Method for generating fitting catenary through point cloud data

Abstract

The invention discloses a method for generating a fitting catenary through point cloud data. The method is used for designing or maintaining a target electric power facility. The method comprises the following steps: acquiring point cloud data of a target electric power facility through sensing equipment; preprocessing the collected data, including denoising, segmentation and coordinate transformation, so as 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; solving the parameters of the mathematical model by using an optimization algorithm, and minimizing the deviation between the model and the key point data; and finally, according to a fitting calculation result, generating a geometrical shape and parameterized description of the catenary. According to the method, point cloud data processing and catenary modeling technologies are combined, the catenary characteristics in the electric power facility are efficiently and accurately fitted, and the method is suitable for engineering requirements in catenary form analysis and electric power facility design and maintenance.

Description

Technical Field

[0001] The present invention relates to the technical field of power data processing, and in particular to a method for generating a fitted catenary through point cloud data. Background Art

[0002] In the prior art, the catenary morphology analysis and modeling of power facilities is an important part of power engineering design and maintenance. Traditional methods usually rely on manual measurement or simple geometric models, which have certain 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 used to obtain geometric information of power facilities, and catenary fitting through 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 parameter characteristics of the catenary more scientific.

[0003] However, the existing technology has significant problems in point cloud data processing, key point extraction and catenary fitting. First, the interference of noise and background data leads to inaccurate point cloud preprocessing results; second, the fitting method based on simplified models is difficult to fully reflect the actual physical characteristics of the catenary; third, the limitations of the optimization algorithm easily cause the model to fall into a local optimal solution and the fitting accuracy cannot be guaranteed. The above problems limit the widespread application of point cloud data in catenary fitting, and also affect the efficiency and reliability of power facility design and maintenance to a certain extent.

[0004] In order to solve the above problems, the present invention proposes a new method for generating a fitting catenary through point cloud data. Summary of the invention

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

[0006] The present application provides a method for generating a fitted catenary using point cloud data, comprising:

[0007] Collecting point cloud data for describing target power facilities through sensing equipment;

[0008] Preprocessing the collected point cloud data to extract key point data related to the catenary; wherein the preprocessing includes denoising, segmentation and coordinate conversion;

[0009] Based on the preprocessed key point data, a catenary mathematical model is established, wherein the catenary mathematical model includes parameters of gravity, tension and catenary length;

[0010] The optimization algorithm is used to solve the parameters of the catenary mathematical model to minimize the deviation between the model and the key point data;

[0011] Based on the results of the fitting calculation, the geometric shape and parameterized description of the catenary are generated for the design or maintenance of the target power facility.

[0012] Furthermore, the point cloud data for describing the target power facility collected by the sensor device includes:

[0013] According to the location and type of the target power facility, determine the spatial range of point cloud data to be collected, which includes the starting point, end point and path area of ​​the catenary, and consider the impact of the surrounding environment on data collection, including the presence of obstacles or interferences;

[0014] Select sensing equipment, including lidar, 3D scanner or other high-precision measuring equipment, according to the scope of the target area and the specific characteristics of the power facilities, and set the working parameters of the equipment, including scanning angle, resolution, sampling frequency and measurement distance;

[0015] The sensing equipment is placed at multiple viewing points in the target area and scanned in sequence 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] Perform preliminary processing on the collected point cloud data to remove discrete noise points caused by sensor equipment errors or environmental interference, and use spatial density filtering method to smooth the point cloud data to retain high-quality point data related to the target power facilities;

[0018] According to 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 area related to the catenary from the background data in the point cloud data, while excluding equipment or environmental information that is not related to the catenary;

[0019] In the region of interest, the set of candidate points that may belong to the catenary is identified through curvature analysis, point density distribution, and vertical height change characteristics, and point data that do not conform to the geometric characteristics of the catenary are eliminated based on the continuity and connectivity of the candidate points;

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

[0021] The extracted catenary key points are transformed into coordinates and unified into a standardized coordinate system centered on the target power facility, and the spatial positions of the key points are normalized.

[0022] Furthermore, the catenary mathematical model is established based on the preprocessed key point data, including:

[0023] Analyze the geometric and physical characteristics of the key point data of the catenary extracted by preprocessing, including the horizontal distribution of the key points, the vertical height change and the distance characteristics between the key points, and obtain the initial conditions and constraint parameters for catenary modeling;

[0024] According to the basic physical characteristics of the catenary, a parametric mathematical model of the catenary is constructed based on the positions of the starting point, the end point and the key points in the path of the catenary, wherein the model includes the gravity factor, the tension factor and the length of the catenary as parameter inputs;

[0025] Combined with the distribution characteristics of key points, statistical and analytical methods are used to estimate the initial parameter values ​​of the catenary mathematical model, including the coordinates of the starting and end points, the lowest point position of the catenary, and the initial values ​​of the tension and curvature of the model, providing initial input for subsequent fitting calculations;

[0026] Embed physical constraints in the catenary mathematical model, including the tension balance relationship of the catenary, the proportional relationship between gravity and 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 the power facility;

[0027] Based on the preliminary constructed catenary mathematical model, the framework of 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 method of solving the parameters of the catenary mathematical model by using an optimization algorithm 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 connection line of the point cloud key point data, the initial values ​​of the catenary model parameters are determined, including the gravity factor, the tension factor and the catenary length, and used as the input of the optimization iteration;

[0030] Based on the matching relationship between the catenary physical model and the point cloud data, an error function is constructed, wherein 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, wherein the tension and gravity constraints are determined by the vertical distribution trend of the key points of the point cloud;

[0031] According to the matching degree between the distribution density of key points in the point cloud and the catenary shape, dynamic weights are adaptively assigned to each error term in the error function to enhance the fitting accuracy in low-density key point areas while ensuring that physical constraints dominate the optimization process.

[0032] During the optimization process, the current parameter combination is gradually disturbed in small amplitudes, combined with the feedback of the error function, to update the parameter value, and the disturbance range is adaptively shrunk based on the local characteristics of the key point data, so as to gradually approach the global optimal solution;

[0033] At the same time, 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 results with the smallest error are used to guide the parameter combinations of other paths to avoid falling into local optimal solutions.

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

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

[0036] (1) Through high-precision acquisition and preprocessing of point cloud data, the present application can effectively extract key point data related to the catenary, and solve the catenary mathematical model in combination with the optimization algorithm, significantly reducing the deviation between the model and the point cloud key point data, thereby improving the accuracy and efficiency of catenary fitting. (2) The preprocessing steps of the present application include denoising, segmentation and coordinate transformation, which can effectively filter environmental noise and irrelevant data, and integrate multi-view point cloud data at the same time 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 by the present application not only considers geometric parameters, but also introduces physical parameters such as gravity, tension and catenary length, which can fully 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 the optimization algorithm, the present application comprehensively considers the distribution of point cloud key points and physical constraints in the fitting process, which can effectively avoid the optimization process from falling into the local optimal solution, ensuring that the fitting results are closer to the global optimal solution, thereby improving the reliability and engineering application value of the catenary analysis of power facilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flowchart of a method for generating a fitted catenary using point cloud data provided in the first embodiment of the present application. DETAILED DESCRIPTION

[0038] Many specific details are described in the following description to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar generalizations without violating the connotation of the present application, so the present application is not limited by the specific implementation disclosed below.

