Method for extracting and analyzing power line crossing information based on point cloud

Abstract

The invention discloses a method for extracting and analyzing power line crossing information based on a point cloud, and the method comprises the following steps: S1, obtaining point cloud data of a power transmission line, carrying out the differential modeling of the shape of the power transmission line, and obtaining a curvilinear equation of the power transmission line; s2, substituting the curvilinear equation of the power transmission lines into the original three-dimensional coordinate system of the laser point cloud, calculating a linear equation of the projection of the power transmission lines on the horizontal plane, and solving the projection position of the crossing point of the two power transmission lines on the horizontal plane; and S3, substituting the projection positions of the intersection points into the curve equation of the power transmission lines to obtain accurate coordinates of the intersection points of the two power transmission lines, and calculating the intersection distance.

Description

Technical Field

[0001] The present invention relates to the field of electric power technology, and in particular to a method for analyzing crossover information of electric power lines based on point cloud extraction. Background Art

[0002] In power engineering surveying, crossing refers to the difference in height from the ground between two or more transmission lines of different directions. It is used to measure whether the space between two sets of crossing lines meets the requirements in power line inspection, and is used to plan a reasonable height for crossing lines in line design. In recent years, the State Grid has actively promoted the three-dimensional digital design of power grid projects and proposed the application of laser point clouds in power projects. Many power companies have made attempts to varying degrees, generally focusing on survey and design and power line inspection. Airborne laser radar measurement technology has been widely used in the survey and design of transmission line projects in mountainous areas, greatly improving the work efficiency of survey and design. However, the information extraction and analysis of crossing lines is mainly based on manual interpretation and recognition.

[0003] The invention patent with the prior art application publication number CN118212469A discloses a method and device, electronic device, and storage medium for post-processing of power line classification based on point cloud. First, the power line point cloud is extracted from the original point cloud data; then the power line point cloud is segmented and clustered to determine the target number of power lines, then the line type is determined according to the target number of lines, and a single power line point cloud is obtained in different ways according to different line types; then the single power line point cloud is fitted according to a parabola, and the fitted point cloud is sampled and filled according to a preset step size to obtain a simulated power line point cloud; finally, a KD tree is used to search for laser points at a preset distance from the simulated power line point cloud, and the searched laser points are used as points corresponding to the root simulated power line point cloud, and the category of the laser points is set to power line. The scheme disclosed in the present invention reduces the workload of manual inspection and correction of power line classification results in the later stage, and improves the accuracy and efficiency of power line point cloud classification. Summary of the invention

[0004] Traditional cross-over measurements generally use industrial surveying methods. Surveyors need to travel back and forth between various lines and key points at the project site, with the help of traditional surveying and mapping equipment such as GPS, rangefinders, etc., and require the cooperation of multiple people to complete the task. This is inefficient and there are also greater safety risks under complex terrain conditions. In addition, the results of the cross-over wire measurement are not intuitive enough.

[0005] In order to solve the above problems, the technical solution provided by the present invention is: a method for analyzing cross-over information of power lines based on point cloud extraction, characterized in that it includes the following steps: S1. Obtain the point cloud data of the transmission line, perform differential modeling on the shape of the transmission line, and obtain the curve equation of the transmission line; S2. Substitute the curve equation of the transmission line into the original three-dimensional coordinate system of the laser point cloud, and calculate the straight line equation of the projection of the transmission line on the horizontal plane, and solve to obtain the projection position of the intersection point of the two transmission lines on the horizontal plane; S3. Substitute the projection position of the intersection point into the curve equation of the transmission line to obtain the precise coordinates of the intersection point where the two transmission lines cross, and calculate the crossing distance.

[0006] Among them, the transmission line is in the shape of a catenary in the vertical plane, and the mathematical expression after differential modeling of the transmission line in S1 is a hyperbolic cosine function.

[0007] In particular, after the hyperbolic cosine function of the transmission line is calculated in S1, the parabolic equation is used to approximate the original hyperbolic cosine function of the transmission line to obtain the parabolic equation of the transmission line.

