A method for detecting the linear shape of an arch ring based on three-dimensional laser scanning

Abstract

The present invention relates to the technical field of arch ring linear detection of arch bridges, and in particular to an arch ring linear detection method based on three-dimensional laser scanning; comprising the following steps: obtaining the arch ring point cloud data of the arch bridge, and retaining the arch ring bottom point cloud; fitting the arch ring bottom point cloud to form a straight line, rotating the straight line by a first angle, so that the rotated straight line is parallel to the X-Z plane; using a polynomial fitting surface algorithm, fitting the arch ring bottom point cloud on the rotated straight line, and obtaining a polynomial point cloud surface; obtaining the Z value corresponding to the polynomial fitting surface at every preset distance along the X-axis direction; interpolating all Z values ​​with a three-dimensional spline curve to obtain a high-precision arch ring linear shape; rotating the arch ring linear shape counterclockwise around the Z axis by a first angle, thereby obtaining the arch ring linear shape spatial posture. The purpose of the present invention is to solve the problem that it is difficult to ensure that the reflective sheet is attached to the same straight line, resulting in low precision of the curve fitted by the collected points.

Description

Technical Field

[0001] The invention relates to the technical field of arch bridge arch ring linear shape detection technology, and in particular to an arch ring linear shape detection method based on three-dimensional laser scanning. Background Art

[0002] Arch bridges have a large spanning capacity and can fully use local materials. Compared with beam bridges, they can save a lot of steel and cement, have good durability, and have low maintenance and repair costs. For many bridges such as beam bridges, their own line shape has little effect on the constant load internal force of the bridge, but for arch bridges, the line shape of the arch ring has a significant impact on its own constant load internal force. Arch ring line shape monitoring is a crucial task in arch bridge construction, especially vertical deformation, which is one of the main control factors for arch bridge construction monitoring.

[0003] At present, when detecting the linear shape of the arch ring, the traditional total station is used to collect data on the limited feature points of the arch ring. The specific method is: first, reflective sheets are equidistantly affixed to the center line of the lower edge of the arch ring. Taking all factors into consideration, reflective sheets are generally affixed at intervals of 3m to 10m, and the center of the reflective sheet is exactly on the line segment; then the total station is used to collect data on the reflective sheet while ensuring that it is in the same coordinate system as the construction coordinates.

[0004] However, the current method of detecting the arch line shape using a traditional total station has the following shortcomings: it is difficult to ensure that the reflective sheet is attached to the same straight line. In addition, it is difficult to ensure the accuracy of the curve fitted by the points collected by the reflective sheet at intervals of 3m to 10m using the total station. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes an arch ring linear detection method based on three-dimensional laser scanning to solve the problem that the reflective sheet is attached to the center line of the lower edge of the arch ring, and it is difficult to ensure that the reflective sheet is attached to the same straight line, resulting in low accuracy of the curve fitted by the collected points.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for detecting the linear shape of an arch ring based on three-dimensional laser scanning, comprising the following steps:

[0007] Acquire the arch ring point cloud data in the target state of the arch bridge, and retain the arch ring bottom point cloud in the arch ring point cloud data;

[0008] Project the point cloud of the bottom of the arch ring onto the XY plane in the three-dimensional coordinate system, fit a straight line containing the point cloud of the bottom of the arch ring, determine a first angle between the straight line and the positive direction of the X-axis, and rotate the straight line clockwise around the Z axis by the first angle so that the rotated straight line is parallel to the XZ plane;

[0009] The polynomial point cloud surface is obtained by fitting the point cloud of the bottom of the arch ring on the rotated straight line using a polynomial fitting surface algorithm.

[0010] The polynomial fitting surface is fitted at preset distances along the X-axis direction, and the midpoint value of the corresponding point on the Y-axis is obtained to obtain the Z value corresponding to the polynomial fitting surface;

[0011] All Z values ​​are interpolated with three-dimensional spline curves to obtain high-precision arch line shape;

[0012] The arch ring line shape is rotated counterclockwise around the Z axis by the first angle, so as to obtain the arch ring line shape in space.