[0039] The first embodiment of the present application provides a method for generating a fitting catenary curve through point cloud data. Figure 1 , which is a schematic diagram of the first embodiment of the present application. Figure 1 A method for generating a fitted catenary using point cloud data is described in detail in the first embodiment of the present application.

[0040] Step S101: collecting point cloud data for describing target power facilities through sensing equipment.

[0041] Step S101 is a key step for collecting point cloud data for describing the target power facility through sensor equipment. This step requires reasonable configuration of the sensor equipment and its working parameters in combination with the spatial location, environmental conditions and equipment type of the target power facility to ensure that the collected data meets the accuracy requirements of subsequent processing and fitting.

[0042] First, determine the spatial scope of the target power facility, including the starting and ending points of the catenary and the areas where the catenary path may pass. Through preliminary on-site surveys, clarify the layout of the sensor equipment to avoid dead angles or blind spots in data collection due to occlusion, reflection or complex terrain. If the target facility has the characteristics of a large height or span, multiple sensor devices can be set up in different areas and viewing angles to cover the entire collection range.

[0043] Next, select the appropriate sensing equipment according to the characteristics and accuracy requirements of the target area. For example, you can choose a lidar for high-precision point cloud scanning over a large area, or a 3D scanner for collecting local features of catenary curves with more details. The working parameters of the sensing equipment need to be adjusted according to the environmental conditions, including but not limited to scanning angle, scanning accuracy, sampling frequency, measurement distance, and scanning path. In order to improve the collection efficiency and data accuracy, you can combine the multi-view collection method and use a rotating or mobile device for multi-angle scanning to ensure that the point cloud data within the coverage area is not missed or over-crowded.

[0044] In the actual acquisition process, it is necessary to consider the impact of external factors such as ambient light, weather conditions, and background interference on the performance of the sensor equipment. For example, in strong light or rainy and snowy environments, equipment with ambient light compensation function or adding external light sources can be used to reduce interference. During the acquisition process, the equipment operator needs to calibrate the equipment regularly to eliminate data drift and errors, and adjust the scanning path and acquisition strategy according to the on-site conditions.

[0045] After the acquisition is completed, the point cloud data is stored in the form of a file. The file format can be a common 3D point cloud format (such as .ply, .las, .pcd) for subsequent data processing. To ensure the traceability of the data, it is recommended to record the acquisition time, equipment parameters, and location information of the sensor equipment at the same time, and store them in association with the point cloud data for subsequent analysis.

[0046] Furthermore, the point cloud data for describing the target power facility collected by the sensor device includes:

[0047] According to the location and type of the target power facility, determine the spatial range of point cloud data to be collected, which includes the starting point, end point and path area of ​​the catenary, and consider the impact of the surrounding environment on data collection, including the presence of obstacles or interferences;

[0048] Select sensing equipment, including lidar, 3D scanner or other high-precision measuring equipment, according to the scope of the target area and the specific characteristics of the power facilities, and set the working parameters of the equipment, including scanning angle, resolution, sampling frequency and measurement distance;

[0049] The sensing equipment is placed at multiple viewing points in the target area and scanned in sequence 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, the point cloud data used to describe the target power facility collected by the sensor device is the basis of the entire catenary fitting method. To ensure that the collected data meets the accuracy and applicability of the catenary fitting calculation, it is necessary to systematically plan the collection steps, reasonably configure the equipment and parameters, and fully consider the characteristics of the target power facility and the influence of its surrounding environment.

[0051] First, determine the spatial scope of point cloud data collection based on the location and type of the target power facility. The target facility may be a conductor between high-voltage transmission towers or other similar catenary structures, and its spatial scope is usually composed of the starting point, end point and path area of ​​the catenary. The definition of the path area needs to cover the maximum curvature of the catenary and the possible vibration or deviation range. In addition, surrounding environmental factors such as obstacles (such as trees, buildings) or interference (such as reflective surfaces, weather conditions) may interfere with the collection process. These factors need to be considered when planning the collection scope. For example, for areas that may be obstructed, spare scanning points should be added to reduce blind spots, and for areas with strong reflection interference, the angle or surface filtering settings of the sensing equipment should be adjusted.

[0052] After determining the target area, select appropriate sensing equipment based on the geometric characteristics of the power facility and the collection requirements. LiDAR is a common choice due to its high precision and long-distance measurement capabilities, and is suitable for large-scale catenary collection. For local areas that require high detail resolution, more accurate equipment such as 3D scanners can be selected. The choice of equipment needs to match the characteristics of the facility. For example, for long-distance wires in the sky, LiDAR with tilt scanning function can be preferred to cover a larger area; and for complex node areas (such as the connection points between wires and insulators), handheld 3D scanners can be used to capture more details. The working parameters of the equipment, such as scanning angle, resolution, sampling frequency and measurement distance, need to be optimized according to the site conditions. For example, the resolution can be appropriately reduced to improve efficiency when scanning a large area, while the resolution needs to be increased in the key connection point area to capture more details.

[0053] The acquisition process is completed by placing the sensing device at multiple viewing points in the target area and scanning them in sequence. The selection of viewing points must ensure coverage of the entire catenary path and minimize blind spots. For example, the device can be placed near the starting point and end point of the catenary, and several intermediate points can be selected to be distributed along the path of the catenary to form a multi-point and multi-view scanning layout. When scanning at each viewing point, the stability of the sensing device must be ensured to avoid a decrease in data accuracy due to device shaking. In addition, in order to reduce possible occlusions and data errors in overlapping areas, the scanning angle or device height can be adjusted appropriately. For example, in areas with more occlusions, the pitch angle of the device can be increased; and in scenes with large terrain undulations, the position of the device can be moved to capture more comprehensive data.

[0054] During the data collection process, special attention should be paid to the impact of environmental conditions on data quality. For example, in strong light or rainy and snowy weather, the lidar may be affected by reflection interference or signal attenuation. The collection effect can be optimized by selecting a low-reflection wavelength or adding an auxiliary light source. In addition, for environments with high wind speeds, measures must be taken to stabilize the equipment, such as adding support devices or using anti-vibration bases.

[0055] After the acquisition is completed, the data of each viewpoint is integrated into a complete point cloud data set. During the integration process, coordinate alignment and deduplication processing are required to ensure that there is no deviation or overlap between the data. After integration, the data set can also be checked for quality to confirm whether the details of key areas such as the start, end and connection points of the catenary are fully recorded, and to supplement the collection of missing parts.

[0056] Through the above detailed steps planning and implementation, point cloud data that meets the requirements of catenary fitting can be effectively collected, providing high-quality input data for subsequent fitting calculations. This process covers the planning of the target range, equipment selection and setting, scanning layout, and environmental adaptation to ensure the comprehensiveness, accuracy, and efficiency of the collection results.

[0057] Step S102: pre-processing the collected point cloud data to extract key point data related to the catenary; wherein the pre-processing includes denoising, segmentation and coordinate conversion.

