CN112967256A - Tunnel ovalization detection method based on spatial distribution - Google Patents

Tunnel ovalization detection method based on spatial distribution Download PDF

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CN112967256A
CN112967256A CN202110257311.6A CN202110257311A CN112967256A CN 112967256 A CN112967256 A CN 112967256A CN 202110257311 A CN202110257311 A CN 202110257311A CN 112967256 A CN112967256 A CN 112967256A
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ellipse
tunnel
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张雅欣
张甘露
赵俊龙
张康茹
徐永安
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Abstract

The invention discloses a tunnel ovalization detection method based on spatial distribution in the technical field of tunnel detection, which comprises the following steps: (1) scanning the outer edge of the tunnel for one circle by using a three-dimensional laser scanner, collecting a data point coordinate every i mm, and forming a simulation data set by all collected data points; (2) filtering out all data points with large errors to form a new data point set { M1,M2,M3,... Mg }; (3) fitting an ellipse according to the new set of data points; (4) calculating the ellipticity according to the fitted ellipse parameters; wherein g is the number of data points in the data point set, MkThe data point is the kth data point, and k is more than or equal to 1 and less than or equal to g; the invention has the advantages of high detection speed and better detectionAnd the stability and the detection precision are high.

Description

Tunnel ovalization detection method based on spatial distribution
Technical Field
The invention belongs to the technical field of tunnel detection, and particularly relates to a tunnel ovalization detection method based on spatial distribution.
Background
With the progress of urbanization and the large-scale development of cities, the subway construction is being tightened in China to solve the increasingly serious traffic jam problem. Due to the rapid expansion of the tunnel scale, the workload of tunnel detection increases rapidly, and due to the influence of various factors such as the wide China territory, the large differences of geological structures and natural environments from east to west, south to north, the change of the surrounding environment, the vibration of trains during operation and the like, various diseases can occur in the subway tunnel, and the deformation detection of the tunnel engineering structure is an extremely important work in the subway construction and operation maintenance processes.
The tunnel profile is theoretically required to be circular, but over time the tunnel tends to ovalize. Ovality is an important parameter for quantitatively calculating tunnel ovalization, hidden danger of tunnel deformation is found in time, and tunnel diseases are early warned, so that detection of tunnel ovality is increasingly important. The conventional tunnel deformation detection methods include plumb-hang method measurement, precision leveling measurement, total station measurement, measurement robot measurement and the like, but the monitoring methods are slow in speed, high in manpower requirement, time-consuming and labor-consuming, and meanwhile, measurement points are scattered and sparse, and the integral deformation condition of the tunnel section cannot be reflected.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides the tunnel ovalization detection method based on spatial distribution, solves the technical problem of low detection speed in the prior art, and has the advantages of high detection speed, more stable detection and high detection precision.
The purpose of the invention is realized as follows: a tunnel ovalization detection method based on spatial distribution comprises the following steps:
(1) scanning the outer edge of the tunnel for one circle by using a three-dimensional laser scanner, collecting a data point coordinate every i mm, and forming a simulation data set by all collected data points;
(2) filtering out all data points with large errors to form a new data point set { M1,M2,M3,...Mg};
(3) Fitting an ellipse according to the new set of data points;
(4) calculating the ellipticity according to the fitted ellipse parameters;
wherein g is the number of data points in the data point set, MkThe data point is the kth data point, and k is more than or equal to 1 and less than or equal to g.
