A method for determining cable force of a stay cable based on three-dimensional laser point cloud

Abstract

The application discloses a method for measuring cable force of a cable-stayed cable based on three-dimensional laser point clouds, which is characterized by the following steps: obtaining point cloud data of the cable-stayed cable by three-dimensional laser scanning, fitting the measured linear shape of the cable-stayed cable, combining with a finite element calculation method, finding the linear shape of a finite element model of the cable-stayed cable which is the same as the measured linear shape of the cable-stayed cable, and determining the actual cable force of the cable-stayed cable, so as to accurately measure the cable force of the cable-stayed cable. The three-dimensional laser scanning technology is introduced into the measurement of the cable force of the cable-stayed cable, and the non-contact measurement, high measurement accuracy and high measurement efficiency of the three-dimensional laser scanning technology are utilized to realize the rapid measurement of the linear shape and the cross-sectional size of the cable-stayed cable. On the basis of the finite element calculation and analysis, the method for measuring the cable force of the cable-stayed cable based on the three-dimensional laser point clouds is provided, and the rapid and efficient measurement of the cable force of the cable-stayed cable is realized.

Description

Technical Field

[0001] This invention belongs to the field of point cloud reverse modeling, and particularly relates to a method for measuring the cable force of a cable-stayed bridge based on three-dimensional laser point clouds. Background Technology

[0002] Cable-stayed bridges are a mature cable-stayed bridge structure with greater spanning capacity than traditional beam bridges, and are widely used in river and sea crossing projects. Cable-stayed bridges have several symmetrically distributed stay cables and are classified as highly statically indeterminate structures, making them one of the most complex structural forms in terms of stress distribution. The stay cables connect the towers and the main girder, responsible for transferring the load between the towers and the main girder, and are crucial load-bearing components of the cable-stayed bridge. Therefore, accurately measuring the cable forces is of great significance for assessing the operational status of cable-stayed bridges.

[0003] In engineering practice, commonly used methods for measuring cable force in stay cables include the pressure sensor method, the electromagnetic field method, and the vibration frequency method. The pressure sensor method is generally only applicable to measuring cable force during the tensioning process in stay cable construction. The electromagnetic field method requires prior determination of the cable material properties and fabrication of induction coils, which is very costly. The vibration frequency method is an indirect method for cable force identification. It first requires accurate determination of the fundamental frequency or several frequencies of the stay cable, and then the cable force is calculated based on relevant theories. This method demands high accuracy from the vibration pickup used to identify the stay cable frequency and the vibration test signal.

[0004] In recent years, the application of 3D laser scanning technology in bridge surveying has shown a gradual increasing trend. 3D laser scanning technology uses high-speed laser scanning to rapidly acquire large-area, high-resolution 3D coordinate data of the surface of the object being measured, enabling the rapid and large-scale collection of spatial point information to form point cloud data. Therefore, how to utilize 3D laser scanning technology to determine the cable force of cable stays has become a major research topic in this field. Summary of the Invention

[0005] Purpose of the invention: To address the shortcomings of existing methods for measuring the cable force of cable-stayed bridges, the present invention aims to provide a method for measuring the cable force of cable-stayed bridges based on three-dimensional laser point clouds, which can quickly and efficiently complete the measurement of the cable force of cable-stayed bridges.

[0006] Technical solution: The present invention provides a method for determining the cable force of a cable-stayed bridge based on three-dimensional laser point clouds, comprising the following steps:

[0007] Step 1: Use a 3D laser scanner to scan the cable surface of the cable-stayed bridge under test to obtain point cloud data {x,y,z} of a single cable;

[0008] Step 2: Fit the cross-sectional dimensions of a single stay cable to the point cloud data {x,y,z} to determine the cross-sectional dimension r of the stay cable. r and the measured linear coordinates of the cable-stayed bridge {x ci,y ci ,z ci};

[0009] Step 3: Establish the finite element model of the cable-stayed bridge;

[0010] Step 4: Perform calculation and analysis on the finite element model of the cable-stayed bridge, and extract the linear coordinates {x} of the cable-stayed bridge obtained from the calculation of the finite element model. Fi ,z Fi} and cable tension;

[0011] Step 5: Calculate the linear coordinates of the stay cable obtained from the finite element model of the stay cable {x}. Fi ,z Fi After fitting, the coordinates of the cable-stayed bridge are compared with the measured linear coordinates of the cable. ci ,y ci ,z ci If the two lines are the same, the cable force calculated by the finite element model of the cable is the actual cable force. If the two lines are different, the cable tension is added to the finite element model of the cable, and steps 3 to 5 are repeated until the two lines are the same, and the actual cable force is obtained.

[0012] Furthermore, step 1 specifically includes the following steps:

[0013] Step 1.1: After scanning the cable surface of the cable-stayed bridge under test using a 3D laser scanner, the point cloud data of the cable surface under test is collected;

[0014] Step 1.2: Rotate the coordinate system of the cable surface point cloud data to a coordinate system with the cable length direction horizontal. In the coordinate system, the cable length direction is the x-axis, the horizontal direction perpendicular to the cable length direction is the y-axis, and the cable height direction is the z-axis. Then extract the point cloud data {x,y,z} of a single cable from it.

