A method, system, device and medium for quickly determining the force of a main cable and the force of a sling of a suspension bridge based on a three-dimensional point cloud

Abstract

The application discloses a kind of based on three-dimensional point cloud suspension bridge main cable force and sling force fast determination method, system, equipment and medium, comprising the following steps: the main cable and sling of the suspension bridge to be measured are scanned to obtain original point cloud data, after being preprocessed, the main cable section point cloud data and sling point cloud data between adjacent slings are obtained;Cross-section fitting is carried out on the main cable section point cloud data, and the main cable section linear coordinate is extracted;According to the x-axis coordinate of the intersection point of each sling and main cable in the global cartesian coordinate system, the geometric shape parameters of each main cable section are obtained by overall fitting based on the segmented catenary theory according to the main cable section linear coordinate and the x-axis coordinate of the intersection point of sling and main cable;The actual main cable horizontal force is calculated using the unstressed state catenary theory;According to the actual main cable horizontal force and the tangent angle of the main cable at the end point of each main cable section, the corresponding sling force is calculated.The application can accurately determine the main cable force and sling force of suspension bridge.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring, and in particular relates to a method, system, equipment and medium for rapid determination of main cable force and suspension cable force of suspension bridge based on three-dimensional point cloud. Background Technology

[0002] As a cable-stayed bridge structure, the main cable and suspenders are key load-bearing components of a suspension bridge. Their stress state directly affects the overall structural safety and is a crucial indicator for assessing the structural condition of a suspension bridge. Abnormal stress on the main cable or suspenders can easily lead to structural damage or even collapse, and in severe cases, may even cause the bridge to collapse. Therefore, accurately assessing the changes in the main cable and suspender forces of in-service suspension bridges is crucial for ensuring the safety assessment and maintenance of bridge structures.

[0003] Currently, the commonly used method for determining sling force is the vibration frequency method. This method requires precise determination of the sling's fundamental frequency or a specific order frequency before calculating the sling force based on relevant theories. This process demands high precision from the vibration pickup and high-quality vibration test signals. Furthermore, the vibration frequency method can only be used for individual sling measurements, resulting in low overall efficiency. The vibration frequency method is unsuitable for determining main cable force because the main cable is not a simplified, hinged cable component like a sling. The main cable is a complex load-bearing system composed of multiple strands of steel wire, with complex boundary conditions. This makes it difficult to accurately establish the theoretical relationship between vibration frequency and cable force, and the frequency response signal is easily interfered with, making it impossible to determine cable force through simple vibration pickup as with slings.

[0004] In recent years, existing technologies have utilized three-dimensional laser scanning to determine the main cable force and suspender force, but significant drawbacks remain: when fitting the main cable alignment, existing methods typically ignore the elevation continuity constraint of adjacent segments at the suspender intersection, leading to inaccurate fitting of segmented catenary parameters; furthermore, cable force determination often relies on design parameters such as the main beam's self-weight, which are difficult to obtain precisely. These parameters vary with dead load in actual bridges and are difficult to determine accurately, thus directly transmitting errors to the cable force measurement results and affecting the overall measurement accuracy. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a rapid method for measuring the main cable force and suspension cable force of a suspension bridge based on three-dimensional point clouds, so as to achieve high-precision calculation of the main cable force and suspension cable force and effectively avoid parameter transmission errors.

[0006] The second objective of this invention is to provide a rapid measurement system for the main cable force and suspension cable force of a suspension bridge based on three-dimensional point clouds.

[0007] A third objective of this invention is to provide an electronic device.

[0008] A fourth objective of this invention is to provide a computer-readable storage medium.

[0009] Technical Solution: To achieve the above objectives, this invention discloses a rapid method for determining the main cable force and suspension cable force of a suspension bridge based on three-dimensional point clouds, comprising the following steps:

[0010] (1) The main cable and suspenders of the suspension bridge under test are scanned to obtain the original point cloud data. After preprocessing, the point cloud data of the main cable segments between adjacent suspenders are obtained. and cable point cloud data ;

[0011] (2) Point cloud data of main cable segments Perform cross-sectional fitting to extract the linear coordinates of the main cable segments. ;

[0012] (3) Based on the point cloud data of the suspension cable Determine the x-axis coordinate of each intersection point of the suspender and the main cable in the global Cartesian coordinate system. ;

[0013] (4) Based on the main cable segment coordinates extracted in step (2) The x-axis coordinates of each intersection point of the sling and the main cable determined in step (3) Based on the segmented catenary theory, the geometric morphological parameters of each main cable segment are obtained by performing an overall fitting on each main cable segment. The geometric parameters of each main cable segment include horizontal distance. Elevation difference between the two endpoints and the tangent angle of the main cable at both ends and ;

[0014] (5) Based on the geometric parameters of each main cable segment determined in step (4), the actual horizontal force of the main cable is calculated using the catenary theory in the stress-free state. ;

[0015] (6) The actual horizontal force of the main cable calculated according to step (5) And using the tangent angle of the main cable at the end of each main cable segment obtained in step (4), the corresponding suspending cable force is calculated using the principle of nodal force balance. .

[0016] Optionally, step (1) specifically includes the following steps:

[0017] (1.1) Use a 3D laser scanner to scan the main cable and suspenders of the suspension bridge under test to obtain the original point cloud data of the main cable and suspenders;

[0018] (1.2) Transform the original point cloud data of the main cable and suspenders to the global Cartesian coordinate system to obtain the point cloud data of the main cable and suspenders. In the global Cartesian coordinate system The axis is the longitudinal direction of the bridge. The axis is in the transverse direction of the bridge. The axis is in the height direction of the main cable;

[0019] (1.3) Point cloud data The data is segmented to separate the point cloud data of the main cable segments between adjacent suspension cables. and cable point cloud data The point cloud data of the suspension cables includes cable clips.

