Structural plane automatic identification optimization method based on self-optimization grouping of dominant structural plane

Abstract

The application discloses a structure surface automatic identification optimization method based on self-optimization grouping of dominant structure surfaces, establishes a new evaluation index of fuzzy clustering effect, and obtains an optimal clustering number by comparing the clustering effects under different clustering numbers. Thus, the use range of the fuzzy clustering is expanded, and the clustering number does not need to be manually specified. The structure surface data set can be quickly clustered under the condition that the clustering number is unknown, the self-optimization grouping of the dominant structure surfaces is realized, and the structure surface identification is completed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of data mining and surveying engineering, and particularly relates to a structural plane automatic identification optimization method based on self-optimization grouping of dominant structural planes. BACKGROUND

[0002] Clustering analysis, also known as unsupervised learning, is widely used to find natural grouping and composition patterns in data. Clustering is completed by calculating the similarity of each element in the data set. Fuzzy clustering (Fuzzy C Means, FCM) uses membership as a dissimilarity index, and uses membership function Jm (objective function) and minimum as an evaluation index to achieve clustering analysis of the data set. Since the dissimilarity index (membership) of fuzzy clustering is fuzzy, the classification of elements is in the form of probability (membership), which is beneficial to the classification of complex data. At the same time, the introduction of fuzziness makes the weight of observation values far from the centroid approach zero faster than the weight of observation values near the original centroid, greatly reducing the influence of far points on the determination of the centroid, so fuzzy clustering is less affected by outliers than other classification methods.

[0003] Three-dimensional laser scanning can record the spatial information of the structural plane of the slope and present it in the form of point cloud. In the point cloud, the structural plane of the slope rock mass is a "plane" with certain fluctuations and changes, which can be regarded as a plane within a certain spatial range, so the spatial information of the structural plane can be approximately described by using the geometric information of the plane. In geological survey, the spatial information of a structural plane is described by using inclination and dip angle. At the same time, the structural planes of the slope rock mass often appear in groups, and the structural planes in the same group have small differences in inclination and dip angle, and have obvious centroids that can be used for clustering, so the method of fuzzy clustering can be used to realize the identification of the structural plane. There are examples of realization in the identification of the structural plane of the tunnel (Liu Changjun, et al. Fuzzy clustering analysis of tunnel rock mass structural plane based on laser measurement and FKM clustering algorithm[J]. Journal of Jilin University (Earth Science Edition), 2014(44), 01:285-294.). When applied to other engineering such as slope engineering, the clustering result is greatly affected by the clustering number set by the human, and different people may get different results, which makes it difficult to ensure the accuracy of the clustering result.

[0004] Based on the advantages of fuzzy clustering, fuzzy clustering is widely used in data mining, image segmentation, data grouping and other fields. However, the clustering result of fuzzy clustering is greatly affected by the clustering number, especially in the identification of the structural plane, which requires certain prior knowledge before use. In the absence of prior knowledge (unknown clustering number), further research is needed to quickly estimate the optimal clustering number. At the same time, effective indicators for evaluating the effect or quality of fuzzy clustering are also indispensable. SUMMARY

[0005] The application aims to provide a structural surface automatic identification optimization method based on self-optimization grouping of dominant structural surfaces, establish a new evaluation index of fuzzy clustering effect, and obtain the optimal clustering number by comparing the clustering effects under different clustering numbers.

[0006] To solve the technical problems, the technical scheme of the application is:

[0007] The structural surface automatic identification optimization method based on self-optimization grouping of dominant structural surfaces comprises the following steps:

[0008] S1: Obtain point cloud data of a slope, establish a slope triangular mesh model by using a Delaunay triangulation algorithm, calculate the outer normal vector of each triangular surface in the triangular mesh model, and form a data set N;

[0009] S2: Determine the clustering number j=2, perform fuzzy clustering on the data set N, and obtain a membership function matrix U nj ;

[0010] S3: Sort the first dimension of the membership function matrix U nj , i.e. each row element, and transform the membership function matrix U nj into a matrix C nj ;

[0011] S4: Each row of the membership function matrix corresponds to each element of the data set one by one, the column serial number is the corresponding group, and the column where the maximum value of each row is located is the group of the element, and the classification result R n is obtained by traversing all elements;

[0012] S5: Determine the maximum value of each row of the membership function matrix U nj , which represents the intra-group similarity of the corresponding element, and the intra-group similarity index is obtained by summing the squares of the maximum values of each row of the membership function, i.e.

