter combination of other paths to avoid getting trapped in local optima.

[0034] When the fitting results of all paths meet the convergence condition of the error function, and the error of the fitting model in the key point region is lower than the preset threshold, the final catenary model parameters and geometric shape are output.

[0035] The beneficial effects of the technical solution provided in this application include:

[0036] (1) Through high-precision acquisition and preprocessing of point cloud data, this application can effectively extract key point data related to the catenary and solve the mathematical model of the catenary by combining optimization algorithms, which significantly reduces the deviation between the model and the key point data of the point cloud, thereby improving the accuracy and efficiency of the catenary fitting. (2) The preprocessing steps of this application include denoising, segmentation and coordinate transformation, which can effectively filter environmental noise and irrelevant data, and integrate multi-view point cloud data to ensure that the point cloud data used in the fitting process has high quality and consistency, thereby improving the robustness and applicability of point cloud data processing. (3) The catenary mathematical model established in this application not only considers geometric parameters, but also introduces physical parameters such as gravity, tension and catenary length, which can comprehensively reflect the actual characteristics of the catenary and provide a more scientific and reliable model basis for the design and maintenance of target power facilities. (4) Through the design of optimization algorithms, this application comprehensively considers the distribution of key points of the point cloud and physical constraints in the fitting process, which can effectively avoid the optimization process from getting trapped in local optima and ensure that the fitting results are closer to the global optimum, thereby improving the reliability and engineering application value of the catenary analysis of power facilities. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for generating a fitted catenary from point cloud data, provided in the first embodiment of this application. Detailed Implementation

[0038] Many specific details are set forth in the following description to provide a full understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific implementations disclosed below.

[0039] The first embodiment of this application provides a method for generating a fitted catenary from point cloud data. Please refer to... Figure 1 This figure is a schematic diagram of the first embodiment of this application. The following is in conjunction with... Figure 1 The first embodiment of this application provides a method for generating a fitted catenary from point cloud data, which will be described in detail below.

[0040] Step S101: Collect point cloud data to describe the target power facility using sensing devices.

[0041] Step S101 is a crucial step in acquiring point cloud data to describe the target power facility using sensing devices. This step requires the appropriate configuration of sensing devices and their operating parameters based on the spatial location of the target power facility, environmental conditions, and equipment type to ensure that the acquired data meets the accuracy requirements for subsequent processing and fitting.

[0042] First, determine the spatial scope of the target power facility, including the start and end points of the catenary and the areas the catenary path may traverse. Through preliminary site surveys, clarify the placement of sensor equipment to avoid blind spots or dead zones in data collection caused by obstructions, reflections, or complex terrain. If the target facility has significant height or span, multiple sensor devices can be deployed in different areas and from different perspectives to cover the entire data collection range.

[0043] Next, select appropriate sensing equipment based on the characteristics and accuracy requirements of the target area. For example, a lidar can be chosen for large-area, high-precision point cloud scanning, or a 3D scanner can be selected for acquiring detailed local features of catenary lines. The operating parameters of the sensing equipment need to be adjusted according to environmental conditions, including but not limited to scanning angle, scanning accuracy, sampling frequency, measurement distance, and scanning path. To improve acquisition efficiency and data accuracy, multi-view acquisition methods can be combined, utilizing rotation or mobile devices for multi-angle scanning to ensure that no point cloud data is missed or over-dense within the coverage area.

[0044] During actual data acquisition, the impact of external factors such as ambient light, weather conditions, and background interference on the performance of sensing equipment must be considered. For example, in environments with strong light or rain and snow, equipment with ambient light compensation or additional external light sources can be used to reduce interference. During the acquisition process, equipment operators need to periodically calibrate the equipment to eliminate data drift and errors, and adjust the scanning path and acquisition strategy according to the site conditions.

[0045] After data acquisition, store the point cloud data as files. The file format can be a common 3D point cloud format (such as .ply, .las, .pcd) for subsequent data processing. To ensure data traceability, it is recommended to also record the acquisition time, device parameters, and sensor location information, and store these information in association with the point cloud data for easy subsequent analysis.

[0046] Furthermore, the acquisition of point cloud data for describing the target power facility via sensing devices includes:

[0047] Based on the location and type of the target power facility, determine the spatial range in which point cloud data needs to be collected. The range includes the starting point, ending point and path area of ​​the catenary. At the same time, consider the impact of the surrounding environment on data collection. The surrounding environment includes the presence of obstacles or interference.

[0048] Based on the scope of the target area and the specific characteristics of the power facilities, select sensing devices, including lidar, 3D scanners or other high-precision measuring devices, and set the operating parameters of the devices, including scanning angle, resolution, sampling frequency and measurement distance.

[0049] The sensing device is placed at multiple viewpoints in the target area and scanned sequentially to collect point cloud data of the target power facilities, ensuring that the details of the key parts of the catenary and its connection points are fully recorded, while avoiding the occurrence of data blind spots.

[0050] In this embodiment, collecting point cloud data to describe the target power facility using sensing devices is the foundation of the entire catenary fitting method. To ensure that the collected data meets the accuracy and applicability requirements of the catenary fitting calculation, it is necessary to systematically plan the data collection steps, rationally configure the equipment and parameters, and fully consider the characteristics of the target power facility and the influence of its surrounding environment.

[0051] First, the spatial range for point cloud data acquisition is determined based on the location and type of the target power facility. The target facility may be conductors between high-voltage transmission towers or other similar catenary structures, and its spatial range typically consists of the catenary's starting point, ending point, and path area. The path area definition must cover the maximum curvature of the catenary and the possible range of vibration or offset. Furthermore, surrounding environmental factors such as obstacles (e.g., trees, buildings) or interfering objects (e.g., reflective surfaces, weather conditions) may interfere with the acquisition process, and these factors must be carefully considered when planning the acquisition range. For example, for areas that may be obstructed, additional backup scanning points should be added to reduce blind spots, while for areas with strong reflection interference, the angle of the sensing equipment or surface filtering settings should be adjusted.

[0052] After determining the target area, select appropriate sensing equipment based on the geometric characteristics of the power facility and the data acquisition requirements. LiDAR (Light Detection and Ranging) is a common choice due to its high precision and long-range measurement capabilities, suitable for large-scale catenary data acquisition. For localized areas requiring high detail resolution, higher-precision equipment such as 3D scanners can be selected. The equipment selection must match the characteristics of the facility. For example, for long-distance conductors at high altitudes, LiDAR with tilt scanning capabilities is preferred to cover a larger area; while for complex node areas (such as the connection points between conductors and insulators), handheld 3D scanners can be used to capture more details. The equipment's operating parameters, such as scanning angle, resolution, sampling frequency, and measurement distance, need to be optimized according to site conditions. For example, the resolution can be appropriately reduced to improve efficiency during large-scale scanning, while the resolution needs to be increased in critical connection point areas to capture more details.

[0053] The data acquisition process involves sequentially scanning the target area from multiple viewpoints using sensors. The selection of viewpoints must ensure full coverage of the catenary path and minimize blind spots. For example, the sensors can be positioned near the start and end points of the catenary, with several intermediate points distributed along the path to create a multi-point, multi-view scanning layout. During scanning at each viewpoint, the stability of the sensors must be ensured to prevent data accuracy degradation due to device movement. Furthermore, to reduce data errors caused by potential occlusion and overlapping areas, the scanning angle or device height can be adjusted appropriately. For instance, in areas with significant occlusion, the device's pitch angle can be increased; and in scenarios with significant terrain undulations, the device's position can be adjusted to capture more comprehensive data.