[0020] Optionally, step (2) specifically includes the following steps:

[0021] (2.1) Point cloud data of main cable segments Slice the bridge at equal intervals along its longitudinal direction, with horizontal spacing. Step size, The value range is 0.1m to 1m, and the thickness of the slice is... , The value range is 0.01m to 0.02m, generating point cloud slices. ;

[0022] (2.2) Slice the point cloud Projected to By projecting point cloud slices onto the cross-section of the main cable in the axial plane, a cross-sectional point cloud is obtained. Point clouds from cross-section Randomly sample 3 points and calculate the center coordinates and radius of the circle formed by the 3 points; repeat the above steps. The radius sample was obtained the next time. , The number of points in the point cloud slice; then the radius sample Perform probability density statistics and take the radius value corresponding to the peak value of the probability density. and the center ; Retain With center at and radius at, Point cloud data within the range, The tolerance threshold is determined by the minimum distance between the main cable surface and the auxiliary facilities, and the calculation formula is as follows:

[0023] ,

[0024] Finally, the denoised cross-sectional point cloud is obtained. ;

[0025] (2.3) Then based on the design radius of the main cable The least squares method is used to fit the circular curve of the cross section of the point cloud slice. Let the equation of the circular curve be:

[0026] ,

[0027] In the formula, The coordinates of the center of the circular curve;

[0028] The coordinates of the center of the circular curve were calculated using the least squares method. The calculation formula is:

[0029] ,

[0030] (2.4) Based on the coordinates of the center of the fitted circular curve Computational point cloud slicing Centroid coordinates inside The calculation formula is:

[0031] ,

[0032] In the formula, Slicing point clouds middle The maximum value; Slicing point clouds middle The minimum value;

[0033] (2.5) Repeat steps (2.2) to (2.4) to calculate the centroid coordinates of all point cloud slices in all main cable segments. Main cable segment coordinates Centroid coordinates of all point cloud slices in all main cable segments A set of.

[0034] Optionally, step (3) specifically includes the following steps:

[0035] (3.1) From the point cloud data of the suspension cable In the process, the point cloud data of the cable clamp area is separated and removed, while the point cloud data of the main cable body between the upper and lower anchoring ends is retained. ;

[0036] (3.2) Calculate the point cloud data of the main body of the suspension cable exist Midpoint of the axis The midpoint is the intersection point of each sling and the main cable in the global Cartesian coordinate system. The formula for calculating the axis coordinates is:

[0037] .

[0038] Optionally, step (4) specifically includes the following steps:

[0039] (4.1) The alignment of each main cable segment follows the catenary equation. Assume that the first segment... The alignment of each main cable segment satisfies the catenary equation:

[0040] ,

[0041] In the formula, , and The parameters for the catenary equations are as follows: since the horizontal force is the same in each main cable segment, the corresponding segmented catenary equations are... They are all the same; Let be the independent variable of the equation. It is a hyperbolic cosine function. For the first The catenary equation satisfied by the alignment of each main cable segment;

[0042] (4.2) The coordinates of the main cable segments Project to From the plane, we obtain the two-dimensional linear coordinates of the main cable segment. Establish the objective function that minimizes the sum of squared residuals. The expression is:

[0043] ,

[0044] In the formula, Where N is the number of main cable segments, N is the number of linear coordinate points in each main cable segment, and P is the parameter vector of the catenary equation. The two-dimensional linear coordinates of the nth linear coordinate point in each main cable segment. It is the sum of squared residuals;

[0045] (4.3) Based on the intersection of each sling and the main cable Axis coordinates To satisfy the elevation continuity condition, a system of continuity constraint equations is established, expressed as follows:

[0046] ,

[0047] In the formula, g represents the system of continuous constraint equations. The catenary equation satisfied by the alignment of the first main cable segment. The catenary equation satisfied by the alignment of the second main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. The first sling intersects with the main cable. Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates;

[0048] (4.4) Based on the objective function and constraint equations obtained in steps (4.2) and (4.3), the Levenberg-Marquardt algorithm is used for iterative solution. The iterative formula is as follows:

[0049] ,

[0050] In the formula, For the residual vector, For the first The residual vector of each main cable segment For the first The first main cable segment Two-dimensional linear coordinates of a linear coordinate point The residual, For transpose, For Jacobian matrices, It is the identity matrix. The damping factor, For the first The parameter vector of the catenary equation in the next iteration. For the first The catenary equation parameter vector for the next iteration;

[0051] The iteration termination condition is as follows:

[0052] ,

[0053] in, For the iterative parameter threshold, The recommended value is 10. -6 ;

[0054] Finally, the parameters of the catenary equation for each segment of the main cable were obtained. , and ;

[0055] (4.5) Based on the piecewise catenary equation parameters obtained by fitting in step (4.4) , and Calculate the geometric parameters of each main cable segment, the first... The formula for calculating the geometric parameters of each main cable segment is as follows:

[0056] ,

[0057] In the formula, For the first The horizontal distance between each main cable segment; For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The x-axis coordinates of the intersection points of the suspenders and the main cable; For the first The elevation difference between the two ends of each main cable segment; and The first The tangent angle of the main cable at both ends of each main cable segment; It is a hyperbolic sine function. It is the arctangent function.

[0058] Optionally, step (5) specifically includes the following steps:

[0059] (5.1) Assume the initial horizontal force on the main cable is According to the mechanical characteristics of suspension bridges, the horizontal force of each main cable segment remains constant; based on the result obtained in step (4), the first... Horizontal distance of each main cable segment and the angle of the main cable tangent at the endpoint Using the catenary theory in a stress-free state, the initial horizontal force on the main cable is calculated. Under the action of the first Theoretical elevation difference of each main cable segment The calculation formula is:

[0060] ,

[0061] In the formula, For the first Vertical force at the end of each main cable segment; L 0,m For the first The stress-free length of each main cable segment is determined by the horizontal distance. Calculated; The elastic modulus of the main cable. The cross-sectional area of ​​the main cable. The unit weight of the main cable. , , All were obtained from design data; It is an inverse hyperbolic sine function. It is the tangent function;

[0062] (5.2) Establishing the theoretical elevation difference The elevation difference between the two endpoints obtained in step (4) The objective function for the sum of squared residuals is expressed as:

[0063] ,

[0064] In the formula, Number of main cable segments Let the objective function be the sum of squared residuals;

[0065] (5.3) By adjusting the initial horizontal force of the main cable , so that the objective function The minimum value corresponds to the actual horizontal force on the main cable. .