[0015] Furthermore, step 2 specifically includes the following steps:

[0016] Step 2.1: Cable-stayed bridge point cloud data segmentation: In the cable-stayed bridge point cloud data {x,y,z}, extract point cloud segments {x} along the x-axis direction at horizontal lengths of ΔL. i ,y i ,z i},as follows:

[0017]

[0018]

[0019] Among them, m is the number of point cloud segments, rounded up, and the value of ΔL ranges from 0.1 meter to 1 meter, ensuring that there are enough points for the circular curve fitting of the cross-section of the point cloud segment to reduce the fitting random error; x max is the maximum value of x in the point cloud segment {x i , y i , z i}; x i is the minimum value of x in the point cloud segment {x min , y i , z i , z i}.

[0020] Step 2.2: Determination of the projection angle of the cross-section of the point cloud segment: Determine the projection angle α according to two points in the point cloud segment {x i , y i , z i}. Point A (x A , y A , z A ) is the point corresponding to the minimum value in the z-axis direction in {x i , y i , z i}, and point B (x B , y B , z B ) is the point corresponding to the minimum value in the z-axis direction on the side corresponding to point A in the x-axis direction. The calculation is as follows:

[0021]

[0022] Among them, x i,zA and y i,zA are the x and y coordinate values of the point corresponding to the minimum value z i , y i , z i} in {x i , and x i,min and y i,zB are the x and y coordinate values of the point corresponding to the minimum value z i,zB on the side corresponding to point A in the x-axis direction in {x i , y i , z i )};

[0023] ) Project point A and point B onto the xz-axis plane. At this time, the coordinates of point A are (x A , z A ), and the coordinates of point B are (x B , z B ). Calculate the projection angle α of the point cloud segment according to point A and point B as follows:​​​​​

[0024]

[0025] Step 2.3: Projection of the cross-section of the point cloud segment: Point cloud segment {x i ,y i ,z i Taking point A as the reference point, rotate the point cloud in the xz-axis plane by an angle α to obtain the rotated point cloud segment {x w ,y w ,z w The calculation is as follows:

[0026] x w =(x i -x A )cosα-(z i -z A sinα+x A

[0027] y w =y i

[0028] z w =(x i -x A )sinα+(z i -z A cosα+z A

[0029] In the formula, α is the projection angle of the point cloud segment;

[0030] Cut the rotated point cloud into segments {x w ,y w ,z w Projecting the point cloud segments onto the yz-axis plane completes the projection of the point cloud segments onto the cross-section perpendicular to the cable tangent, obtaining the cross-sectional point cloud {y w ,z w};

[0031] Step 2.4: Circular Curve Fitting of Point Cloud Segment Cross-Section: The least squares method is used to fit the circular curve of the point cloud segment cross-section. Let the circular curve be:

[0032] (yy r ) 2 +(zz r ) 2 =r 2

[0033] The cross-sectional point cloud {y} is calculated using the least squares method. w ,z w The center coordinates (y) of the fitted circular curve r ,zr And the radius r, as follows:

[0034]

[0035]

[0036]

[0037] in

[0038]

[0039] b=n∑y w z w -∑y w ∑z w

[0040]

[0041]

[0042]

[0043] In the formula, n represents the cross-sectional point cloud {y} w ,z w The number of midpoints;

[0044] Step 2.5: Fitting the circular curve of the cross-section of the point cloud segment with low arc coverage: When the cross-section point cloud {y w ,z w When the coverage on the arc is low, the cross-sectional point cloud {y} w ,z w The estimation of the radius has a large error. It is necessary to estimate the coordinates of the center of the circle given the radius of the circular curve. Let the circular curve be:

[0045] (yy r ) 2 +(zz r ) 2 =r0 2

[0046] In the formula, r0 is the radius of the circular curve obtained from the cross-section of the point cloud segment with high arc coverage. Then, the cross-sectional point cloud {y} is calculated according to the least squares method in step 2.4. w ,z w The center coordinates (y) of the fitted circular curve r ,z r );

[0047] Step 2.6: Calculate the linear coordinates of the point cloud segments: Based on the radius r and center coordinates (y) of the fitted circular curve. r ,zr ) Calculate point cloud segments {x w ,y w ,z w The centroid coordinates (x0, y0, z0) within the area are calculated as follows:

[0048]

[0049] y0=y r

[0050] z0=z r

[0051] In the formula, x A Let A be the x-axis coordinate value, and ΔL be the horizontal length of the point cloud segment along the x-axis.