[0054] During data acquisition, special attention must be paid to the impact of environmental conditions on data quality. For example, in strong sunlight or rain / snow, lidar may be affected by reflection interference or signal attenuation. The acquisition effect can be optimized by selecting low-reflection wavelengths or adding auxiliary light sources. Furthermore, in environments with high wind speeds, measures must be taken to stabilize the equipment, such as adding support devices or using vibration-resistant bases.

[0055] After data collection, the data from each viewpoint is integrated into a complete point cloud dataset. During integration, coordinate alignment and deduplication are performed to ensure there is no deviation or overlap between data points. After integration, the dataset undergoes a quality check to confirm that details of key areas such as the start and end points of catenaries and connection points are fully recorded, and any missing data is supplemented.

[0056] By planning and implementing the above detailed steps, point cloud data that meets the requirements for catenary fitting can be effectively collected, providing high-quality input data for subsequent fitting calculations. This process covers target area planning, equipment selection and setup, scanning layout, and environmental adaptation, ensuring the comprehensiveness, accuracy, and efficiency of the acquisition results.

[0057] Step S102: Preprocess the collected point cloud data to extract key point data related to the catenary; wherein, the preprocessing includes denoising, segmentation and coordinate transformation.

[0058] Step S102 is a crucial step in preprocessing the collected point cloud data to extract key point data related to the catenary. This step involves data denoising, segmentation, and coordinate transformation to convert the original point cloud data into a simplified dataset that facilitates subsequent mathematical modeling and calculation, highlighting the catenary feature points.

[0059] First, in the data denoising stage, invalid and noisy points in the point cloud data caused by sensor errors, environmental interference, or acquisition conditions need to be removed. Statistical filtering algorithms can be used to detect outliers in the point cloud. This method identifies noise points by calculating the distribution characteristics of the surrounding neighborhood points of each point. Furthermore, voxelization downsampling techniques can be combined to downsample the point cloud, reducing the amount of data while preserving the main geometric features of the target power facility, thereby improving processing efficiency.

[0060] Next, the region of interest (ROI) is segmented. By analyzing the spatial distribution characteristics of the point cloud data, the portion containing the catenary is selected, while other irrelevant parts such as background objects or non-power facility areas are excluded. A region-growing method can be used, starting from seed points at the beginning or end of the catenary and expanding the region according to the Euclidean distance or height difference between points, gradually extracting data from the catenary region. Simultaneously, to enhance segmentation accuracy, the curvature characteristics of the point cloud can be analyzed to assist in identifying the catenary portion, ensuring that the detailed information of the catenary is fully preserved.

[0061] After segmentation, the resulting point cloud data undergoes coordinate transformation to unify the catenary-related point cloud data into a standard coordinate system. For example, the starting point of the catenary can be set as the origin, and the entire point cloud can be translated and rotated to ensure that the catenary lies within a unified geometric reference frame. This transformation facilitates parameter simplification and optimization in subsequent mathematical modeling, improving fitting accuracy and computational efficiency.

[0062] Finally, based on the segmented point cloud data, key point data related to the catenary are extracted. By analyzing the geometric features and spatial distribution of the point cloud within the catenary region, the starting point, ending point, and other representative key points of the catenary are selected, such as inflection points with significant morphological changes or locations with large curvature. Key point extraction can be combined with methods such as density analysis, local extremum detection, and curvature change rate analysis to ensure that the extracted key points accurately reflect the overall geometric shape of the catenary.

[0063] Through the above preprocessing steps, the point cloud data is transformed from its original state into a simplified dataset for catenary, providing high-quality data input for the establishment of the catenary mathematical model and parameter solving.

[0064] Furthermore, the preprocessing of the collected point cloud data to extract key point data related to the catenary includes:

[0065] The collected point cloud data is preliminarily processed to remove discrete noise points caused by sensor errors or environmental interference, and spatial density filtering is used to smooth the point cloud data, retaining high-quality point data related to the target power facilities.

[0066] Based on the geometric shape and spatial location of the target power facility, a segmentation algorithm based on region growth or boundary features is used to separate the catenary-related region in the point cloud data from the background data, while excluding equipment or environmental information unrelated to the catenary.

[0067] Within the region of interest, a set of candidate points that may belong to the catenary is identified by curvature analysis, point density distribution, and vertical height variation characteristics. Point data that do not conform to the geometric characteristics of the catenary are then eliminated based on the continuity and connectivity of the candidate points.

[0068] Extract key points of the catenary from the candidate point set. Key points include the starting point, ending point and extreme points or turning points on the path of the catenary. Determine the specific location of the key points by comprehensively analyzing the spatial distribution and physical characteristics of the points.

[0069] The extracted catenary key points are subjected to coordinate transformation to unify them into a standardized coordinate system centered on the target power facility. The spatial positions of the key points are also normalized to improve the consistency and computational efficiency of subsequent fitting calculations.

[0070] The preprocessing step in this embodiment aims to refine the acquired point cloud data, extracting high-quality key point data related to the catenary from the complex raw data, providing accurate input for subsequent catenary fitting. This step encompasses multiple stages, including denoising, segmentation, candidate point selection, and key point extraction, and combines coordinate transformation and normalization to ensure data consistency and usability.

[0071] Preprocessing begins with noise reduction. Acquired point cloud data typically contains discrete noise points introduced by equipment errors or environmental disturbances, which can interfere with subsequent analysis. To address this, statistical filtering algorithms can be used to remove noise points. These algorithms identify and remove points with abnormal density by calculating the local point density distribution around each point. Furthermore, spatial density filtering methods can be applied to smooth the point cloud data. By adjusting the local density of the point cloud, noise caused by uneven distribution is reduced while preserving the main geometric features of the target power facility. This process ensures high-quality point cloud data and reduces the complexity of subsequent processing.

[0072] The next step is segmentation. The goal of segmentation is to extract the catenary-related region from the point cloud data while removing irrelevant background information. Based on the geometry and spatial location of the target power facility, a region-growing segmentation algorithm can be used. Starting from the beginning or end of the catenary, the region is gradually expanded using distance and angular relationships with neighboring points to identify the part containing the catenary. Furthermore, boundary feature analysis can be combined, using the edge characteristics of the point cloud to separate the catenary region from the background data. For example, the boundary of a catenary typically appears as a continuous and smooth curve, contrasting sharply with the irregular distribution in the background region. These methods effectively focus on the catenary region, providing a precise data range for subsequent point selection.

[0073] Within the defined region of interest, the candidate point set for the catenary needs to be further filtered. This step identifies points that may belong to the catenary by analyzing the geometric characteristics of the point cloud data, such as curvature, point density distribution, and vertical height variation. For example, the local curvature of a catenary typically exhibits small and smooth variations, unlike the irregular variations found in other interference regions; in terms of point density distribution, the points along the catenary are usually relatively uniform; and regarding vertical height variation, the height of the catenary changes regularly with horizontal distance. By comprehensively judging these characteristics, a set of points that may belong to the catenary can be selected, while points that do not conform to the geometric characteristics of the catenary can be eliminated. This process significantly reduces data redundancy and improves data relevance.

[0074] Based on the candidate point set, key points of the catenary are further extracted. The selection of key points requires a comprehensive analysis combining the geometric and physical characteristics of the catenary to ensure that the selected key points accurately represent its morphological features. Key points include the starting and ending points of the catenary, as well as extreme points or turning points along the path. By analyzing the spatial distribution of candidate points, local extremum detection methods can be used to determine the maximum and minimum values ​​of the height, while spatial continuity is used to judge the rationality between key points. For example, the lowest point of the catenary usually corresponds to a critical extreme point, while the connection points at both ends of the catenary need to satisfy the characteristics of physical connection. Through these analyses, a key point set can be constructed, providing the necessary basic data for fitting the catenary.