[0066] Optionally, step (6) specifically includes the following steps:

[0067] (6.1) At the intersection of the suspender and the main cable, the vertical forces of adjacent main cable segments satisfy the equilibrium condition. The static equilibrium equation of the suspender is established as follows:

[0068] ,

[0069] In the formula, For the first Vertical force at the endpoints of each main cable segment For the first The suspender force corresponding to each main cable segment The vertical force at the end point of the (m+1)th main cable segment;

[0070] (6.2) Based on the tangent angle of the main cable at both ends of each main cable segment obtained in step (4) and the actual horizontal force H of the main cable obtained in step (5), calculate the corresponding suspender force using the vertical force balance equation. The calculation formula is:

[0071] ,

[0072] in For the first The tangent angle of the main cable at the end of each main cable segment. For the first The tangent angle of the main cable at the end of each main cable segment. and They share the same sling.

[0073] Based on the same inventive concept, this invention discloses a rapid measurement system for the main cable force and suspension cable force of a suspension bridge based on three-dimensional point clouds, comprising:

[0074] The point cloud data preprocessing module is used to scan the main cable and suspenders of the suspension bridge under test to obtain raw point cloud data, and then preprocess the data to obtain point cloud data of the main cable segments between adjacent suspenders. and cable point cloud data ;

[0075] The linear coordinate extraction module is used for the point cloud data of the main cable segments. Perform cross-sectional fitting to extract the linear coordinates of the main cable segments. ;

[0076] The intersection point coordinate determination module is used to determine the coordinates of the intersection points based on the cable point cloud data. Determine the x-axis coordinate of each intersection point of the suspender and the main cable in the global Cartesian coordinate system. ;

[0077] The morphological parameter fitting module is used to fit the linear coordinates of the main cable segments. x-axis coordinates of each sling intersection with the main cable Based on the segmented catenary theory, the geometric morphological parameters of each main cable segment are obtained by performing an overall fitting on each main cable segment. The geometric parameters of each main cable segment include horizontal distance. Elevation difference between the two endpoints and the tangent angle of the main cable at both ends and ;

[0078] The main cable force calculation module is used to calculate the actual horizontal force on the main cable based on the geometric parameters of each main cable segment and using the catenary theory in a stress-free state. ;

[0079] The cable force calculation module is used to calculate the actual horizontal force of the main cable. And the tangent angle of the main cable at the end of each main cable segment, using the principle of nodal force balance, to calculate the corresponding suspender force. .

[0080] Based on the same inventive concept, the present invention provides an electronic device including a processor and a storage medium;

[0081] The storage medium is used to store instructions;

[0082] The processor is configured to operate according to the instructions to perform the steps of the method described above.

[0083] Based on the same inventive concept, the computer-readable storage medium of the present invention stores a computer program thereon, characterized in that the program, when executed by a processor, implements the steps of the method described above.

[0084] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0085] (1) In the process of fitting the segmented catenary, the present invention introduces the elevation continuity constraint condition at the intersection of the suspension cable and the main cable, which effectively solves the problem of misalignment of the fitting line shape of adjacent segments at the connection point, and ensures the smooth transition of the overall line shape of the main cable, thereby significantly improving the extraction accuracy of key geometric parameters such as horizontal distance, elevation difference and endpoint tangent angle.

[0086] (2) This invention proposes an iterative solution method that combines the catenary theory. By establishing the residual function between the theoretical elevation difference and the measured elevation difference, the main cable force and the suspending cable force can be calculated quickly and accurately. This method does not rely on parameters such as the self-weight of the main beam, which are difficult to obtain accurately. It can realize the rapid and high-precision calculation of the main cable force and the suspending cable force by only using the geometric shape and material properties of the main cable itself. It effectively avoids parameter transmission errors and improves the calculation efficiency and accuracy at the same time. Attached Figure Description

[0087] Figure 1 This is a flowchart of the present invention;

[0088] Figure 2 This is a schematic diagram of point cloud data segmentation in this invention;

[0089] Figure 3 This is a schematic diagram of point cloud slicing denoising in this invention;

[0090] Figure 4 This is a schematic diagram illustrating the calculation of the x-axis coordinate of the intersection point of the suspender cable and the main cable in this invention;

[0091] Figure 5 This is a flowchart for calculating the horizontal force of the main cable in this invention;

[0092] Figure 6 This is a schematic diagram of the process for calculating the sling force in this invention. Detailed Implementation

[0093] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0094] Example 1: As Figure 1 As shown, this invention discloses a rapid method for determining the main cable force and suspension cable force of a suspension bridge based on three-dimensional point clouds, comprising the following steps:

[0095] (1) The main cable and suspenders of the suspension bridge under test are scanned to obtain the original point cloud data. After preprocessing, the point cloud data of the main cable segments between adjacent suspenders are obtained. and cable point cloud data .

[0096] like Figure 2As shown, step (1) specifically includes the following steps:

[0097] (1.1) Use a three-dimensional laser scanner to scan the main cable and suspenders of the suspension bridge under test to obtain the original point cloud data of the main cable and suspenders.

[0098] (1.2) Transform the original point cloud data of the main cable and suspenders to the global Cartesian coordinate system to obtain the point cloud data of the main cable and suspenders. In the global Cartesian coordinate system The axis is the longitudinal direction of the bridge. The axis is in the transverse direction of the bridge. The axis is in the height direction of the main cable.

[0099] (1.3) Point cloud data The data is segmented to separate the point cloud data of the main cable segments between adjacent suspension cables. and cable point cloud data The point cloud data of the suspension cables includes cable clips.

[0100] (2) Point cloud data of main cable segments Perform cross-sectional fitting to extract the linear coordinates of the main cable segments. .

[0101] like Figure 3 As shown, step (2) specifically includes the following steps:

[0102] (2.1) Point cloud data of main cable segments Slice the bridge at equal intervals along its longitudinal direction, with horizontal spacing. Step size, The value range is 0.1m to 1m, and the thickness of the slice is... , The value range is 0.01m to 0.02m, generating point cloud slices. ; and The value of needs to simultaneously satisfy the conditions that the point cloud slice has a sufficient number of points and that the shape of the point cloud slice can ignore the influence of sag, so as to suppress the random error of cross-sectional fitting.

