A concave polygonal inclined coal mining face segmentation method for surface subsidence prediction

Abstract

The present invention discloses a concave polygon inclined coal mining working face segmentation method for surface subsidence prediction, which is applicable to the field of concave polygon inclined coal mining assessment. The vertex coordinate data of the working face to be predicted is obtained, and points are interpolated at fixed intervals on the polygon edge and interior to establish two large triangles covering the polygon working face. The interpolated points are inserted into the large triangles one by one according to the triangle circumscribed circle criterion, and all data points are constructed into segmented triangles. Then, the coordinates of the centroids of each segmented triangle are collected, and it is determined whether each centroid is on the polygon edge or inside the polygon working face. All segmented triangles of the concave polygon coal mining working face are obtained according to the principle of whether to keep or not. Considering that different segmentation units of the inclined coal seam correspond to different coal seam parameters. The network construction algorithm based on the interpolation point is theoretically rigorous and the geometric logic is appropriate. It is applicable to the concave polygon inclined coal mining working face, and the segmentation accuracy is perfect, which helps to improve the prediction accuracy of the surface movement and deformation of the concave polygon inclined coal mining working face.

Description

Technical Field

[0001] The invention relates to a concave polygon inclined coal mining working face subdivision method for surface subsidence prediction, belonging to the technical field of surface movement and deformation prediction during polygon inclined coal mining working face mining. Technical Background

[0002] Coal mining disrupts the stress balance of the original underground rock formations. The presence of goaf allows stress to be transmitted to the surface, causing ground subsidence, threatening the safety of farmland and structures and shortening their service life. Predicting the surface movement and deformation caused by coal mining before mining can help prevent and plan for secondary surface disasters, achieving a win-win situation for coal mining and environmental protection.

[0003] Extensive research has been conducted on surface subsidence prediction methods for coal mining, and surface subsidence prediction methods that meet conventional geological mining conditions have been established. In particular, the probability integral method has become the most mature and widely used method for predicting mining subsidence. When using the probability integral method to predict surface movement and deformation during coal mining, the large size of the working face often requires face segmentation to improve prediction accuracy. Conventional mining working faces are often rectangular strips, and rectangular segmentation can achieve fine-scale division of the working face. However, irregular working faces often suffer from jagged edges when using rectangular segmentation, resulting in incomplete face segmentation and insufficient prediction accuracy. Therefore, triangulation has been introduced to face segmentation. Triangulation can divide irregular working faces into small triangles by interpolating points within the working face. Its varied shapes can be aligned with the edges of irregular polygons, reducing edge precision losses. However, when the triangulation algorithm is applied to concave polygonal coal mining working faces, illegal triangles are generated in the polygonal concave areas. This phenomenon greatly reduces the applicability of the triangulation algorithm to the field of arbitrary polygonal triangulation processing. How to solve the problem of illegal triangles generated by concave polygonal triangulation processing has become an urgent problem to be solved, which is of great significance to improving the accuracy of surface subsidence prediction in coal mining. Summary of the Invention

[0004] To address the shortcomings of the above-mentioned technologies, a concave polygon inclined coal mining face segmentation method for surface subsidence prediction is provided. This method has rigorous theory, appropriate geometric logic, low programming time complexity, and perfect segmentation accuracy, which helps to improve the prediction accuracy of surface movement and deformation of irregular coal mining faces.

[0005] To achieve the above technical objectives, the present invention provides a concave polygon inclined coal mining face segmentation method for surface subsidence prediction. For an inclined coal mining face whose plan view is a concave polygon, the steps are as follows:

[0006] The information of the concave polygonal inclined coal seam is obtained through the existing mining data of the mining area, including the coordinates of each vertex of the mining working face polygon space and the mining depth of each vertex, i.e., the mining depth. The vertex coordinates are arranged and stored in the order of counterclockwise distribution of the working face plane diagram;

[0007] By default, the mining thickness of inclined coal seams is uniform. The polygonal working surface is simplified into a plan view. The edges and interior of the polygonal working surface are marked with interpolation points according to the principle of first edges and then interior. The spacing of the interpolation points is determined based on work experience or a fixed ratio. The fixed ratio is the depth from the roof of the working surface to the ground surface, that is, one-fifth of the mining depth.