In order to further improve the detection accuracy, the step of filtering out data points with large errors in the step (2) is specifically,
(201) establishing a tunnel end surface plane right angle system xOy by taking the position of the laser generator as an origin O, and respectively taking a horizontal line and a vertical line passing through the origin as an x axis and a y axis, and setting discrete data points as (x)α,yα) (alpha is 1, 2.. g'), calculating the mass center of the analog data set, taking the mass center as the center, taking a horizontal line passing through the mass center as an initial straight line, drawing a straight line by sequentially anticlockwise spacing an angle omega of the initial straight line, and drawing a straight line by y1、y2、,...ynN 180/ω, the data point is divided into a plurality of regions, Ω12,...Ωm,m=2n;
(202) Setting g' to g;
(203) randomly selecting data points with the proportion of eta from each region, selecting p times in total, fitting p ellipses, solving the parameter of each ellipse, taking the parameter average value as the parameter of the ellipse subjected to preliminary fitting, solving two focuses of the ellipse subjected to preliminary fitting, calculating the sum of the distances from each data point in a new data point set to the two focuses, and setting a distance threshold value d;
(204) setting k to 0, i' to 1;
(205)k’=k+1;
(206) if k 'is less than or equal to g', adding 1 to k, entering the step (207), otherwise, turning to the step (208);
(207) if M isk‘If > d, the data point M is setk’Remove from the new data point set, add 1 to i', i ″ -1, return to step(205);
(208) g ═ g-i ", set j ═ 0;
(209)j’=j+1,j’≤jsetting upGo to step (210), otherwise end;
(210) re-dividing the rest data points into regions, and rotating the straight line for dividing the original region counterclockwise by thetaj', each new region is formed, and the procedure returns to step (203);
wherein,
Figure BDA0002968053370000031
jsetting upIs a set number of iterations.
In order to further realize the fitting of the ellipse, in the step (3), the step of fitting the ellipse is specifically,
(301) an elliptical expression is defined and,
Figure BDA0002968053370000032
(302) from discrete data points { xα,yα} (α ═ 1, 2.. g') defines algebraic distances
Figure BDA0002968053370000033
(303) The matrices ξ and θ are defined: ,
Figure BDA0002968053370000034
θ=(A,B,C,D,E,F)T (4);
(304) the elliptical expression may be rewritten to a compact format,
(ξ,θ)=0 (5);
(305) define ξ α at a certain point (x)α,yα) The matrix xi on the upper part, and further expresses the algebraic distance again,
Figure BDA0002968053370000035
the matrix M is a matrix of a number,
Figure BDA0002968053370000041
(306) the constraints of the ellipse are constructed such that,
(θ,Nθ)=c (8);
(307) the minimum algebraic distance is set to min J, order
minJ=(θ,Mθ)
Let (θ, N θ) be c (9);
(308) solving for M θ ═ λ N θ, finding the matrix N that minimizes the covariance and bias,
Figure BDA0002968053370000042
wherein:
Figure BDA0002968053370000043
Figure BDA0002968053370000044
(xc,yc) For discrete data points { xα,yαG'), f0 is a proportionality constant, and c is a non-zero constant.
In order to further realize the detection of the tunnel ovalization, in the step (4), the step of calculating the ovality is specifically,
(401) determining the center position of an ellipse
Figure BDA0002968053370000051
Figure BDA0002968053370000052
(402) The major semi-axis a of the ellipse is calculated, and the intersection point of the straight line L1 where the major axis is located and the ellipse is (x)1,y1) And (x)2,y2),
Figure BDA0002968053370000053
(403) The ellipticity T is calculated and the ellipticity T is calculated,
Figure BDA0002968053370000054
wherein, a is the long half shaft of the tunnel, b is the short half shaft of the tunnel, and D is the outer diameter of the tunnel.
The method comprises the steps of firstly forming a plurality of detected tunnel outer edge data points into a simulation data set, dividing the data points in the simulation data set into a plurality of regions, randomly taking a part of points from each region each time, fitting a certain number of ellipses, constructing an initial ellipse through average analysis, filtering out original data with large errors, removing noise points, repeating iteration to obtain a new data set of the final ellipse to be fitted, meshing the ellipses by utilizing the new data set to obtain ellipse parameters, better fitting the ellipse by combining a new point cloud denoising method and an ellipse fitting method, and improving the detection precision, wherein the method has the advantages that the detected data are more accurate and stronger in robustness especially in a strong noise environment; obtaining an index of tunnel ovalization through the fitted ellipse parameters, and judging an accumulated deformation value of the tunnel and judging the structural damage risk level according to the calculated index of tunnel ovalization in practical application; the method can be applied to tunnel detection.