[0058] Step S102 is a key step to pre-process the collected point cloud data to extract the key point data related to the catenary. This step requires data denoising, segmentation and coordinate conversion operations to convert the original point cloud data into a streamlined data set that is convenient for subsequent mathematical modeling and calculation, with a focus on the characteristic points of the catenary.

[0059] First, in the data denoising stage, invalid points and noise points caused by sensor equipment errors, environmental interference or acquisition conditions need to be removed from the point cloud data. Statistical filtering algorithms can be used to detect outliers in the point cloud. This method determines noise points by calculating the distribution characteristics of the neighborhood points around each point. In addition, voxel downsampling technology can be combined to downsample the point cloud to reduce the amount of data while retaining the main geometric features of the target power facility to improve processing efficiency.

[0060] Next, the region of interest is segmented. By analyzing the spatial distribution characteristics of the point cloud data, the part containing the catenary is screened out, and other irrelevant parts such as background objects or non-power facility areas are excluded. A method based on regional growth can be used, starting from the seed point at the starting point or end point of the catenary, and the region is expanded according to the Euclidean distance or height difference between the points, and the data of the catenary area is gradually extracted. At the same time, in order to enhance the segmentation accuracy, the curvature characteristics of the point cloud can also be analyzed to assist in identifying the catenary part, ensuring that the detailed information of the catenary is completely preserved.

[0061] After the segmentation is completed, the coordinate transformation of the segmented point cloud data is performed to unify the point cloud data related to the catenary into a standard coordinate system. For example, the starting point of the catenary can be set as the coordinate origin, and the coordinate translation and rotation operations can be performed on the entire point cloud to ensure that the catenary is located in a unified geometric reference frame. This transformation helps to simplify and optimize the parameters in the subsequent mathematical modeling process and improve the accuracy of fitting and the calculation efficiency.

[0062] Finally, based on the segmented point cloud data, the key point data related to the catenary is extracted. By analyzing the geometric characteristics and spatial distribution of the point cloud in the catenary area, the starting point, end point and other representative key points of the catenary are selected, such as the inflection point with obvious morphological changes or the position with a large arc. The extraction of key points can be combined with density analysis, local extreme point detection and curvature change rate analysis to ensure that the extracted key points can accurately reflect the overall geometric morphology of the catenary.

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

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

[0065] Perform preliminary processing on the collected point cloud data to remove discrete noise points caused by sensor equipment errors or environmental interference, and use spatial density filtering method to smooth the point cloud data to retain high-quality point data related to the target power facilities;

[0066] According to 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 area related to the catenary from the background data in the point cloud data, while excluding equipment or environmental information that is not related to the catenary;

[0067] In the region of interest, the set of candidate points that may belong to the catenary is identified through curvature analysis, point density distribution, and vertical height change characteristics, and point data that do not conform to the geometric characteristics of the catenary are eliminated based on the continuity and connectivity of the candidate points;

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

[0069] The extracted catenary key points are transformed into coordinates and unified into a standardized coordinate system centered on the target power facility, and the spatial positions of the key points are normalized to ensure the uniformity and efficiency of subsequent fitting calculations.

[0070] The preprocessing step of this embodiment is to perform fine processing on the collected point cloud data, extract high-quality key point data related to the catenary from the complex original data, and provide accurate input for the subsequent fitting of the catenary. This step covers multiple links such as denoising, segmentation, candidate point screening and key point extraction, and combines coordinate transformation and normalization processing to ensure the uniformity and availability of data.

[0071] Preprocessing starts with denoising. The collected point cloud data usually contains discrete noise points introduced by equipment errors or environmental interference, and the presence of these points will interfere with subsequent analysis. To this end, a statistical filtering algorithm can be used to remove noise points. The algorithm calculates the local point density distribution around each point, identifies points with abnormal density and removes them. In addition, a spatial density filtering method can be applied to smooth the point cloud data. By adjusting the local density of the point cloud, the noise caused by uneven distribution can be reduced, while retaining the main geometric features of the target power facility. This process ensures the high quality of the point cloud data and reduces the complexity of subsequent processing.

[0072] Next comes the segmentation process. The goal of segmentation is to extract the area related to the catenary from the point cloud data, while removing interference information in the background that is not related to the target. According to the geometric shape and spatial position of the target power facility, a segmentation algorithm based on region growth can be used. Starting from the starting point or end point of the catenary, the area is gradually expanded through the distance and angle relationship of the adjacent points to identify the part where the catenary is located. In addition, the edge characteristics of the point cloud can be used in combination with boundary feature analysis to separate the catenary area from the background data. For example, the boundary of the catenary is usually manifested as a continuous and smooth curve, which is in sharp contrast to the irregular distribution in the background area. Through these methods, the catenary area can be effectively focused, providing an accurate data range for subsequent point screening.

[0073] In the determined area of ​​interest, it is necessary to further screen the candidate point set of the catenary. This step identifies points that may belong to the catenary by analyzing the geometric features of the point cloud data, such as curvature, point density distribution, and vertical height change. For example, the local curvature of the catenary usually presents small and smooth changes, which is different from the irregular change points in other interference areas; in terms of point density distribution, the point distribution of the catenary is usually more uniform; and in terms of vertical height change characteristics, the height of the catenary changes regularly with horizontal distance. Through the comprehensive judgment of these features, the point set that may belong to the catenary can be screened out, and points that do not meet the geometric characteristics of the catenary can be eliminated. This process significantly reduces data redundancy and improves data relevance.

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

[0075] Finally, the extracted key point data is transformed and normalized. The coordinate transformation unifies the position of the key points into the standardized coordinate system of the target power facility. For example, the starting point of the catenary is used as the origin, and a local coordinate system is established along the catenary direction. This transformation can eliminate the coordinate deviation caused by the different original data acquisition angles or equipment positions, and ensure the uniformity of the key point data. In addition, the spatial position of the key points is normalized so that all coordinates are expressed in consistent units and ranges, which helps to improve the efficiency of subsequent fitting calculations and simplify parameter optimization.

[0076] Through the above detailed preprocessing steps, high-quality catenary key point data can be extracted from the original point cloud data, providing accurate input for the mathematical model of fitting the catenary. This process covers comprehensive processing of data denoising, segmentation, candidate point screening, key point extraction, and coordinate standardization to ensure the reliability and applicability of the preprocessing results.

[0077] Step S103: establishing a catenary mathematical model based on the preprocessed key point data, wherein the catenary mathematical model includes parameters of gravity, tension and catenary length.

[0078] Step S103 is the core step of establishing a catenary mathematical model based on the preprocessed key point data. Its goal is to generate a mathematical model suitable for fitting calculation based on the physical properties of the catenary and the geometric distribution of the key points. The implementation of this step needs to comprehensively consider the physical properties, geometric characteristics and parametric expression of the catenary to ensure that the model has 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 positions of the starting point, the end point and other key points on the path. Based on the relative height and horizontal distance of these points, the span range of the catenary and the approximate position of the lowest point are preliminarily determined. These features provide basic data for the definition of model parameters and the setting of constraints.