[0103] (2.2) Slice the point cloud Projecting the point cloud slices onto the yz-axis plane, the point cloud slices are projected onto the cross-section of the main cable to obtain the cross-sectional point cloud. Point clouds from cross-section Randomly sample 3 points and calculate the center coordinates and radius of the circle formed by the 3 points; repeat the above steps. The radius sample was obtained the next time. , The number of points in the point cloud slice; then the radius sample Perform probability density statistics and take the radius value corresponding to the peak value of the probability density. and the center To filter out noise points, retain the following: With center at and radius at, The point cloud data within the range, where q is the tolerance threshold. The value of the tolerance threshold is determined by the minimum distance between the surface of the main cable and the auxiliary facilities, and the calculation formula is as follows:

[0104] ,

[0105] After denoising, the final denoised cross-sectional point cloud is obtained. .

[0106] (2.3) Then based on the design radius of the main cable The least squares method is used to fit the circular curve of the cross section of the point cloud slice. Let the equation of the circular curve be:

[0107] ,

[0108] In the formula, The coordinates of the center of the circular curve;

[0109] The coordinates of the center of the circular curve were calculated using the least squares method. The calculation formula is:

[0110] .

[0111] (2.4) Based on the coordinates of the center of the fitted circular curve Computational point cloud slicing Centroid coordinates inside The calculation formula is:

[0112] ,

[0113] In the formula, Slicing point clouds middle The maximum value; Slicing point clouds middle The minimum value.

[0114] (2.5) Repeat steps (2.2) to (2.4) to calculate the centroid coordinates of all point cloud slices in all main cable segments. Main cable segment coordinates Centroid coordinates of all point cloud slices in all main cable segments A set of.

[0115] (3) Based on the point cloud data of the suspension cable Determine the x-axis coordinate of each intersection point of the suspender and the main cable in the global Cartesian coordinate system. .

[0116] like Figure 4 As shown, step (3) specifically includes the following steps:

[0117] (3.1) From the point cloud data of the suspension cable In the process, the point cloud data of the cable clamp area is separated and removed, while the point cloud data of the main cable body between the upper and lower anchoring ends is retained. .

[0118] (3.2) Calculate the point cloud data of the main body of the suspension cable At the midpoint of the x-axis The midpoint is the intersection point of each sling and the main cable in the global Cartesian coordinate system. The formula for calculating the axis coordinates is:

[0119] .

[0120] (4) If directly based on the coordinates of the main cable segment Fitting catenary parameters is prone to inaccuracies due to measurement errors and data dispersion, leading to significant deviations in the obtained geometric parameters. To improve the accuracy and reliability of parameter identification, this invention combines the main cable segment linear coordinates obtained in step (2). The x-axis coordinates of each sling-to-main-cable intersection point determined in step (3) in the global Cartesian coordinate system. Based on the segmented catenary theory, each main cable segment is fitted as a whole. Through the fitting process, the geometric parameters of each main cable segment can be determined more accurately. The geometric parameters of each main cable segment include horizontal distance. Elevation difference between the two endpoints and the tangent angle of the main cable at both ends and .

[0121] Step (4) specifically includes the following steps:

[0122] (4.1) The alignment of each main cable segment follows the catenary equation. Assume that the alignment of the m-th main cable segment satisfies the catenary equation:

[0123] ,

[0124] In the formula, a and b m and c m represents the parameters of the catenary equation; since the horizontal force is the same for each main cable segment, the corresponding segmented catenary equation 'a' is the same; 'e' is the independent variable of the equation. It is a hyperbolic cosine function. Let m be the catenary equation satisfied by the alignment of the m-th main cable segment.

[0125] (4.2) The coordinates of the main cable segments Project to From the plane, we obtain the two-dimensional linear coordinates of the main cable segment. Establish the objective function that minimizes the sum of squared residuals. The expression is:

[0126] ,

[0127] In the formula, Where N is the number of main cable segments, N is the number of linear coordinate points in each main cable segment, and P is the parameter vector of the catenary equation. The two-dimensional linear coordinates of the nth linear coordinate point in each main cable segment. This is the sum of squared residuals.

[0128] (4.3) Based on the intersection of each sling and the main cable Axis coordinates To satisfy the elevation continuity condition, a system of continuity constraint equations is established, expressed as follows:

[0129] ,

[0130] In the formula, g represents the system of continuous constraint equations. The catenary equation satisfied by the alignment of the first main cable segment. The catenary equation satisfied by the alignment of the second main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. The first sling intersects with the main cable. Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates.

[0131] (4.4) Based on the objective function and constraint equations obtained in steps (4.2) and (4.3), the Levenberg-Marquardt algorithm is used for iterative solution. The iterative formula is as follows:

[0132] ,

[0133] In the formula, For the residual vector, For the first The residual vector of each main cable segment For the first The first main cable segment Two-dimensional linear coordinates of a linear coordinate point The residual, For transpose, For Jacobian matrices, It is the identity matrix. The damping factor, For the first The parameter vector of the catenary equation in the next iteration. For the first The catenary equation parameter vector for the next iteration;

[0134] The iteration termination condition is as follows:

[0135] ,

[0136] Where ε is the threshold value for the iteration parameter, and the recommended value for ε is 10. -6 ;

[0137] Finally, the parameters a and b of the catenary equation for the main cable segment are obtained. m and c m .

[0138] (4.5) Based on the piecewise catenary equation parameters obtained by fitting in step (4.4) , and Calculate the geometric parameters of each main cable segment, the first... The formula for calculating the geometric parameters of each main cable segment is as follows:

[0139] ,

[0140] In the formula, For the first The horizontal distance between each main cable segment; For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The x-axis coordinates of the intersection points of the suspenders and the main cable; For the first The elevation difference between the two ends of each main cable segment; and The first The tangent angle of the main cable at both ends of each main cable segment; It is a hyperbolic sine function. It is the arctangent function.

[0141] (5) Based on the geometric parameters of each main cable segment determined in step (4), calculate the horizontal force H of the main cable using the catenary theory in the stress-free state.

[0142] like Figure 5 As shown, step (5) specifically includes the following steps:

[0143] (5.1) Assume the initial horizontal force on the main cable is According to the mechanical characteristics of suspension bridges, the horizontal force of each main cable segment remains constant; based on the result obtained in step (4), the first... Horizontal distance of each main cable segment and the angle of the main cable tangent at the endpoint Using the catenary theory in a stress-free state, the initial horizontal force on the main cable is calculated. Under the action of the first Theoretical elevation difference of each main cable segment The calculation formula is:

[0144] ,

[0145] In the formula, For the first Vertical force at the end of each main cable segment; L 0,m For the first The stress-free length of each main cable segment is determined by the horizontal distance. Calculated; The elastic modulus of the main cable. The cross-sectional area of ​​the main cable. The unit weight of the main cable. , , All were obtained from design data; It is an inverse hyperbolic sine function. It is the tangent function.