[0013] Preferably, after retaining the arch ring bottom point cloud in the arch ring point cloud data, the arch ring bottom point cloud is subjected to denoising processing of small-scale noise.

[0014] Preferably, the denoising process for the small-scale noise is performed by using a triangular pyramid method.

[0015] Preferably, the polynomial fitting surface algorithm is specifically:

[0016] According to the actual height Z of the point cloud at the bottom of the arch i and fitting difference ξ i , we can get the surface fitting height z i Function:

[0017] z i =Z i -ξ i (1);

[0018] Among them, the fitting error ξ i With plane coordinate x i y i The function between them is:

[0019] ξ i =f(x,y)+ε i (2);

[0020] In formula (2): ε i is a random error;

[0021]

[0022] In formula (3): p≥0 and is an integer, a 0 , a 1 , a 2 , a j , a m-1 is the conversion parameter;

[0023] When there are n known points: Z i 、zi Point and x i ,y i When n≥m, according to formula (2) in ∑ε 2 =min, the least square method is used to obtain a j = the least squares estimate of (j=0,1,2,…m-1);

[0024] Then a j The coordinates of the undetermined point and the undetermined elevation are simultaneously substituted into ξ = f(x, y), and then the point z of the surface fitting elevation is obtained by equation (1): i .

[0025] Preferably, the ξ in the known point is L i express:

[0026] Formula (2) can be converted into a matrix:

[0027] L = AX + ε (4);

[0028] In formula (4):

[0029] Among them, n≥m is based on the condition that the mathematical expectation of ε E(ε)=0, and its least square solution is obtained, which is specifically:

[0030] X=(A T PA) -1 (A T PL) (5);

[0031] In formula (5), P is the unit weight matrix of the known point observation value.

[0032] Preferably, when the number of x in formula (3) is 4 or 5 and the number of y is 1, the fitting error ξ i Minimum.

[0033] Preferably, the specific steps of fitting the polynomial surface at preset distances along the X-axis direction are:

[0034] Using a cutting plane perpendicular to the XY plane, the fitting surface parallel to the XZ plane is divided into multiple micro-segments with an X-axis spacing of 0.1-0.2 m and the midpoint value of the Y axis of the corresponding point to obtain the Z value corresponding to the polynomial fitting surface.

[0035] Preferably, the arch point cloud data is acquired by scanning and collecting using a three-dimensional laser scanner.

[0036] Preferably, if the arch ring point cloud data collected under the target state of the arch bridge is incomplete, multiple stations are set for the incompletely collected area to collect the arch ring point cloud data using multiple perspectives to obtain multi-perspective arch ring point cloud data, and the collected arch ring point cloud data are spliced ​​at multiple stations to obtain complete arch ring point cloud data.

[0037] Compared with the prior art, the beneficial effects of this solution are:

[0038] 1. By collecting the point cloud data of the arch ring of the arch bridge, the straight line fitting is performed based on the point cloud at the bottom of the arch ring of the arch bridge, without the need for manual assistance to paste reflective sheets, thereby reducing manual operations, and the operation is relatively simple and efficient. At the same time, the polynomial fitting surface algorithm is used to fit the point cloud at the bottom of the arch ring multiple times to obtain the optimal polynomial point cloud surface. Based on the polynomial point cloud surface extraction, the high-precision arch ring line shape is obtained. The data processing method is simple and has high precision, and the three-dimensional line shape of the arch ring line shape can be extracted to obtain the high-precision arch ring line shape space posture.

[0039] 2. By using the triangular pyramid method to denoise the point cloud at the bottom of the arch ring of the arch bridge, the accuracy of the fitting straight line is improved, thereby improving the accuracy of obtaining the linear spatial posture of the arch ring.