[0075] Finally, the extracted key point data undergoes coordinate transformation and normalization. Coordinate transformation unifies the key point locations to a standardized coordinate system of the target power facility, for example, establishing a local coordinate system along the catenary direction with the origin as the origin. This transformation eliminates coordinate deviations caused by differences in the original data acquisition angle or equipment location, ensuring the consistency of the key point data. Furthermore, normalizing the spatial locations of the key points ensures that all coordinates are represented in consistent units and ranges, which helps improve the efficiency of subsequent fitting calculations and simplify parameter optimization.

[0076] Through the detailed preprocessing steps described above, high-quality catenary keypoint data can be extracted from the raw point cloud data, providing accurate input for fitting the mathematical model of the catenary. This process encompasses comprehensive processing including data denoising, segmentation, candidate point selection, keypoint extraction, and coordinate standardization, ensuring the reliability and applicability of the preprocessing results.

[0077] Step S103: Based on the preprocessed key point data, establish a catenary mathematical model, which includes parameters such as gravity, tension, and catenary length.

[0078] Step S103 is the core step in establishing a mathematical model of the catenary based on the preprocessed keypoint data. Its goal is to generate a mathematical model suitable for fitting calculations, based on the physical properties of the catenary and the geometric distribution of the keypoints. The implementation of this step requires comprehensive consideration of the catenary's physical properties, geometric features, and parametric representation to ensure the model has both computational efficiency and physical meaning.

[0079] First, the geometric distribution of the catenary is analyzed from the key point data extracted in step S102, including the spatial locations of the starting point, ending point, and other key points along the path. Based on the relative height and horizontal distance of these points, the span range of the catenary and the approximate location of its lowest point are preliminarily determined. These features provide basic data for defining model parameters and setting constraints.

[0080] Next, considering the physical properties of the catenary, the main parameters of the model are determined. A catenary is a curve subjected to gravity and tension, and its shape is influenced by the gravity factor, tension factor, and the total length of the catenary. Therefore, the model needs to include these three core parameters: the gravity factor describes the degree to which the catenary is affected by gravity; the tension factor reflects the distribution of tension on the catenary; and the catenary length is a geometric parameter of the curve, used to constrain the actual span of the fitted curve. These parameters are linked to key point data through mathematical expressions, enabling the model to reflect the geometric and physical properties of the catenary.

[0081] In parametric modeling, the morphology of the catenary is expressed as a continuous mathematical function to facilitate subsequent fitting calculations. The standard equation of the catenary is generally used, which parametrically expresses the relationship between the horizontal position and vertical height of key points, and uses the gravity factor, tension factor, and catenary length as input variables for the model. Specifically, the equation must be based on the spatial position of the key points, ensuring geometric constraints at the start and end points, while also considering the relative distance and height variations between key points.

[0082] To ensure the model accurately reflects the actual conditions of the target power facility, physical constraints need to be introduced. These constraints include the tension balance of the catenary, the ratio of tension to gravity, and the geometric consistency between the catenary length and the spacing between key points. Embedding these constraints not only improves the physical accuracy of the model but also prevents it from deviating from the actual catenary characteristics during the fitting process.

[0083] Finally, the model construction needs to support subsequent optimization calculations. An error evaluation mechanism needs to be defined to measure the deviation between the fitted curve and the keypoint data, while also providing a clear objective function and computational framework for solving the parameters of the optimization algorithm. By organically combining geometric and physical properties, a catenary mathematical model with clear physical meaning and high computational efficiency is ultimately generated.

[0084] Through the above steps, the model can fully express the physical and geometric characteristics of the target power facility's catenary, providing a high-quality foundation for subsequent optimization calculations.

[0085] Furthermore, the establishment of a catenary mathematical model based on the preprocessed key point data includes:

[0086] Geometric and physical property analysis is performed on the preprocessed and extracted catenary key point data, including the horizontal distribution of key points, vertical height variation and distance characteristics between key points, to obtain the initial conditions and constraint parameters for catenary modeling;

[0087] Based on the basic physical properties of the catenary, a parametric mathematical model of the catenary is constructed, taking the positions of the starting point, ending point and key points in the path of the catenary as the basis. The model includes the gravity factor, tension factor and length of the catenary as parameter inputs.

[0088] Based on the distribution characteristics of key points, the initial parameter values ​​of the catenary mathematical model are estimated using statistical and analytical methods, including the coordinates of the start and end points, the position of the lowest point of the catenary, and the initial values ​​of the tension and curvature of the model, so as to provide initial input for subsequent fitting calculations.

[0089] Physical constraints are embedded in the catenary mathematical model, including the tension balance relationship of the catenary, the ratio of gravity to tension, and the dependence of the catenary length on the distance between key points, to ensure that the mathematical model conforms to the actual physical characteristics of power facilities.

[0090] Based on the initially constructed catenary mathematical model, a framework for model optimization is defined, including parameter optimization objectives, error evaluation criteria, and optimization iteration process, laying the model foundation for fitting calculations.

[0091] This embodiment establishes a catenary mathematical model based on preprocessed key point data, providing a solid theoretical foundation for subsequent fitting and optimization processes. This model integrates geometric and physical property analysis, parametric modeling, initial parameter estimation, embedding of physical constraints, and definition of the optimization framework to ensure the model's accuracy and practical applicability.

[0092] First, geometric and physical characteristics are analyzed from the keypoint data extracted during preprocessing. Keypoint data for a catenary typically includes the start point, end point, lowest point, and other important points along the path. Their horizontal distribution, vertical height variation, and distance characteristics between keypoints are the core basis for modeling. Analyzing the horizontal distribution of keypoints allows for a preliminary assessment of the catenary's span and morphological trend; while the vertical height variation provides preliminary information on the catenary's curvature characteristics and physical form. Furthermore, the distance characteristics between keypoints reveal the total length and curvature distribution of the catenary. This information collectively provides the initial conditions and constraint parameters for constructing the mathematical model of the catenary.

[0093] After completing the characteristic analysis, based on the fundamental physical properties of the catenary, a parametric mathematical model is constructed using the starting point, ending point, and key points along the path. The catenary is a typical curve subjected to gravity and tension; its shape is determined by the gravity factor, tension factor, and total length of the catenary. The parametric expression of the model is established through the geometric relationships between these factors and key points, allowing the curve to be fully described by a finite set of parameters. This parametric modeling method provides a clear mathematical expression for subsequent calculations, while also possessing good scalability and adaptability.

[0094] Model construction requires reasonable estimation of initial parameter values ​​to provide a stable starting point for subsequent optimization. By combining the distribution characteristics of key points and utilizing statistical and analytical methods, the coordinates of the start and end points, the location of the lowest point of the catenary, and the initial values ​​of the model's tension and curvature can be preliminarily determined. Specifically, the coordinates of the start and end points can be directly obtained from the endpoints of the horizontal position and height in the key point set; the location of the lowest point can be determined by the minimum height value of the key point, while ensuring its rationality in conjunction with the horizontal distribution; the initial values ​​of tension and curvature can be estimated based on the span and height difference of the catenary, and these values ​​can be adjusted according to physical laws to meet the basic physical requirements of the model.

[0095] When constructing the model, necessary physical constraints must be embedded into the mathematical model. These constraints include the tension balance relationship of the catenary, the ratio of gravity to tension, and the dependency relationship between the total length of the catenary and the spacing between key points. The tension balance relationship ensures that the model can accurately reflect the overall equilibrium state of the forces acting on the catenary; the ratio of gravity to tension, combined with the height and horizontal distribution characteristics of the key points, constrains the physical rationality of the model's solution; the dependency relationship between the total length and the spacing between key points constrains the curve shape through geometric consistency, making it consistent with the actual power facility structure. The embedding of these physical constraints enhances the physical meaning and practicality of the model, ensuring a high degree of consistency between the mathematical expression and engineering reality.