[0146] (5.2) Establishing the theoretical elevation difference The elevation difference between the two endpoints obtained in step (4) The objective function for the sum of squared residuals is expressed as:

[0147] ,

[0148] In the formula, M is the number of main cable segments. Let be the objective function for the sum of squared residuals.

[0149] (5.3) By adjusting the horizontal force H0 of the main cable, the objective function is made more efficient. The minimum value corresponds to the actual horizontal force H of the main cable.

[0150] (6) The actual horizontal force of the main cable calculated according to step (5) And using the tangent angle of the main cable at the end of each main cable segment obtained in step (4), the corresponding suspending cable force is calculated using the principle of nodal force balance. .

[0151] like Figure 6 As shown, step (6) specifically includes the following steps:

[0152] (6.1) At the intersection of the suspender and the main cable, the vertical forces of adjacent main cable segments satisfy the equilibrium condition. The static equilibrium equation of the suspender is established as follows:

[0153] ,

[0154] In the formula, For the first Vertical force at the endpoints of each main cable segment For the first The suspender force corresponding to each main cable segment This represents the vertical force at the endpoint of the (m+1)th main cable segment.

[0155] (6.2) Based on the tangent angle of the main cable at both ends of each main cable segment obtained in step (4) and the actual horizontal force H of the main cable obtained in step (5), calculate the corresponding suspender force using the vertical force balance equation. The calculation formula is:

[0156] ,

[0157] in For the first The tangent angle of the main cable at the end of each main cable segment. For the first The tangent angle of the main cable at the end of each main cable segment. and They share the same sling.

[0158] Example 2: This invention discloses a rapid measurement system for the main cable force and suspension cable force of a suspension bridge based on three-dimensional point clouds, comprising:

[0159] The point cloud data preprocessing module is used to scan the main cable and suspenders of the suspension bridge under test to obtain raw point cloud data, and then preprocess the data to obtain point cloud data of the main cable segments between adjacent suspenders. and cable point cloud data .

[0160] The point cloud data preprocessing module uses a 3D laser scanner to scan the main cable and suspenders of the suspension bridge under test to obtain the raw point cloud data of the main cable and suspenders.

[0161] The original point cloud data of the main cable and suspenders are transformed into a global Cartesian coordinate system to obtain the point cloud data of the main cable and suspenders. In the global Cartesian coordinate system The axis is the longitudinal direction of the bridge. The axis is in the transverse direction of the bridge. The axis is in the height direction of the main cable;

[0162] Point cloud data The data is segmented to separate the point cloud data of the main cable segments between adjacent suspension cables. and cable point cloud data The point cloud data of the suspension cables includes cable clips.

[0163] The linear coordinate extraction module is used for the point cloud data of the main cable segments. Perform cross-sectional fitting to extract the linear coordinates of the main cable segments. .

[0164] The linear coordinate extraction module extracts point cloud data from main cable segments. Slice the bridge at equal intervals along its longitudinal direction, with horizontal spacing. Step size, The value range is 0.1m to 1m, and the thickness of the slice is... , The value range is 0.01m to 0.02m, generating point cloud slices. ; and The value of needs to simultaneously satisfy the conditions that the point cloud slice has a sufficient number of points and that the shape of the point cloud slice can ignore the influence of sag, so as to suppress the random error of cross-sectional fitting.

[0165] Slice the point cloud Projecting the point cloud slices onto the yz-axis plane, the point cloud slices are projected onto the cross-section of the main cable to obtain the cross-sectional point cloud. Point clouds from cross-section Randomly sample 3 points and calculate the center coordinates and radius of the circle formed by the 3 points; repeat the above steps. The radius sample was obtained the next time. , The number of points in the point cloud slice; then the radius sample Perform probability density statistics and take the radius value corresponding to the peak value of the probability density. and the center To filter out noise points, retain the following: With center at and radius at, The point cloud data within the range, where q is the tolerance threshold. The value of the tolerance threshold is determined by the minimum distance between the surface of the main cable and the auxiliary facilities, and the calculation formula is as follows:

[0166] ,

[0167] After denoising, the final denoised cross-sectional point cloud is obtained. .

[0168] Then based on the design radius of the main cable The least squares method is used to fit the circular curve of the cross section of the point cloud slice. Let the equation of the circular curve be:

[0169] ,

[0170] In the formula, The coordinates of the center of the circular curve;

[0171] The coordinates of the center of the circular curve were calculated using the least squares method. The calculation formula is:

[0172] ,

[0173] Based on the coordinates of the center of the fitted circular curve Computational point cloud slicing Centroid coordinates inside The calculation formula is:

[0174] ,

[0175] In the formula, Slicing point clouds middle The maximum value; Slicing point clouds middle The minimum value.

[0176] The centroid coordinates of all point cloud slices in all main cable segments were calculated. Main cable segment coordinates Centroid coordinates of all point cloud slices in all main cable segments A set of.

[0177] The intersection point coordinate determination module is used to determine the coordinates of the intersection points based on the cable point cloud data. Determine the x-axis coordinate of each intersection point of the suspender and the main cable in the global Cartesian coordinate system. .

[0178] The intersection coordinate determination module is derived from the point cloud data of the suspension cable. In the process, the point cloud data of the cable clamp area is separated and removed, while the point cloud data of the main cable body between the upper and lower anchoring ends is retained. .

[0179] Calculate the point cloud data of the main body of the suspension cable At the midpoint of the x-axis The midpoint is the intersection point of each sling and the main cable in the global Cartesian coordinate system. The formula for calculating the axis coordinates is:

[0180] .

[0181] The morphological parameter fitting module is used to fit the linear coordinates of the main cable segments. x-axis coordinates of each sling intersection with the main cable Based on the segmented catenary theory, the geometric morphological parameters of each main cable segment are obtained by performing an overall fitting on each main cable segment. The geometric parameters of each main cable segment include horizontal distance. Elevation difference between the two endpoints and the tangent angle of the main cable at both ends and .