[0008] In the approximation process, the parabola equation and the hyperbolic cosine function equation of the transmission line both pass through three points, namely the bottom point of the open upward concave arc, and two intersection points that are symmetrical about the z-axis and intersect the x-axis at a distance of r.

[0009] By substituting the bottom point and two intersection points of the concave arc into the unknown parabola equation and the calculated hyperbolic cosine function equation to solve the equations together, we can get a transcendental equation composed of the coefficients of the hyperbolic cosine function equation. The parabola equation of the transmission line can be calculated by solving it using Newton's iteration method.

[0010] Among them, in S2, the parabola equation of the transmission line is substituted into the original three-dimensional coordinate system of the laser point cloud to obtain the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud, and its projection in the horizontal plane is a straight line. In S2, the straight line equations of the two transmission lines projected in the horizontal plane are combined to calculate the intersection of the two transmission line projection lines. The intersection of the two transmission line projection lines is the projection position of the intersection of the two transmission lines on the horizontal plane.

[0011] In S3, the X-axis and Y-axis coordinates of the intersection of the two transmission line projection lines are substituted into the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud to calculate the precise coordinates of the intersection of the two transmission lines. The Z-axis height difference of the precise coordinates of the intersection of the two transmission lines is the crossing distance.

[0012] The beneficial effects of the present invention are as follows: by using the laser point cloud application in the existing three-dimensional digital design of power grid projects to obtain the data model of the transmission line, the cross-span measurement is calculated and realized with higher efficiency, and there is no need for surveyors to travel back and forth between the lines and key points at the project site. With the help of traditional surveying and mapping equipment such as GPS, rangefinders, etc., it is more concise and convenient. At the same time, there are still great safety risks under complex terrain conditions. The present invention avoids the safety risks of outdoor measurement through model calculation, and can intuitively display the measurement results through graphic representation information and software applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The figure is a flow chart of the method of the present invention.

[0014] Figure 2 Graphs showing the shape of the hyperbolic cosine function and the fitted parabola of the transmission line in the embodiment.

[0015] Figure 3 It is a function graph of the difference between the hyperbolic cosine function and the fitted parabola of the transmission line in the embodiment.

[0016] Figure 4 This is the result diagram of the cross-span surveying in Example 1.

[0017] Figure 5 This is the result of the cross-span surveying of Example 2. DETAILED DESCRIPTION

[0018] Embodiment 1: A method for analyzing crossover information of power lines based on point cloud extraction, such as Figure 1 As shown, the following steps are included: S1. Obtain the point cloud data of the transmission line, perform differential modeling on the shape of the transmission line, and obtain the curve equation of the transmission line; S2. Substitute the curve equation of the transmission line into the original three-dimensional coordinate system of the laser point cloud, and calculate the straight line equation of the projection of the transmission line on the horizontal plane, and solve to obtain the projection position of the intersection point of the two transmission lines on the horizontal plane; S3. Substitute the projection position of the intersection point into the curve equation of the transmission line to obtain the precise coordinates of the intersection point where the two transmission lines cross, and calculate the crossing distance.

[0019] Among them, to extract the cross-over line information, we must first determine the shape curve of the crossing wire. Under windless conditions, the transmission line is only affected by the suspension of the power tower and its own gravity. At this time, the transmission line will form a catenary in the vertical plane. The shape of the transmission line is differentially modeled and solved in this plane. It can be seen that its mathematical expression is a hyperbolic cosine function. The mathematical expression of the differential modeling of the transmission line in S1 is a hyperbolic cosine function, and its expression is as follows: A and B are the coefficients of the function. The reason why z and X are different in capital letters is that z here has the same meaning and value as z in the original coordinates P(x,y,z) of the laser point cloud; while X is the new horizontal coordinate of each point after the original coordinates are rotated counterclockwise around the z axis by an angle of θ, that is: Where θ is the angle between the projection (straight line) of the transmission line in the horizontal plane and the positive direction of the original x-axis, which can be obtained by performing Hough transform in the horizontal plane. After the above calculation, the new vertical coordinate of each point on the transmission line will become a constant, that is, Y = C, where C is the distance from the origin of the coordinate to the projection straight line.

