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

Abstract

The invention discloses a tunnel ovalization detection method based on spatial distribution in the technical field of tunnel detection, comprising the following steps: (1) Scan the outer edge of the tunnel with a three-dimensional laser scanner, and collect the coordinates of a data point every 1 mm , all the collected data points constitute a simulated data set; (2) filter out all data points with large errors to form a new data point set {M ₁ , M ₂ , M ₃ ,...Mg}; (3) According to Fit the ellipse to the new data point set; (4) Calculate the ellipseness according to the fitted ellipse parameters; where g is the number of data points in the data point set, M _k data point is the kth data point, 1≤k ≤g; the detection speed is fast, the detection is more stable, and the detection precision is high.

Description

A detection method of tunnel ovalization based on spatial distribution

technical field

The invention belongs to the technical field of tunnel detection, and in particular relates to a method for detecting ovalization of tunnels based on spatial distribution.

Background technique

With the process of urbanization and the large-scale development of cities, my country is stepping up the construction of subways to solve the increasingly serious traffic jam problem. Due to the rapid expansion of the tunnel scale, the workload of tunnel inspection has increased sharply. In addition to the vast territory of China, the geological structure and natural environment from east to west and from south to north are very different. Under the influence of various factors such as vibration, various diseases will occur in subway tunnels. In the process of subway construction and operation and maintenance, deformation detection of tunnel engineering structures is an extremely important task.

The tunnel section is theoretically required to be circular, but over time, the tunnel will tend to ovalize. The ellipticity is an important parameter to quantitatively calculate the ovalization of the tunnel. It can detect the hidden danger of tunnel deformation in time and give early warning of tunnel diseases. Therefore, the detection of tunnel ovality is increasingly important. Conventional tunnel deformation detection methods include hanging plumb method measurement, precision leveling measurement, total station measurement, measurement robot measurement, etc., but these monitoring methods are slow, require high manpower, time-consuming and labor-intensive, and the measurement points are also very discrete and sparse. It cannot reflect the overall deformation of the tunnel section.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies in the prior art, and provide a method for detecting tunnel ovalization based on spatial distribution, which solves the technical problem of slow detection speed in the prior art. More stable and high detection accuracy.

The object of the present invention is achieved in this way: a kind of tunnel ovalization detection method based on spatial distribution, comprising the following steps:

(1) Use a three-dimensional laser scanner to scan the outer edge of the tunnel, collect a data point coordinate every 1 mm, and all the collected data points form a simulated data set;

(2) Filter out all data points with large errors to form a new data point set {M ₁ , M ₂ , M ₃ ,...Mg};

(3) Fitting an ellipse according to the new data point set;

(4) Calculate the ellipticity according to the fitted ellipse parameters;

Among them, g is the number of data points in the data point set, M _k data point is the kth data point, 1≤k≤g.

In order to further improve the detection accuracy, in the step (2), the step of filtering out data points with large errors is specifically:

(201) Taking the position of the laser generator as the origin O, and taking the horizontal and vertical lines passing through the origin as the x-axis and y-axis respectively, establish the tunnel end plane right angle system xOy, and set the discrete data points as (x _α , y _α )(α =1, 2,...g'), calculate the centroid of the simulated data set, take the centroid as the center, the horizontal line passing through the centroid is the initial straight line, and draw a straight line with the initial straight line counterclockwise at an angle ω, y ₁ , y ₂ ,,...y _n , n=180/ω, divide the data point into multiple regions, Ω ₁ ,Ω ₂ ,...Ω _m , m=2n;

(202) set g'=g;

(203) randomly select data points with a proportion of n from each area, select p times in total, fit p ellipses, obtain the parameters of each ellipse, take the average value of the parameters, and use the average parameter value as the ellipse of the preliminary fitting parameter, find the two foci of the initially fitted ellipse, calculate the sum of the distances from each data point in the new data point set to the two foci, and set the distance threshold d;

(204) set k=0, i'=1;

(205) k'=k+1;

(206) If k'≤g', add 1 to k, and go to step (207), otherwise go to step (208);

(207) If M _k' >d, remove the data point M _k' from the new data point set, add 1 to i', i"=i'-1, and return to step (205);

(208) g'=g-i", set j=0;

(209) j'=j+1, j'≤j _{is set} , go to step (210), otherwise end;

(210) the remaining data points are re-divided into regions, and the straight line that divides the original region is rotated counterclockwise by θ _j ' to form each new region, and returns to step (203);

j_设定为设定好的迭代次数。in,

j _{is set} to the 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) define an ellipse expression,

(302) Define algebraic distances according to discrete data points {x _α , y _α } (α=1, 2, ... g')

(303) define matrices ξ and θ:,

θ = (A, B, C, D, E, F) ^T (4);

(304) Ellipse expressions can be rewritten in compact form,

(ξ,θ)=0 (5);