[0008] Mark the coordinates of all interpolation points, and then sort the coordinates of all interpolation points from small to large X coordinates and store them in the array Vertices. The array Vertices records the coordinate values ​​(X, Y) of each interpolation point.

[0009] Extract the largest X coordinates of the vertices of the concave polygon coal mining face max With the largest Y max Coordinates, minimum X min With Y min Coordinates, create two large triangles covering the concave polygon of the coal mining face plan, and store them in the triangle list Triangles, which records the coordinates of the three vertices of each triangle;

[0010] The plan view of the concave polygonal coal mining face is triangulated. The specific process is as follows:

[0011] Traverse all the interpolation point coordinates stored in the array Vertices. If the interpolation point coordinates are inside or on the circumcircle of a triangle in the triangle list Triangles, delete the triangle from the list, then connect the current point to the three vertices of the triangle just deleted to form three subdivided triangles, and add the coordinates of the three subdivided triangles to the triangle list Triangles; if the interpolation point coordinates are outside the circumcircle of a triangle in the triangle list Triangles, directly add the coordinates of the triangle to the triangle list Triangles;

[0012] After traversing all the interpolation point coordinates recorded in the array Vertices, the coordinates of the two large triangles are deleted from the triangle list Triangles. The remaining triangles are the subdivision triangles of all preliminary triangulations.

[0013] Since illegal triangles exist after the initial subdivision of the concave polygon is completed, the centroid coordinates of each subdivided triangle are calculated using the triangle centroid theorem. If the centroid is located inside the working surface coordinate range, the triangle is retained; if the centroid is located outside the polygon working surface coordinate range or on the edge, the triangle is removed. Finally, all the subdivided triangles of the irregular working surface are obtained.

[0014] Furthermore, due to the existence of the dip angle of the inclined coal seam, the use of the average mining depth in the subsequent surface movement and deformation prediction process will make the predicted value deviate from reality; based on the distance from the center of gravity of each subdivided triangle to each vertex of the polygonal working surface as the weight, and the mining depth of each vertex of the polygonal working surface as the calculated value, the weighted average calculation can obtain the mining depth corresponding to each subdivided triangle.

[0015] Create the UDelTris class, which is used to record the information of each subdivision unit, including the coordinates of the three vertices of the triangle, the triangle serial number, the coordinates of the triangle center of gravity, and the mining depth corresponding to the triangle.

[0016] Furthermore, the steps for determining the positional relationship between the interpolation point M and the center of the triangle circumscribed circle are as follows:

[0017] Suppose the coordinates of the three vertices of a triangle are: A(x1,y1), B(x2,y2), C(x3,y3), then the coordinates of the center of the triangle are P(X / D,Y / D). Then, by comparing the distance MP from the interpolated point M to the center of the triangle P with the distance AP from the triangle A to the center of the triangle P, the positional relationship between the interpolated point and the center of the triangle's circumcircle can be determined.

[0018] in:

[0019] D=(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))*2,

[0020] X=(x1 2 +y1 2 )*(y2-y3)+(x2 2 +y2 2 )*(y3-y1)+(x3 2 +y3 2 )*(y1-y2),

[0021] Y=(x1 2 +y1 2 )*(x3-x2)+(x2 2 +y2 2 )*(x1-x3)+(x3 2 +y3 2 )*(x2-x1);

[0022] If MP = AP, it is determined that the interpolation point M is on the circumcircle of the triangle; if MP > AP, it is determined that the interpolation point M is outside the circumcircle of the triangle; if MP < AP, it is determined that the interpolation point M is inside the circumcircle of the triangle.