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FIG. 1 is a block diagram of the algorithm for filtering noise points according to the present invention.
Fig. 2 is a graph of the primary region division in the present invention.
Fig. 3 is a graph of the next division of the area according to the present invention.
Fig. 4 is a tunnel simulation point cloud data diagram in the present invention.
Fig. 5 is a partial enlarged view of the point cloud data.
FIG. 6 is an ellipse fitting image of the present invention.
FIG. 7 is a partial enlarged view of an ellipse fitting image in the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
A tunnel ovalization detection method based on spatial distribution comprises the following steps:
(1) scanning the outer edge of the tunnel for one circle by using a three-dimensional laser scanner, collecting a data point coordinate every i mm, and forming a simulation data set by all collected data points;
(2) filtering out all data points with large errors to form a new data point set { M1,M2,M3,...Mg};
(3) Fitting an ellipse according to the new set of data points;
(4) calculating the ellipticity according to the fitted ellipse parameters;
wherein g is the number of data points in the data point set, MkThe data point is the kth data point, and k is more than or equal to 1 and less than or equal to g.
In order to further improve the detection accuracy, the step of filtering out data points with large errors in the step (2) is specifically,
(201) establishing a tunnel end surface plane right angle system xOy by taking the position of the laser generator as an origin O, and respectively taking a horizontal line and a vertical line passing through the origin as an x axis and a y axis, and setting discrete data points as (x)α,yα) (alpha is 1, 2.. g'), calculating the mass center of the analog data set, taking the mass center as the center, taking a horizontal line passing through the mass center as an initial straight line, drawing a straight line by sequentially anticlockwise spacing an angle omega of the initial straight line, and drawing a straight line by y1、y2、,...ynN 180/ω, the data point is divided into a plurality of regions, Ω12,...Ωm,m=2n;
(202) Setting g' to g;
(203) randomly selecting data points with the proportion of eta from each region, selecting p times in total, fitting p ellipses, solving the parameter of each ellipse, taking the parameter average value as the parameter of the ellipse subjected to preliminary fitting, solving two focuses of the ellipse subjected to preliminary fitting, calculating the sum of the distances from each data point in a new data point set to the two focuses, and setting a distance threshold value d;
(204) setting k to 0, i' to 1;
(205)k’=k+1;
(206) if k 'is less than or equal to g', adding 1 to k, entering the step (207), otherwise, turning to the step (208);
(207) if M isk‘If > d, the data point M is setk’Removing from the new data point set, adding 1 to i ', i ″, i' -1, and returning to step (205);
(208) g ═ g-i ", set j ═ 0;
(209)j’=j+1,j’≤jsetting upGo to step (210), otherwise end;
(210) re-dividing the rest data points into regions, and rotating the straight line for dividing the original region counterclockwise by thetaj', each new region is formed, and the procedure returns to step (203);
wherein,
Figure BDA0002968053370000071
jsetting upIs a set number of iterations.
In order to further realize the fitting of the ellipse, in the step (3), the step of fitting the ellipse is specifically,
(301) an elliptical expression is defined and,
Figure BDA0002968053370000072
(302) from discrete data points { xα,yα} (α ═ 1, 2.. g') defines algebraic distances
Figure BDA0002968053370000081
(303) The matrices ξ and θ are defined: ,
Figure BDA0002968053370000082
θ=(A,B,C,D,E,F)T (4);
(304) the elliptical expression may be rewritten to a compact format,
(ξ,θ)=0 (5);
(305) define ξ α at a certain point (x)α,yα) The matrix xi on the upper part, and further expresses the algebraic distance again,
Figure BDA0002968053370000083
the matrix M is a matrix of a number,
Figure BDA0002968053370000084
(306) the constraints of the ellipse are constructed such that,
(θ,Nθ)=c (8);
(307) the minimum algebraic distance is set to min J, order
minJ=(θ,Mθ)
Let (θ, N θ) be c (9);
(308) solving for M θ ═ λ N θ, finding the matrix N that minimizes the covariance and bias,
Figure BDA0002968053370000085
wherein:
Figure BDA0002968053370000091
Figure BDA0002968053370000092
(xc,yc) Is composed ofDiscrete data points { xα,yαCoordinates of the center of mass of } (α ═ 1, 2.. g'), f0Is a constant of proportionality, and c is a non-zero constant.
