A power transmission line laser point cloud segmentation method based on model matching

Abstract

The present application relates to a kind of power transmission line laser point cloud segmentation method based on model matching, the method includes improved RANSAC power transmission line model reconstruction and model constrained power transmission line laser point cloud segmentation.The method of the present application can automatically identify noise point in the point cloud segmentation process, with good precision, while still having good universality under complex background environment such as point cloud noise, data missing.

Description

Technical Field

[0001] This invention belongs to the technical field of power transmission line segmentation methods, and in particular relates to a laser point cloud segmentation method for power transmission lines based on model matching. Background Technology

[0002] High-voltage and ultra-high-voltage transmission lines, as carriers of long-distance power transmission, are a key focus of power grid operation, maintenance, and management. Traditional ground inspections mainly rely on manual observation along the lines, which is inefficient, labor-intensive, and suffers from "blind spots" inaccessible to personnel. In recent years, with the rapid development of UAV platforms and lidar sensors, onboard / unmanned lidar systems have seen rapid advancements. These systems can acquire high-precision, high-density three-dimensional spatial geographic information data—laser point clouds—of transmission lines with only a single flight, requiring fewer ground control points. They offer advantages such as fast scanning speed and high automation, overcoming the limitations of traditional manual ground measurements and spaceborne optical sensors, which are restricted by geographical conditions and have low data resolution. This has become a hot topic in research on the informatization of transmission lines and the intelligent application of power grid inspection technology. Currently, laser point cloud transmission line inspection mainly includes four parts: acquisition of laser point cloud data of transmission lines, extraction of transmission lines from point cloud data, modeling of transmission lines from point cloud data, simulation of transmission line operating conditions from point cloud data, and health status inspection / monitoring. Among them, extraction of transmission lines from point cloud data is the foundation of laser point cloud transmission line inspection, and its results directly affect the accuracy of subsequent transmission line model reconstruction and the reliability of status inspection / monitoring.

[0003] A single-span, single-line transmission line is the smallest unit for the reconstruction and analysis of transmission line models. The transmission lines extracted from the original point cloud data also include the phenomenon of multiple transmission lines coexisting. Transmission line point cloud segmentation is to divide the transmission line point cloud extracted from the original transmission line point cloud data into several independent subsets, each of which contains complete single-line transmission line points.

[0004] Common point cloud segmentation methods for power transmission lines can be summarized into two categories: indirect segmentation based on two-dimensional space and direct segmentation based on three-dimensional point clouds. The former utilizes the linear distribution characteristics of power transmission lines to transform the three-dimensional point cloud into an image in a horizontal plane or a vertical plane perpendicular to the cross-section. By establishing a mapping relationship between two-dimensional space and point cloud space, it indirectly achieves three-dimensional point cloud segmentation based on line detection or projection point clustering in two-dimensional digital images. It features simple operation and high segmentation efficiency, with typical examples including the Hough transform method and feature space clustering method. The latter utilizes the spatial distribution characteristics of closely connected single power transmission lines and separate different power transmission lines. It directly achieves three-dimensional point cloud segmentation based on the connectivity of power transmission lines in the point cloud space, offering the advantage of high point cloud segmentation accuracy. Typical examples include three-dimensional point cloud density clustering method and connectivity analysis method.

[0005] Literature review found that existing laser point cloud segmentation methods for transmission lines have good segmentation results in relatively ideal environments such as complete point cloud data and low noise. However, there is a lack of research on background environments that are more common in power grid engineering applications, such as severe point cloud loss and a large number of noise points. The main technical difficulties are: (1) Point cloud loss disrupts the spatial continuity of transmission lines. Under normal conditions, laser point clouds are uniformly distributed along the surface of transmission lines. When there are missing segments in the point cloud, the spatial continuity of transmission lines is disrupted, causing abnormal feature calculations based on the two-dimensional indirect segmentation method. At the same time, the direct segmentation method based on the connectivity of three-dimensional point clouds fails; (2) Point cloud noise changes the spatial distribution rules of transmission lines. Noise points have greater dispersion and are extremely irregular in shape. These points are close to the transmission line points, changing the normal extension direction of the connectivity of the transmission line point cloud. This leads to incorrect results in the direct segmentation method based on three-dimensional point clouds. In addition, due to the presence of noise points, the linear feature representation ability of transmission lines in the point cloud space is weakened, causing the straight line detection algorithm to fail to obtain ideal results in the segmentation of transmission line point clouds; (3) Split conductors have a small spatial scale and complex structure. To suppress corona discharge and reduce line reactance, high-voltage and ultra-high-voltage transmission lines typically employ a split conductor installation method. Unlike conventional non-split conductors, split conductors are "constrained" into bundles at certain intervals along the line by polygonal spacers. In the point cloud space, the individual conductors are relatively close to each other. At the same time, the spacers and other non-transmission line points alter the spatial independence characteristics of the conductors, making it more difficult to identify and segment the point cloud of a single transmission line.