[0020] Since the hyperbolic cosine function is an exponential function, it is inconvenient to calculate. Therefore, after the hyperbolic cosine function of the transmission line is calculated in S1, the parabolic equation is used to approximate the original hyperbolic cosine function of the transmission line to obtain the parabolic equation of the transmission line.

[0021] The general formula of the parabola equation is: z = aX 2 +bX+c The parabola equation and the hyperbolic cosine function equation of the transmission line both pass through three points, namely the bottom point of the concave arc that opens upward, and two intersection points that are symmetrical about the z-axis and intersect the x-axis at a distance of r. By substituting the bottom point of the concave arc and the two intersection points into the unknown parabola equation and the calculated hyperbolic cosine function equation for simultaneous equation solving, we can obtain a transcendental equation composed of the coefficients of the hyperbolic cosine function equation.

[0022] Transcendental equation is a concept in mathematics, which refers to an equation of transcendental functions containing unknown variables. Transcendental functions are those functions that do not satisfy any algebraic equation (i.e. polynomial equation), such as exponential functions, logarithmic functions, trigonometric functions (sine, cosine, tangent, etc.) and their inverse functions.

[0023] Solving transcendental equations is often more difficult than solving algebraic equations because they do not usually involve simple solutions to polynomial equations (e.g. factorization, root formulas, etc.). Solutions to transcendental equations may need to be obtained through numerical methods (e.g. iteration, approximation, etc.), or in some special cases through transformations and algebraic techniques.

[0024] This embodiment uses the Newton's iteration method to solve the parabolic equation of the transmission line. Newton's iteration method, also known as the Newton-Raphson method, is a method proposed by Newton in the 17th century to approximately solve equations in the real number domain and the complex number domain. The basic principle of the Newton's iteration method is to make a tangent line at an initial point (x0, f(x0)) and the tangent line intersects with the X-axis to obtain the coordinates of the next iteration point x1, and then make a tangent line at (x1, f(x1)), and so on, until an approximate solution that satisfies the accuracy is obtained.

[0025] Specifically, let r be the root of f(x) = 0, and select x0 as the initial approximation of r. Draw a tangent line L to the curve y = f(x) through the point (x0, f(x0)), and the equation of L is y = f(x0) + f'(x0)(x-x0). Calculate the horizontal coordinate x1 = x0-f(x0) / f'(x0) of the intersection of L and the x-axis, and call x1 the first-order approximation of r. Then draw a tangent line to the curve y = f(x) through the point (x1, f(x1)), and calculate the horizontal coordinate x2 = x1-f(x1) / f'(x1) of the intersection of the tangent line and the x-axis, and call x2 the second-order approximation of r. Repeat the above process to obtain a sequence of approximations of r, among which x(n+1) = x(n)-f(x(n)) / f'(x(n)), which is called the n+1th-order approximation of r. The above formula is the Newton iteration formula.

[0026] The application of Newton's iteration method needs to meet certain conditions: the function f(x) must be continuous, and the zero point to be found must be isolated; at the same time, there is a region around the zero point, and as long as the initial value is in this neighboring region, Newton's method will converge.

[0027] In addition, if f'(x0) = 0, the Newton-Raphson method may fail because the slope of the tangent line cannot be calculated. If the initial guess value is close to the inflection point of the function f(x) in the equation f(x) = 0, the Newton-Raphson method may start to deviate from the root and then converge back to the root. Therefore, in actual application, you need to know the general situation of the model you want to solve and make reasonable adjustments.

[0028] The specific process is as follows: Assume that both curves pass through three points: (-r, 0), (r, 0), (0, s), that is, they are both symmetrical about the z-axis, intersecting the x-axis at ±r and the z-axis at s, and are upward-opening concave arcs. Substituting the coordinates of the three points into the parabola equation, we get: It can be solved as: b=0;c=s Substituting the coordinates of the three points into the hyperbola equation, we get: It can be solved as: The first minor equation is a transcendental equation about A, which can be solved by Newton's iteration method: In order to quantitatively measure the difference between the two curves, assume a set of parameters: r = 250m, s = -10m (this set of values ​​is consistent with the span and sag magnitude of many actual high-voltage power lines), so the equations of the two curves can be completely determined, and the shapes of the two curves can be drawn according to this equation. Figure 2 As shown, Figure 2 The thick line is the result of drawing a parabola, and the thin line is the result of drawing a hyperbolic cosine line. The difference between the two is shown in the curve Figure 3 As shown, the shapes of the two curves are similar to Figure 2 As shown in the figure, the shapes of the parabola and the hyperbola are almost completely overlapped, and the maximum difference is 0.00133m. Compared with the absolute sag of |s|=10m, the relative difference is only 0.000133, which is a very small amount. Therefore, it can be considered that the parabola can be used instead of the hyperbola to describe the shape of the wire.