[0182] In the morphological parameter fitting module, the alignment of each main cable segment follows the catenary equation. Assume the alignment of the m-th main cable segment satisfies the catenary equation:

[0183] ,

[0184] In the formula, a and b m and c m represents the parameters of the catenary equation; since the horizontal force is the same for each main cable segment, the corresponding segmented catenary equation 'a' is the same; 'e' is the independent variable of the equation. It is a hyperbolic cosine function. Let m be the catenary equation satisfied by the alignment of the m-th main cable segment.

[0185] The linear coordinates of the main cable segment Project to From the plane, we obtain the two-dimensional linear coordinates of the main cable segment. Establish the objective function that minimizes the sum of squared residuals. The expression is:

[0186] ,

[0187] In the formula, Where N is the number of main cable segments, N is the number of linear coordinate points in each main cable segment, and P is the parameter vector of the catenary equation. The two-dimensional linear coordinates of the nth linear coordinate point in each main cable segment. This is the sum of squared residuals.

[0188] Based on the intersection of each sling and the main cable Axis coordinates To satisfy the elevation continuity condition, a system of continuity constraint equations is established, expressed as follows:

[0189] ,

[0190] In the formula, g represents the system of continuous constraint equations. The catenary equation satisfied by the alignment of the first main cable segment. The catenary equation satisfied by the alignment of the second main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. The first sling intersects with the main cable. Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates.

[0191] Based on the objective function and the set of constraint equations, the Levenberg-Marquardt algorithm is used for iterative solution. The iterative formula is as follows:

[0192] ,

[0193] In the formula, For the residual vector, For the first The residual vector of each main cable segment For the first The first main cable segment Two-dimensional linear coordinates of a linear coordinate point The residual, For transpose, For Jacobian matrices, It is the identity matrix. The damping factor, For the first The parameter vector of the catenary equation in the next iteration. For the first The parameter vector of the catenary equation in the next iteration.

[0194] The iteration termination condition is as follows:

[0195] ,

[0196] Where ε is the threshold value for the iteration parameter, and the recommended value for ε is 10. -6 ;

[0197] Finally, the parameters a and b of the catenary equation for the main cable segment are obtained. m and cm .

[0198] Based on the fitted piecewise catenary equation parameters , and Calculate the geometric parameters of each main cable segment, the first... The formula for calculating the geometric parameters of each main cable segment is as follows:

[0199] ,

[0200] In the formula, For the first The horizontal distance between each main cable segment; For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The x-axis coordinates of the intersection points of the suspenders and the main cable; For the first The elevation difference between the two ends of each main cable segment; and The first The tangent angle of the main cable at both ends of each main cable segment; It is a hyperbolic sine function. It is the arctangent function.

[0201] The main cable force calculation module is used to calculate the actual horizontal force on the main cable based on the geometric parameters of each main cable segment and using the catenary theory in a stress-free state. .

[0202] The main cable force calculation module assumes the initial horizontal force of the main cable is... According to the mechanical characteristics of suspension bridges, the horizontal force in each main cable segment remains constant; based on the first Horizontal distance of each main cable segment and the angle of the main cable tangent at the endpoint Using the catenary theory in a stress-free state, the initial horizontal force on the main cable is calculated. Under the action of the first Theoretical elevation difference of each main cable segment The calculation formula is:

[0203] ,

[0204] In the formula, For the first Vertical force at the end of each main cable segment; L 0,m For the first The stress-free length of each main cable segment is determined by the horizontal distance. Calculated; The elastic modulus of the main cable. The cross-sectional area of ​​the main cable. The unit weight of the main cable. , , All were obtained from design data; It is an inverse hyperbolic sine function. It is the tangent function.

[0205] Establish theoretical height difference Elevation difference between the two endpoints The objective function for the sum of squared residuals is expressed as:

[0206] ,

[0207] In the formula, M is the number of main cable segments. Let be the objective function for the sum of squared residuals.

[0208] By adjusting the horizontal force H0 of the main cable, the objective function is achieved. The minimum value corresponds to the actual horizontal force H of the main cable.

[0209] The cable force calculation module is used to calculate the actual horizontal force of the main cable. And the tangent angle of the main cable at the end of each main cable segment, using the principle of nodal force balance, to calculate the corresponding suspender force. .

[0210] In the sling force calculation module, at the intersection of the sling and the main cable, the vertical forces of adjacent main cable segments satisfy the equilibrium condition, and the static equilibrium equation of the sling is established, expressed as follows:

[0211] ,

[0212] In the formula, For the first Vertical force at the endpoints of each main cable segment For the first The suspender force corresponding to each main cable segment This represents the vertical force at the endpoint of the (m+1)th main cable segment.

[0213] Based on the tangent angle of the main cable at both ends of each main cable segment and the actual horizontal force H of the main cable, the corresponding suspender force is calculated using the vertical force balance equation. The calculation formula is:

[0214] ,

[0215] in For the first The tangent angle of the main cable at the end of each main cable segment. For the first The tangent angle of the main cable at the end of each main cable segment. and They share the same sling.

[0216] Example 3: An electronic device according to the present invention includes a processor and a storage medium;

[0217] Storage media are used to store instructions;

[0218] The processor is configured to operate according to the instructions to perform the steps of the method described above.

[0219] Example 4: The computer-readable storage medium of the present invention stores a computer program thereon, which, when executed by a processor, implements the steps of the method described above.