[0006] Existing laser point cloud segmentation methods for power transmission lines have shortcomings such as poor noise resistance and low universality. Furthermore, the segmentation process treats the split conductors as a whole, ignoring the differences in the spatial morphology of individual power transmission lines, which reduces the accuracy of laser point cloud power transmission line model reconstruction. Summary of the Invention

[0007] The present invention aims to address the aforementioned problems and deficiencies by providing a method for segmenting laser point clouds over power transmission lines based on model matching.

[0008] The present invention is implemented using the following technical solution.

[0009] A method for segmenting laser point clouds over power transmission lines based on model matching is characterized by comprising improved RANSAC power transmission line model reconstruction and model-constrained segmentation of laser point clouds over power transmission lines.

[0010] The improved RANSAC transmission line model reconstruction of this invention is as follows: the three-dimensional parabolic equation of the transmission line is decomposed into a straight-parabolic equation, as shown in formula (1), where... For linear model parameters, For parabolic model parameters, The x-coordinate of the laser point cloud projected onto the vertical plane;

[0011] (1)

[0012] The linear model parameters are solved using the least squares method and the random consistency sampling algorithm.

[0013] The least squares method described in this invention includes:

[0014] (1) Improve the selection principles and number of initial sample points;

[0015] Along the horizontal direction of the transmission line, the laser point cloud is divided into K' segments. From each segment, one sample point is randomly selected to combine with K' initial seed points as the sample dataset for solving the initial model parameters. K' is greater than the minimum sample point for solving the model parameters and less than the maximum sample dataset N.

[0016] (2) Solve for the initial model parameters using the least squares method;

[0017] The least squares method is introduced to solve the overall model parameters for K' sample datasets.

[0018] The improved RANSAC transmission line model of this invention includes the following steps:

[0019] Step 1: Calculate the number of iterations according to formula (2) ,in This represents the proportion of transmission line points, i.e., the probability of an interior point. This represents the confidence probability (typically ranging from 0.95 to 0.99). Indicates the number of random sampling points:

[0020] (2)

[0021] Step 2: Divide the laser point cloud into K' segments along the span and randomly select laser points from each segment to form K' sample datasets. Use the least squares method to solve the linear and parabolic model parameter solutions in formula (1) to reconstruct the initial model of the spatial parabola.

[0022] Step 3: Use the initial model to test the overall point cloud dataset, calculate and count the number of valid points of the model. If the number of valid points is the largest, then mark the current model as the optimal model.

[0023] Step 4: If the number of valid points of the current optimal model is greater than the set threshold and the algorithm converges early or the number of iterations is greater than the set number, then the iteration stops; otherwise, repeat Step 2 to Step 3.

[0024] Step 5: Output the optimal model parameters and the best model. The algorithm execution ends.

[0025] In this invention, K' represents the initial number of sample points selected, with a value ranging from 30 to 45.

[0026] The model-constrained transmission line laser point cloud segmentation described in this invention specifically includes:

[0027] Laser point cloud of single-span power transmission line

[0028] ,

[0029] Set parameters K', d, j = 0.

[0030] Improved RANSAC transmission line model reconstruction;

[0031] Extraction and labeling of single transmission line points

[0032] ,

[0033] Search for the point cloud to be segmented

[0034] ,

[0035] Determine if N is large enough. If yes, return to the improved RANSAC transmission line model reconstruction step; otherwise, mark it as a noise point.