[0023] Furthermore, the method for calculating the centroid coordinates of each triangulated triangle is as follows: The coordinates of the three vertices of a certain triangle are A(x1, y1), B(x2, y2), and C(x3, y3), then the centroid coordinates of this triangle are P((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3).

[0024] Furthermore, the steps for determining the positional relationship between the centroid point of a triangle and the working surface of a concave polygon are as follows: Denote the coordinates of the centroid point of a certain triangle as P. Draw a horizontal ray to the left or right from point P. If the number of intersection points of this ray and the working surface of the polygon is odd, then point P is inside the working surface of the polygon; if the number of intersection points of this ray and the polygon is even or 0, then point P is outside the working surface of the polygon.

[0025] Furthermore, the method for calculating the mining depth corresponding to each triangulated triangle is as follows: Let the mining depths of the vertices of the polygon be H1, H2, …, H n , and the distances from the centroid of the triangulated triangle to each vertex be d1, d2, …, d n , then the mining depth corresponding to this triangulated triangle is

[0026] Advantageous Effects

[0027] The present invention uses a triangulation algorithm to generate unit triangulated triangles with a large number of vertical sides in the case of pre-interpolating working surface points, which is beneficial for determining the upper and lower limits of double integrals during subsequent prediction of surface movement and deformation, and ensures the accuracy of polygon edge triangulation. In the invention, a geometrically rigorous algorithm for judging the positional relationship between points and polygons and the triangle centroid theorem are used to remove illegal triangles generated in irregular concave polygons. Considering the differences in information parameters of different triangulation units in inclined coal seams, a weighted average method is adopted and classes are created to integrate each triangle triangulation unit, so that the triangulation processing method of the present invention can be used for predicting the surface movement and deformation values of working surfaces of polygons with arbitrary mining shapes. Description of the Drawings

[0028] <000011​​​​​​​​​​​ Figure 3 (b) is a schematic diagram of the working surface edge and internal insertion points of the present invention.

[0032] Figure 4 (a) Schematic diagram of two large triangles for establishing the working surface of the present invention.

[0033] Figure 4 (b) is a schematic diagram of the preliminary triangulation without removing illegal triangles according to the present invention.

[0034] Figure 4 (c) is a schematic diagram of the final triangulation of the working surface of the present invention. DETAILED DESCRIPTION

[0035] The present invention will be further described in detail below with reference to the figures and specific implementation process:

[0036] The concave polygon inclined coal mining working face segmentation method for surface subsidence prediction of the present invention first uses the existing mining data of the mining area, usually CAD files, such as Figure 1 and Figure 2 As shown in the figure, due to the large difference in mining depth of each vertex of the inclined coal seam, the mining depths of each vertex of the concave polygon mining working face H1, H2, ..., H n The vertex coordinates are stored in counterclockwise order, without tilted seams such as (x1, y1), (x2, y2), (x3, y3), ..., (x n ,y n );

[0037] Take one fifth of the average mining depth To fix the interval, first interpolate the points on the polygon edge, and then generate the vertical rectangular grid points circumscribing the polygon based on the interval. Remove the points outside the polygon and the points whose distance from the polygon is less than D / 2, and keep the grid points inside the polygon, such as Figure 3 As shown in (a), the polygon edge and all internal interpolation interval points are obtained, as shown in Figure 3 As shown in (b), all interpolation point coordinates are sorted from smallest to largest in the X coordinate order and stored in the array Vertices to record the (X, Y) coordinates of each interpolation point.

[0038] Extract the maximum X and Y, and the minimum X and Y according to the vertex coordinates of the working surface, and follow the following order: ①{(minimum X, maximum Y), (minimum X, minimum Y), (maximum X, minimum Y)}, ②{(maximum X, minimum Y), (maximum X, maximum Y), (minimum X, maximum Y)}, to create two large triangles covering the working surface and store them in the triangle list Triangles. Figure 4(a), establish the following two large triangles: ①{(x1,y8), (x1,y2), (x7,y2)}, ②{(x7,y2), (x7,y8), (x1,y8)}.