[0013]

[0014] S6: Calculate the inter-group similarity index B j ; determine the second maximum value of each row of the membership function, which represents the inter-group similarity of the corresponding element, and the inter-group similarity index is obtained by summing the squares of the second maximum values of each row of the membership function, i.e.

[0015] S7: Calculate the evaluation index Op j of the fuzzy clustering; and the evaluation index calculation expression of the fuzzy clustering is:

[0016] When the fuzzy clustering classification result corresponds to the actual class number of the data set, the clustering number is the optimal clustering number, at this time, the within-group similarity index A j and the between-group similarity index B j are obtained to obtain the relative maximum value.

[0017] S8: the optimal clustering number is obtained by iteration; the value of j (j=3, 4, 5,...) is changed to calculate O pj under the corresponding j value according to steps S2-S7; the optimal clustering number is the clustering group number j corresponding to the maximum value of O pj , that is, when Op j >Op j-1 and Op j >Op j+1 , j is the optimal clustering number, at this time, j is the same as the number of dominant structural surface groups.

[0018] S9: the classification result R n is output, that is, the self-optimizing grouping of the dominant structural surface is completed.

[0019] Further, the point cloud data of the slope is obtained by using a three-dimensional laser scanner.

[0020] Further, the data set N is an n*3 matrix; n is the number of data set elements, that is, the number of triangles in the triangular mesh, and the coordinates (x, y, z) of the outer normal vector of the triangle corresponding to each row are stored in the matrix in turn.

[0021] Further, the membership function matrix is an n*j matrix, the mth column is the probability of each triangle belonging to the mth group, 1≤m≤j, and m is a positive integer.

[0022] Further, the membership function matrix U nj is obtained, and the elements of the ith row are u i1 , u i2 , …, u ij in turn. nj In C i1 , the elements of the row are assigned values c im = u i2 , c i2 = u ij , …, c i1 = u im in turn, where u i2 ≥ u i1 ≥…≥ u .

[0023] Further, the within-group similarity index A jThe index represents the accuracy of each triangle grouping when the cluster number is j, and the greater the value, the more accurate the classification result, and the maximum value is 1, and when the classification boundary is fuzzy, the intra-group similarity index is not 1.

[0024] Further, the inter-group similarity index B j The index represents the error of each triangle grouping when the cluster number is j, and the smaller the value, the more accurate the classification result, and the minimum value is 0, but when the classification boundary is fuzzy, the intra-group similarity index is not 0.

[0025] Further, the evaluation index Op j of fuzzy clustering is calculated j The index reflects the principle of minimizing the inter-class similarity, i.e. j The inter-group similarity index B j reaches the minimum value, and maximizing the intra-class similarity, i.e. j The intra-group similarity index A j reaches the maximum value.

[0026] Compared with the prior art, the advantages of the present application are:

[0027] The present application studies the optimal cluster number estimation method of fuzzy clustering, expands the use range of fuzzy clustering, and enables it to quickly cluster the data set under unknown cluster number; when the number of advantage structural plane groups of a slope is unknown or cannot be determined, the optimal cluster number estimation can be completed within 1 minute (point cloud data does not exceed 2*10 7 ) by using the method, the evaluation index realizes self-optimization grouping of structural planes, and optimizes the structural plane automatic identification algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 : The generated data set graph (data4 is uniformly distributed noise);

[0029] Figure 2 : Fuzzy clustering result graph (a cluster number 2; b cluster number 3, data4 is noise; c cluster number 4, data5 is noise; d cluster number 5, data6 is noise);

[0030] Figure 3 : Comparison graph of the method and the contour coefficient index;

[0031] Figure 4 : Example slope triangular mesh model graph;

[0032] Figure 5 : Slope structural plane automatic grouping result (group number 4) graph;