[0036] ,

[0037] Segmentation results ,Finish.

[0038] The beneficial effects of this invention are as follows: laser point cloud segmentation of transmission lines is an important aspect of single-span, single-line transmission line extraction. Starting from laser point cloud data of a single-span transmission line, this invention uses the linear-parabolic equation as the theoretical model for single-line transmission line reconstruction, and proposes a model-constrained transmission line point cloud segmentation method based on the basic idea of ​​identifying and segmenting each transmission line. The main contributions of this invention include two aspects:

[0039] (1) Improved the reconstruction of the transmission line model of random consistency sampling laser point cloud. By improving the initial seed point selection principle and the number of seed points K' in the global scope, and introducing the least squares method for initial model reconstruction, the accuracy of identifying and reconstructing the model from laser point cloud data has been improved.

[0040] (2) A model-constrained transmission line point cloud segmentation method is proposed. Using an improved random consistency sampling laser point cloud transmission line model as a constraint, a single transmission line point set is identified by setting a distance threshold. The basic idea of ​​identifying each transmission line sequentially is adopted to achieve transmission line laser point cloud segmentation, overcoming the dependence of local feature-based transmission line point cloud segmentation methods on data integrity and point cloud continuity. Experimental results show that, compared with existing K'-means clustering and density clustering laser point cloud segmentation methods, the method of this invention can automatically identify noise points during point cloud segmentation, has better accuracy, and still has good universality in complex background environments such as point cloud noise and missing data.

[0041] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0042] Figure 1 Reconstruction results of laser point cloud model of single-span power transmission line; (a) reconstruction of the original RANSAC model, (b) reconstruction of the improved RANSAC model;

[0043] Figure 2 Flowchart of laser point cloud transmission line segmentation technology;

[0044] Figure 3 Experimental point cloud data of laser transmission line; (a) point cloud of experimental data 1, (b) point cloud of experimental data 2;

[0045] Figure 4 Experimental data segmentation results of different methods: (a) K' mean clustering, (b) density clustering, (c) the method of this invention;

[0046] Figure 5 Experimental data segmentation results of different methods: (a) K' mean clustering, (b) density clustering, (c) the method of this invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0048] Therefore, the following detailed description of embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0049] 1. Improved RANSAC transmission line model reconstruction

[0050] Generally, the main factors affecting the accuracy of 3D model reconstruction of power transmission lines based on discrete 3D laser point cloud data are the quality of the laser point cloud data, model selection, and the method for solving model parameters.

[0051] Depending on the load distribution, the spatial morphology of transmission lines can be described by the catenary equation and the parabolic equation. The catenary equation is the theoretical model of the transmission line, while the parabolic equation is an approximate expression of the points in the catenary equation. However, based on the reconstruction of the transmission line model using laser point clouds, the parabolic equation has higher model reconstruction accuracy and efficiency, and is universally applicable in power grid engineering applications. Since the length of the transmission line's suspension curve is much greater than its cross-sectional diameter, under natural conditions, the transmission line only bears vertical loads and is suspended between two towers in a static equilibrium state. At this time, the suspension curve of the transmission line is distributed in a vertical plane that passes through the line connecting the suspension points and is perpendicular to the horizontal plane. Therefore, the three-dimensional spatial parabolic equation of the transmission line can be decomposed into a straight-parabolic equation, as shown in formula (1), where For linear model parameters, For parabolic model parameters, The x-coordinate is the projection of the laser point cloud onto the vertical plane.

[0052] (1)

[0053] Most methods for solving linear model parameters draw on numerical analysis theories and methods, with the least squares method and the random consistency sampling algorithm being common. The difference between the two lies in the selection scheme of the initial sample points. The former uses all sample points as the initial sample dataset for solving the model parameters, which has the advantages of strong stability and fast convergence speed. However, its sample point selection principle makes the accuracy of model parameter solution limited by the interference of noise points. The latter, on the other hand, randomly selects the smallest sample point as the initial sample dataset for solving the model parameters. The iterative calculation process of this algorithm can make good use of the former's lack of noise factors. However, its random sample selection principle will lead to a decrease in the stability and efficiency of model parameter solution. In short, neither method can simultaneously achieve stability and noise resistance, which is not conducive to the rapid and accurate identification of a single transmission line from point cloud data.