[0080] Next, the main parameters of the model are determined in combination with the physical properties of the catenary. The catenary is a curve affected by gravity and tension, and its shape is affected by the gravity factor, the tension factor, and the total length of the catenary. Therefore, the model needs to include these three core parameters: the gravity factor is used to describe 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 the geometric characteristic parameter of the curve, which is used to constrain the actual span of the fitted curve. These parameters are associated with key point data through mathematical expressions, so that the model can reflect the geometric and physical characteristics of the catenary.

[0081] In parametric modeling, the shape 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 expresses the relationship between the horizontal position and vertical height of the key points through parameterization, and uses the gravity factor, tension factor and catenary length as input variables of the model. Specifically, the equation needs to be based on the spatial position of the key points, ensure the geometric constraints of the starting point and the end point, and consider the relative distance and height changes between the key points.

[0082] In order to make the model conform to the actual situation of the target power facility, physical constraints need to be introduced. These constraints include the tension balance relationship of the catenary, the proportional relationship between tension and gravity, and the geometric consistency between the catenary length and the key point spacing. The embedding of these conditions not only improves the physical accuracy of the model, but also prevents the model from deviating from the actual catenary characteristics during the fitting process.

[0083] Finally, the construction of the model needs to provide support for subsequent optimization calculations. It is necessary to define the model's error evaluation mechanism to measure the degree of deviation between the fitting curve and the key point data, and provide a clear objective function and calculation framework for the parameter solution of the optimization algorithm. By organically combining geometric and physical properties, a catenary mathematical model with clear physical meaning and high computational efficiency is finally generated.

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

[0085] Furthermore, the catenary mathematical model is established based on the preprocessed key point data, including:

[0086] Analyze the geometric and physical characteristics of the key point data of the catenary extracted by preprocessing, including the horizontal distribution of the key points, the vertical height change and the distance characteristics between the key points, and obtain the initial conditions and constraint parameters for catenary modeling;

[0087] According to the basic physical characteristics of the catenary, a parametric mathematical model of the catenary is constructed based on the positions of the starting point, the end point and the key points in the path of the catenary, wherein the model includes the gravity factor, the tension factor and the length of the catenary as parameter inputs;

[0088] Combined with the distribution characteristics of key points, statistical and analytical methods are used to estimate the initial parameter values ​​of the catenary mathematical model, including the coordinates of the starting and end points, the lowest point position of the catenary, and the initial values ​​of the tension and curvature of the model, providing initial input for subsequent fitting calculations;

[0089] Embed physical constraints in the catenary mathematical model, including the tension balance relationship of the catenary, the proportional relationship between gravity and 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 the power facility;

[0090] Based on the preliminary constructed catenary mathematical model, the framework of 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 for the preprocessed key point data, providing a solid theoretical basis for the subsequent fitting and optimization process. The model combines multiple aspects of geometric and physical property analysis, parametric modeling, initial parameter estimation, physical constraint embedding and optimization framework definition to ensure the accuracy and practical applicability of the model.

[0092] First, the geometric and physical characteristics are analyzed from the key point data extracted by preprocessing. The key point data of the catenary usually includes the starting point, the end point, the lowest point and other important points on the path. Its horizontal distribution, vertical height change and the distance characteristics between key points are the core basis for modeling. By analyzing the horizontal distribution of key points, the span range and morphological trend of the catenary can be preliminarily determined; and the vertical height change of key points provides preliminary information on the curvature characteristics and physical morphology of the catenary. In addition, the distance characteristics between key points reveal the total length and curvature distribution of the catenary. This information together provides the initial conditions and constraint parameters for the construction of the mathematical model of the catenary.

[0093] After completing the characteristic analysis, a parametric mathematical model is constructed based on the basic physical characteristics of the catenary, the starting point, the end point and the location of the key points in the path of the catenary. The catenary is a typical curve under the action of gravity and tension, and its shape is determined by the gravity factor, the tension factor and the total length of the catenary. The parametric expression of the model is established through the geometric relationship between these factors and the key points, so that the curve can be fully described by a limited set of parameters. This parametric modeling method provides a clear mathematical expression for subsequent calculations, and has good scalability and adaptability.

[0094] The construction of the model requires reasonable estimation of the initial parameter values ​​to provide a stable starting point for the subsequent optimization process. Combined with the distribution characteristics of the key points, the coordinates of the starting and ending points, the position of the lowest point of the catenary, and the initial values ​​of the tension and curvature of the model can be preliminarily determined using statistical and analytical methods. Specifically, the coordinates of the starting and ending points can be directly obtained through the endpoints of the horizontal position and height in the key point set; the position of the lowest point can be determined by the minimum height of the key point, and its rationality can be ensured by combining 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 in combination with physical laws to meet the basic physical requirements of the model.

[0095] When constructing the model, it is also necessary to embed necessary physical constraints in the mathematical model. These constraints include the tension balance relationship of the catenary, the proportional relationship between gravity and tension, and the dependency of the total length of the catenary on the distance between key points. The tension balance relationship ensures that the model can correctly reflect the overall equilibrium state of the catenary force; the proportional relationship between gravity and tension, combined with the height and horizontal distribution characteristics of the key points, restricts the model solution to be physically reasonable; the dependency of the total length on the distance between key points constrains the curve shape through geometric consistency, making it consistent with the actual structure of the power facility. 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 practice.

[0096] Finally, based on the preliminary constructed catenary mathematical model, it is necessary to define the framework of model optimization. The optimization framework includes parameter optimization objectives, error evaluation criteria and optimization iteration process, aiming to make the model closer to the actual catenary shape through systematic optimization means. The parameter optimization goal is to minimize the geometric and physical deviations between the model and the key point data by adjusting the model's gravity factor, tension factor and total length parameters. The error evaluation criterion needs to comprehensively consider the vertical distance error from the key point to the model curve and the degree of conformity of the model parameters to the physical constraints. These criteria provide clear evaluation indicators for optimization. The optimization iteration process gradually adjusts the parameters and continuously improves the model based on error feedback, ultimately achieving the global optimal fit.

[0097] Through the above steps, we can accurately establish the mathematical model of the catenary based on the key point data, providing a reliable basis for subsequent fitting and optimization. The geometric and physical characteristics, parametric expression and optimization framework of the model together constitute the complete system of the model, ensuring that it can meet the actual engineering needs and has a wide range of applicability.

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

[0099] Step S104 is a key step to solve the parameters of the catenary mathematical model using an optimization algorithm. Its goal is to adjust the model parameters through the optimization algorithm so that they are highly matched with the preprocessed key point data and minimize the deviation between the model and the key points. This process requires the comprehensive application of the search, evaluation and adjustment mechanisms of the optimization algorithm to ensure that the model accurately reflects the catenary characteristics of the target power facility.

[0100] First, initialize the parameters of the optimization algorithm. According to the catenary mathematical model established in step S103, the initial values ​​of the gravity factor, tension factor and catenary length are preliminarily set. These initial values ​​can be estimated based on the geometric distribution characteristics of the key point data. For example, the initial length is calculated by the horizontal distance between the starting point and the end point of the catenary, the range of the gravity factor is determined by the range of the key point height variation, and the initial value of the tension factor is set by the density of the key point distribution. The rationality of the initial value directly affects the convergence speed of the optimization process and the accuracy of the final result.