[0033] Figure 6 : Four-group structural plane occurrence distribution graph;

[0034] Figure 7Flowchart for structural surface identification. Detailed Implementation

[0035] The specific implementation of the present invention is described below with reference to embodiments:

[0036] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0037] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0038] Example 1:

[0039] like Figure 7 As shown, this embodiment includes the following steps:

[0040] (1) Obtain the point cloud data of the slope and use the Delaunay triangulation algorithm to establish a slope triangular network model, and then calculate the outward normal vector of each triangle face in the triangular network. Form a dataset N, which is an n*3 matrix (n is the number of elements in the dataset, i.e. the number of triangles in the triangular network), and store the coordinates (x, y, z) of the outward normal vector of the corresponding triangle in each row.

[0041] (2) Fuzzy Clustering. Since the number of clusters in dataset N is unknown, fuzzy clustering is first performed on dataset N with a cluster number j=2 to obtain the membership function matrix U. nj The membership function matrix is ​​an n*j matrix, and the m-th column represents the probability that each triangle belongs to the m-th group (1≤m≤j, and m is a positive integer).

[0042] (3) Sort the membership function matrix and sort along the membership function matrix U. nj Sort the elements of the first dimension (each row) and then sort the membership function matrix U. nj Transform into matrix C nj For example, for U nj The i-th row contains elements that are u in sequence. i1 u i2 ,…,u ij Then in C nj The elements in this row are assigned the value c in sequence. i1 =uim , c i2 = u i2 , …, c ij = u i1 , where u im > u i2 > … > u i1 .

[0043] (4) Get the classification result R n . Each row of the membership function matrix corresponds to each element of the data set, and the column number is the corresponding group. The column where the maximum value of each row is located is the group of the element, and the classification result R n is obtained by traversing all elements. For example, also for the i-th row described in step (3), since u im is the maximum value, the i-th row element r n = m in R i .

[0044] (5) Calculate the intra-group similarity index A j proposed in this method, which represents the accuracy of each triangle group under the condition of clustering number j. The larger the value, the more accurate the classification result, and the maximum value is 1. However, when the classification boundary is fuzzy, the intra-group similarity index cannot reach 1. This method considers that the maximum value of each row of the membership function matrix U nj represents the intra-group similarity of the element, and the intra-group similarity index is obtained by summing the squares of the maximum values of each row of the membership function, that is,

[0045] (6) Calculate the inter-group similarity index B j proposed in this method, which represents the error degree of each triangle group under the condition of clustering number j. The smaller the value, the more accurate the classification result, and the minimum value is 0. However, when the classification boundary is fuzzy, the intra-group similarity index cannot reach 0. This method considers that the second maximum value of each row of the membership function is the inter-group similarity of the element, and the inter-group similarity index is obtained by summing the squares of the second maximum values of each row of the membership function, that is,

[0046] (7) Calculate the fuzzy clustering index Op j proposed in this method. This index reflects the clustering principle of "minimizing inter-class similarity (inter-group similarity index B j reaches the minimum value, and maximizing intra-class similarity (intra-group similarity index A j reaches the maximum value)". The evaluation index calculation expression of the fuzzy clustering proposed in this method is:

[0047]

[0048] The method considers that when the fuzzy clustering classification result corresponds to the actual class number of the data set, the clustering number is the optimal clustering number. At this time, the within-group similarity index A j and the between-group similarity index B j reach the relative maximum value.

[0049] (8) The optimal clustering number is obtained by iteration. Change the value of j (j = 3, 4, 5, …) to calculate O pj under the corresponding j value according to steps (2)-(7). The optimal clustering number is the clustering group number j corresponding to the maximum value of O pj . When Op j > Op j-1 and Op j > Op j+1 , j is the optimal clustering number, and at this time, j is the same as the number of dominant structure plane groups.

[0050] (9) Output the classification result R n of this time, and complete the self-optimization grouping of the dominant structure plane.