[0040] 3. By projecting the point cloud of the bottom of the arch ring onto the XY plane in the three-dimensional coordinate system, a straight line is fitted to determine the first angle between the straight line and the positive direction of the X-axis; the straight line is rotated clockwise around the Z axis by the first angle to make it parallel to the XZ plane, further ensuring the accuracy of the polynomial point cloud surface obtained by the polynomial fitting surface algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the specific implementation of the present invention, the following will briefly introduce the drawings required for use in the specific implementation. In all the drawings, each element or part is not necessarily drawn according to the actual scale.

[0042] Figure 1 It is a flowchart of the arch line shape detection method based on three-dimensional laser scanning of the present invention;

[0043] Figure 2 It is an effect diagram of the arch bottom point cloud in the arch line shape detection method based on three-dimensional laser scanning of the present invention after the triangular pyramid method is used to denoise it;

[0044] Figure 3 It is an effect diagram of the polynomial point cloud surface fitting of the arch bottom point cloud in the arch line shape detection method based on three-dimensional laser scanning of the present invention;

[0045] Figure 4 It is a line diagram of the spatial posture of the arch line shape in the arch line shape detection method based on three-dimensional laser scanning of the present invention. DETAILED DESCRIPTION

[0046] The following embodiments of the technical solution of the present invention are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only used as examples, and cannot be used to limit the protection scope of the present invention.

[0047] See also Figure 1-Figure 4 , a method for detecting the linear shape of an arch ring based on three-dimensional laser scanning, comprising the following steps:

[0048] S1. Please also refer to Figure 1 , obtain the arch ring point cloud data in the target state of the arch bridge, and retain the arch ring bottom point cloud in the arch ring point cloud data. In this embodiment, the arch ring point cloud data uses professional point cloud processing software to delete redundant point clouds, such as deleting the arch ring side and other on-site structure point clouds, and only retaining the arch ring bottom point cloud.

[0049] At the same time, in order to prevent noise from interfering with the point cloud at the bottom of the arch ring, the triangular pyramid method is used to denoise the small-scale noise at the bottom of the arch ring. By denoising the point cloud at the bottom of the arch ring of the arch bridge using the triangular pyramid method, the accuracy of the fitted straight line is improved, thereby improving the accuracy of obtaining the linear spatial posture of the arch ring.

[0050] Among them, in order to obtain the point cloud of the bottom of the arch ring in the target state of the arch bridge, the bottom of the arch ring is first scanned using a three-dimensional laser scanner to collect the complete point cloud data of the arch ring in the target state of the arch bridge.

[0051] At the same time, when the bottom of the arch ring of the arch bridge is blocked by other obstructions after completion, multiple stations are set up for the areas with obstructions in the arch ring, and multiple perspectives are used to collect the arch ring point cloud data for the incomplete areas. For example, 2 or 3 stations use 3D laser scanners to collect the arch ring point cloud data using multiple perspectives. Then, when the collected arch ring point cloud data is imported into Geomagic Control, 2 or 3 stations are spliced ​​to obtain complete arch ring point cloud data.

[0052] S2. Project the point cloud of the bottom of the arch ring onto the XY plane in the three-dimensional coordinate system, fit a straight line containing the point cloud of the bottom of the arch ring, determine the first angle between the straight line and the positive direction of the X-axis, rotate the straight line clockwise around the Z axis by the first angle, so that the rotated straight line is parallel to the XZ plane or located on the XZ plane. In this embodiment, the positive direction of the Z axis in the three-dimensional coordinate system can be vertically upward, the positive direction of the X axis can be horizontally to the right, and the positive direction of the Y axis can be perpendicular to the XZ plane and forward. By projecting the point cloud of the bottom of the arch ring onto the XY plane in the three-dimensional coordinate system, a straight line is fitted, and the first angle between the straight line and the positive direction of the X axis is determined; the straight line is rotated clockwise around the Z axis by the first angle to make it parallel to the XZ plane, and the accuracy of the polynomial point cloud surface obtained by the polynomial fitting surface algorithm is further guaranteed.