[0029] By simulating the shape of the crossing line, we can extract information such as the direction, line height, and crossing distance of the crossing line.

[0030] The following is the derivation process of the extraction calculation method of the intersection distance: In S2, the parabolic equation of the transmission line is substituted into the original three-dimensional coordinate system of the laser point cloud to obtain the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud, and its projection in the horizontal plane is a straight line.

[0031] The equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud is: Let m = cosθ, n = -sinθ, then the above formula can be simplified as: In S2, the linear equations of the projections of the two transmission lines in the horizontal plane are simultaneously established to calculate the intersection of the two transmission line projection lines. The intersection of the two transmission line projection lines is the projection position of the intersection of the two transmission lines on the horizontal plane.

[0032] The projection of the transmission line in the horizontal plane is a straight line, and the equation of the line is as follows: nx+my=C The projection of two space parabolas with different directions on the ground gives two intersecting straight lines, whose intersection point K(x,y) is determined by the set of simultaneous equations: In S3, the X-axis and Y-axis coordinates of the intersection of the two transmission line projection lines are substituted into the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud to calculate the precise coordinates of the intersection of the two transmission lines. The Z-axis height difference of the precise coordinates of the intersection of the two transmission lines is the crossing distance.

[0033] The specific process is as follows: The points whose projection points are K on the two space parabolas are P1(x, y, z1) and P2(x, y, z2), and the height difference △H=|z1-z2| is defined as the crossing distance.

[0034] After obtaining the coordinates of point K (x, y) from the equations of the two crossing lines, substitute them back into the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud to obtain the vertical coordinates z1 and z2 of P1 and P2, and the crossing distance △H can be obtained.

[0035] This embodiment develops an algorithm through the above method for the integrated sky-ground surveying and mapping platform of power engineering projects, and uses the existing line point cloud as the basic data. When using the "Crossing and Spanning Surveying and Mapping" toolbar, the software will automatically generate a rectangle based on the profile width, automatically search for point cloud data within the rectangular range, and display the direction, line height, crossing distance and other information of the crossing and spanning line in the form of a point cloud profile in the crossing and spanning surveying and mapping window, and can output the crossing and spanning information in the line cross-section diagram with one click.

[0036] Through the application of laser point cloud in the existing three-dimensional digital design of power grid projects, the data model of the transmission line is obtained, and the cross-span measurement is calculated. The above method is applied to some lines of Jingxing Fudi 110kV line, and the following results can be obtained: Figure 3 Cross-over survey map shown.

[0037] The cross in the figure is the crossing point of the two lines. The extracted crossing point coordinates are (#1,577992.889,3163268.789,113.528). The bottom line is a schematic diagram of the route based on the point cloud data fitting.

[0038] Embodiment 2: A method for analyzing crossover information of power lines based on point cloud extraction, such as Figure 1 As shown, the following steps are included: S1. Obtain the point cloud data of the transmission line, perform differential modeling on the shape of the transmission line, and obtain the curve equation of the transmission line; S2. Substitute the curve equation of the transmission line into the original three-dimensional coordinate system of the laser point cloud, and calculate the straight line equation of the projection of the transmission line on the horizontal plane, and solve to obtain the projection position of the intersection point of the two transmission lines on the horizontal plane; S3. Substitute the projection position of the intersection point into the curve equation of the transmission line to obtain the precise coordinates of the intersection point where the two transmission lines cross, and calculate the crossing distance.