[0096] Finally, based on the initially constructed catenary mathematical model, a framework for model optimization needs to be defined. This framework includes parameter optimization objectives, error evaluation criteria, and an optimization iteration process, aiming to make the model more closely resemble the actual catenary shape through systematic optimization methods. The parameter optimization objective is to minimize the geometric and physical deviations between the model and the keypoint data by adjusting parameters such as the gravity factor, tension factor, and total length of the model. The error evaluation criteria need to comprehensively consider the vertical distance error from the keypoints to the model curve and the degree to which the model parameters conform to physical constraints; these criteria provide clear evaluation indicators for optimization. The optimization iteration process involves gradually adjusting parameters and continuously improving the model based on error feedback, ultimately achieving a globally optimal fit.

[0097] Through the above steps, a mathematical model of the catenary can be accurately established based on key point data, providing a reliable foundation for subsequent fitting and optimization. The model's geometric and physical properties, parametric expression, and optimization framework together constitute a complete system, ensuring that it can meet practical engineering needs and has wide applicability.

[0098] Step S104: Use an optimization algorithm to solve for the parameters of the catenary mathematical model to minimize the deviation between the model and the key point data.

[0099] Step S104 is a crucial step in solving the parameters of the catenary mathematical model using an optimization algorithm. Its goal is to adjust the model parameters through the optimization algorithm to ensure a high degree of match with the preprocessed key point data and to minimize the deviation between the model and the key points. This process requires the comprehensive application of the optimization algorithm's search, evaluation, and adjustment mechanisms to ensure that the model accurately reflects the catenary characteristics of the target power facility.

[0100] First, the parameters of the optimization algorithm are initialized. Based on the catenary mathematical model established in step S103, initial values ​​for the gravity factor, tension factor, and catenary length are set. These initial values ​​can be estimated based on the geometric distribution characteristics of the keypoint data. For example, the initial length can be estimated by the horizontal distance between the start and end points of the catenary, the range of the gravity factor can be determined using the range of keypoint height variations, and the initial value of the tension factor can be set based on the density of keypoint distribution. The rationality of the initial values ​​directly affects the convergence speed of the optimization process and the accuracy of the final result.

[0101] During optimization, an error function is constructed to quantify the deviation between the model and the keypoint data. The design of the error function needs to comprehensively consider geometric deviations and physical constraints, specifically including the vertical distance deviation from the keypoints to the fitted curve, and the mechanical equilibrium relationship of the catenary. The error function effectively measures the merits of the current parameter combination, providing clear guidance for subsequent adjustments.

[0102] Subsequently, the parameters are iteratively adjusted using an optimization algorithm. This algorithm employs a stepwise perturbation search strategy, making small adjustments to the gravity factor, tension factor, and catenary length in each iteration and calculating the adjusted error function value. If the new error function value is smaller than the current value, the new parameter combination is accepted; otherwise, it reverts to the previous parameter combination. To avoid getting trapped in local optima, a multi-path parallel search mechanism can be introduced. This involves simultaneously running optimization paths for multiple initial parameter combinations, comparing the results between paths to select the path with the smallest error as a reference, and using the results of the optimal path to guide the parameter adjustment direction of other paths.

[0103] After each iteration, the convergence of the error function is evaluated. If the error function value remains stable and below the preset convergence threshold across multiple iterations, the optimization process is considered complete, and the final parameter results are output. If the error function fails to meet the convergence condition, the perturbation range or optimization direction needs further adjustment. For example, when the error value changes small, the parameter adjustment range is gradually narrowed to improve the optimization precision; when the error value changes large or fluctuates significantly, the parameter adjustment range can be widened to enhance the search capability.

[0104] During optimization, special attention must be paid to the satisfaction of physical constraints, such as the tension balance and length constraints of the catenary. Any parameter combinations that do not conform to physical reality should be eliminated. In addition, intermediate results and error value changes during the optimization process should be recorded to evaluate and fine-tune the optimization path.

[0105] Through the above steps, the optimization algorithm can effectively adjust the parameters of the catenary mathematical model, making the fitting results highly consistent with the key point data of the point cloud.

[0106] Furthermore, the step of using an optimization algorithm to solve for the parameters of the catenary mathematical model to minimize the deviation between the model and the key point data includes:

[0107] By analyzing the geometric center, distance distribution, and curvature of the key point lines in the point cloud data, the initial values ​​of the catenary model parameters are determined. These initial values ​​include the gravity factor, tension factor, and catenary length, and are used as inputs for optimization iteration.

[0108] Based on the matching relationship between the catenary physical model and the point cloud data, an error function is constructed. The error function includes the vertical distance error from the key point to the catenary fitting curve and the deviation of the tension and gravity constraints. The tension and gravity constraints are determined by the vertical distribution trend of the key points in the point cloud.

[0109] Based on the matching degree between the distribution density of key points in the point cloud and the catenary morphology, dynamic weights are adaptively assigned to each error term in the error function to enhance the fitting accuracy in low-density key point regions, while ensuring that physical constraints play a dominant role in the optimization process.

[0110] During the optimization process, the parameter values ​​are updated by gradually and slightly perturbing the current parameter combination and combining the feedback of the error function. The perturbation range is adaptively shrunk based on the local characteristics of the key point data, thereby gradually approaching the global optimal solution.

[0111] Simultaneously, multiple sets of initial parameters are used to perform optimization calculations in parallel, and the fitting results of different paths are compared and interacted with each other. The path result with the smallest error is used to guide the parameter combination of other paths to avoid getting trapped in local optima.

[0112] When the fitting results of all paths meet the convergence condition of the error function, and the error of the fitting model in the key point region is lower than the preset threshold, the final catenary model parameters and geometric shape are output.

[0113] This embodiment uses an optimization algorithm to solve for the parameters of the catenary mathematical model, aiming to minimize the deviation between the model and the key point data in the point cloud. The optimization process combines geometric analysis, physical constraints, and dynamic weight adjustment, adopts a multi-path parallel optimization strategy, and achieves the global optimum through stepwise approximation, ultimately outputting accurate catenary model parameters and geometric shape.

[0114] First, the initial parameter values ​​of the catenary model are determined through geometric center, distance distribution, and curvature analysis of the keypoint data in the point cloud. These initial values ​​include the gravity factor, tension factor, and catenary length, reflecting the morphological characteristics of the catenary in the gravitational field, the distribution of tension it bears, and its physical length, respectively. The calculation of the geometric center provides the initial symmetrical position of the catenary in space, the distance distribution reflects the distribution range of keypoints along the path, and the curvature analysis helps determine the initial tension parameters by detecting the bending characteristics of the curve. These analyses ensure that the initial parameters are reasonable, providing stable input for subsequent optimization.

[0115] Based on the matching relationship between the physical model of the catenary and the point cloud data, an error function is constructed to quantify the model's fitting accuracy. The error function integrates the vertical distance deviation from keypoints to the fitted curve, as well as the physical constraint deviation of the catenary. The vertical distance deviation directly reflects the geometric deviation between the model and the keypoint data, while the physical constraint deviation (such as the balance between tension and gravity) is determined by the vertical distribution trend of the point cloud keypoints, ensuring the physical rationality of the model. The error function provides a clear objective and evaluation criterion for the optimization process.