[0053] S3. Please also refer to Figure 3 , using the polynomial fitting surface algorithm, fit the arch bottom point cloud on the rotated straight line to obtain the polynomial point cloud surface. Among them, the degree of x in the polynomial is 1, the degree of y is 1, the degree of x is 2, the degree of y is 1, the degree of x is 3, the degree of y is 1... Let the actual height of the arch bottom point cloud be Z i , the surface fitting elevation is z i , the fitting error is ξ i ; Calculate the fitting degree Z of each group of polynomials respectively i , z i ,ξ i , determine the minimum ξ i The corresponding polynomials are the degrees of x and y. When the degree of x is 4 or 5 and the degree of y is 1, the fitting error is ξ i The polynomial fitting surface has high accuracy and good robustness. In order to achieve the best fitting effect, the best fitting surface is defined. The best fitting surface should meet two requirements: first, the standard deviation should be less than a given threshold; second, the standard deviation of the selected surface should be less than that of the high-order surface.

[0054] In this embodiment, the polynomial fitting surface algorithm is specifically:

[0055] According to the actual height Z of the point cloud at the bottom of the arch i and fitting difference ξ i , we can get the surface fitting height z i Function:

[0056] z i =Z i -ξ i (1).

[0057] Among them, the fitting error ξ i With plane coordinate x i y i The function between them is:

[0058] ξ i =f(x,y)+ε i (2).

[0059] In formula (2): ε i is a random error.

[0060]

[0061] In formula (3): p≥0 and is an integer, a 0 , a 1 , a 2 , a j , a m-1 is the conversion parameter.

[0062] When there are n known points: Z i 、z i Point and x i ,y i When n≥m, according to formula (2) in ∑ε 2 =min, the least square method is used to obtain a j =The least squares estimate of (j=0,1,2,…m-1).

[0063] Then a j The coordinates of the undetermined point and the undetermined elevation are simultaneously substituted into ξ = f(x, y), and then the point z of the surface fitting elevation is obtained by equation (1): i .

[0064] At the same time, in order to distinguish the ξ of the known point from the ξ of the undetermined point, the ξ of the known point is replaced by L i express:

[0065] Formula (2) can be converted into a matrix:

[0066] L=AX+ε (4).

[0067] In formula (4):

[0068] Among them, n≥m is based on the condition that the mathematical expectation of ε E(ε)=0, and its least square solution is obtained, which is specifically:

[0069] X=(A T PA) -1 (A T PL) (5).

[0070] In formula (5), P is the unit weight matrix of the known point observation value.

[0071] S4, the polynomial fitting surface is fitted at preset distances along the X-axis direction, and the midpoint value of the corresponding point on the Y-axis is obtained to obtain the Z value corresponding to the polynomial fitting surface.

[0072] Specifically: using a cutting plane perpendicular to the XY plane, the fitting surface parallel to the XZ plane is divided into multiple micro-segments, the X-axis spacing of the micro-segments is 0.1, and the midpoint value of the Y axis of the corresponding point is obtained, that is, the Z value corresponding to the polynomial fitting surface is obtained. At the same time, the X-axis spacing of the micro-segments can also be selected as 0.15 or 0.2.

[0073] Please also refer to Figure 4 , interpolate all Z values ​​with three-dimensional spline curves to obtain a high-precision arch shape. Rotate the arch shape counterclockwise around the Z axis by a first angle to obtain the arch shape's spatial posture.

[0074] The above technical solution collects the point cloud data of the arch ring of the arch bridge, and fits the straight line based on the point cloud at the bottom of the arch ring of the arch bridge, without the need for manual assistance to paste reflective sheets, thereby reducing manual operations, and the operation is relatively simple and efficient. At the same time, the point cloud at the bottom of the arch ring is fitted multiple times through the polynomial fitting surface algorithm to obtain the optimal polynomial point cloud surface. Based on the polynomial point cloud surface extraction, a high-precision arch ring linear shape is obtained, the data processing method is simple and has high precision, and the three-dimensional linear shape of the arch ring can be extracted to obtain a high-precision arch ring linear shape spatial posture.