[0052] Point A (x A ,z A Using y0, y0, z0 as the reference point, rotate the centroid coordinates (x0, y0, z0) in the xz-axis plane to the initial point cloud segment {x i ,y i ,z i The position of point cloud segment is obtained by rotating it in the xz-axis plane with point A as the reference point by an angle of -α. c ,y c ,z c The details are as follows:

[0053] x c =(x0-x A cos(-α)-(z0-z) A sin(-α)+x A

[0054] y c =y0

[0055] z c =(x0-x A sin(-α)+(z0-z) A cos(-α)+z A

[0056] Step 2.7: Calculation of measured linear coordinates and cross-sectional dimensions of the stay cable: Repeat steps 2.2 to 2.6 to calculate the linear coordinates (x, y, x) of all point cloud segments of the stay cable. c ,y c ,z c ) and the radius r of the fitted circular curve of the cross section, and the measured coordinates of the cable-stayed cable's linear shape at point {x ci ,y ci ,z ci} represents the linear coordinates (x, y) of all point cloud segments. c ,yc ,z c The measured cross-sectional dimensions of the stay cable are the average value of the radius r of the fitted circular curve of all point cloud segments. r The calculation is as follows:

[0057]

[0058]

[0059] In the formula, m is the number of point cloud segments.

[0060] Furthermore, step 3 specifically includes the following steps:

[0061] Step 3.1: Establishing the straight section of the stay cable: Establish the measured linear coordinates of the stay cable at {x... ci ,y ci ,z ci Project the coordinates (x, z) of the connection point P1 between the stay cable and the main beam onto the xz-axis plane. P1 ,z P1 ) and the coordinates (x) of the connection point P2 between the cable and the tower. P2 ,z P2 A two-dimensional straight component for the cable-stayed bridge is established using points P1 and P2.

[0062] Step 3.2: Set cross-section properties: Assign cross-section properties to the stay cable component, setting the cross-section type to solid circle and the cross-section radius to the measured cross-section size r of the stay cable. r ;

[0063] Step 3.3: Material Property Setting: For the cable-stayed bridge material properties, obtain the elastic modulus E, density ρ, and coefficient of linear expansion α from the cable-stayed bridge engineering drawings. c Three parameters;

[0064] Step 3.4: Boundary condition setting: Set both ends of the cable-stayed cable component to be hinged, that is, do not constrain the rotation angle, but constrain the displacement in the x, y, and z directions;

[0065] Step 3.5: Element type selection: Assign the cable-stayed component as a beam element, and select B21 two-node planar linear beam element;

[0066] Step 3.6: Apply gravity load: In the finite element model of the cable stays, a gravitational acceleration g is set vertically downward in the z-axis direction to simulate the self-weight of the cable stays. The g value is 9.8 m / s². 2 ;

[0067] Step 3.7: Initial Temperature Calculation of the Temperature Field: By "cooling" the stay cable by a temperature difference Δt, the stay cable is shortened. Due to the constraints of the boundary conditions, a tension force ΔT is generated in the stay cable. The simulation of applying a tension force ΔT in the stay cable is calculated as follows:

[0068]

[0069] In the formula, E is the elastic modulus of the cable, A is the cross-sectional area of ​​the cable, and α is the elastic modulus of the cable. c The linear expansion coefficient of the cable-stayed bridge;

[0070] Step 3.8: Temperature field setting: In the temperature field analysis step, set the temperature field for the finite element model of the cable stay, and reduce the temperature from Δt to 0℃ to simulate the tensioning process of the cable stay.

[0071] Furthermore, step 4 specifically includes the following steps:

[0072] Step 4.1: Finite element model analysis and calculation of the stay cables;

[0073] Step 4.2: Cable-stayed unit node coordinates {x} Fi ,z Fi} and support reaction force R F After the finite element model calculation of the cable-stayed bridge is completed, the coordinates of all element nodes {x} are extracted. Fi ,z Fi The support reaction force R at the connection point P1 between the cable and the beam. F .

[0074] Furthermore, step 5 specifically includes the following steps:

[0075] Step 5.1: Determining the line shape of the finite element model of the cable stay: Determine the coordinates of the nodal nodes of the cable stay elements {x Fi ,z Fi Two adjacent points within a line are fitted together using multiple line segments f. i To approximate the shape of the cable-stayed bridge's linear curve using (x), let f be a multi-segment linear function. i (x) is:

[0076] f i (x)=a i x+b i

[0077] Among them, a i Let b be the slope of the line between any two adjacent points. i The intercepts of the line between each pair of adjacent points are as follows:

[0078]

[0079] b i =z F(i) -a i x F(i)

[0080] In the formula, x F(i) and x F(i+1)The x-axis coordinates of two adjacent points in the coordinate system of a cable-stayed unit are given by z. F(i) and z F(i+1) The z-axis coordinate value of two adjacent points in the coordinate system of the cable-stayed unit node;

[0081] Step 5.2: Calculation of corresponding points of the measured alignment coordinates of the stay cable: The measured alignment coordinates of the stay cable {x...} ci ,y ci ,z ci Projecting onto the xz-axis plane, calculate the measured linear coordinates of the stay cables in multiple linear function f. i For points with the same x-axis coordinate in (x), the x-axis coordinates of the cable-stayed bridge will be used to represent the x-axis coordinates of the cable-stayed bridge. ci Substitute f i (x), calculate the z-axis coordinate of the corresponding point. di Then the corresponding point is {x} ci ,z di The calculation is as follows:

[0082] z di =f i (x ci )

[0083] Step 5.3: Calculation of the distance between the measured coordinate points of the cable-stayed cable and the corresponding points: Since the measured coordinates {x ci ,z ci} and corresponding point {x ci ,z di If the x-axis coordinates of the two objects are the same, then the average distance Z between them is:

[0084]

[0085] In the formula, n is the number of measured linear coordinates of the cable-stayed bridge;

[0086] Step 5.4: Comparison of cable alignment: The smaller Z is, the closer the measured alignment of the cable is to the alignment calculated by the finite element model. Determine whether Z meets the allowable error ε, as follows:

[0087] |Z|≤ε

[0088] If this condition is met, it means that the measured alignment of the stay cable is approximately the same as the alignment calculated by the finite element model of the stay cable. Under this condition, the support reaction force R is obtained. F The actual cable force R is obtained by increasing the initial tension ΔT in step 3.7 and repeating steps 3 to 5 to make the alignment calculated by the finite element model of the cable approximate the actual alignment of the cable until the condition is met. F .

[0089] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0090] This invention introduces three-dimensional laser scanning technology for the determination of cable-stayed bridge forces. Addressing the shortcomings of commonly used methods, it proposes a cable-stayed bridge force determination method based on three-dimensional laser point clouds. This method utilizes the non-contact measurement, high accuracy, and high efficiency of three-dimensional laser scanning technology to achieve rapid measurement of the cable's alignment and cross-sectional dimensions. Based on finite element analysis, it identifies the alignment of a finite element model of the cable that matches the measured alignment, thereby determining the actual cable force and achieving rapid and efficient determination of the cable force. Attached Figure Description

[0091] Figure 1 This is a flowchart illustrating the overall steps of a method for determining cable tension based on three-dimensional laser point clouds according to the present invention.

[0092] Figure 2 This is a further schematic diagram of step 1 of the present invention;

[0093] Figure 3 The following is a more detailed flowchart of step 2 of the present invention;

[0094] Figure 4 This is a schematic diagram illustrating the calculation of the projection angle α of the point cloud segment cross-section in step 2.2 of this invention;

[0095] Figure 5 The following is a flowchart of further detailed steps 3 to 5 of the present invention. Detailed Implementation

[0096] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0097] This invention selects two stay cables, A6 and A26, from a cable-stayed bridge in China as examples. The actual cable force data for these two cables allows for comparative verification of the technical solution proposed in this invention. Figures 1 to 5 As shown, a method for determining the cable force of a cable-stayed bridge based on three-dimensional laser point clouds includes the following steps:

[0098] Step 1: Use a 3D laser scanner to scan the cable surface of the cable-stayed bridge under test to obtain the point cloud data {x,y,z} of a single cable of the cable-stayed bridge under test.

[0099] Step 2: Fit the cross-sectional dimensions of the stay cable to determine the cross-sectional dimension r of the stay cable. r and the measured linear coordinates of the cable-stayed bridge {x ci ,y ci ,z ci The specific steps are as follows:

[0100] Step 2.1: Cable-stayed bridge point cloud data segmentation. From the cable-stayed bridge point cloud data, extract point cloud segments along the x-axis in 0.5-meter horizontal segments {x...} i ,y i ,z i The calculation is as follows:

[0101]

[0102]

[0103] Where m is the number of point cloud segments, rounded up.

[0104] Step 2.2: Determine the projection angle of the cross-section of the point cloud segment. Based on the point cloud segment {x i ,y i ,z i Point A (x) inside} A ,y A ,z A ) and point B (x B ,y B ,z B The projection angle α is calculated as follows:

[0105]

[0106] Where, x i,zA and y i,zA For {x i ,y i ,z i}inner z i Minimum value z i,min The x and y coordinates of the corresponding point. i,zB and y i,zB For {x i ,y i ,z i The z-axis of point A on the side corresponding to point A in the x-axis direction. i Minimum value z i,min，xB The x and y coordinates of the corresponding point.

[0107] like Figure 4 As shown, points A and B are projected onto the xz-axis plane. At this time, the coordinates of point A are (x... A ,z A The coordinates of point B are (x, y). B ,z B The projection angle α of the point cloud segment is calculated based on points A and B, as follows:

[0108]

[0109] Step 2.3: Projection of the cross-section of the point cloud segment. Point cloud segment {x}i ,y i ,z i Taking point A as the reference point, rotate the point cloud in the xz-axis plane by an angle α to obtain the rotated point cloud segment {x w ,y w ,z w The calculation is as follows:

[0110] x w =(x i -x A )cosα-(z i -z A sinα+x A

[0111] y w =y i

[0112] z w =(x i -x A )sinα+(z i -z A cosα+z A

[0113] Then cut the rotated point cloud into segments {x} w ,y w ,z w Projecting this onto the yz-axis plane yields the point cloud cross-section of the point cloud segment {y w ,z w}