[0116] During the optimization process, dynamic weights are assigned to each error term in the error function. These dynamic weights are adaptively adjusted based on the distribution density of keypoints in the point cloud and the matching degree of the catenary morphology to enhance the fitting accuracy in low-density regions while ensuring that physical constraints play a dominant role in the optimization. For example, for regions with sparse keypoint distribution, the weight of the vertical distance deviation term is increased to improve the model's sensitivity to these regions; and for physical constraints, the weight adjustment ensures that the model maintains mechanical balance while satisfying geometric fitting requirements.

[0117] Parameter optimization is achieved through a gradual perturbation and error feedback mechanism. In each iteration, a small perturbation is applied to the current parameter combination, the adjusted error function value is calculated, and the parameters are updated based on the error feedback. The perturbation range is dynamically adjusted based on the local characteristics of the keypoint data. For example, the perturbation range is gradually reduced in regions where the error converges quickly to improve optimization accuracy, while the perturbation range is expanded in regions with larger errors to enhance global search capabilities. This gradual approximation method effectively avoids the optimization from getting trapped in local optima.

[0118] To further enhance the optimization effect, multiple sets of initial parameters are used to perform optimization calculations in parallel. Each set of initial parameters forms an independent optimization path, and the different paths guide each other through result comparison and interaction. Specifically, the optimal path is selected based on the error function value of each path, and the results of this path are used to provide a reference for adjusting the parameters of other paths, thereby accelerating the convergence process and improving the stability of the global optimal solution.

[0119] The optimization process ends when the fitting results of all paths satisfy the convergence condition of the error function and the error of the fitted model in the key point region is lower than the preset threshold. Finally, the optimized catenary model parameters and geometry are output. These parameters and geometry not only accurately describe the actual state of the catenary but also provide reliable basic data for the design and maintenance of target power facilities.

[0120] Through the optimization process described above, an accurate catenary model can be efficiently constructed from point cloud keypoint data, ensuring that the geometric fitting accuracy and physical plausibility of the model are consistent. This method offers significant accuracy advantages and engineering value in the analysis and design of catenary systems for power facilities.

[0121] Furthermore, the initial values ​​of the catenary model parameters are determined through analysis of the geometric center, distance distribution, and curvature of the lines connecting the key points in the point cloud data, including:

[0122] This embodiment comprehensively analyzes the geometric center, distance distribution, and curvature of the lines connecting key points in the point cloud data to calculate the initial parameter values ​​of the catenary mathematical model, including the gravity factor, tension factor, and catenary length. These initial values ​​are the basis for optimization calculations and directly affect the accuracy and convergence speed of the fitting results. The following details how to implement this step.

[0123] The initial value of the gravity factor G0 of the catenary mathematical model is determined according to the following formula (1):

[0124]

[0125] Among them, z i The height value of the i-th keypoint in the point cloud represents its position in the vertical direction;

[0126] The average height of all key points in the point cloud is used to describe the overall vertical distribution characteristics of the point cloud.

[0127] n represents the number of key points in the point cloud, reflecting the density of the data points;

[0128] w i The weight of the i-th keypoint in the geometric center distribution is calculated according to the following formula (2):

[0129]

[0130] Where, d i Represents the Euclidean distance from the i-th keypoint to the geometric center, used to measure the relative importance of the keypoint in space; ∈ is a small positive number to prevent division by zero;

[0131] Using the above formula, the initial value of the gravity factor can dynamically reflect the vertical distribution of the point cloud and its force on the catenary.

[0132] The initial value T0 of the tension factor in the catenary mathematical model is determined using the following formula (2):

[0133]

[0134] Where m is κ i The number of segments in the line connecting keypoints indicates the total number of line segments between keypoints in the point cloud; κ j Let be the local curvature value of line segment j, reflecting the degree of curvature of the line segment. The local curvature is calculated using the three-point fitted circle method. Specifically, three consecutive points on the line segment are selected, a circle is fitted to the line segment, and the curvature is defined as the reciprocal of the radius of curvature of that circle. j Let j be the length of line segment j;

[0135] The initial value L0 of the catenary length is determined by the following formula (3):

[0136]

[0137] Among them, (x i ,y i (x) represents the coordinates of the i-th keypoint in the point cloud on the horizontal plane; (x) i+1 ,y i+1 ) represents the coordinates of the (i+1)th point cloud keypoint on the horizontal plane; n is the number of point cloud keypoints.

[0138] Through the above steps, the initial parameter values ​​of the catenary model can be accurately calculated based on the geometric and physical characteristics of the key points in the point cloud, providing high-quality input conditions for subsequent optimization solutions. This method is efficient and applicable, dynamically adapting to the characteristics of different point cloud data distributions, ensuring the stability of the fitting process and the accuracy of the final results.

[0139] Furthermore, the construction of the error function based on the matching relationship between the catenary physical model and the point cloud data includes:

[0140] The error function is constructed according to the following formula (4):

[0141]

[0142] Where E is the total error function value, used to measure the overall deviation between the catenary fitting curve and the key points and physical constraints of the point cloud; x i Let z be the horizontal coordinate of the i-th keypoint in the point cloud, representing the position of the i-th keypoint in the horizontal direction; i Let be the vertical coordinate of the i-th keypoint in the point cloud, representing the position of the i-th keypoint in the vertical direction; f(x) is the curve function of the catenary mathematical model, representing the geometric shape of the fitted catenary; x c Indicates the distance between the catenary and the key point (x). i ,z i The horizontal coordinates of the points where the vertical projections intersect; f ′ (x c ) and f″(x c ) represents the first and second derivatives of the catenary function;

[0143] T j The tension value on the j-th catenary segment is obtained through mechanical calculations based on the catenary model; g j Let be the gravity distribution value on the j-th catenary segment, calculated based on the vertical distribution trend of key points in the point cloud; m is the number of catenary segments.

[0144] Δh i Δx represents the vertical height difference between the i-th keypoint and the (i+1)-th keypoint. i θ represents the difference in horizontal distance between the i-th keypoint and the (i+1)-th keypoint; i The tangent angle of the catenary fitted curve between keypoints i and i+1 is represented by p; p is the number of keypoints; α i β and γ are weighting factors.

[0145] Weighting factor α i β and γ can be obtained from experimental data or set directly based on expert knowledge, or they can be dynamically adjusted. For details on dynamic adjustment, please refer to the following instructions.

[0146] Furthermore, the step of adaptively assigning dynamic weights to each error term in the error function based on the matching degree between the distribution density of key points in the point cloud and the catenary morphology includes:

[0147] The weighting factor α is calculated according to the following formula (5). i :

[0148]

[0149] Where, d iLet be the local density of key point i in the point cloud. The local density is calculated by counting the number of points in the neighborhood of the key point and is used to describe the spatial distribution characteristics of the key point.

[0150] d mean The average density of all key points is used to compare the difference between the local density of each point and the overall distribution.

[0151] n is the number of key points in the point cloud;

[0152] k is a weighting factor. The larger the value, the more significant the impact of density changes on the weight. It can be obtained based on empirical data or experimental data.

[0153] δ i This is the deviation value of the matching degree between the i-th point cloud key point and the fitted curve. Its value is calculated from the matching degree of the fitted curve to the key point, and is used to reflect the contribution of the key point to the overall fitting.

[0154] Calculate the weighting factor β according to the following formula (5):

[0155]

[0156] Among them, f i The physical constraint strength of the i-th keypoint in the point cloud is calculated using the catenary mechanics formula, specifically the ratio of tension to gravity, reflecting the degree of physical equilibrium of the keypoint; n is the number of keypoints in the point cloud; ω i The vertical distribution trend weight of the i-th key point in the point cloud is calculated according to the following formula (7):

[0157]

[0158] Among them, z i This represents the height of the i-th key point in the point cloud; It is the average height of all key points in the point cloud; Indicates the height of all point cloud keypoints and The maximum value among the absolute values ​​of the differences;

[0159] Calculate the weighting factor γ according to the following formula (8):

[0160]

[0161] Where n is the number of key points in the point cloud.