[0054] Based on this, the basic principle of least squares is introduced to improve the original random sampling consensus algorithm. The main improvements include the following two points:

[0055] (1) Improve the selection principles and number of initial sample points.

[0056] Along the horizontal direction of the transmission line, the laser point cloud is divided into K' segments. One sample point is randomly selected from each segment to form K' initial seed points as the sample dataset for solving the initial model parameters. K' is greater than the minimum sample point for solving the model parameters and less than the maximum sample dataset N. Taking the parabola equation model parameter solution as an example, 3 < K' < N.

[0057] (2) Introduce the least squares method to solve the initial model parameters.

[0058] The least squares method, which has fast convergence speed and high stability, is introduced to solve the overall model parameters of the K' sample datasets, so as to improve the convergence speed of the random consistency sampling algorithm.

[0059] By randomly selecting initial sample points from the global scope, the model parameters are prevented from getting stuck in local optima by the original random sampling principle; by selecting more sample data, the randomness of the initial sample point selection is weakened; by introducing the least squares model parameter solution and the original random consistency algorithm iterative optimization process, the improved random consistency model parameter solution results can simultaneously take into account stability and noise resistance.

[0060] The improved process for solving transmission line model parameters and reconstructing the model mainly includes five steps.

[0061] Step 1: Calculate the number of iterations according to formula (2) ,in This represents the proportion of transmission line points, i.e., the probability of an interior point. K represents the confidence probability (typically ranging from 0.95 to 0.99), and K' represents the number of random sampling points.

[0062] (2)

[0063] Step 2: Divide the laser point cloud into K' segments along the span and randomly select laser points from each segment to form K' sample datasets. Use the least squares method to solve the linear and parabolic model parameter solutions in formula (1) to reconstruct the initial model of the spatial parabola.

[0064] Step 3: Use the initial model to test the overall point cloud dataset, calculate and count the number of valid points of the model. If the number of valid points is the largest, then mark the current model as the optimal model.

[0065] Step 4: If the number of valid points of the current optimal model is greater than the set threshold and the algorithm converges early or the number of iterations is greater than the set number of iterations, then the iteration stops; otherwise, repeat Step 2 to Step 3.

[0066] Step 5: Output the optimal model parameters and the best model. The algorithm execution ends.

[0067] Figure 1 The model reconstruction results of the original random sampling consensus algorithm and the improved random sampling consensus algorithm are shown. The blue dots represent the laser point cloud of a single transmission line, and the red curve represents the model reconstruction result.

[0068] The original random consensus sampling algorithm's single-span transmission line model curves crisscross among the laser point clouds and are relatively close to a small number of point clouds. The improved random consensus model curves uniformly pass through the middle of a single laser point cloud and fit well with the discrete single transmission line laser point cloud, indicating that the improved random consensus algorithm has higher accuracy in representing the morphology of a single transmission line and in model reconstruction.

[0069] It should be noted that the original random consensus algorithm has poor stability. Figure 1 (a) The curve shown is the result of random selection in the experiment. In addition, the improved random consistency sampling algorithm has the best effect when the number of initial sample points K' is 30~45. The specific value depends on the density of the point cloud. The higher the density of the point cloud, the larger the value, and vice versa.

[0070] 2. Model-constrained laser point cloud segmentation of transmission lines

[0071] The power grid ledger data of the power transmission line design and management department contains the coordinate data of the power transmission line towers. It can extract the point cloud data of power transmission lines with different directions and elevations in a single file. Therefore, the research object of this invention is the single file of power transmission line point cloud data extracted from the coordinate ledger.

[0072] In the point cloud space, a single transmission line suspended from two fixed towers is approximately parallel to each other and maintains a certain spatial distance from each other. The improved random consistency sampling algorithm can reconstruct the single transmission line model from the single transmission line point cloud data. The laser point cloud of the single transmission line is tightly surrounded by the curve of the three-dimensional spatial model, while the other noise points and transmission line points are isolated from the transmission line model curve.