[0039] Traverse the interpolation points in Vertices, and judge the positional relationship between an interpolation point M and the circumcircle of a certain triangle in Triangles (denote the coordinates of the three vertices of a certain triangle as: A(x1,y1), B(x2,y2), C(x3,y3), and denote D = (x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2)) * 2, X = (x1 2 + y1 2 ) * (y2 - y3) + (x2 2 + y2 2 ) * (y3 - y1) + (x3 2 + y3 2 ) * (y1 - y2), Y = (x1 2 + y1 2 ) * (x3 - x2) + (x2 2 + y2 2 ) * (x1 - x3) + (x3 2 + y3 2 ) * (x2 - x1), then the centroid coordinates of this triangle are P(X / D, Y / D), and then compare the magnitudes of MP and AP. If MP = AP, then point M is on the circumcircle of this triangle; if MP > AP, then point M is outside the circumcircle of this triangle; if MP < AP, then point M is inside the circumcircle of this triangle, and thus the positional relationship between this point and the center of the circumcircle of the triangle can be determined). If the point is inside or on the circumcircle of this triangle, then delete this triangle from the list, and then connect point M to the three vertices of the just-deleted triangle, thereby forming three new triangles, and add these three new triangles to the list Triangles. If point M is outside the circumcircle of this triangle, add this triangle to the list Triangles. When all the points in Vertices have been traversed, delete the two originally constructed large triangles, and the finally formed list Triangles is all the triangulated triangles obtained by the preliminary triangulation.

[0040] Calculate the centroid coordinates of each triangulated triangle: Denote the coordinates of the three vertices of a certain triangle as: A(x1,y1), B(x2,y2), C(x3,y3), then the centroid coordinates of this triangle are P((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3).

[0041] Determine the positional relationship between the center of gravity point and the polygon working surface: let the coordinates of a certain center of gravity point be P, and draw a horizontal ray from point P to the left or right. If the number of intersections between the ray and the polygon is odd, then point P is inside the polygon. If the number of intersections between the ray and the polygon is even or 0, then point P is outside the polygon.

[0042] If the centroid is inside the polygonal working surface, the triangle is retained; if the centroid is outside the polygonal working surface or on the edge, the triangle is removed. In this way, all the subdivided triangles of the concave polygonal working surface are obtained.

[0043] Due to the existence of the dip angle of the inclined coal seam, the use of average mining depth in the subsequent surface movement and deformation prediction process will make the predicted value out of touch with reality. The mining depth corresponding to each subdivided triangle is obtained by weighted average calculation based on the distance from the center of gravity of each subdivided triangle to each vertex of the polygon working surface as the calculation value. The specific method is to set the mining depth of each vertex of the polygon as H1, H2, ..., H n , the distance from the centroid of a certain triangle to each vertex is d1, d2, ..., d n , then the corresponding mining depth of the subdivided triangle is

[0044] To facilitate data management and reflect the integrity of the inclined coal seam working face segmentation method, the coordinates and parameter information of the segmented triangles are stored in the UDelTris class. This class is used to record the information of each segmentation unit, which can realize the integration of the segmentation unit information of the coal mining working face, including the coordinates of the three vertices of the triangle, the triangle sequence number, the coordinates of the triangle center of gravity, and the mining depth corresponding to the triangle, which is beneficial to the subsequent movement deformation prediction and other related scenarios.

[0045] The C# code is as follows.

[0046]

[0047] Implementation Example

[0048] Step 1: Figure 2 As shown, assume that the mining depth of each vertex of the concave polygon mining working face is h1=340m, h2=260m, h3=260m, h4=280m, h5=280m, h6=260m, h7=260m, h8=340m, the average mining depth is H=285m, and the coordinates of the corner points are stored in the array Vertices in counterclockwise order: (x1, y1), (x2, y2), (x3, y3), (x4, y4), (x5, y5), (x6, y6), (x7, y7), (x8, y8).