[0162] Furthermore, during the optimization process, the parameter values ​​are updated by gradually making small perturbations to the current parameter combination and combining this with feedback from the error function, including:

[0163] Based on the current catenary model parameters, including gravity factor, tension factor and catenary length, a set of initial small perturbation values ​​are generated. The amplitude of each perturbation value is controlled by a preset perturbation range. The perturbation range is dynamically adjusted according to the distribution density of key points in the point cloud. A larger perturbation range is set for low-density areas to enhance the model's adaptability.

[0164] The generated perturbation values ​​are applied one by one to the current parameter combination to form multiple new parameter combinations. Each parameter combination adds or subtracts a perturbation value of a specific magnitude based on the current parameters. At the same time, the error function value corresponding to each parameter combination is recorded to measure its fitting effect.

[0165] Based on the feedback results of the error function, the fitting effects of different perturbation parameter combinations are compared, and higher weights are assigned to parameter combinations with smaller errors. The basic parameter combination for the next round of optimization is determined by calculating the weighted average value, thereby gradually approaching the global optimum.

[0166] This embodiment continuously optimizes the model parameters by gradually and slightly perturbing them, and by combining the feedback results of the error function, gradually bringing the model parameters closer to the global optimum. The key to this process lies in reasonably setting the perturbation value and range, combining it with a dynamic adjustment mechanism, and using the error function results to guide the selection and updating of parameter combinations.

[0167] In the initial optimization phase, a set of small perturbation values ​​are generated for the parameters of the current catenary model, including the gravity factor, tension factor, and catenary length. The magnitude of each perturbation value is determined by a preset perturbation range, which is dynamically adjusted according to the distribution density of keypoints in the point cloud. Specifically, for regions with low keypoint density, a larger perturbation range is set to enhance the model's adaptability in sparse data regions; for regions with high density, the perturbation range is appropriately reduced to improve the stability of parameter updates and the accuracy of local fitting. This dynamic adjustment ensures that the perturbation range matches the data distribution characteristics, enabling both exploration of the global parameter space and fine-grained optimization in local regions.

[0168] Next, the generated perturbation values ​​are applied one by one to the current parameter combination, forming multiple new parameter combinations. Each parameter combination has a perturbation value increased or decreased by a certain amount based on the current one, forming a candidate parameter set with diverse characteristics. This operation effectively avoids the model parameters from getting trapped in local optima and provides a wider search space for the global optimum. After each parameter combination is generated, its fitting effect is calculated using an error function, and the error function value corresponding to each parameter combination is recorded. These error values ​​reflect the geometric deviation and physical consistency between the model fitting curve and the key points of the point cloud, providing a clear evaluation basis for subsequent parameter updates.

[0169] Based on the feedback results of the error function, the fitting effects of different combinations of perturbation parameters are compared and analyzed. By comparing the error values, parameter combinations with smaller errors are selected and assigned higher weights, with the weight values ​​inversely proportional to the performance of their error functions. This weighting strategy ensures that parameter combinations with better fitting effects contribute more to the next round of optimization, while retaining a certain proportion of high-error parameter combinations to maintain the diversity of parameter search. Subsequently, the weighted average of all parameter combinations is calculated to generate the basic parameter combinations for the next round of optimization. This weighted averaging strategy improves the stability of parameter updates while maintaining the model's ability to explore the global optimum.

[0170] Throughout the optimization process, a combination of gradual, small-scale perturbations and error feedback is used. By dynamically adjusting the perturbation range and weight allocation, precise control over parameter updates is achieved. Finally, when the error function value stabilizes after multiple iterations and reaches the preset convergence condition, the optimization process terminates, and the current parameter combination is output as the final catenary model parameters.

[0171] This method achieves a balance between global search and local optimization by gradually perturbing the parameters, providing error feedback, and adjusting the weights, ensuring that the fitting results are both highly accurate and reflect the actual physical characteristics of the catenary.

[0172] Furthermore, the simultaneous parallel execution of optimization calculations using multiple sets of initial parameters, and the comparison and interaction of fitting results from different paths, using the path result with the smallest error to guide parameter combinations for other paths, avoids getting trapped in local optima, including:

[0173] Based on the geometric distribution of key points in the point cloud and the physical characteristics of the catenary model, multiple sets of initial parameter combinations are randomly generated. These parameter combinations include gravity factor, tension factor, and catenary length.

[0174] Each initial parameter combination is assigned an independent optimization path, and optimization calculations are performed separately. Each path independently runs the error function calculation and parameter update process.

[0175] After each round of optimization iteration, the current error value and parameter combination of all paths are collected, the error results between paths are compared, the path with the smallest error value is selected as the reference path, and the optimization result of the path is marked as the current best fit result.

[0176] Based on the fitting results of the reference path, the parameter combinations of other paths are adjusted in a guiding manner, including narrowing the range of parameter perturbation, increasing the weight of the key fitting region, or modifying the optimization direction, so as to guide other paths to approach the global optimum while maintaining the diversity between paths to avoid premature convergence.

[0177] In this embodiment, when optimizing the catenary model parameters, multiple sets of initial parameters are used simultaneously to perform optimization calculations in parallel. This fully utilizes the diversity of different parameter combinations, expands the search space, and increases the probability of finding the global optimum. This method, based on the comparison and interaction of results between paths, avoids the optimization process getting trapped in local optima, ensuring high accuracy and physical plausibility of the model fit.

[0178] In the initial stage of optimization computation, multiple sets of initial parameter combinations are randomly generated based on the geometric distribution of key points in the point cloud and the physical characteristics of the catenary model. These parameter combinations include gravity factor, tension factor, and catenary length. Each set of parameters is randomly distributed within a reasonable range to cover the possible morphological features of the catenary. The diversity of initial parameters is crucial to the success of optimization; therefore, when generating these combinations, it is necessary to ensure that the parameter distribution can represent the overall characteristics of the point cloud data while retaining a certain degree of randomness to explore more possible solutions.

[0179] Each generated initial parameter combination is assigned to an independent optimization path, and each path runs optimization computation independently, including error function calculation and parameter update. Within each path, the error function is used to quantify the fitting effect of the current parameter combination, including the geometric error from keypoints to the fitted curve and the physical constraint deviation of the catenary model. In each iteration, the optimization algorithm within the path updates the parameters based on the feedback from the error function, gradually improving the fitting results. This parallel computing mechanism can accelerate the optimization process of different parameter combinations without mutual interference, while providing rich data support for comparison and interaction between subsequent paths.

[0180] After each optimization iteration, the current error values ​​of all paths and their corresponding parameter combinations are collected and analyzed. By comparing the error results among the paths, the path with the smallest error value is selected as the reference path. The reference path represents the parameter combination with the best fit in the current iteration, and its optimization result is marked as the current best fit result. The selection of the reference path provides guidance for the interaction between subsequent paths and also lays the foundation for the gradual approximation of the global optimum.

[0181] Based on the fitting results of the reference path, the parameter combinations of other paths are adjusted in a guiding manner. This adjustment method includes multiple levels. First, the range of parameter perturbation is narrowed, that is, the magnitude of parameter variation is reduced in the region where the error value is close to that of the reference path, so as to enhance the precision of optimization. Second, the weight of key fitting regions is increased, especially in regions where the distribution of key points in the point cloud is sparse or the curvature changes greatly. By assigning higher error weights to these regions, the optimization direction is guided. Finally, the optimization direction of the path is modified. For example, in paths with large error values, the parameter trends of the reference path or the regions of priority are introduced, so that other paths gradually move closer to the global optimum.