[0073] Using the improved random consistency sampling algorithm to reconstruct the straight-parabola spatial model of the transmission line as a constraint, the points within a certain range around the model curve are divided into a set of points of a single transmission line. Based on the basic idea of ​​identifying each transmission line one by one, a laser point cloud segmentation method for transmission lines with model constraints is proposed.

[0074] First, set the parameters K' and d, where d represents the distance threshold between the point cloud to be segmented and the model curve. In an ideal environment, the laser point cloud is uniformly distributed on the surface of a single power transmission line in a spatially curved cylindrical shape, and the model curve passes through the center of the circle of the power transmission line cross-section. Considering the discrete rows of the laser point cloud, the distance threshold... The radius of the transmission line cross-section is taken as 3 to 5 times. When the distance between the laser point and the model curve is less than a threshold, the point is marked as a single transmission line identification point cloud dataset under the constraint of the model curve and is marked as a segmented point. Otherwise, it is marked as a point to be segmented. The above operation is repeated until the number of remaining points is small, the point cloud segmentation is completed, and the remaining points are marked as noise points. Finally, the point cloud segmentation of a single transmission line in a single span is tested. The main technical process is as follows: Figure 2 As shown.

[0075] 3. Experiment and Analysis

[0076] Two typical single-span power transmission line laser point clouds were selected as experimental data, such as... Figure 3 As shown. Experimental data 1 is a point cloud of a single-span non-split transmission line acquired by a manned airborne lidar system, containing 5 transmission lines (2 lightning protection wires and 3 non-split conductive wires). This experimental data contains a total of 5932 laser points. The conductive wire point cloud exhibits severe missing data and a small number of noise points, such as... Figure 3 As shown in (a); Experimental data 2 is a four-split conductive line point cloud acquired by an UAV-borne lidar system, consisting of four single conductors with a spatial distance of 0.4m between them. This experimental data contains a total of 7589 laser points. The point cloud data includes non-transmission line points such as spacer points and numerous noise points, as shown in (a). Figure 3 As shown in (b). In summary, the selected experimental data is generally representative of power grid engineering and represents a key technical challenge in airborne laser point cloud segmentation processing for power transmission lines.

[0077] Figure 4 The experiment data of a single-span transmission line using different methods is shown, with color display being randomly selected. Figure 4 (a~c) show the segmentation results of single-span transmission line point clouds using the two-dimensional feature space indirect segmentation method (Reference 23, referred to as K'-means clustering), the three-dimensional point cloud-based direct segmentation method (Reference 25, referred to as density clustering), and the method of this invention, respectively. When there are missing data in the transmission line point cloud, the K'-means clustering method sets the number of segments equal to the number of transmission lines through prior knowledge, ensuring the correct number of segmentation target categories. However, the K'-means clustering method treats missing data segments and non-missing segments as equivalent to K' classification targets, without considering the impact of missing data segments on the reduction of the number of classification object categories. This leads to chaotic labeling of the point cloud segmentation results for missing data segments, resulting in incorrect segmentation results, such as... Figure 3 (a) shows that the same single transmission line contains multiple segmentation categories; when there are missing data in the laser point cloud, the missing segments change the interconnectedness of the transmission lines, causing a single transmission line to be segmented into multiple target categories and the number of segmented targets in the point cloud deviates significantly from the number of transmission lines, resulting in oversegmentation, such as... Figure 3As shown in (b), the method of the present invention overcomes the limitations of K' mean clustering and density clustering on the continuity and integrity of point clouds in the local area by randomly selecting multiple seed points from the global range. It weakens the impact of missing fragments of point cloud data on the segmentation results of power transmission line point clouds. The single power transmission line is marked with the same target category label and the number of segments is consistent with the number of power transmission lines. This indicates that when there are missing laser point clouds, the power transmission line point cloud segmentation results of the method of the present invention are completely correct and have good applicability.

[0078] Figure 5 The experimental data of the split conductor point cloud are shown, with red dots representing noise points identified during the segmentation process and other colored dots representing single transmission line points. All three methods achieve an ideal number of segments. However, density clustering and the method of this invention can identify non-transmission line points such as spacers and noise points interspersed between single conductors during point cloud segmentation. Compared to density clustering, the method of this invention performs better in identifying noise points near transmission lines, indicating that the method of this invention has a strong noise resistance advantage.