(305) Define the matrix ξ of ξα at a certain point (x _α , y _α ), and then re-express the algebraic distance,

The matrix M is,

(306) Constraints for constructing an ellipse,

(θ, Nθ) = c (8);

(307) The minimum algebraic distance is set as min J, let

minJ=(θ, Mθ)

Suppose (θ, Nθ) = c (9);

(308) Solve Mθ=λNθ, find the matrix N that minimizes the covariance and deviation,

in:

(x_c，y_c)为离散数据点{x_α，y_α}(α＝1，2，...g’)的质心坐标，f0是一个比例常数，c为一非零常数。

(x _c , y _c ) are the coordinates of the centroid of the discrete data points {x _α , y _α } (α=1, 2,...g'), f0 is a proportionality constant, and c is a non-zero constant.

In order to further realize the detection of tunnel ovalization, in the step (4), the step of calculating the ellipticity is specifically:

(401) Determine the center position of the ellipse

(402) Calculate the semi-major axis a of the ellipse, and the intersection points of the straight line L1 where the long axis is located and the ellipse are (x ₁ , y ₁ ) and (x ₂ , y ₂ ),

(403) Calculate the ellipticity T,

Among them, a is the long semi-axis of the tunnel, b is the short semi-axis of the tunnel, and D is the outer diameter of the tunnel.

In the present invention, a number of detected data points on the outer edge of the tunnel constitute a simulated data set, and the data points in the simulated data set are divided into several regions, and a part of points is randomly selected from each region each time, and a certain number of ellipses are fitted to fit a certain number of ellipses. The average analysis constructs the initial ellipse, filters out the original data with large error, removes the noise, repeats iteratively, and obtains a new data set of the final ellipse to be fitted. The cloud denoising method and the ellipse fitting method are combined to better fit the ellipse and improve the detection accuracy, especially in a strong noise environment, the present invention has greater advantages, and the detected data is more accurate and robust; The index of tunnel ellipse is obtained by fitting the ellipse parameters. In practical application, the accumulated deformation value of the tunnel and the risk level of structural damage will be judged according to the calculated ellipse index of the tunnel; it can be applied to the work of tunnel inspection. middle.

Description of drawings

FIG. 1 is a flow chart of an algorithm for filtering noise points in the present invention.

FIG. 2 is a coordinate diagram of the first divided area in the present invention.

FIG. 3 is a coordinate diagram of the next divided area in the present invention.

FIG. 4 is a data diagram of a tunnel simulation point cloud in the present invention.

Figure 5 is an enlarged view of a part of the point cloud data.

FIG. 6 is an ellipse fitting image of the present invention.

FIG. 7 is a partial enlarged view of the ellipse fitting image in the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings.

A method for detecting tunnel ovalization based on spatial distribution, comprising the following steps:

(1) Use a three-dimensional laser scanner to scan the outer edge of the tunnel, collect a data point coordinate every 1 mm, and all the collected data points form a simulated data set;

(2) Filter out all data points with large errors to form a new data point set {M ₁ , M ₂ , M ₃ ,...Mg};

(3) Fitting an ellipse according to the new data point set;

(4) Calculate the ellipticity according to the fitted ellipse parameters;

Among them, g is the number of data points in the data point set, M _k data point is the kth data point, 1≤k≤g.

In order to further improve the detection accuracy, in the step (2), the step of filtering out data points with large errors is specifically:

(201) Taking the position of the laser generator as the origin O, and taking the horizontal and vertical lines passing through the origin as the x-axis and y-axis respectively, establish the tunnel end plane right angle system xOy, and set the discrete data points as (x _α , y _α )(α =1, 2,...g'), calculate the centroid of the simulated data set, take the centroid as the center, the horizontal line passing through the centroid is the initial straight line, and draw a straight line with the initial straight line counterclockwise at an angle ω, y ₁ , y ₂ ,,...y _n , n=180/ω, divide the data point into multiple regions, Ω ₁ ,Ω ₂ ,...Ω _m , m=2n;

(202) set g'=g;

(203) randomly select data points with a proportion of n from each area, select p times in total, fit p ellipses, obtain the parameters of each ellipse, take the average value of the parameters, and use the average parameter value as the ellipse of the preliminary fitting parameter, find the two foci of the initially fitted ellipse, calculate the sum of the distances from each data point in the new data point set to the two foci, and set the distance threshold d;

(204) set k=0, i'=1;

(205) k'=k+1;

(206) If k'≤g', add 1 to k, and go to step (207), otherwise go to step (208);

(207) If M _k' >d, remove the data point M _k' from the new data point set, add 1 to i', i"=i'-1, and return to step (205);

(208) g'=g-i", set j=0;

(209) j'=j+1, j'≤j _{is set} , go to step (210), otherwise end;