[0182] To avoid premature convergence between paths, maintaining a certain degree of path diversity during optimization is crucial. Even when guided by a reference path, parameter updates for other paths must retain a degree of randomness and independence to continuously explore potential improvement directions. This mechanism ensures that paths can both learn from and improve upon each other while maintaining sufficient flexibility in the global search.

[0183] Finally, the optimization process terminates when the error values ​​of multiple paths all reach the preset convergence condition and the differences in optimization results between paths decrease. At this point, the parameter combination of the reference path is selected as the final result of the catenary model. Through this parallel optimization and path interaction approach, those skilled in the art can efficiently avoid local optima problems and obtain the best fitting results that conform to the characteristics of point cloud data and the physical properties of catenaries. This method combines computational efficiency and global search capability, and is suitable for catenary model fitting problems under complex point cloud data.

[0184] Step S105: Based on the fitting calculation results, generate the geometry and parametric description of the catenary for use in the design or maintenance of the target power facility.

[0185] Step S105 is a crucial step in generating the geometry and parametric description of the catenary based on the fitting calculation results, to meet the design or maintenance requirements of the target power facility. This step requires transforming the optimized catenary mathematical model into a visual and operable form, while outputting relevant data based on actual application needs.

[0186] First, based on the catenary model parameters optimized in step S104, including the gravity factor, tension factor, and catenary length, the catenary mathematical model is transformed into the specific geometric shape of the curve. This process requires calculating the set of points within the defined range of the model using the catenary parameterized expression, including the horizontal position and vertical height of each point on the curve. The calculation must incorporate the actual coordinates of the starting and ending points to ensure that the fitted curve accurately covers the catenary area of ​​the target power facility.

[0187] The generated catenary geometry is then visualized as 3D point cloud data. This allows 3D modeling tools to connect the discrete point sets of the catenary into a continuous curve, generating a graphical representation for design or maintenance. For example, the 3D shape of the curve can be exported to common 3D model formats (such as STL or OBJ) for further analysis and use by power engineers in design software.

[0188] Alongside generating the geometry, a parametric description of the catenary must also be output. This parametric description includes the catenary's mathematical equations, key point locations, total length, maximum curvature, and tension values ​​at the start and end points. These parameters provide a quantitative description of the catenary's physical properties and can be directly used for engineering design or maintenance calculations of power facilities. For example, the total length and maximum curvature of the catenary can be used to assess the strength requirements of cable materials, and the tension values ​​can be used to detect stress areas exceeding design specifications.

[0189] Furthermore, to facilitate engineering applications, the generated geometric shapes and parametric descriptions need to be standardized. The geometric shapes must be unified to the coordinate system of the power facility; for example, coordinate transformations should be performed with the starting point as the origin to ensure that the generated curves are consistent with the spatial location of the actual facility. The parametric descriptions need to have their unit systems and output formats adjusted according to power engineering design specifications; for example, length should be expressed in meters (m) and tension in Newtons (N). This standardization process ensures that the output results can be seamlessly integrated into existing design and maintenance workflows.

[0190] Finally, depending on the actual needs, the generated geometry and parametric description can be stored or transmitted to relevant systems. For example, the output can be recorded as an electronic document and linked to point cloud data or power facility design files; or it can be transmitted to engineering design software or remote maintenance systems via data interfaces for direct use by other processes.

[0191] The above steps generate clear and accurate catenary geometry and parametric descriptions, providing strong support for the design or maintenance of target power facilities and ensuring the efficiency and reliability of the fitting results in practical applications.

[0192] A second embodiment of this application provides an electronic device, the electronic device comprising:

[0193] processor;

[0194] The memory is used to store a program, which, when read and executed by the processor, performs the method for generating a fitted catenary from point cloud data provided in the first embodiment of this application.

[0195] The fourth embodiment of this application provides a computer-readable storage medium storing a computer program thereon. When the program is executed by a processor, it performs the method for generating a fitted catenary from point cloud data provided in the first embodiment of this application.

[0196] Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of this application. Therefore, the scope of protection of this application should be determined by the scope defined in the claims of this application.

Claims

1. A method for generating a fitted catenary from point cloud data, characterized in that, include: Point cloud data used to describe the target power facility is collected through sensing devices; The collected point cloud data is preprocessed to extract key point data related to the catenary; wherein, the preprocessing includes denoising, segmentation and coordinate transformation; Based on the preprocessed key point data, a catenary mathematical model is established, which includes parameters such as gravity, tension, and catenary length. The parameters of the catenary mathematical model are solved using an optimization algorithm to minimize the deviation between the model and the key point data. Based on the fitting calculation results, the geometry and parametric description of the catenary are generated for the design or maintenance of the target power facility; The step of establishing a catenary mathematical model based on preprocessed key point data includes: Geometric and physical property analysis is performed on the preprocessed and extracted catenary key point data, including the horizontal distribution of key points, vertical height variation and distance characteristics between key points, to obtain the initial conditions and constraint parameters for catenary modeling; Based on the basic physical properties of the catenary, a parametric mathematical model of the catenary is constructed, taking the positions of the starting point, ending point and key points in the path of the catenary as the basis. The model includes the gravity factor, tension factor and length of the catenary as parameter inputs. Based on the distribution characteristics of key points, the initial parameter values ​​of the catenary mathematical model are estimated using statistical and analytical methods, including the coordinates of the start and end points, the position of the lowest point of the catenary, and the initial values ​​of the tension and curvature of the model, so as to provide initial input for subsequent fitting calculations. Physical constraints are embedded in the catenary mathematical model, including the tension balance relationship of the catenary, the ratio of gravity to tension, and the dependence of the catenary length on the distance between key points, to ensure that the mathematical model conforms to the actual physical characteristics of power facilities. Based on the initially constructed catenary mathematical model, a framework for model optimization is defined, including parameter optimization objectives, error evaluation criteria, and optimization iteration process, laying the model foundation for fitting calculations.

2. The method for generating a fitted catenary from point cloud data according to claim 1, characterized in that, The point cloud data collected through sensing devices to describe the target power facilities includes: Based on the location and type of the target power facility, determine the spatial range in which point cloud data needs to be collected. The range includes the starting point, ending point and path area of ​​the catenary. At the same time, consider the impact of the surrounding environment on data collection. The surrounding environment includes the presence of obstacles or interference. Based on the scope of the target area and the specific characteristics of the power facilities, select sensing equipment, including lidar, 3D scanner or other high-precision measuring equipment, and set the operating parameters of the equipment, including scanning angle, resolution, sampling frequency and measurement distance. The sensing device is placed at multiple viewpoints in the target area and scanned sequentially to collect point cloud data of the target power facilities, ensuring that the details of the key parts of the catenary and its connection points are fully recorded, while avoiding the occurrence of data blind spots.

3. The method for generating a fitted catenary from point cloud data according to claim 1, characterized in that, The preprocessing of the collected point cloud data to extract key point data related to the catenary includes: The collected point cloud data is preliminarily processed to remove discrete noise points caused by sensor errors or environmental interference, and spatial density filtering is used to smooth the point cloud data, retaining high-quality point data related to the target power facilities. Based on the geometric shape and spatial location of the target power facility, a segmentation algorithm based on region growth or boundary features is used to separate the catenary-related region in the point cloud data from the background data, while excluding equipment or environmental information unrelated to the catenary. Within the region of interest, a set of candidate points that may belong to the catenary is identified by curvature analysis, point density distribution, and vertical height variation characteristics. Point data that do not conform to the geometric characteristics of the catenary are then eliminated based on the continuity and connectivity of the candidate points. Extract key points of the catenary from the candidate point set. Key points include the starting point, ending point and extreme points or turning points on the path of the catenary. Determine the specific location of the key points by comprehensively analyzing the spatial distribution and physical characteristics of the points. The extracted catenary key points are subjected to coordinate transformation to be unified into a standardized coordinate system centered on the target power facility, and the spatial position of the key points is normalized.