[0079] Using the manual segmentation results as a standard reference, the number of noise points identified (M / point), the maximum and minimum accuracy rates were selected as the accuracy evaluation indicators for the laser point cloud segmentation results of transmission lines. Accuracy rate represents the ratio of the segmentation result of a single transmission line to the standard reference. A comparison of the transmission line point cloud segmentation results using the three methods is shown in Table 1. The method of this invention is insensitive to the type of transmission line, exhibiting high segmentation accuracy for both non-split transmission lines and split conductors. When noise and missing data exist in the transmission line point cloud, the point cloud segmentation accuracy of the method of this invention is close to 100%, significantly better than K'-means clustering and density clustering. It should be noted that this accuracy comparison result is a statistical analysis of the accuracy results from multiple repeated experiments, demonstrating that the method of this invention has advantages such as good stability, strong universality, and insensitivity to noise and missing data.

[0080] Table 1. Statistical analysis of point cloud segmentation accuracy in experimental data.

[0081]

[0082] The method of this invention involves the initial seed point selection number K' and the noise identification threshold. Although the paper provides a reference for parameter selection, using these two key parameters as prior knowledge reduces the automation level of the method. Future research will focus on how to improve the adaptability of parameter selection.

[0083] The above descriptions are merely some specific embodiments of the present invention. Commonly known details or common knowledge in the solutions are not described in detail here (including but not limited to abbreviations, acronyms, and units conventionally used in the art). It should be noted that the above embodiments do not limit the present invention in any way. For those skilled in the art, any technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for segmenting laser point clouds over power transmission lines based on model matching, characterized in that, The method includes improved RANSAC transmission line model reconstruction and model-constrained transmission line laser point cloud segmentation; The improved RANSAC transmission line model is reconstructed as follows: the three-dimensional parabolic equation of the transmission line is decomposed into a straight-parabolic equation, as shown in formula (1), where... For linear model parameters, For parabolic model parameters, The x-coordinate of the laser point cloud projected onto the vertical plane; （1） The linear model parameters are solved using the least squares method and the random consistency sampling algorithm. The least squares method includes: (1) Improve the selection principles and number of initial sample points; Along the horizontal direction of the transmission line, the laser point cloud is divided into K' segments. One sample point is randomly selected from each segment to combine with K' initial seed points as initial model parameters to solve the sample dataset. K' is greater than the minimum sample point and less than the maximum sample dataset N. (2) Solve for the initial model parameters using the least squares method; The least squares method is introduced to solve the overall model parameters for K' sample datasets; The model-constrained transmission line laser point cloud segmentation specifically includes... Laser point cloud of single-span power transmission line ， Set parameters K', d, j = 0, where d represents the distance threshold between the point cloud to be segmented and the model curve. Improved RANSAC transmission line model reconstruction; Extraction and labeling of single transmission line points ， Search for the point cloud to be segmented ， Determine if N is large enough. If yes, return to the improved RANSAC transmission line model reconstruction step; otherwise, mark it as a noise point. ， Segmentation results ,Finish.

2. The method according to claim 1, characterized in that, The improved RANSAC transmission line model includes the following steps: Step 1: Calculate the number of iterations according to formula (2) ,in This represents the proportion of transmission line points, i.e., the probability of an interior point. This represents the confidence probability (typically ranging from 0.95 to 0.99). Indicates the number of random sampling points: （2） Step 2: Divide the laser point cloud into K' segments along the span and randomly select laser points from each segment to form K' sample datasets. Use the least squares method to solve the linear and parabolic model parameter solutions in formula (1) to reconstruct the initial model of the spatial parabola. Step 3: Use the initial model to test the overall point cloud dataset, calculate and count the number of valid points of the model. If the number of valid points is the largest, then mark the current model as the optimal model. Step 4: If the number of valid points of the current optimal model is greater than the set threshold and the algorithm converges early or the number of iterations is greater than the set number, then the iteration stops; otherwise, repeat Step 2 to Step 3. Step 5: Output the optimal model parameters and the best model. The algorithm execution ends.

3. The method according to claim 1, characterized in that, K' represents the initial number of sample points selected, with a value ranging from 30 to 45.

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