[0114] Step 2.4: Circular curve fitting of the cross-section of the point cloud segment. The point cloud cross-section {y} is calculated using the least squares method. w ,z w The center coordinates (y) of the fitted circular curve r ,z r Given the radius r, the following calculations are performed:

[0115] Let the circular curve be:

[0116] (yy r ) 2 +(zz r ) 2 =r 2

[0117] The cross-sectional point cloud {y} is calculated using the least squares method. w ,z w The center coordinates (y) of the fitted circular curve r ,z r And the radius r, as follows:

[0118]

[0119]

[0120]

[0121] in

[0122]

[0123] b=n∑y w z w -∑y w ∑z w

[0124]

[0125]

[0126]

[0127] In the formula, n represents the cross-sectional point cloud {y} w ,z w The number of points in the middle of the}.

[0128] Step 2.5: Circular curve fitting for the cross-section of a point cloud segment with low arc coverage. When the arc coverage of the point cloud segment's cross-section is low, the coordinates of the circle center are estimated given a circle radius. The given circle radius is the radius of the circular curve obtained from the cross-section of the point cloud segment with high arc coverage. Then, the point cloud {y} of the cross-section is calculated using the least squares method in Step 2.4. w ,z w The center coordinates (y) of the fitted circular curve r ,z r ).

[0129] Step 2.6: Calculate the linear coordinates of the point cloud segments. Based on the fitted circular curve radius r and center coordinates (y... r ,z r ) Calculate point cloud segments {x i ,y i ,z i Linear coordinates (x) within} c ,y c ,z c The calculation is as follows:

[0130]

[0131] y0=y r

[0132] z0=z r

[0133] In the formula, x A Let A be the x-axis coordinate value, and ΔL be the horizontal length of the point cloud segment along the x-axis.

[0134] Point A (x A ,z A Using y0, y0, z0 as the reference point, rotate the centroid coordinates (x0, y0, z0) in the xz-axis plane to the initial point cloud segment {x i ,y i ,z i The position of point cloud segment is obtained by rotating it in the xz-axis plane with point A as the reference point by an angle of -α. c ,y c ,z c The details are as follows:

[0135] x c =(x0-x A cos(-α)-(z0-z) A sin(-α)+x A

[0136] y c =y0

[0137] z c =(x0-x A sin(-α)+(z0-z) A cos(-α)+z A

[0138] Step 2.7: Calculation of measured alignment coordinates and cross-sectional dimensions of the stay cable. Measured alignment coordinates of the stay cable {x ci ,y ci ,z ci} represents the linear coordinates (x, y) of all point cloud segments. c ,y c ,z c The measured cross-sectional dimensions of the stay cable are the average value of the radius r of the fitted circular curve of all point cloud segments. r The calculation is as follows:

[0139]

[0140]

[0141] In the formula, m is the number of point cloud segments.

[0142] Table 1 shows the comparison of the measured cross-sectional dimensions of the stay cables.

[0143] Table 1 Measured Cross-sectional Dimensions of Stay Cables

[0144]

[0145] Step 3: The finite element model of the stay cable is established and analyzed using ABAQUS finite element analysis software. The specific steps for establishing the finite element model of the stay cable are as follows:

[0146] Step 3.1: Establishing the straight section of the stay cable. The measured coordinates of the stay cable's alignment points {x... ci ,y ci ,z ci Project the coordinates (x, z) of the cable-stayed beam connection point P1 onto the xz-axis plane. P1 ,z P1 The coordinates (x) of the connection point P2 of the tower and the cable tower P2 ,z P2 Establish a two-dimensional straight component for the cable-stayed bridge using points P1 and P2.

[0147] Step 3.2: Set Section Properties. Assign section properties to the stay cable component, setting the section type to solid circle and the section radius to r. r .

[0148] Step 3.3: Setting material properties. Elastic modulus E, density ρ, and coefficient of linear expansion α. c All of these were obtained from the engineering drawings of the cable-stayed bridge.

[0149] Step 3.4: Boundary Condition Setting. Set both ends of the stay cable component to hinged, i.e., do not constrain rotation angles, but constrain displacement in the x, y, and z directions.

[0150] Step 3.5: Element type selection. Assign the cable-stayed components as beam elements, and select B21 two-node planar linear beam elements.

[0151] Step 3.6: Apply gravity load. In the finite element model of the stay cable, a gravitational acceleration g is set vertically downwards along the z-axis to simulate the self-weight of the stay cable; g is 9.8 m / s². 2 .

[0152] Step 3.7: Initial Temperature Calculation of the Temperature Field. By "cooling" the stay cable by a temperature difference Δt, the cable shortens. Due to boundary constraints, a tension force ΔT is generated in the stay cable. The simulation of applying tension force ΔT in the stay cable is calculated as follows:

[0153]

[0154] In the formula, E is the elastic modulus of the cable, A is the cross-sectional area of ​​the cable, and α is the elastic modulus of the cable. c is the linear expansion coefficient of the cable-stayed bridge.