(210) the remaining data points are re-divided into regions, and the straight line that divides the original region is rotated counterclockwise by θ _j ' to form each new region, and returns to step (203);

j_设定为设定好的迭代次数。in,

j _{is set} to the 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) define an ellipse expression,

(302) Define algebraic distances according to discrete data points {x _α , y _α } (α=1, 2, ... g')

(303) define matrices ξ and θ:,

θ = (A, B, C, D, E, F) ^T (4);

(304) Ellipse expressions can be rewritten in compact form,

(ξ,θ)=0 (5);

(305) Define the matrix ξ of ξα at a certain point (x _α , y _α ), and then re-express the algebraic distance,

The matrix M is,

(306) Constraints for constructing an ellipse,

(θ, Nθ) = c (8);

(307) The minimum algebraic distance is set as min J, let

minJ=(θ, Mθ)

Suppose (θ, Nθ) = c (9);

(308) Solve Mθ=λNθ, find the matrix N that minimizes the covariance and deviation,

in:

(x_c，y_c)为离散数据点{x_α，y_α}(α＝1，2，...g’)的质心坐标，f₀是一个比例常数，c为一非零常数。

(x _c , y _c ) are the coordinates of the centroid of the discrete data points {x _α , y _α } (α=1, 2, ... g'), f ₀ is a proportionality constant, and c is a non-zero constant.

In order to further realize the detection of tunnel ovalization, in the step (4), the step of calculating the ellipticity is specifically:

(401) Determine the center position of the ellipse

(402) Calculate the semi-major axis a of the ellipse, and the intersection points of the straight line L1 where the long axis is located and the ellipse are (x ₁ , y ₁ ) and (x ₂ , y ₂ ),

(403) Calculate the ellipticity T,

Among them, a is the long semi-axis of the tunnel, b is the short semi-axis of the tunnel, and D is the outer diameter of the tunnel.

In the present invention, a number of detected data points on the outer edge of the tunnel constitute a simulated data set, and the data points in the simulated data set are divided into several regions, and a part of points is randomly selected from each region each time, and a certain number of ellipses are fitted to fit a certain number of ellipses. The average analysis constructs the initial ellipse, filters out the original data with large error, removes the noise, repeats iteratively, and obtains a new data set of the final ellipse to be fitted. The cloud denoising method and the ellipse fitting method are combined to better fit the ellipse and improve the detection accuracy, especially in a strong noise environment, the present invention has greater advantages, and the detected data is more accurate and robust; The index of tunnel ellipse is obtained by fitting the ellipse parameters. In practical application, the accumulated deformation value of the tunnel and the risk level of structural damage will be judged according to the calculated ellipse index of the tunnel; it can be applied to the work of tunnel inspection. middle.

Use the detection method in the present invention to perform simulation. In this embodiment, take ω=45°, i is 4, m is 8, step (201) is divided into areas as shown in Figure 2, and the next divided area is as shown in Figure 2 3; j is set to 6, η = 60%, p = 200; assuming that the long axis of the tunnel ovalization is 5.5m, the short axis is 5.4m, and the ellipse center coordinate is (0,0), because Tunnel measurement can only measure the data points above the foundation, so the lower half short axis is 4.7m, and i is taken as 2. In this application, disturbance noise is added to the simulation of the data point set to simulate the actual tunnel point cloud, as shown in Figures 4 and 5 .

In addition, other detection methods and the detection method in the present invention are adopted to carry out comparative tests, which are respectively:

I. Using HyperLS to directly fit the ellipse to the simulated data set;

II. Use LS to directly fit the ellipse to the simulated data set;

III. Use RANSAC&HyperLS to directly fit the ellipse to the simulated data set;

IV. Use RANSAC&LS to directly fit the ellipse to the simulated data set;

V. the detection method in this application;

VI. After obtaining a new data set using the method in this application, use the LS method to fit an ellipse to the new data set.

As can be seen from Figure 7, the line V is closest to the standard data point, the fitting effect of the line VI is second, and the traditional detection method has a poor fitting effect. The detection is more stable, the detection accuracy is improved, and the detection accuracy is high.

The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some of the technical features according to the disclosed technical contents without creative work. Modifications, replacements 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, M_kThe 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，y_α) (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、,...y_nN 180/ω, the data point is divided into a plurality of regions, Ω₁,Ω₂,...Ω_m，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 is_k‘If > d, the data point M is set_k’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’≤j_{setting up}Go 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 theta_j', each new region is formed, and the procedure returns to step (203);

wherein,

j_{setting up}Is 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 { x_α，y_α} (α ═ 1, 2.. g') defines algebraic distances

(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，y_α) The matrix xi on the upper part, and further expresses the algebraic distance again,

the matrix M is a matrix of a number,

(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,

wherein:

(x_c，y_c) For discrete data points { x_α，y_αCoordinates 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

(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)，

(403) The ellipticity T is calculated and the ellipticity T is calculated,

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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