[0051] Example 2:

[0052] (1) A Gaussian mixture model is used to generate three categories (data1, 2, 3, each category satisfies a normal distribution with a mean as a center point, a dimension 1 variance of 5, and a dimension 2 variance of 10, and two dimensions represent the occurrence of a structure plane: inclination and dip angle. One data point is a structure plane), and a data set N with n = 330 elements (each element has two dimensions, dimension 1: 0-90, dimension 2: 0-360, ) is generated, of which 30 elements are noise (data4, uniformly distributed in this area). The specific classification is shown in FIG. 1. Figure 1 ;

[0053] (2) After completing steps (2)-(7) of the scheme, the result is shown in FIG. 2. Figure 2 When the optimal clustering number corresponds to the actual class number of the data set, the fuzzy clustering classification result is the best (the best agreement with the generated data set classification, FIG. 2b), indicating that the optimal clustering number determined by the method is accurate. Figure 2

[0054] (3) The difference between the accuracy of the optimal clustering number and the silhouette coefficient and the superiority are shown in FIG. 3. Both the evaluation index Op of the method and the silhouette coefficient index can obtain the optimal clustering number 3, but in this example, the Op is about 12 times faster than the silhouette coefficient. Figure 3

[0055] Example 3:

[0056] The specific implementation of the method will be described below with reference to specific examples:

[0057] ​​(1) In this example, the point cloud data of the slope is obtained by using a three-dimensional laser scanner, and a triangular mesh model of the slope is established by using the Delaunay triangulation algorithm (the triangular mesh contains 423423 triangles, attached Figure 4 ), and the outer normal vector of each triangle in the triangular mesh is calculated. Form a data set N, N is a 423423*3 matrix, each row stores the coordinates (x, y, z) of the outer normal vector of the corresponding triangle in the row.

[0058] (2) Fuzzy clustering. Since the number of clusters of data set N is unknown, first use the number of clusters j = 2 to perform fuzzy clustering on data set N to obtain membership function matrix U2. The membership function matrix is a 423423*2 matrix, the mth column is the probability of each triangle belonging to the mth group (1≤m≤2, and m is a positive integer).

[0059] (3) Sort the membership function matrix, sort the elements along the first dimension (each row) of the membership function matrix U2, and transform the membership function matrix U2 into matrix C2. For example, for the 34th row of U2, the elements in the row are 0.724, 0.276 in turn, then in C2 the elements in the row are assigned values c 34，1 = 0.724, c 34，2 = 0.276.

[0060] (4) Get the classification result R n . Each row of the membership function matrix corresponds to each element of the data set, and the column number is the corresponding group. The column where the maximum value of each row is located is the group of the element, and the classification result R n is obtained by traversing all elements. For example, for the 34th row described in step (3), since 0.724 is the maximum value, the 34th element r 34 = 1 in R n . That is, the triangle corresponding to this row is divided into the first group.

[0061] (5) Calculate the intra-group similarity index A2 proposed in this method,

[0062] A2 = 0.2715.

[0063] (6) Calculate the inter-group similarity index B2 proposed in this method,

[0064] B2 = 0.0544.

[0065] (7) Calculate the fuzzy clustering index Op2 proposed in this method.

[0066] (8) The optimal cluster number is obtained by iteration. Change the value of j (j=3, 4, 5,...) to calculate O pj . O p3 = 10.4911, O p4 = 19.9856, O p5 = 15.5159. O p4 is the maximum value, so the optimal cluster number is 4.

[0067] (9) The classification result R n with the cluster number of 4 is output, and the self-optimizing grouping of the dominant structural plane is completed (see the attached Figure 5 ).

[0068] (10) The stereographic projection map is drawn, and it is checked that the four groups of structural planes all have cluster centers and are separated from each other, and the clustering result is good (see the attached Figure 6 ).

[0069] The preferred embodiments of the present application are described in detail above, but the present application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present application.

[0070] Many other changes and modifications can be made without departing from the spirit and scope of the present application. It should be understood that the present application is not limited to a particular embodiment, and the scope of the present application is defined by the appended claims.