[0049] Step 2: Take one fifth of the mining depth, i.e. D = H / 5 = 57m, as a fixed interval to interpolate points on the edge and interior of the polygonal working surface, such as Figure 3 As shown in (b). Store all the insertion point coordinates sorted in ascending order of the X coordinate first.

[0050] Step 3: Extract the maximum and minimum X and Y from the corner point coordinates of the working face. As shown in Figure 4 (a), establish the following two large triangles: ①{(x1,y8), (x1,y2), (x7,y2)}, ②{(x7,y2), (x7,y8), (x1,y8)}, and store them in the triangle list Triangles.

[0051] Step 4: Traverse the points in Vertices and judge the position relationship between a certain point M and the circumcircle of a certain triangle in Triangles (denote the coordinates of the three vertices of a certain triangle as: A(x1,y1), B(x2,y2), C(x3,y3), denote D=(x1*(y2 - y3)+x2*(y3 - y1)+x3*(y1 - y2))*2, X=(x1 2 +y1 2 )*(y2 - y3)+(x2 2 +y2 2 )*(y3 - y1)+(x3 2 +y3 2 )*(y1 - y2), Y=(x1 <000,0042>+y1 2 )*(x3 - x2)+(x2 <, 2 +y2 2 )*(x1 - x3)+(x3 2 +y3 2 )*(x2 - x1), then the centroid coordinates of this triangle are P(X / D, Y / D). Then compare the sizes of MP and AP. If MP = AP, then point M is on the circumcircle of this triangle; if MP > AP, then point M is outside the circumcircle of this triangle; if MP < AP, then point M is inside the circumcircle of this triangle. Thus, the position relationship between this point and the center of the circumcircle of the triangle can be determined.). If the point is inside or on the circumcircle of this triangle, then delete this triangle from the list, and then connect point M to the three vertices of the just-deleted triangle to form three new triangles, and add these three new triangles to the list Triangles. If point M is outside the circumcircle of this triangle, add this triangle to the list Triangles. When all the points in Vertices have been traversed, delete the two originally constructed large triangles. The finally formed list Triangles is all the triangulation triangles obtained by the preliminary triangulation.

[0052] Step 5: Calculate the coordinates of the center of gravity of each subdivided triangle: Let the coordinates of the three vertices of a triangle be: A(x1,y1), B(x2,y2), C(x3,y3), then the coordinates of the center of gravity of the triangle are P((x1+x2+x3) / 3,(y1+y2+y3) / 3).

[0053] Step 6: Determine the positional relationship between the center of gravity and the polygonal working surface: Let the coordinates of a certain center of gravity be P, and draw a horizontal ray from point P to the left. If the number of intersections between the ray and the polygon is odd, then point P is inside the polygon. If the number of intersections between the ray and the polygon is even or 0, then point P is outside the polygon. Figure 4 As shown in (b), the centroids of the triangles in the red area are outside the polygon, which are illegal triangles and should be removed.

[0054] Step 7: If the centroid is inside the polygonal working surface, keep the triangle; if the centroid is outside the polygonal working surface or on the edge, remove the triangle. In this way, all the subdivided triangles of the concave polygonal working surface are obtained, such as Figure 4 As shown in (c), a total of 252 triangles are obtained.

[0055] Step 8: Based on the distance from the center of gravity of each subdivided triangle to each vertex of the polygon working surface as the weight, and the mining depth of each vertex of the polygon working surface as the calculation value, the weighted average calculation is performed to obtain the mining depth corresponding to each subdivided triangle. The specific method is to set the mining depth of each vertex of the polygon as H1, H2, ..., H n , the distance from the centroid of a certain triangle to each vertex is d1, d2, ..., d n , then the corresponding mining depth of the subdivided triangle is

[0056] Step 9: Create the UDelTris class, which is used to record the information of each subdivision unit and integrate the subdivision unit information of the coal mining working face, including the coordinates of the three vertices of the triangle (x1, y1), (x2, y2), (x3, y3), the triangle serial number GZMSerial, the coordinates of the triangle center of gravity (GzmFocusX, GzmFocusY), and the mining depth H corresponding to the triangle.