4. The method for generating a fitted catenary from point cloud data according to claim 1, characterized in that, The step of using optimization algorithms to solve for the parameters of the catenary mathematical model, minimizing the deviation between the model and the key point data, includes: By analyzing the geometric center, distance distribution, and curvature of the key point lines in the point cloud data, the initial values ​​of the catenary model parameters are determined. These initial values ​​include the gravity factor, tension factor, and catenary length, and are used as inputs for optimization iteration. Based on the matching relationship between the catenary physical model and the point cloud data, an error function is constructed. The error function includes the vertical distance error from the key point to the catenary fitting curve and the deviation of the tension and gravity constraints. The tension and gravity constraints are determined by the vertical distribution trend of the key points in the point cloud. Based on the matching degree between the distribution density of key points in the point cloud and the catenary morphology, dynamic weights are adaptively assigned to each error term in the error function to enhance the fitting accuracy in low-density key point regions, while ensuring that physical constraints play a dominant role in the optimization process. During the optimization process, the parameter values ​​are updated by gradually and slightly perturbing the current parameter combination and combining the feedback of the error function. The perturbation range is adaptively shrunk based on the local characteristics of the key point data, thereby gradually approaching the global optimal solution. Simultaneously, multiple sets of initial parameters are used to perform optimization calculations in parallel, and the fitting results of different paths are compared and interacted with each other. The path result with the smallest error is used to guide the parameter combination of other paths to avoid getting trapped in local optima. When the fitting results of all paths meet the convergence condition of the error function, and the error of the fitting model in the key point region is lower than the preset threshold, the final catenary model parameters and geometric shape are output.

5. The method for generating a fitted catenary from point cloud data according to claim 4, characterized in that, The initial values ​​of the catenary model parameters are determined by analyzing the geometric center, distance distribution, and curvature of the lines connecting key points in the point cloud data, including: Get the Height values ​​of key points in a point cloud ; The initial value of the gravity factor for the catenary mathematical model is determined according to the following formula (1). : ； in, The average height of all key points in the point cloud; The number of key points in the point cloud; For the first The weights of each keypoint in the point cloud in the geometric center distribution are calculated according to the following formula (2): ； in, Indicates the first Euclidean distance from each key point to the geometric center; To prevent small positive numbers from being divided by zero; The initial value of the tension factor in the catenary mathematical model is determined using the following formula (2). : ； in, for The number of segments in the line connecting key points indicates the total number of line segments between key points in the point cloud; For line segments The local curvature value is calculated using the three-point fitted circle method; For line segments Length; The initial value of the catenary length is determined using the following formula (3). : ； in, Indicates the first The coordinates of key points in the point cloud on the horizontal plane; Indicates the first The coordinates of key points in the point cloud on the horizontal plane; This represents the number of key points in the point cloud.

6. The method for generating a fitted catenary from point cloud data according to claim 4, characterized in that, The error function is constructed based on the matching relationship between the catenary physical model and the point cloud data, including: Construct the error function according to the following formula (4): ； in, The total error function value is used to measure the overall deviation between the catenary fitting curve and the key points and physical constraints of the point cloud; For the first The horizontal coordinates of the nth keypoint in the point cloud represent the... The horizontal position of the key points; For the first The vertical coordinates of the nth point cloud keypoints represent the... The vertical position of the key points; is the curve function of the mathematical model of the catenary, representing the geometric shape of the fitted catenary; Indicates the connection between the catenary and the key point. The horizontal coordinates of the points where the vertical projections intersect; and These are the first and second derivatives of the catenary function; For the first The tension values ​​on each catenary segment are obtained based on mechanical calculations using the catenary model. For the first The gravity distribution values ​​on each catenary segment are calculated based on the vertical distribution trend of key points in the point cloud. The number of segments for the catenary; For the first The key point and the first Vertical height difference between key points; For the first The key point and the first The difference in horizontal distance between key points; This indicates the catenary fitted curve at key points. and The angle of inclination of the tangents between them; The number of key points; , and This is the weighting factor.

7. The method for generating a fitted catenary from point cloud data according to claim 6, characterized in that, The method of adaptively assigning dynamic weights to each error term in the error function based on the matching degree between the distribution density of key points in the point cloud and the catenary morphology includes: Calculate the weighting factor according to the following formula (5). : ； in, Key points of point cloud Local density; The average density of all key points; The number of key points in the point cloud; As a weighting factor; For the first The deviation value of the matching degree between the key points of the point cloud and the fitted curve is obtained by calculating the geometric and physical constraints of the fitted curve on the key points. Calculate the weighting factor according to the following formula (5). : ； in, For the first The physical constraint strength of each key point in the point cloud is calculated by the catenary mechanics formula, specifically the ratio of tension to gravity. The number of key points in the point cloud; For the first The vertical distribution trend weights of the key points in the point cloud are calculated according to the following formula (7): ； in, Indicates the first The height of key points in the point cloud; It is the average height of all key points in the point cloud; Indicates the height of all point cloud keypoints and The maximum value among the absolute values ​​of the differences; Calculate the weighting factor according to the following formula (8). : ； in, This represents the number of key points in the point cloud.

8. The method for generating a fitted catenary from point cloud data according to claim 4, characterized in that, During the optimization process, the parameter values ​​are updated by gradually and slightly perturbing the current parameter combination, combined with feedback from the error function, including: Based on the current catenary model parameters, including gravity factor, tension factor and catenary length, a set of initial small perturbation values ​​are generated. The amplitude of each perturbation value is controlled by a preset perturbation range. The perturbation range is dynamically adjusted according to the distribution density of key points in the point cloud. A larger perturbation range is set for low-density areas to enhance the model's adaptability. The generated perturbation values ​​are applied one by one to the current parameter combination to form multiple new parameter combinations. Each parameter combination adds or subtracts a perturbation value of a specific magnitude based on the current parameters. At the same time, the error function value corresponding to each parameter combination is recorded to measure its fitting effect. Based on the feedback results of the error function, the fitting effects of different perturbation parameter combinations are compared, and higher weights are assigned to parameter combinations with smaller errors. The basic parameter combination for the next round of optimization is determined by calculating the weighted average value, thereby gradually approaching the global optimum.

9. The method for generating a fitted catenary from point cloud data according to claim 4, characterized in that, The process involves simultaneously performing optimization calculations using multiple sets of initial parameters in parallel, comparing and interacting with the fitting results of different paths, and using the path result with the smallest error to guide the parameter combinations of other paths to avoid getting trapped in local optima. This includes: Based on the geometric distribution of key points in the point cloud and the physical characteristics of the catenary model, multiple sets of initial parameter combinations are randomly generated. These parameter combinations include gravity factor, tension factor, and catenary length. Each initial parameter combination is assigned an independent optimization path, and optimization calculations are performed separately. Each path independently runs the error function calculation and parameter update process. After each round of optimization iteration, the current error value and parameter combination of all paths are collected, the error results between paths are compared, the path with the smallest error value is selected as the reference path, and the optimization result of the path is marked as the current best fit result. Based on the fitting results of the reference path, the parameter combinations of other paths are adjusted in a guiding manner, including narrowing the range of parameter perturbation, increasing the weight of the key fitting region, or modifying the optimization direction, so as to guide other paths to approach the global optimum while maintaining the diversity between paths to avoid premature convergence.

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