Claims

1. A structural plane automatic identification optimization method based on a self-optimization grouping of dominant structural planes, characterized in that, The method comprises: S1: obtaining point cloud data of the slope, and establishing a triangular mesh model of the slope by using a Delaunay triangulation algorithm, and calculating an outer normal vector of each triangular face in the triangular mesh model to form a data set N; S2: determine the cluster number j = 2, fuzzy cluster the data set N to obtain the membership function matrix U nj ; S3: along the first dimension of the membership function matrix U nj , i.e. each row element is sorted in descending order, the membership function matrix U nj is transformed into matrix C nj ; S4: each row of the membership function matrix corresponds to each element of the data set, the column number is the corresponding group, the column where the maximum value of each row is located is the group of the element, and all elements are traversed to obtain the classification result R n ; S5: Determine the membership function matrix U nj The maximum value of each row of the membership function matrix U represents the similarity within the corresponding group. The similarity index within the group is obtained by summing the square of the maximum value of each row of the membership function matrix, i.e. S6: Calculate the inter-group similarity index B j ; determine the second maximum value of each row of the membership function, which represents the inter-group similarity of the corresponding element, and obtain the inter-group similarity index by summing the squares of the second maximum values of each row of the membership function, i.e. S7: Calculate evaluation index Op of fuzzy clustering j ; Determine evaluation index calculation table of fuzzy clustering The expression is: When the fuzzy clustering classification result corresponds to the actual class number of the data set, the clustering number is the optimal clustering number, at this time, the within-group similarity index A j and the between-group similarity index B j reach the relative maximum or minimum value. S8: find the optimal cluster number by iteration; change j (j=3, 4, 5,...) value to calculate O pj of corresponding j value according to steps S2-S7 pj ; the optimal cluster number is the cluster group number j corresponding to the maximum value of O j j-1 and Op j >Op j+1 , j is the optimal cluster number, at this time j is the same as the dominant structure plane group number.​ S9: output the classification result R n That is, the self-optimizing grouping of the dominant structural plane is completed.

2. The structural plane automatic identification optimization method based on the self-optimization grouping of dominant structural planes according to claim 1, characterized in that, A three-dimensional laser scanner is used to obtain point cloud data of the slope.

3. The structural plane automatic identification optimization method based on the self-optimization grouping of dominant structural planes according to claim 1, characterized in that, The data set N is an n*3 matrix; n is the number of elements of the data set, that is, the number of triangles in the triangular mesh, and each row of the matrix stores the coordinates (x, y, z) of the outer normal vector of the corresponding triangle in the row.

4. The structural plane automatic identification optimization method based on the self-optimization grouping of dominant structural planes according to claim 1, characterized in that, The membership function matrix is an n*j matrix, the mth column is the probability of each triangle belonging to the mth group, 1≤m≤j, and m is a positive integer.

5. The structural plane automatic identification optimization method based on the self-optimization grouping of the dominant structural plane according to claim 1, characterized in that, The matrix U of membership functions nj The i-th row of U has elements u i1 , u i2 , …, u ij , then the i-th row of C nj has elements c i1 = u im , c i2 = u i2 , …, c ij = u i1 , where u im ≥ u i2 ≥ … ≥ u i1 .

6. The structural plane automatic identification optimization method based on the self-optimization grouping of dominant structural planes according to claim 1, characterized in that, The intra-group similarity index A j The index represents the accuracy of each triangle grouping in the case of clustering number j, the larger the value, the more accurate the classification result, the maximum value is 1, and the intra-group similarity index is not 1 when the classification boundary is fuzzy.

7. The structural plane automatic identification optimization method based on the self-optimization grouping of dominant structural planes according to claim 1, characterized in that, the inter-group similarity index B j The index represents the error degree of each triangle group when the cluster number is j. The smaller the value, the more accurate the classification result. The minimum value is 0, but the intra-group similarity index is not 0 when the classification boundary is ambiguous.

8. The structural plane automatic identification optimization method based on the self-optimization grouping of dominant structural planes according to claim 1, characterized in that, An evaluation index Op of fuzzy clustering is calculated j which reflects a clustering principle of minimizing the similarity between classes, i.e., a between-group similarity index B j reaching a minimum value, and maximizing the similarity within classes, i.e., a within-group similarity index A j reaching a maximum value.

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