[0155] Step 3.8: Temperature Field Setup. In the temperature field analysis step, set the temperature field for the finite element model of the cable-stayed bridge, with the temperature decreasing from Δt to 0℃ to simulate the cable-stayed bridge tensioning process.

[0156] Step 4: Perform calculation and analysis on the finite element model of the stay cable, and extract the linear coordinates {x} of the stay cable obtained from the calculation of the finite element model. Fi ,z Fi} and cable force R of the stay cable F The specific steps are as follows:

[0157] Step 4.1: Finite element model analysis and calculation of the cable-stayed bridge.

[0158] Step 4.2: Cable-stayed unit node coordinates {x} Fi ,z Fi} and support reaction force R F Extraction. After the finite element model calculation of the cable-stayed bridge is completed, the coordinates of all element node points {x} are extracted. Fi ,z Fi The support reaction force R at the connection point P1 between the cable and the beam. F .

[0159] Step 5.1: Determining the linearity of the finite element model of the stay cable. Determine the nodal coordinates of the stay cable elements {x... Fi ,z Fi Two adjacent points within a line are fitted together using multiple line segments f. i (x) is used to approximate the shape of the cable-stayed bridge's linear curve. Let f be a multi-segment linear function. i (x) is:

[0160] f i (x)=a i x+b i

[0161] Among them, a i Let b be the slope of the line between any two adjacent points. i The intercepts of the line between each pair of adjacent points are as follows:

[0162]

[0163] b i =z F(i) -a i x F(i )

[0164] In the formula, x F(i) and x F(i+1) The x-axis coordinates of two adjacent points in the coordinate system of a cable-stayed unit are given by z. F(i) and z F(i+1) The z-axis coordinates of two adjacent points in the coordinate system of the cable-stayed unit node are given.

[0165] Step 5.2: Calculate the corresponding points of the measured alignment coordinates of the stay cable. The measured alignment coordinates of the stay cable {x...} ci ,y ci,z ci Projecting this onto the xz-axis plane, the x-axis coordinates of the measured linear coordinates of the cable-stayed cable are... ci Substitute f i (x), calculate the z-axis coordinate of the corresponding point. di Then the corresponding point is {x} ci ,z di The calculation is as follows:

[0166] z di =f i (x ci )

[0167] Step 5.3: Calculate the distance between the measured coordinate points of the cable-stayed bridge and the corresponding points. Since the measured coordinates {x...} ci ,z ci} and corresponding point {x ci ,z di If the x-axis coordinates of the two objects are the same, then the average distance Z between them is:

[0168]

[0169] In the formula, n is the number of measured linear coordinates of the cable-stayed bridge.

[0170] Step 5.4: Comparison of cable alignment. The smaller Z is, the closer the measured cable alignment is to the alignment calculated by the finite element model. Determine if Z satisfies the allowable error ε as follows:

[0171] |Z|≤ε

[0172] If this condition is met, it means that the measured alignment of the stay cable is approximately the same as the alignment calculated by the finite element model of the stay cable. Under this condition, the support reaction force R is obtained. F This represents the actual cable force of the stay cable. If the condition is not met, the initial tension ΔT in step 3.7 needs to be increased, and steps 3 to 5 need to be repeated to make the alignment calculated by the finite element model of the stay cable approximate the actual alignment of the stay cable until the condition is met, thus obtaining the actual cable force R of the stay cable. F .