[0075] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for detecting the linear shape of an arch ring based on three-dimensional laser scanning, characterized in that: The following steps are involved: Acquire the arch ring point cloud data in the target state of the arch bridge, and retain the arch ring bottom point cloud in the arch ring point cloud data; Project the point cloud of the bottom of the arch ring onto the XY plane in the three-dimensional coordinate system, fit a straight line containing the point cloud of the bottom of the arch ring, determine a first angle between the straight line and the positive direction of the X-axis, and rotate the straight line clockwise around the Z axis by the first angle so that the rotated straight line is parallel to the XZ plane; The polynomial point cloud surface is obtained by fitting the point cloud of the bottom of the arch ring on the rotated straight line using a polynomial fitting surface algorithm. The polynomial fitting surface is fitted at preset distances along the X-axis direction, and the midpoint value of the corresponding point on the Y-axis is obtained to obtain the Z value corresponding to the polynomial fitting surface; All Z values ​​are interpolated with three-dimensional spline curves to obtain high-precision arch line shape; Rotate the arch ring line shape counterclockwise around the Z axis by the first angle, so as to obtain the arch ring line shape spatial posture; The polynomial fitting surface algorithm is specifically as follows: According to the actual height Z of the point cloud at the bottom of the arch i and fitting difference ξ i , we can get the surface fitting height z i Function: With i =Z i -ξ i (1); Among them, the fitting error ξ i With plane coordinate x i y i The function between them is: x i =f(x,y)+ε i (2); In formula (2): ε i is a random error; In formula (3): p≥0 and is an integer, a0, a1, a2, a j , a m-1 is the conversion parameter; When there are n known points: Z i 、z i Point and x i ,y i When n≥m, according to formula (2) in ∑ε 2 =min, the least square method is used to obtain a j = the least squares estimate of (j=0,1,2,…m-1); Then a j The coordinates of the undetermined point and the undetermined elevation are simultaneously substituted into ξ = f(x, y), and then the point z of the surface fitting elevation is obtained by equation (1): i ; The ξ in the known point is L i express: Formula (2) can be converted into a matrix: L = AX + ε (4); In formula (4): Among them, n≥m is based on the condition that the mathematical expectation of ε E(ε)=0, and its least square solution is obtained, which is specifically: X=(A T PA) -1 (A T PL) (5); In formula (5), P is the unit weight matrix of the known point observation value.

2. The method for detecting the arch line shape based on three-dimensional laser scanning according to claim 1, characterized in that: After retaining the arch bottom point cloud in the arch point cloud data, the arch bottom point cloud is subjected to denoising processing of small-scale noise.

3. The method for detecting the arch line shape based on three-dimensional laser scanning according to claim 2, characterized in that: The denoising process for the small-scale noise is performed by using a triangular pyramid method.

4. The method for detecting the arch line shape based on three-dimensional laser scanning according to claim 1, characterized in that: When the order of x in formula (3) is 4 or 5 and the order of y is 1, the fitting error ξ i Minimum.

5. The method for detecting the arch line shape based on three-dimensional laser scanning according to claim 1, characterized in that: The specific steps of fitting the polynomial surface at preset distances along the X-axis direction are: Using a cutting plane perpendicular to the XY plane, the fitting surface parallel to the XZ plane is divided into multiple micro-segments with an X-axis spacing of 0.1-0.2 m and the midpoint value of the Y axis of the corresponding point to obtain the Z value corresponding to the polynomial fitting surface.

6. The method for detecting the arch line shape based on three-dimensional laser scanning according to claim 1, characterized in that: The arch point cloud data is scanned and acquired using a three-dimensional laser scanner.

7. The method for detecting the arch line shape based on three-dimensional laser scanning according to claim 6, characterized in that: If the arch ring point cloud data collected under the target state of the arch bridge is incomplete, multiple stations are set up for the incomplete collection area to collect the arch ring point cloud data using multiple perspectives to obtain multi-perspective arch ring point cloud data, and the collected arch ring point cloud data are spliced ​​at multiple stations to obtain complete arch ring point cloud data.

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