[0101] During the optimization process, an error function is constructed to quantify the deviation between the model and the key point data. The design of the error function needs to comprehensively consider the geometric deviation and physical constraints, including the vertical distance deviation from the key point to the fitting curve, and the mechanical balance relationship of the catenary. The error function can effectively measure the advantages and disadvantages of the current parameter combination and provide a clear guide for subsequent adjustments.

[0102] Subsequently, the optimization algorithm is used to iteratively adjust the parameters. The optimization algorithm can adopt a step-by-step 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 falls back to the previous parameter combination. In order to avoid falling into a local optimal solution, a multi-path parallel search mechanism can be introduced, that is, the optimization paths of multiple initial parameter combinations are run simultaneously, and the path with the smallest error is selected as a reference by comparing the results between the paths. At the same time, the results of the optimal path are used to guide the parameter adjustment direction of other paths.

[0103] After each round of iteration, evaluate the convergence of the error function. If the error function value remains stable in multiple consecutive iterations and is lower than the preset convergence threshold, the optimization process is considered complete and the final parameter result is output. If the error function does not meet the convergence conditions, it is necessary to further adjust the perturbation range or optimization direction. For example, when the error value changes slightly, gradually narrow the parameter adjustment range to improve the refinement of the optimization; when the error value changes greatly or fluctuates significantly, the parameter adjustment range can be relaxed to enhance the search capability.

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

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

[0106] Furthermore, the method of solving the parameters of the catenary mathematical model by using an optimization algorithm 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 connection line of the point cloud key point data, the initial values ​​of the catenary model parameters are determined, including the gravity factor, the tension factor and the catenary length, and used as the input of the optimization iteration;

[0108] Based on the matching relationship between the catenary physical model and the point cloud data, an error function is constructed, wherein 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, wherein the tension and gravity constraints are determined by the vertical distribution trend of the key points of the point cloud;

[0109] According to the matching degree between the distribution density of key points in the point cloud and the catenary shape, dynamic weights are adaptively assigned to each error term in the error function to enhance the fitting accuracy in low-density key point areas while ensuring that physical constraints dominate the optimization process.

[0110] During the optimization process, the current parameter combination is gradually disturbed in small amplitudes, combined with the feedback of the error function, to update the parameter value, and the disturbance range is adaptively shrunk based on the local characteristics of the key point data, so as to gradually approach the global optimal solution;

[0111] At the same time, 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 results with the smallest error are used to guide the parameter combinations of other paths to avoid falling into local optimal solutions.

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

[0113] This embodiment solves the parameters of the catenary mathematical model through an optimization algorithm, aiming to minimize the deviation between the model and the key point data of 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 optimal solution through stepwise approximation, and finally outputs accurate catenary model parameters and geometric shapes.

[0114] First, the initial parameter values ​​of the catenary model are determined by analyzing the geometric center, distance distribution, and curvature of the key point connection line of the point cloud key point data. These initial values ​​include the gravity factor, tension factor, and catenary length, which respectively reflect the morphological characteristics of the catenary in the gravity field, the tension distribution it bears, and its physical length. The calculation of the geometric center provides the initial symmetrical position of the catenary in space, the distance distribution reflects the distribution range of the key points on the path, and the curvature analysis assists in determining the initial tension parameters by detecting the bending characteristics of the curve. These analyses ensure that the initial parameters are reasonable and provide 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 fitting accuracy of the model. The error function combines the vertical distance deviation from the key point to the fitting curve and the physical constraint deviation of the catenary. The vertical distance deviation directly reflects the geometric deviation between the model and the key point data, while the physical constraint deviation (such as the balance relationship between tension and gravity) is determined by the vertical distribution trend of the key points of the point cloud to ensure the physical rationality of the model. The error function provides a clear goal and evaluation criteria for the optimization process.

[0116] During the optimization process, dynamic weights are assigned to each error in the error function. The dynamic weights are adaptively adjusted according to the distribution density of the key points of the point cloud and the matching degree of the catenary shape to enhance the fitting accuracy of low-density areas while ensuring that physical constraints dominate the optimization. For example, for areas with sparse distribution of key points, the weight of the vertical distance deviation term is increased to increase the sensitivity of the model to these areas; and for physical constraints, the weight adjustment ensures that the model maintains mechanical balance while satisfying geometric fitting.

[0117] Parameter optimization is achieved through a stepwise 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 key point data. For example, the perturbation range is gradually reduced in areas where the error converges faster to improve the optimization accuracy, while the perturbation range is expanded in areas where the error is larger to enhance the global search capability. This stepwise approximation method can effectively avoid the optimization from falling into the local optimal solution.

[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 mutual guidance is achieved between different paths 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 reference for parameter adjustment of other paths, thereby accelerating the convergence process and improving the stability of the global optimal solution.

[0119] When the fitting results of all paths meet the convergence conditions of the error function and the error of the fitting model in the key point area is lower than the preset threshold, the optimization process ends. Finally, the optimized catenary model parameters and geometric shapes are output. These parameters and shapes can not only accurately describe the actual state of the catenary, but also provide reliable basic data for the design and maintenance of the target power facilities.

[0120] Through the above optimization process, an accurate catenary model can be efficiently constructed from the key point data of the point cloud, and the geometric fitting accuracy of the model can be ensured to be consistent with the physical rationality. The application of this method in the analysis and design of catenary of power facilities has significant accuracy advantages and engineering value.

[0121] Furthermore, the initial values ​​of the catenary model parameters are determined by analyzing the geometric center, distance distribution and curvature of the key point connection line of the point cloud key point data, including:

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

[0123] The initial value of the gravity factor G of the catenary mathematical model is determined according to the following formula (1): 0 :

[0124]

[0125] Among them, z i Represents the height value of the i-th point cloud key point, indicating its position in the vertical direction;

[0126] It is the average height of all key points of the point cloud, which is used to describe the vertical distribution characteristics of the point cloud as a whole;

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

[0128] w iis the weight of the i-th point cloud key point in the geometric center distribution, calculated according to the following formula (2):

[0129]

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

[0131] Through 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] Use the following formula (2) to determine the initial value of the tension factor T of the catenary mathematical model: 0 :

[0133]

[0134] Where m is κ i The number of segments of the key point connection line, indicating the total number of line segments between the key points of the point cloud; κ j is the local curvature value of line segment j, reflecting the curvature of the line segment. The local curvature is calculated by the three-point fitting circle method, which is to select three consecutive points on the line segment, fit a circle, and define the curvature as the inverse of the radius of curvature of the circle. j is the length of line segment j;

[0135] The initial value L of the catenary length is determined by the following formula (3): 0 :

[0136]

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

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

[0139] Furthermore, the error function is constructed based on the matching relationship between the catenary physical model and the point cloud data, including:

[0140] According to the following formula (4), the error function is constructed:

[0141]

[0142] Where E is the total error function value, which is used to measure the overall deviation between the catenary fitting curve and the key points of the point cloud and the physical constraints; x i is the horizontal coordinate of the i-th point cloud key point, indicating the position of the i-th key point in the horizontal direction; z i is the vertical coordinate of the i-th key point of the point cloud, indicating the position of the i-th key point in the vertical direction; f(x) is the curve function of the catenary mathematical model, indicating the geometric shape of the fitted catenary; x c Indicates the catenary line and the key point (x i ,z i ) is the horizontal coordinate of the curve point where the vertical projection intersects; f ′ (x c ) and f″(x c ) are the first and second derivatives of the catenary function;

[0143] T j is the tension value on the jth catenary segment, obtained based on the mechanical calculation of the catenary model; g j is the gravity distribution value on the jth catenary segment, calculated based on the vertical distribution trend of the key points of the point cloud; m is the number of catenary segments;

[0144] Δh i is the vertical height difference between the i-th key point and the i+1-th key point; Δx i is the horizontal distance difference between the i-th key point and the i+1-th key point; θ i represents the tangent inclination angle of the catenary fitting curve between key points i and i+1; p is the number of key points; α i , β and γ are weight factors.