Claims

1. A method for determining the cable force of a cable-stayed bridge based on three-dimensional laser point clouds, characterized in that, Includes the following steps: Step 1: Use a 3D laser scanner to scan the cable surface of the cable-stayed bridge under test to obtain point cloud data {x, y, z} of a single cable; Step 2: Fit the cross-sectional dimensions of a single stay cable to the point cloud data {x, y, z} to determine the cross-sectional dimension r of the stay cable. r and the measured linear coordinates of the cable-stayed bridge {x ci , y ci , z ci }; Step 3: Establish the finite element model of the cable-stayed bridge; Step 3 specifically includes the following steps: Step 3.1: Establishing the straight section of the stay cable: Establish the measured linear coordinates of the stay cable at {x... ci , y ci , z ci Project the coordinates (x, z) of the connection point P1 between the stay cable and the main beam onto the xz-axis plane. P1 , z P1 ) and the coordinates (x) of the connection point P2 between the cable and the tower. P2 , z P2 A two-dimensional straight component for the cable-stayed bridge is established using points P1 and P2. Step 3.2: Set cross-section properties: Assign cross-section properties to the stay cable component, setting the cross-section type to solid circle and the cross-section radius to the measured cross-section size r of the stay cable. r ; Step 3.3: Material Property Setting: For the cable-stayed bridge material properties, obtain the elastic modulus E, density ρ, and coefficient of linear expansion α from the cable-stayed bridge engineering drawings. c Three parameters; Step 3.4: Boundary condition setting: Set both ends of the cable-stayed cable component to be hinged, that is, do not constrain the rotation angle, but constrain the displacement in the x, y, and z directions; Step 3.5: Element type selection: Assign the cable-stayed component as a beam element, and select B21 two-node planar linear beam element; Step 3.6: Apply gravity load: In the finite element model of the cable stays, a gravitational acceleration g is set vertically downward in the z-axis direction to simulate the self-weight of the cable stays. The g value is 9.8 m / s². 2 ; Step 3.7: Initial Temperature Calculation of the Temperature Field: By "cooling" the stay cable by a temperature difference ∆t, the stay cable is shortened. Due to the constraints of the boundary conditions, a tension force ∆T is generated in the stay cable. The simulation of applying the tension force ∆T in the stay cable is calculated as follows: ； In the formula, E is the elastic modulus of the cable, A is the cross-sectional area of ​​the cable, and α is the elastic modulus of the cable. c The linear expansion coefficient of the cable-stayed bridge; Step 3.8: Temperature field setting: In the temperature field analysis step, set the temperature field for the finite element model of the cable stay, and reduce the temperature from ∆t to 0℃ to simulate the tensioning process of the cable stay. Step 4: Perform calculation and analysis on the finite element model of the cable-stayed bridge, and extract the linear coordinates {x} of the cable-stayed bridge obtained from the calculation of the finite element model. Fi , z Fi } and cable tension; Step 5: Calculate the linear coordinates of the stay cable obtained from the finite element model of the stay cable {x}. Fi , z Fi After fitting, the coordinates of the cable-stayed bridge are compared with the measured linear coordinates of the cable. ci , y ci , z ci If the two lines are the same, the cable force calculated by the finite element model of the cable is the actual cable force; if the two lines are different, the cable tension is added to the finite element model of the cable, and steps 3 to 5 are repeated until the two lines are the same, and the actual cable force is obtained. Step 5 specifically includes the following steps: Step 5.1: Determining the line shape of the finite element model of the cable stay: Determine the coordinates of the nodal nodes of the cable stay elements {x Fi , z Fi Two adjacent points within a line are fitted together using multiple line segments f. i To approximate the shape of the cable-stayed bridge's linear curve using (x), let f be a multi-segment linear function. i (x) is: ； Among them, a i Let b be the slope of the line between any two adjacent points. i The intercepts of the line between each pair of adjacent points are as follows: ； In the formula, x F(i) and x F(i+1) The x-axis coordinates of two adjacent points in the coordinate system of a cable-stayed unit are given by z. F(i) and z F(i+1) The z-axis coordinate value of two adjacent points in the coordinate system of the cable-stayed unit node; Step 5.2: Calculation of corresponding points of the measured alignment coordinates of the stay cable: The measured alignment coordinates of the stay cable {x...} ci , y ci , z ci Projecting onto the xz-axis plane, calculate the measured linear coordinates of the stay cables in multiple linear function f. i For points with the same x-axis coordinate in (x), the x-axis coordinates of the cable-stayed bridge will be used to represent the x-axis coordinates of the cable-stayed bridge. ci Substitute f i (x), calculate the z-axis coordinate of the corresponding point. di Then the corresponding point is {x} ci ,z di The calculation is as follows: ； Step 5.3: Calculation of the distance between the measured coordinate points of the cable-stayed cable and the corresponding points: Since the measured coordinates {x ci , z ci } and corresponding point {x ci , z di If the x-axis coordinates of the two objects are the same, then the average distance Z between them is: ； In the formula, n is the number of measured linear coordinates of the cable-stayed bridge; Step 5.4: Comparison of cable alignment: The smaller Z is, the closer the measured alignment of the cable is to the alignment calculated by the finite element model. Determine whether Z meets the allowable error ε, as follows: ； If this condition is met, it means that the measured alignment of the stay cable is approximately the same as the alignment calculated by the finite element model of the stay cable. Under this condition, the support reaction force R is obtained. F The actual cable force R is obtained by increasing the initial tension ∆T in step 3.7 and repeating steps 3 to 5 to make the alignment calculated by the finite element model of the cable approximate the actual alignment of the cable until the condition is met, thus obtaining the actual cable force R. F .

2. The method for determining the cable force of a cable-stayed bridge based on three-dimensional laser point clouds according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: After scanning the cable surface of the cable-stayed bridge under test using a 3D laser scanner, the point cloud data of the cable surface under test is collected; Step 1.2: Rotate the coordinate system of the cable surface point cloud data to a coordinate system with the cable length direction horizontal. In the coordinate system, the cable length direction is the x-axis, the horizontal direction perpendicular to the cable length direction is the y-axis, and the cable height direction is the z-axis. Then extract the point cloud data {x, y, z} of a single cable.