Claims

1. A concave polygonal inclined coal mining face segmentation method for surface subsidence prediction, characterized by: For an inclined coal mining face with a concave polygon as the plan view, the steps are as follows: Obtain the information of the inclined coal seam of the concave polygon through the existing mining data of the mining area, including the coordinates of each vertex of the polygon space of the mining face and the mining depth of each vertex, that is, the mining depth. Arrange the vertex coordinates in the counterclockwise order of the plan view of the working face and store them; Assume that the mining thickness of the inclined coal seam is uniform. Simplify the polygon working face into a plan view. According to the principle of first the side line and then the interior, interpolating points are marked on the side line and inside of the plan view of the polygon working face. The spacing of the interpolating points is based on work experience or a fixed ratio. The fixed ratio is one-fifth of the depth from the upper roof of the working face to the ground surface, that is, the mining depth; Mark the coordinates of all interpolating points, and then sort and store all the interpolating point coordinates into an array Vertices according to the principle of increasing X coordinates from small to large. The array Vertices records the coordinate values (X, Y) of each interpolating point; Extract the largest X coordinates of the vertices of the concave polygon coal mining face max With the largest Y max Coordinates, minimum X min With Y min Coordinates, create two large triangles covering the concave polygon of the coal mining face plan, and store them in the triangle list Triangles, which records the coordinates of the three vertices of each triangle; Perform triangulation on the plan view of the concave polygon coal mining face. The specific process is as follows: ​ ​ ​ ​ ​ ​ ​ <h2 style=";text-align:left;direction:ltr">X=(x1<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +y1<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> )*(y2-y3)+(x2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +y2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> )*(y3-y1)+(x3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +y3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> )*(y1-y2), Y=(x1 2 +y1 2 )*(x3-x2)+(x2 2 +y2 2 )*(x1-x3)+(x3 2 +y3 2 )*(x2-x1); ​ 2. The method for segmenting a concave polygonal inclined coal mining face for surface subsidence prediction according to claim 1, characterized in that: Due to the existence of the dip angle of the inclined coal seam, the use of the average mining depth in the subsequent surface movement and deformation prediction process will make the predicted value deviate from reality; the distance from the centroid of each triangular segmentation triangle to each vertex of the polygonal working surface is used as the weight, and the mining depth of each vertex of the polygonal working surface is used as the calculation value. The weighted average calculation can obtain the mining depth corresponding to each triangular segmentation triangle; considering that different triangular segmentation units in the inclined coal seam have different corresponding coal seam parameters, the UDelTris class is created to integrate the coordinates and parameter information corresponding to the triangulation units.

3. The method for segmenting a concave polygonal inclined coal mining face for surface subsidence prediction according to claim 1, characterized in that: The method for calculating the centroid coordinates of each subdivided triangle is: the coordinates of the three vertices of a triangle are: A(x1,y1), B(x2,y2), C(x3,y3), then the centroid coordinates of the triangle are P((x1+x2+x3) / 3,(y1+y2+y3) / 3).

4. The method for segmenting a concave polygonal inclined coal mining face for surface subsidence prediction according to claim 3, characterized in that: The steps to determine the positional relationship between the centroid of a triangle and the concave polygon working surface are as follows: let the coordinates of the centroid of a triangle be P, and draw a horizontal ray from point P to the left or right. If the number of intersections between the ray and the polygon working surface is odd, then point P is inside the polygon working surface. If the number of intersections between the ray and the polygon is even or 0, then point P is outside the polygon working surface.

5. The method for segmenting a concave polygonal inclined coal mining face for surface subsidence prediction according to claim 2, characterized in that: The method for calculating the mining depth corresponding to each subdivided triangle is: let the mining depth of each vertex of the polygon be H1, H2, ..., H n , the distance from the centroid of the triangle to each vertex is d1, d2, ..., d n , then the corresponding mining depth of the subdivided triangle is

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