[0145] Weight factor α i , β and γ can be obtained based on experimental data or directly set based on expert knowledge, or can be adjusted dynamically. The dynamic adjustment can be specifically referred to the following instructions.

[0146] Furthermore, according to the matching degree between the distribution density of the key points of the point cloud and the catenary shape, each error term in the error function is adaptively assigned a dynamic weight, including:

[0147] According to the following formula (5), the weight factor α is calculated i :

[0148]

[0149] Among them, di is the local density of the key point i of the point cloud. The local density is calculated by counting the number of points in the neighborhood of the key point to describe the spatial distribution characteristics of the key point.

[0150] d mean is the average density of all key points, which 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 weight factor. The larger the value, the more significant the impact of density change on the weight. It can be obtained based on empirical data or experimental data.

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

[0154] According to the following formula (5), the weight factor β is calculated:

[0155]

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

[0157]

[0158] Among them, z i Indicates the height of the i-th point cloud key point; is the average height of all key points of the point cloud; Indicates the height and The maximum absolute value of the difference;

[0159] According to the following formula (8), the weight factor γ is calculated:

[0160]

[0161] Among them, n is the number of key points in the point cloud.

[0162] Furthermore, in the optimization process, the current parameter combination is gradually and slightly disturbed, combined with the feedback of the error function, to update the parameter value, including:

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

[0164] The generated disturbance values ​​are applied to the current parameter combination one by one to form multiple new parameter combinations. Each parameter combination increases or decreases the disturbance value of a specific amplitude 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] According to the feedback results of the error function, the fitting effects of different disturbance parameter combinations are compared, and higher weights are given to parameter combinations with smaller errors. The basic parameter combination for the next round of optimization is determined by calculating the weighted average, thereby gradually approaching the global optimal solution.

[0166] This embodiment gradually perturbs the parameters of the current catenary model in small increments and combines the feedback results of the error function to continuously optimize the model parameters so that it gradually approaches the global optimal solution. The key to this process is to reasonably set the perturbation value and range, combine the dynamic adjustment mechanism, and use the error function results to guide the selection and update of parameter combinations.

[0167] In the initial stage of optimization, 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 amplitude of each perturbation value is determined by the preset perturbation range, which is dynamically adjusted according to the distribution density of the point cloud key points. Specifically, for areas with low density of point cloud key points, a larger perturbation range is set to enhance the adaptability of the model in sparse data areas; for areas with higher 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, which can not only explore the global parameter space, but also achieve fine optimization in local areas.

[0168] Next, the generated disturbance values ​​are applied to the current parameter combination one by one to form multiple new parameter combinations. Each parameter combination increases or decreases the disturbance value by a certain amplitude on the current basis to form a candidate parameter set with diverse characteristics. Through this operation, the model parameters can be effectively prevented from falling into the local optimal solution, and a wider search space can be provided for the global optimal solution. After each parameter combination is generated, the error function is used to calculate its fitting effect, 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] According to the feedback results of the error function, the fitting effects of different perturbation parameter combinations are compared and analyzed. By comparing the error values, parameter combinations with smaller errors are screened out, and these combinations are given higher weights, and the weight values ​​are inversely proportional to the performance of their error functions. This weighted 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 basic parameter combination for the next round of optimization is generated by calculating the weighted average of all parameter combinations. This weighted average strategy improves the stability of parameter updates while maintaining the model's ability to explore the global optimal solution.

[0170] During the entire optimization process, gradual small perturbations and error feedback are combined to achieve precise control of parameter updates by dynamically adjusting the perturbation range and weight distribution. Finally, when the error function value stabilizes in multiple consecutive 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 can strike a balance between global search and local optimization through gradual perturbation of parameters, error feedback and weight adjustment, ensuring that the fitting results are both highly accurate and reflect the actual physical properties of the catenary.

[0172] Furthermore, the optimization calculation is performed in parallel using multiple sets of initial parameters, and the fitting results of different paths are compared and interacted with each other, and the path result with the smallest error is used to guide the parameter combination of other paths to avoid falling into the local optimal solution, including:

[0173] Based on the geometric distribution of key points of the point cloud and the physical characteristics of the catenary model, a plurality of groups of initial parameter combinations are randomly generated, wherein the parameter combinations include a gravity factor, a tension factor and a catenary length;

[0174] Assign an independent optimization path to each initial parameter combination, perform optimization calculations separately, and run error function calculation and parameter update process independently for each path;

[0175] After each round of optimization iteration, the current error values ​​and parameter combinations of all paths are collected, the error results between the 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, guiding adjustments are made to the parameter combinations of other paths, including shrinking the parameter perturbation range, increasing the weight of the key fitting area, or modifying the optimization direction, so as to guide other paths to move closer to the global optimal solution, while maintaining the diversity between paths to avoid premature convergence.

[0177] When optimizing the parameters of the catenary model, this embodiment uses multiple sets of initial parameters to perform optimization calculations in parallel, so as to make full use of the diversity of different parameter combinations, expand the search space, and improve the probability of finding the global optimal solution. This method is based on the comparison and interaction of results between paths, avoids the optimization process from falling into the local optimum, and ensures the high accuracy and physical rationality of model fitting.

[0178] In the initial stage of the optimization calculation, multiple sets of initial parameter combinations are randomly generated based on the geometric distribution of the key points of the point cloud and the physical characteristics of the catenary model. These parameter combinations include gravity factors, tension factors, and catenary lengths. Each set of parameters is randomly distributed within a reasonable range to cover the possible morphological characteristics of the catenary. The diversity of initial parameters is crucial to the success of the 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 set of initial parameter combinations generated is assigned to an independent optimization path, and each path runs the optimization calculation independently, including error function calculation and parameter update process. In each path, the error function is used to quantify the fitting effect of the current parameter combination, including the geometric error from the key point to the fitting curve and the physical constraint deviation of the catenary model. In each iteration, the optimization algorithm in the path updates the parameters according to the feedback of the error function and gradually improves the fitting results. This parallel computing mechanism can accelerate the optimization process of different parameter combinations without interfering with each other, and provide rich data support for the comparison and interaction between subsequent paths.

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

[0181] Based on the fitting results of the reference path, the parameter combinations of other paths are adjusted in a guided manner. This adjustment method includes multiple levels. The first is to shrink the parameter perturbation range, that is, to reduce the parameter change range in the area where the error value is close to the reference path to enhance the refinement of the optimization; the second is to increase the weight of the key fitting area, especially the area where the key points of the point cloud are sparsely distributed or the curvature changes greatly, and guide the optimization direction by giving these areas a higher error weight; the last is to modify the optimization direction of the path. For example, in the path with a large error value, the parameter trend of the reference path or the area of ​​priority attention is introduced to make other paths gradually approach the global optimal solution.