3. The method for determining the cable force of a cable-stayed bridge based on three-dimensional laser point clouds according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Cable-stayed bridge point cloud data segmentation: In the cable-stayed bridge point cloud data {x, y, z}, extract point cloud segments {x} along the x-axis direction at horizontal lengths of ΔL. i , y i , z i },as follows: ； Among them, m is the number of point cloud segments, rounded up, and the value of ΔL ranges from 0.1 meter to 1 meter, ensuring that there are enough points for fitting the circular curve of the cross-section of the point cloud segment to reduce the fitting random error; x max is the maximum value of x in the point cloud segment {x i , y i , z i}; x i is the minimum value of x in the point cloud segment {x min , y i , z i , z i}; i ​ Step 2.2: Determining the projection angle of the point cloud segment cross section: Based on the point cloud segment {x i , y i , z i The projection angle α is determined by two points within the plane, and point A (x) A , y A , z A ) is {x i , y i , z i The point B (x) corresponds to the minimum value along the z-axis. B , y B , z B Let A be the point corresponding to the minimum value of the z-axis on the side corresponding to point A in the x-axis direction. The calculation is as follows: ； Where, x i,zA and y i,zA For {x i , y i , z i }inner z i Minimum value z i,min The x and y coordinates of the corresponding point, x i,zB and y i,zB For {x i , y i , z i The z-axis of point A on the side corresponding to point A in the x-axis direction. i Minimum value z i,min，xB The x and y coordinates of the corresponding point; Projecting points A and B onto the xz-axis plane, the coordinates of point A are now (x...). A , z A The coordinates of point B are (x, y). B , z B ), calculate the projection angle α of the point cloud segment based on points A and B, as follows: ； Step 2.3: Projection of the cross-section of the point cloud segment: Point cloud segment {x i , y i , z i Taking point A as the reference point, rotate the point cloud in the xz-axis plane by an angle α to obtain the rotated point cloud segment {x w , y w , z w The calculation is as follows: ； In the formula, α is the projection angle of the point cloud segment; Cut the rotated point cloud into segments {x w , y w , z w Projecting the point cloud segments onto the yz-axis plane completes the projection of the point cloud segments onto the cross-section perpendicular to the cable tangent, obtaining the cross-sectional point cloud {y w , z w }; Step 2.4: Circular Curve Fitting of Point Cloud Segment Cross-Section: The least squares method is used to fit the circular curve of the point cloud segment cross-section. Let the circular curve be: ； The cross-sectional point cloud {y} is calculated using the least squares method. w , z w The center coordinates (y) of the fitted circular curve r , z r And the radius r, as follows: ； in ； In the formula, n represents the cross-sectional point cloud {y} w , z w The number of midpoints; Step 2.5: Fitting the circular curve of the cross-section of the point cloud segment with low arc coverage: When the cross-section point cloud {y w , z w When the coverage on the arc is low, the cross-sectional point cloud {y} w , z w The estimation of the radius has a large error. It is necessary to estimate the coordinates of the center of the circle given the radius of the circular curve. Let the circular curve be: ； In the formula, r0 is the radius of the circular curve obtained from the cross-section of the point cloud segment with high arc coverage. Then, the cross-sectional point cloud {y} is calculated according to the least squares method in step 2.

4. w , z w The center coordinates (y) of the fitted circular curve r , z r ); Step 2.6: Calculate the linear coordinates of the point cloud segments: Based on the radius r and center coordinates (y) of the fitted circular curve. r , z r ) Calculate point cloud segments {x w , y w , z w The centroid coordinates (x0, y0, z0) within the area are calculated as follows: ； In the formula, x A Let A be the x-axis coordinate value, and ΔL be the horizontal length of the point cloud segment along the x-axis. Point A (x A , z A Using y0, y0, z0 as the reference point, rotate the centroid coordinates (x0, y0, z0) in the xz-axis plane to the initial point cloud segment {x i , y i , z i The position of point cloud segment is obtained by rotating it in the xz-axis plane with point A as the reference point by an angle of -α. c , y c , z c The details are as follows: ； Step 2.7: Calculation of measured linear coordinates and cross-sectional dimensions of the stay cable: Repeat steps 2.2 to 2.6 to calculate the linear coordinates (x, y, x) of all point cloud segments of the stay cable. c , y c , z c ) and the radius r of the fitted circular curve of the cross section, and the measured coordinates of the cable-stayed cable's linear shape at point {x ci , y ci , z ci } represents the linear coordinates (x, y) of all point cloud segments. c , y c , z c The measured cross-sectional dimensions of the stay cable are the average value of the radius r of the fitted circular curve of all point cloud segments. r The calculation is as follows: ； In the formula, m is the number of point cloud segments.

4. The method for determining the cable force of a cable-stayed bridge based on three-dimensional laser point clouds according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Finite element model analysis and calculation of the stay cables; Step 4.2: Cable-stayed unit node coordinates {x} Fi , z Fi } and support reaction force R F After the finite element model calculation of the cable-stayed bridge is completed, the coordinates of all element nodes {x} are extracted. Fi , z Fi The support reaction force R at the connection point P1 between the cable and the beam. F .

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