Claims

1. A rapid method for determining the main cable force and suspender force of a suspension bridge based on three-dimensional point clouds, characterized in that, Includes the following steps: (1) The main cable and suspenders of the suspension bridge under test are scanned to obtain the original point cloud data. After preprocessing, the point cloud data of the main cable segments between adjacent suspenders are obtained. and cable point cloud data ; (2) Point cloud data of main cable segments Perform cross-sectional fitting to extract the linear coordinates of the main cable segments. ; (3) Based on the point cloud data of the suspension cable Determine the x-axis coordinate of each intersection point of the suspender and the main cable in the global Cartesian coordinate system. ; (4) Based on the main cable segment coordinates extracted in step (2) The x-axis coordinates of each intersection point of the sling and the main cable determined in step (3) Based on the segmented catenary theory, the geometric morphological parameters of each main cable segment are obtained by performing an overall fitting on each main cable segment. The geometric parameters of each main cable segment include horizontal distance. Elevation difference between the two endpoints and the tangent angle of the main cable at both ends and ; Step (4) specifically includes the following steps: (4.1) The alignment of each main cable segment follows the catenary equation. Assume that the first segment... The alignment of each main cable segment satisfies the catenary equation: ， In the formula, , and The parameters for the catenary equations are as follows: since the horizontal force is the same in each main cable segment, the corresponding segmented catenary equations are... They are all the same; Let be the independent variable of the equation. It is a hyperbolic cosine function. For the first The catenary equation satisfied by the alignment of each main cable segment; (4.2) The coordinates of the main cable segments Project to From the plane, we obtain the two-dimensional linear coordinates of the main cable segment. Establish the objective function that minimizes the sum of squared residuals. The expression is: ， In the formula, Where N is the number of main cable segments, N is the number of linear coordinate points in each main cable segment, and P is the parameter vector of the catenary equation. The two-dimensional linear coordinates of the nth linear coordinate point in each main cable segment. It is the sum of squared residuals; (4.3) Based on the intersection of each sling and the main cable Axis coordinates To satisfy the elevation continuity condition, a system of continuity constraint equations is established, expressed as follows: ， In the formula, g represents the system of continuous constraint equations. The catenary equation satisfied by the alignment of the first main cable segment. The catenary equation satisfied by the alignment of the second main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. The first sling intersects with the main cable. Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates; (4.4) Based on the objective function and constraint equations obtained in steps (4.2) and (4.3), the Levenberg-Marquardt algorithm is used for iterative solution. The iterative formula is as follows: ， In the formula, For the residual vector, For the first The residual vector of each main cable segment For the first The first main cable segment Two-dimensional linear coordinates of a linear coordinate point The residual, For transpose, For Jacobian matrices, It is the identity matrix. The damping factor, For the first The parameter vector of the catenary equation in the next iteration. For the first The catenary equation parameter vector for the next iteration; The iteration termination condition is as follows: ， in, For the iterative parameter threshold, The recommended value is 10. -6 ; Finally, the parameters of the catenary equation for each segment of the main cable were obtained. , and ; (4.5) Based on the piecewise catenary equation parameters obtained by fitting in step (4.4) , and Calculate the geometric parameters of each main cable segment, the first... The formula for calculating the geometric parameters of each main cable segment is as follows: ， In the formula, For the first The horizontal distance between each main cable segment; For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The x-axis coordinates of the intersection points of the suspenders and the main cable; For the first The elevation difference between the two ends of each main cable segment; and The first The tangent angle of the main cable at both ends of each main cable segment; It is a hyperbolic sine function. It is the arctangent function; (5) Based on the geometric parameters of each main cable segment determined in step (4), the actual horizontal force of the main cable is calculated using the catenary theory in the stress-free state. ; (6) The actual horizontal force of the main cable calculated according to step (5) And using the tangent angle of the main cable at the end of each main cable segment obtained in step (4), the corresponding suspending cable force is calculated using the principle of nodal force balance. .

2. The method for rapid determination of main cable force and suspension cable force of a suspension bridge based on three-dimensional point cloud as described in claim 1, characterized in that: Step (1) specifically includes the following steps: (1.1) Use a 3D laser scanner to scan the main cable and suspenders of the suspension bridge under test to obtain the original point cloud data of the main cable and suspenders; (1.2) Transform the original point cloud data of the main cable and suspenders to the global Cartesian coordinate system to obtain the point cloud data of the main cable and suspenders. In the global Cartesian coordinate system The axis is the longitudinal direction of the bridge. The axis is in the transverse direction of the bridge. The axis is in the height direction of the main cable; (1.3) Point cloud data The data is segmented to separate the point cloud data of the main cable segments between adjacent suspension cables. and cable point cloud data The point cloud data of the suspension cables includes cable clips.

3. The method for rapid determination of main cable force and suspension cable force of a suspension bridge based on three-dimensional point cloud as described in claim 1, characterized in that: Step (2) specifically includes the following steps: (2.1) Point cloud data of main cable segments Slice the bridge at equal intervals along its longitudinal direction, with horizontal spacing. Step size, The value range is 0.1m to 1m, and the thickness of the slice is... , The value range is 0.01m to 0.02m, generating point cloud slices. ; (2.2) Slice the point cloud Projected to By projecting point cloud slices onto the cross-section of the main cable in the axial plane, a cross-sectional point cloud is obtained. Point clouds from cross-section Randomly sample 3 points and calculate the center coordinates and radius of the circle formed by the 3 points; repeat the above steps. The radius sample was obtained the next time. , The number of points in the point cloud slice; then the radius sample Perform probability density statistics and take the radius value corresponding to the peak value of the probability density. and the center ; Retain With center at and radius at, Point cloud data within the range, The tolerance threshold is determined by the minimum distance between the main cable surface and the auxiliary facilities, and the calculation formula is as follows: ， Finally, the denoised cross-sectional point cloud is obtained. ; (2.3) Then based on the design radius of the main cable The least squares method is used to fit the circular curve of the cross section of the point cloud slice. Let the equation of the circular curve be: ， In the formula, The coordinates of the center of the circular curve; The coordinates of the center of the circular curve were calculated using the least squares method. The calculation formula is: ， (2.4) Based on the coordinates of the center of the fitted circular curve Computational point cloud slicing Centroid coordinates inside The calculation formula is: ， In the formula, Slicing point clouds middle The maximum value; Slicing point clouds middle The minimum value; (2.5) Repeat steps (2.2) to (2.4) to calculate the centroid coordinates of all point cloud slices in all main cable segments. Main cable segment coordinates Centroid coordinates of all point cloud slices in all main cable segments A set of.