[0039] Among them, to extract the cross-over line information, we must first determine the shape curve of the crossing wire. Under windless conditions, the transmission line is only affected by the suspension of the power tower and its own gravity. At this time, the transmission line will form a catenary in the vertical plane. The shape of the transmission line is differentially modeled and solved in this plane. It can be seen that its mathematical expression is a hyperbolic cosine function. The mathematical expression of the differential modeling of the transmission line in S1 is a hyperbolic cosine function, and its expression is as follows: A and B are the coefficients of the function. The reason why z and X are different in capital letters is that z here has the same meaning and value as z in the original coordinates P(x,y,z) of the laser point cloud; while X is the new horizontal coordinate of each point after the original coordinates are rotated counterclockwise around the z axis by an angle of θ, that is: Where θ is the angle between the projection (straight line) of the transmission line in the horizontal plane and the positive direction of the original x-axis, which can be obtained by performing Hough transform in the horizontal plane. After the above calculation, the new vertical coordinate of each point on the transmission line will become a constant, that is, Y = C, where C is the distance from the origin of the coordinate to the projection straight line.

[0040] Since the hyperbolic cosine function is an exponential function, it is inconvenient to calculate. Therefore, after the hyperbolic cosine function of the transmission line is calculated in S1, the parabolic equation is used to approximate the original hyperbolic cosine function of the transmission line to obtain the parabolic equation of the transmission line.

[0041] The general formula of the parabola equation is: z = aX 2 +bX+c The parabola equation and the hyperbolic cosine function equation of the transmission line both pass through three points, namely the bottom point of the concave arc that opens upward, and two intersection points that are symmetrical about the z-axis and intersect the x-axis at a distance of r. By substituting the bottom point of the concave arc and the two intersection points into the unknown parabola equation and the calculated hyperbolic cosine function equation for simultaneous equation solving, we can obtain a transcendental equation composed of the coefficients of the hyperbolic cosine function equation.

[0042] Transcendental equation is a concept in mathematics, which refers to an equation of transcendental functions containing unknown variables. Transcendental functions are those functions that do not satisfy any algebraic equation (i.e. polynomial equation), such as exponential functions, logarithmic functions, trigonometric functions (sine, cosine, tangent, etc.) and their inverse functions.

[0043] Solving transcendental equations is often more difficult than solving algebraic equations because they do not usually involve simple solutions to polynomial equations (e.g. factorization, root formulas, etc.). Solutions to transcendental equations may need to be obtained through numerical methods (e.g. iteration, approximation, etc.), or in some special cases through transformations and algebraic techniques.

[0044] This embodiment uses the Newton's iteration method to solve the parabolic equation of the transmission line. Newton's iteration method, also known as the Newton-Raphson method, is a method proposed by Newton in the 17th century to approximately solve equations in the real number domain and the complex number domain. The basic principle of the Newton's iteration method is to make a tangent line at an initial point (x0, f(x0)) and the tangent line intersects with the X-axis to obtain the coordinates of the next iteration point x1, and then make a tangent line at (x1, f(x1)), and so on, until an approximate solution that satisfies the accuracy is obtained.

[0045] Specifically, let r be the root of f(x) = 0, and select x0 as the initial approximation of r. Draw a tangent line L to the curve y = f(x) through the point (x0, f(x0)), and the equation of L is y = f(x0) + f'(x0)(x-x0). Calculate the horizontal coordinate x1 = x0-f(x0) / f'(x0) of the intersection of L and the x-axis, and call x1 the first-order approximation of r. Then draw a tangent line to the curve y = f(x) through the point (x1, f(x1)), and calculate the horizontal coordinate x2 = x1-f(x1) / f'(x1) of the intersection of the tangent line and the x-axis, and call x2 the second-order approximation of r. Repeat the above process to obtain a sequence of approximations of r, among which x(n+1) = x(n)-f(x(n)) / f'(x(n)), which is called the n+1th-order approximation of r. The above formula is the Newton iteration formula.

[0046] The application of Newton's iteration method needs to meet certain conditions: the function f(x) must be continuous, and the zero point to be found must be isolated; at the same time, there is a region around the zero point, and as long as the initial value is in this neighboring region, Newton's method will converge.