[0182] In order to avoid premature convergence between paths, it is very important to maintain a certain degree of path diversity during the optimization process. Even under the guidance of the reference path, the parameter updates of other paths must retain a certain degree of randomness and independence to continuously explore possible directions for improvement. This mechanism ensures that paths can learn and improve from each other while maintaining sufficient flexibility in global search.

[0183] Finally, when the error values ​​of multiple paths reach the preset convergence conditions and the differences in the optimization results between the paths are reduced, the optimization process is terminated. 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 method, technicians in this field can efficiently avoid local optimal problems and obtain the best fitting results that meet the characteristics of point cloud data and the physical characteristics of the catenary. This method combines computational efficiency and global search capabilities, and is suitable for catenary model fitting problems under complex point cloud data.

[0184] Step S105: Generate the geometric shape and parameterized description of the catenary according to the result of the fitting calculation, which is used for the design or maintenance of the target power facility.

[0185] Step S105 is to generate the geometric shape and parameterized description of the catenary based on the results of the fitting calculation to meet the key link of the design or maintenance requirements of the target power facility. This step requires converting the optimized catenary mathematical model into a visual and operable form, and outputting relevant data in combination with actual application requirements.

[0186] First, according to the catenary model parameters optimized in step S104, including gravity factor, tension factor and catenary length, the catenary mathematical model is converted into the specific geometric shape of the curve. This process requires the calculation of the point set of the model within the defined range through the catenary parameterized expression, including the horizontal position and vertical height of each point on the curve. The actual coordinates of the starting point and the end point need to be combined during the calculation to ensure that the fitting curve can accurately cover the catenary area of ​​the target power facility.

[0187] The resulting catenary geometry is then visualized and exported in the form of 3D point cloud data. This can be done using 3D modeling tools to connect the catenary's discrete point set 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] While generating the geometry, a parametric description of the catenary is also output. The parametric description includes the catenary's mathematical equation, key point locations, total length, maximum curvature, tension values ​​at the start and end points, etc. These parameters provide a quantitative description of the catenary's physical properties and can be directly used in engineering design or maintenance calculations for power facilities. For example, the total length and maximum curvature of the catenary can be used to assess the strength requirements of the cable material, and the tension value can be used to detect whether there are stress areas that exceed the design specifications.

[0189] In addition, for the convenience of engineering application, the generated geometric shapes and parametric descriptions need to be standardized. The geometric shapes need to be unified into the coordinate system of the power facility. For example, the coordinate transformation is performed with the starting point as the origin to ensure that the generated curve is consistent with the spatial position of the actual facility. The parametric description needs to adjust the unit system and output format according to the power engineering design specifications, such as length in meters (m) and tension in Newtons (N). This standardization process ensures that the output results can be seamlessly integrated into the existing design and maintenance workflow.

[0190] Finally, the generated geometry and parametric description can be stored or transferred to related systems according to actual needs. For example, the output results can be recorded in the form of electronic documents and associated with point cloud data or design files of power facilities; or transmitted to engineering design software or remote maintenance systems through data interfaces for direct call by other links.

[0191] Through the above steps, a clear and accurate catenary geometry and parameterized description can be generated, 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 the present application provides an electronic device, the electronic device comprising:

[0193] processor;

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

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

[0196] Although the present application is disclosed as above in the form of a preferred embodiment, it is not intended to limit the present application. Any technical personnel in this field may make possible changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be based on the scope defined by the claims of the present application.

Claims

1. A method for generating a fitted catenary using point cloud data, characterized in that: include: Collecting point cloud data for describing target power facilities through sensing equipment; Preprocessing the collected point cloud data to extract key point data related to the catenary; wherein the preprocessing includes denoising, segmentation and coordinate conversion; Based on the preprocessed key point data, a catenary mathematical model is established, wherein the catenary mathematical model includes parameters of gravity, tension and catenary length; The optimization algorithm is used to solve the parameters of the catenary mathematical model to minimize the deviation between the model and the key point data; Based on the results of the fitting calculation, the geometric shape and parameterized description of the catenary are generated for the design or maintenance of the target power facility.

2. The method for generating a fitted catenary using point cloud data according to claim 1, characterized in that: The point cloud data used to describe the target power facility is collected by the sensor equipment, including: According to the location and type of the target power facility, determine the spatial range of point cloud data to be collected, which includes the starting point, end point and path area of ​​the catenary, and consider the impact of the surrounding environment on data collection, including the presence of obstacles or interferences; Select sensing equipment, including lidar, 3D scanner or other high-precision measuring equipment, according to the scope of the target area and the specific characteristics of the power facilities, and set the working parameters of the equipment, including scanning angle, resolution, sampling frequency and measurement distance; The sensing equipment is placed at multiple viewing points in the target area and scanned in sequence 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 using 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: Perform preliminary processing on the collected point cloud data to remove discrete noise points caused by sensor equipment errors or environmental interference, and use spatial density filtering method to smooth the point cloud data to retain high-quality point data related to the target power facilities; According to 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 area related to the catenary from the background data in the point cloud data, while excluding equipment or environmental information that is not related to the catenary; In the region of interest, the set of candidate points that may belong to the catenary is identified through curvature analysis, point density distribution, and vertical height change characteristics, and point data that do not conform to the geometric characteristics of the catenary are eliminated based on the continuity and connectivity of the candidate points; Extract the key points of the catenary from the candidate point set. The key points include the starting point, end point, and extreme point or turning point on the path of the catenary. The specific location of the key points is determined by comprehensively analyzing the spatial distribution and physical characteristics of the points. The extracted catenary key points are transformed into coordinates and unified into a standardized coordinate system centered on the target power facility, and the spatial positions of the key points are normalized.

4. The method for generating a fitted catenary using point cloud data according to claim 1, characterized in that: The catenary mathematical model is established based on the pre-processed key point data, including: Analyze the geometric and physical characteristics of the key point data of the catenary extracted by preprocessing, including the horizontal distribution of the key points, the vertical height change and the distance characteristics between the key points, and obtain the initial conditions and constraint parameters for catenary modeling; According to the basic physical characteristics of the catenary, a parametric mathematical model of the catenary is constructed based on the positions of the starting point, the end point and the key points in the path of the catenary, wherein the model includes the gravity factor, the tension factor and the length of the catenary as parameter inputs; Combined with the distribution characteristics of key points, statistical and analytical methods are used to estimate the initial parameter values ​​of the catenary mathematical model, including the coordinates of the starting and end points, the lowest point position of the catenary, and the initial values ​​of the tension and curvature of the model, providing initial input for subsequent fitting calculations; Embed physical constraints in the catenary mathematical model, including the tension balance relationship of the catenary, the proportional relationship between gravity and 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 the power facility; Based on the preliminary constructed catenary mathematical model, the framework of model optimization is defined, including parameter optimization objectives, error evaluation criteria and optimization iteration process, laying the model foundation for fitting calculations.