In order to further realize the detection of the tunnel ovalization, in the step (4), the step of calculating the ovality is specifically,
(401) determining the center position of an ellipse
Figure BDA0002968053370000093
Figure BDA0002968053370000094
(402) The major semi-axis a of the ellipse is calculated, and the intersection point of the straight line L1 where the major axis is located and the ellipse is (x)1,y1) And (x)2,y2),
Figure BDA0002968053370000095
(403) The ellipticity T is calculated and the ellipticity T is calculated,
Figure BDA0002968053370000096
wherein, a is the long half shaft of the tunnel, b is the short half shaft of the tunnel, and D is the outer diameter of the tunnel.
The method comprises the steps of firstly forming a plurality of detected tunnel outer edge data points into a simulation data set, dividing the data points in the simulation data set into a plurality of regions, randomly taking a part of points from each region each time, fitting a certain number of ellipses, constructing an initial ellipse through average analysis, filtering out original data with large errors, removing noise points, repeating iteration to obtain a new data set of the final ellipse to be fitted, meshing the ellipses by utilizing the new data set to obtain ellipse parameters, better fitting the ellipse by combining a new point cloud denoising method and an ellipse fitting method, and improving the detection precision, wherein the method has the advantages that the detected data are more accurate and stronger in robustness especially in a strong noise environment; obtaining an index of tunnel ovalization through the fitted ellipse parameters, and judging an accumulated deformation value of the tunnel and judging the structural damage risk level according to the calculated index of tunnel ovalization in practical application; the method can be applied to tunnel detection.
Simulation is carried out by using the detection method of the present invention, in this embodiment, ω is 45 °, i is 4, m is 8, the region divided in step (201) is as shown in fig. 2, and the next region divided is as shown in fig. 3; j is set to 6, eta is 60%, and p is 200; assuming that the major axis after the tunnel is ellipticized is 5.5m, the minor axis is 5.4m, and the center coordinate of the ellipse is (0,0), since the tunnel measurement can only measure data points above the foundation, the lower semi-minor axis is 4.7m, and i is 2, disturbance noise points are added to the data point set simulation in the application to simulate the actual tunnel point cloud, as shown in fig. 4 and 5.
In addition, other detection methods are adopted to carry out comparison test with the detection method in the invention, which respectively comprise the following steps:
I. fitting an ellipse to the simulation data set directly by using HyperLS;
II, directly fitting an ellipse to the simulation data set by adopting LS;
directly fitting an ellipse to the simulation data set by using RANSAC and HyperLS;
directly fitting an ellipse to the simulation data set by using RANSAC & LS;
v. detection methods in the present application;
and VI, after a new data set is obtained by using the method in the application, fitting an ellipse to the new data set by using an LS method.
As can be seen from fig. 7, the line V is closest to the standard data point, the fitting effect of the line VI is inferior, the fitting effect of the conventional detection method is poor, and the above simulation further verifies that the detection is more stable, the detection accuracy is improved, and the detection precision is high when the detection is performed by using the method of the present invention.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.

Claims (4)

1. A tunnel ovalization detection method based on spatial distribution is characterized by comprising the following steps:
(1) scanning the outer edge of the tunnel for one circle by using a three-dimensional laser scanner, collecting a data point coordinate every i mm, and forming a simulation data set by all collected data points;
(2) filtering out all data points with large errors to form a new data point set { M1,M2,M3,...Mg};
(3) Fitting an ellipse according to the new set of data points;
(4) calculating the ellipticity according to the fitted ellipse parameters;
wherein g is the number of data points in the data point set, MkThe data point is the kth data point, and k is more than or equal to 1 and less than or equal to g.