[0047] In addition, if f'(x0) = 0, the Newton-Raphson method may fail because the slope of the tangent line cannot be calculated. If the initial guess value is close to the inflection point of the function f(x) in the equation f(x) = 0, the Newton-Raphson method may start to deviate from the root and then converge back to the root. Therefore, in actual application, you need to know the general situation of the model you want to solve and make reasonable adjustments.

[0048] The specific process is as follows: Assume that both curves pass through three points: (-r, 0), (r, 0), (0, s), that is, they are both symmetrical about the z-axis, intersecting the x-axis at ±r and the z-axis at s, and are upward-opening concave arcs. Substituting the coordinates of the three points into the parabola equation, we get: It can be solved as: b=0;c=s Substituting the coordinates of the three points into the hyperbola equation, we get: It can be solved as: The first minor equation is a transcendental equation about A, which can be solved by Newton's iteration method: In order to quantitatively measure the difference between the two curves, assume a set of parameters: r = 250m, s = -10m (this set of values ​​is consistent with the span and sag magnitude of many actual high-voltage power lines), so the equations of the two curves can be completely determined, and the shapes of the two curves can be drawn according to this equation. Figure 2 As shown, Figure 2 The thick line is the result of drawing a parabola, and the thin line is the result of drawing a hyperbolic cosine line. The difference between the two is shown in the curve Figure 3 As shown, the shapes of the two curves are similar to Figure 2 As shown in the figure, the shapes of the parabola and the hyperbola are almost completely overlapped, and the maximum difference is 0.00133m. Compared with the absolute sag of |s|=10m, the relative difference is only 0.000133, which is a very small amount. Therefore, it can be considered that the parabola can be used instead of the hyperbola to describe the shape of the wire.

[0049] In the process of fitting the hyperbolic cosine function with a parabola, first select points to substitute into the parabola for fitting, and then calculate the maximum difference between the calculated fitting parabola result and the original function; if the maximum difference is greater than the preset value, it is necessary to reselect points and recalculate the fitting parabola.

[0050] By simulating the shape of the crossing line, we can extract information such as the direction, line height, and crossing distance of the crossing line.

[0051] The following is the derivation process of the extraction calculation method of the intersection distance: In S2, the parabolic equation of the transmission line is substituted into the original three-dimensional coordinate system of the laser point cloud to obtain the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud, and its projection in the horizontal plane is a straight line.

[0052] The equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud is: Let m = cosθ, n = -sinθ, then the above formula can be simplified as: In S2, the linear equations of the projections of the two transmission lines in the horizontal plane are simultaneously established to calculate the intersection of the two transmission line projection lines. The intersection of the two transmission line projection lines is the projection position of the intersection of the two transmission lines on the horizontal plane.

[0053] The projection of the transmission line in the horizontal plane is a straight line, and the equation of the line is as follows: nx+my=C The projection of two space parabolas with different directions on the ground gives two intersecting straight lines, whose intersection point K(x,y) is determined by the set of simultaneous equations: In S3, the X-axis and Y-axis coordinates of the intersection of the two transmission line projection lines are substituted into the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud to calculate the precise coordinates of the intersection of the two transmission lines. The Z-axis height difference of the precise coordinates of the intersection of the two transmission lines is the crossing distance.

[0054] The specific process is as follows: The points whose projection points are K on the two space parabolas are P1(x, y, z1) and P2(x, y, z2), and the height difference △H=|z1-z2| is defined as the crossing distance.

[0055] After obtaining the coordinates of point K (x, y) from the equations of the two crossing lines, substitute them back into the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud to obtain the vertical coordinates z1 and z2 of P1 and P2, and the crossing distance △H can be obtained.

[0056] This embodiment develops an algorithm through the above method for the integrated sky-ground surveying and mapping platform of power engineering projects, and uses the existing line point cloud as the basic data. When using the "Crossing and Spanning Surveying and Mapping" toolbar, the software will automatically generate a rectangle based on the profile width, automatically search for point cloud data within the rectangular range, and display the direction, line height, crossing distance and other information of the crossing and spanning line in the form of a point cloud profile in the crossing and spanning surveying and mapping window, and can output the crossing and spanning information in the line cross-section diagram with one click.