5. The method for generating a fitted catenary using point cloud data according to claim 1, characterized in that: The method of solving the parameters of the catenary mathematical model by using an optimization algorithm to minimize the deviation between the model and key point data includes: By analyzing the geometric center, distance distribution and curvature of the key point connection line of the point cloud key point data, the initial values ​​of the catenary model parameters are determined, including the gravity factor, the tension factor and the catenary length, and used as the input of the optimization iteration; Based on the matching relationship between the catenary physical model and the point cloud data, an error function is constructed, wherein 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, wherein the tension and gravity constraints are determined by the vertical distribution trend of the key points of the point cloud; According to the matching degree between the distribution density of key points in the point cloud and the catenary shape, dynamic weights are adaptively assigned to each error term in the error function to enhance the fitting accuracy in low-density key point areas while ensuring that physical constraints dominate the optimization process. During the optimization process, the current parameter combination is gradually disturbed in small amplitudes, combined with the feedback of the error function, to update the parameter value, and the disturbance range is adaptively shrunk based on the local characteristics of the key point data, so as to gradually approach the global optimal solution; At the same time, 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 results with the smallest error are used to guide the parameter combinations of other paths to avoid falling into local optimal solutions. When the fitting results of all paths meet the convergence conditions of the error function and the errors of the fitting model in the key point area are lower than the preset threshold, the final catenary model parameters and geometric shape are output.

6. The method for generating a fitted catenary using point cloud data according to claim 5, characterized in that: The initial values ​​of the catenary model parameters are determined by analyzing the geometric center, distance distribution and curvature of the key point connection line of the point cloud key point data, including: The initial value G0 of the gravity factor of the catenary mathematical model is determined according to the following formula (1): Among them, z i Represents the height value of the i-th point cloud key point; is the average height of all point cloud key points; n is the number of point cloud key points; w i is the weight of the i-th point cloud key point in the geometric center distribution, calculated according to the following formula (2): Among them, d i represents the Euclidean distance from the i-th key point to the geometric center; ∈ is a small positive number to prevent division by zero; The initial value T0 of the tension factor of the catenary mathematical model is determined using the following formula (2): Where m is κ i The number of segments of the key point connection line, indicating the total number of line segments between the key points of the point cloud; κ j is the local curvature value of line segment j, calculated by the three-point fitting circle method; l j is the length of line segment j; The initial value L0 of the catenary length is determined by the following formula (3): Among them, (x i ,y i ) represents the coordinates of the i-th point cloud key point on the horizontal plane; (x i+1 ,y i+1 ) represents the coordinates of the i+1th point cloud key point on the horizontal plane; n is the number of point cloud key points.

7. The method for generating a fitted catenary using point cloud data according to claim 5, characterized in that: The error function is constructed based on the matching relationship between the catenary physical model and the point cloud data, including: According to the following formula (4), the error function is constructed: Where E is the total error function value, which is used to measure the overall deviation between the catenary fitting curve and the key points of the point cloud and the physical constraints; x i is the horizontal coordinate of the i-th point cloud key point, indicating the position of the i-th key point in the horizontal direction; z i is the vertical coordinate of the i-th key point of the point cloud, indicating the position of the i-th key point in the vertical direction; f(x) is the curve function of the catenary mathematical model, indicating the geometric shape of the fitted catenary; x c Indicates the catenary line and the key point (x i ,z i ) is the horizontal coordinate of the curve point where the vertical projection intersects; f ′ (x c ) and f″(x c ) are the first and second derivatives of the catenary function; T j is the tension value on the jth catenary segment, obtained based on the mechanical calculation of the catenary model; g j is the gravity distribution value on the jth catenary segment, calculated based on the vertical distribution trend of the key points of the point cloud; m is the number of catenary segments; Δh i is the vertical height difference between the i-th key point and the i+1-th key point; Δx i is the horizontal distance difference between the i-th key point and the i+1-th key point; θ i represents the tangent inclination angle of the catenary fitting curve between key points i and i+1; p is the number of key points; α i , β and γ are weight factors.

8. The method for generating a fitted catenary using point cloud data according to claim 7, characterized in that: According to the matching degree between the distribution density of the key points of the point cloud and the catenary shape, each error term in the error function is adaptively assigned a dynamic weight, including: According to the following formula (5), the weight factor α is calculated i : Among them, d i is the local density of the key point i of the point cloud; d mean is the average density of all key points; n is the number of key points in the point cloud; k is the weight factor; δ i is the deviation value of the matching degree between the i-th point cloud key point and the fitting curve, which is calculated by the geometric and physical constraints of the fitting curve on the key point; According to the following formula (5), the weight factor β is calculated: Among them, f i is the physical constraint strength of the i-th point cloud key point, calculated by the catenary mechanics formula, specifically the ratio of tension to gravity; n is the number of point cloud key points; ω i is the vertical distribution trend weight of the i-th point cloud key point, calculated according to the following formula (7): Among them, z i Indicates the height of the i-th point cloud key point; is the average height of all key points of the point cloud; Indicates the height of all point cloud key points and The maximum absolute value of the difference; According to the following formula (8), the weight factor γ is calculated: Where n is the number of key points in the point cloud.

9. The method for generating a fitted catenary using point cloud data according to claim 5, characterized in that: In the optimization process, the current parameter combination is gradually disturbed in small amplitudes, combined with the feedback of the error function, to update the parameter value, including: Based on the current catenary model parameters, including gravity factor, tension factor and catenary length, a set of initial small disturbance values ​​is generated. The amplitude of each disturbance value is controlled by a preset disturbance range. The disturbance range is dynamically adjusted according to the distribution density of the key points of the point cloud. A larger disturbance range is set in the low-density area to enhance the adaptability of the model. The generated disturbance values ​​are applied to the current parameter combination one by one to form multiple new parameter combinations. Each parameter combination increases or decreases the disturbance value of a specific amplitude 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. According to the feedback results of the error function, the fitting effects of different disturbance parameter combinations are compared, and higher weights are given to parameter combinations with smaller errors. The basic parameter combination for the next round of optimization is determined by calculating the weighted average, thereby gradually approaching the global optimal solution.

10. The method for generating a fitted catenary using point cloud data according to claim 5, characterized in that: The method uses multiple sets of initial parameters to perform optimization calculations in parallel, compares and interacts with each other based on the fitting results of different paths, and uses the path results with the smallest error to guide the parameter combinations of other paths to avoid falling into local optimal solutions, including: Based on the geometric distribution of key points of the point cloud and the physical characteristics of the catenary model, a plurality of groups of initial parameter combinations are randomly generated, wherein the parameter combinations include a gravity factor, a tension factor and a catenary length; Assign an independent optimization path to each initial parameter combination, perform optimization calculations separately, and run error function calculation and parameter update process independently for each path; After each round of optimization iteration, the current error values ​​and parameter combinations of all paths are collected, the error results between the 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, guiding adjustments are made to the parameter combinations of other paths, including shrinking the parameter perturbation range, increasing the weight of the key fitting area, or modifying the optimization direction, so as to guide other paths to move closer to the global optimal solution, while maintaining the diversity between paths to avoid premature convergence.

Images