2. The method according to claim 1, wherein the method comprises: in the step (2), the step of filtering out data points with large errors is specifically,
(201) establishing a tunnel end surface plane right angle system xOy by taking the position of the laser generator as an origin O, and respectively taking a horizontal line and a vertical line passing through the origin as an x axis and a y axis, and setting discrete data points as (x)α,yα) (alpha is 1, 2.. g'), calculating the mass center of the analog data set, taking the mass center as the center, taking a horizontal line passing through the mass center as an initial straight line, drawing a straight line by sequentially anticlockwise spacing an angle omega of the initial straight line, and drawing a straight line by y1、y2、,...ynN 180/ω, the data point is divided into a plurality of regions, Ω12,...Ωm,m=2n;
(202) Setting g' to g;
(203) randomly selecting data points with the proportion of eta from each region, selecting p times in total, fitting p ellipses, solving the parameter of each ellipse, taking the parameter average value as the parameter of the ellipse subjected to preliminary fitting, solving two focuses of the ellipse subjected to preliminary fitting, calculating the sum of the distances from each data point in a new data point set to the two focuses, and setting a distance threshold value d;
(204) setting k to 0, i' to 1;
(205)k’=k+1;
(206) if k 'is less than or equal to g', adding 1 to k, entering the step (207), otherwise, turning to the step (208);
(207) if M isk‘If > d, the data point M is setk’Removing from the new data point set, adding 1 to i ', i ″, i' -1, and returning to step (205);
(208) g ═ g-i ", set j ═ 0;
(209)j’=j+1,j’≤jsetting upGo to step (210), otherwise end;
(210) re-dividing the rest data points into regions, and rotating the straight line for dividing the original region counterclockwise by thetaj', each new region is formed, and the procedure returns to step (203);
wherein,
Figure FDA0002968053360000021
jsetting upIs a set number of iterations.
3. The method according to claim 2, wherein the method comprises: in the step (3), the step of fitting the ellipse is specifically,
(301) an elliptical expression is defined and,
Ax2+2Bxy+Cy2+2f0(Dx+Ey)+f0 2F=0 (1);
(302) from discrete data points { xα,yα} (α ═ 1, 2.. g') defines algebraic distances
Figure FDA0002968053360000022
(303) The matrices ξ and θ are defined: ,
ξ=(x2,2xy,y2,2f0x,2f0y,f0 2)T (3);
θ=(A,B,C,D,E,F)T (4);
(304) the elliptical expression may be rewritten to a compact format,
(ξ,θ)=0 (5);
(305) define ξ α at a certain point (x)α,yα) The matrix xi on the upper part, and further expresses the algebraic distance again,
Figure FDA0002968053360000031
the matrix M is a matrix of a number,
Figure FDA0002968053360000032
(306) the constraints of the ellipse are constructed such that,
(θ,Nθ)=c (8);
(307) the minimum algebraic distance is set to min J, order
min J=(θ,Mθ)
Let (θ, N θ) be c (9);
(308) solving for M θ ═ λ N θ, finding the matrix N that minimizes the covariance and bias,
Figure FDA0002968053360000033
wherein:
Figure FDA0002968053360000034
Figure FDA0002968053360000035
(xc,yc) For discrete data points { xα,yαCoordinates of the center of mass of } (α ═ 1, 2.. g'), f0Is a constant of proportionality, and c is a non-zero constant.
4. The method according to claim 2, wherein the method comprises: in the step (4), the step of calculating the ellipticity is specifically,
(401) determining the center position of an ellipse
Figure FDA0002968053360000041
Figure FDA0002968053360000042
(402) The major semi-axis a of the ellipse is calculated, and the intersection point of the straight line L1 where the major axis is located and the ellipse is (x)1,y1) And (x)2,y2),
Figure FDA0002968053360000043
Figure FDA0002968053360000044
(403) The ellipticity T is calculated and the ellipticity T is calculated,
Figure FDA0002968053360000045
wherein, a is the long half shaft of the tunnel, b is the short half shaft of the tunnel, and D is the outer diameter of the tunnel.
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