[0057] Through the application of laser point cloud in the existing three-dimensional digital design of power grid projects, the data model of the transmission line is obtained, and the cross-span measurement is calculated. The above method is applied to some lines of the Huangshan Xianglian-Shuixi 500kV line, and the following can be obtained: Figure 4 Cross-over survey map shown.

[0058] The cross in the figure is the crossing point of the two lines. The extracted crossing point coordinates are (#1619578.41, 3371022.15, 220.54). The top line is a schematic diagram of the route based on the point cloud data fitting.

[0059] The above specific embodiments are only preferred implementations of the present invention, and are not intended to limit the specific implementation structure and implementation scope of the present invention. In fact, some equivalent changes can also be made according to the shape, structure and design purpose of the present invention. Therefore, all equivalent changes made according to the shape, structure and design purpose of the present invention should be included in the protection scope of the present invention, that is, these equivalent changes should be protected by the present invention.

Claims

1. A method for analyzing crossover information of power lines based on point cloud extraction, characterized in that: The steps include: S1. Obtain the point cloud data of the transmission line, perform differential modeling on the shape of the transmission line, and obtain the curve equation of the transmission line; S2. Substitute the curve equation of the transmission line into the original three-dimensional coordinate system of the laser point cloud, and calculate the straight line equation of the projection of the transmission line on the horizontal plane, and solve to obtain the projection position of the intersection point of the two transmission lines on the horizontal plane; S3. Substitute the projection position of the intersection point into the curve equation of the transmission line to obtain the precise coordinates of the intersection point where the two transmission lines cross, and calculate the crossing distance.

2. The method for extracting and analyzing crossover information of power lines based on point cloud according to claim 1 is characterized in that: The transmission line is in the shape of a catenary in the vertical plane, and the mathematical expression after differential modeling of the transmission line in S1 is a hyperbolic cosine function.

3. The method for extracting and analyzing crossover information of power lines based on point cloud according to claim 1 or 2, characterized in that: After the hyperbolic cosine function of the transmission line is calculated in S1, the parabolic equation is used to approximate the original hyperbolic cosine function of the transmission line to obtain the parabolic equation of the transmission line.

4. The method for extracting and analyzing crossover information of power lines based on point cloud according to claim 3 is characterized in that: The parabola equation and the hyperbolic cosine function equation of the transmission line both pass through three points, namely the bottom point of the open upward concave arc, and two intersection points that are symmetrical about the z-axis and intersect the x-axis at a distance r.

5. The method for extracting and analyzing crossover information of power lines based on point cloud according to claim 4 is characterized in that: By substituting the bottom point and two intersection points of the concave arc into the unknown parabola equation and the calculated hyperbolic cosine function equation to solve the equations together, we can get a transcendental equation composed of the coefficients of the hyperbolic cosine function equation. The parabola equation of the transmission line can be calculated by solving it using Newton's iteration method.

6. The method for analyzing crossover information of power lines based on point cloud extraction according to claim 1 is characterized in that: In S2, the parabolic equation of the transmission line is substituted into the original three-dimensional coordinate system of the laser point cloud to obtain the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud, and its projection in the horizontal plane is a straight line.

7. The method for analyzing crossover information of power lines based on point cloud extraction according to claim 1 is characterized in that: In S2, the straight line equations of the projections of the two transmission lines in the horizontal plane are simultaneously established to calculate the intersection of the two transmission line projection lines.

8. The method for analyzing crossover information of power lines based on point cloud extraction according to claim 7 is characterized in that: The intersection of the projection lines of the two transmission lines is the projection position of the intersection of the two transmission lines on the horizontal plane.

9. The method for extracting and analyzing crossover information of power lines based on point cloud according to claim 1, characterized in that: In S3, the X-axis and Y-axis coordinates of the intersection of the two transmission line projection lines are substituted into the equation of the transmission line in the original three-dimensional coordinate system of the laser point cloud to calculate the precise coordinates of the intersection of the two transmission lines.

10. The method for analyzing crossover information of power lines based on point cloud extraction according to claim 1, characterized in that: The Z-axis height difference of the precise coordinates of the intersection point where two transmission lines cross is the crossing distance.

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