4. The method for rapid determination of main cable force and suspension cable force of a suspension bridge based on three-dimensional point cloud as described in claim 1, characterized in that: Step (3) specifically includes the following steps: (3.1) From the point cloud data of the suspension cable In the process, the point cloud data of the cable clamp area is separated and removed, while the point cloud data of the main cable body between the upper and lower anchoring ends is retained. ; (3.2) Calculate the point cloud data of the main body of the suspension cable exist Midpoint of the axis The midpoint is the intersection point of each sling and the main cable in the global Cartesian coordinate system. The formula for calculating the axis coordinates is: 。 5. The method for rapid determination of main cable force and suspension cable force of a suspension bridge based on three-dimensional point cloud as described in claim 1, characterized in that: Step (5) specifically includes the following steps: (5.1) Assume the initial horizontal force on the main cable is According to the mechanical characteristics of suspension bridges, the horizontal force of each main cable segment remains constant; based on the result obtained in step (4), the first... Horizontal distance of each main cable segment and the angle of the main cable tangent at the endpoint Using the catenary theory in a stress-free state, the initial horizontal force on the main cable is calculated. Under the action of the first Theoretical elevation difference of each main cable segment The calculation formula is: ， In the formula, For the first Vertical force at the endpoints of each main cable segment; L 0,m For the first The stress-free length of each main cable segment is determined by the horizontal distance. Calculated; The elastic modulus of the main cable. The cross-sectional area of ​​the main cable. The unit weight of the main cable. , , All were obtained from design data; It is an inverse hyperbolic sine function. It is the tangent function; (5.2) Establishing the theoretical elevation difference The elevation difference between the two endpoints obtained in step (4) The objective function for the sum of squared residuals is expressed as: ， In the formula, Number of main cable segments Let the objective function be the sum of squared residuals; (5.3) By adjusting the initial horizontal force of the main cable , so that the objective function The minimum value corresponds to the actual horizontal force on the main cable. .

6. The method for rapid determination of main cable force and suspension cable force of a suspension bridge based on three-dimensional point cloud as described in claim 1, characterized in that: Step (6) specifically includes the following steps: (6.1) At the intersection of the suspender and the main cable, the vertical forces of adjacent main cable segments satisfy the equilibrium condition. The static equilibrium equation of the suspender is established as follows: ， In the formula, For the first Vertical force at the endpoints of each main cable segment For the first The suspender force corresponding to each main cable segment The vertical force at the end point of the (m+1)th main cable segment; (6.2) Based on the tangent angle of the main cable at both ends of each main cable segment obtained in step (4) and the actual horizontal force H of the main cable obtained in step (5), calculate the corresponding suspender force using the vertical force balance equation. The calculation formula is: ， in For the first The tangent angle of the main cable at the end of each main cable segment. For the first The tangent angle of the main cable at the end of each main cable segment. and They share the same sling.

7. A rapid measurement system for the main cable force and suspender force of a suspension bridge based on three-dimensional point clouds, characterized in that, include: The point cloud data preprocessing module is used to scan the main cable and suspenders of the suspension bridge under test to obtain raw point cloud data, and then preprocess the data to obtain point cloud data of the main cable segments between adjacent suspenders. and cable point cloud data ; The linear coordinate extraction module is used for the point cloud data of the main cable segments. Perform cross-sectional fitting to extract the linear coordinates of the main cable segments. ; The intersection point coordinate determination module is used to determine the coordinates of the intersection points based on the cable point cloud data. Determine the x-axis coordinate of each intersection point of the suspender and the main cable in the global Cartesian coordinate system. ; The morphological parameter fitting module is used to fit the linear coordinates of the main cable segments. x-axis coordinates of each sling intersection with the main cable Based on the segmented catenary theory, the geometric morphological parameters of each main cable segment are obtained by performing an overall fitting on each main cable segment. The geometric parameters of each main cable segment include horizontal distance. Elevation difference between the two endpoints and the tangent angle of the main cable at both ends and ; In the morphological parameter fitting module, the linear shape of each main cable segment follows the catenary equation. Assuming the... The alignment of each main cable segment satisfies the catenary equation: ， In the formula, , and The parameters for the catenary equations are as follows: since the horizontal force is the same in each main cable segment, the corresponding segmented catenary equations are... They are all the same; Let be the independent variable of the equation. It is a hyperbolic cosine function. For the first The catenary equation satisfied by the alignment of each main cable segment; The linear coordinates of the main cable segment Project to From the plane, we obtain the two-dimensional linear coordinates of the main cable segment. Establish the objective function that minimizes the sum of squared residuals. The expression is: ， In the formula, Where N is the number of main cable segments, N is the number of linear coordinate points in each main cable segment, and P is the parameter vector of the catenary equation. The two-dimensional linear coordinates of the nth linear coordinate point in each main cable segment. It is the sum of squared residuals; Based on the intersection of each sling and the main cable Axis coordinates To satisfy the elevation continuity condition, a system of continuity constraint equations is established, expressed as follows: ， In the formula, g represents the system of continuous constraint equations. The catenary equation satisfied by the alignment of the first main cable segment. The catenary equation satisfied by the alignment of the second main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. For the first The catenary equation satisfied by the alignment of each main cable segment. The first sling intersects with the main cable. Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The intersection of the suspender cable and the main cable Axis coordinates; Based on the obtained objective function and constraint equations, the Levenberg-Marquardt algorithm is used for iterative solution. The iterative formula is as follows: ， In the formula, For the residual vector, For the first The residual vector of each main cable segment For the first The first main cable segment Two-dimensional linear coordinates of a linear coordinate point The residual, For transpose, For Jacobian matrices, It is the identity matrix. The damping factor, For the first The parameter vector of the catenary equation in the next iteration. For the first The catenary equation parameter vector for the next iteration; The iteration termination condition is as follows: ， in, For the iterative parameter threshold, The recommended value is 10. -6 ; Finally, the parameters of the catenary equation for each segment of the main cable were obtained. , and ; Based on the fitted piecewise catenary equation parameters , and Calculate the geometric parameters of each main cable segment, the first... The formula for calculating the geometric parameters of each main cable segment is as follows: ， In the formula, For the first The horizontal distance between each main cable segment; For the first The intersection of the suspender cable and the main cable Axis coordinates For the first The x-axis coordinates of the intersection points of the suspenders and the main cable; For the first The elevation difference between the two ends of each main cable segment; and The first The tangent angle of the main cable at both ends of each main cable segment; It is a hyperbolic sine function. It is the arctangent function; The main cable force calculation module is used to calculate the actual horizontal force on the main cable based on the geometric parameters of each main cable segment and using the catenary theory in a stress-free state. ; The cable force calculation module is used to calculate the actual horizontal force of the main cable. And the tangent angle of the main cable at the end of each main cable segment, using the principle of nodal force balance, to calculate the corresponding suspender force. .

8. An electronic device, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 6.

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