Statistical classification and identification method for three-dimensional gaussian mixed model of rock mass discontinuity

Abstract

The application provides a rock mass discontinuity three-dimensional Gaussian mixture model statistical classification and recognition method, and belongs to the field of mining engineering. On the basis of drawing the density mapping of the three-dimensional polar projection of the rock mass, the application utilizes a fast decision density peak value algorithm to automatically decide the optimal grouping number of the rock mass discontinuity. Then, the application utilizes a three-dimensional Gaussian mixture model to statistically analyze the size of the posterior probability of each point belonging to each three-dimensional Gaussian, and through a soft clustering mode, each point is distributed to the three-dimensional Gaussian mixture model with the maximum posterior probability, so as to realize the optimal soft clustering recognition of the number of the three-dimensional Gaussian mixture model, that is, the optimal grouping number, thereby realizing the rock mass discontinuity three-dimensional Gaussian mixture model statistical classification and recognition. The application is simple to realize, has a remarkable effect, and meets the application requirements.

Description

Technical Field

[0001] This invention belongs to the field of mining engineering, and in particular relates to a statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity. Background Technology

[0002] Understanding the distribution, properties, and characteristics of rock mass discontinuities helps in assessing rock mass stability, enabling appropriate measures to be taken during engineering design and construction to reduce the risk of rock mass collapse, sliding, or cave-in. Effectively identifying rock mass discontinuities plays a crucial role in the analysis of rock mass stability.

[0003] Existing methods for identifying rock mass discontinuities mainly employ surface reconstruction, neighborhood search, normal vector calculation, least squares fitting, voxel segmentation, K-means clustering, C-fuzzy clustering, density clustering, region growing algorithms, and tensor voting. By identifying rock mass discontinuities, relevant parameters required for rock mass stability analysis can be calculated, such as discontinuity spacing, the number of volumetric joints, and the rock mass structural grade. Quantitative analysis of these parameters allows for the analysis of rock mass quality, providing effective data support for rock mass slope stability analysis and landslide disaster prediction.

[0004] Existing research generally suffers from two major technical shortcomings. First, the number of discontinuous groups needs to be manually specified when determining it, and cannot be automatically determined. Both K-means clustering and C-fuzzy clustering require the number of discontinuous sets to be manually determined in advance. Second, hard clustering algorithms are usually used in the discontinuous clustering process, which cannot perform statistical optimization clustering analysis on the original data. The commonly used K-means clustering is a hard clustering algorithm, which is highly applicable to spherical clusters, but it is difficult to achieve accurate clustering for highly scattered stereographic projection mappings. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity, which solves the technical problems of automatic decision-making on the optimal number of groups for discontinuity and allocation of the optimal point of detection points, and realizes the statistical classification and identification of three-dimensional Gaussian mixture model of rock mass discontinuity.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity, comprising the following steps:

[0007] Step 1: Generate the density mapping of the rock mass's 3D stereographic projection by calculating the local density of the original rock mass's 3D point cloud dataset, including the following steps:

[0008] Step 1.1: Obtain the original 3D point cloud dataset D of the rock mass. The specific formula is as follows:

[0009] D={P1(x1,y1,z1),P2(x2,y2,z2),…,P n (x n ,y n ,z n )},n∈Z (1)

[0010] Among them, P n (x n ,y n ,z n Z represents the three-dimensional coordinates of the nth point in the original rock mass three-dimensional point cloud dataset D, where Z is a natural integer.

[0011] Step 1.2: Calculate the normal vector of the original rock mass 3D point cloud dataset D and normalize it;

[0012] Let A be the covariance matrix of the original 3D point cloud dataset D of the rock mass. The specific formula is as follows:

[0013]

[0014] Where, x' i ,y' i ,z' i x i ,y i ,z i The first derivative;

[0015] Find the eigenvalues ​​λ of the covariance matrix A i1 , λ i2 and λ i3 and the eigenvector V i1 V i2 and V i3 Among them, V i1 It is the normal vector of each point in the original 3D point cloud dataset D of the rock mass; then it is normalized and represented as V. i ;

[0016] Step 1.3: Calculate the density mapping coordinates P of the three-dimensional stereographic projection of the rock mass for each point in the original three-dimensional point cloud dataset D. pi (x, y, z) is called the pole, and the specific formula is:

[0017] P pi (x,y,z)=P pi (V i (x),V i (y),V i (z)) (3)

[0018] Among them, V i (x),Vi (y),V i (z) represent V i Components in the x, y, and z directions;

[0019] Step 1.4: Calculate the local density ρ of each point in the 3D point cloud dataset D of the rock mass. i The specific formula is as follows:

[0020]

[0021] Where, d c For P pi The cutoff radius of (x,y,z), d ij For P pi Within the cutoff radius of (x,y,z) P pi (x,y,z) and P pj The distance P from (x,y,z) pj (x,y,z) is P pi The neighborhood of the cutoff radius of (x,y,z), where N is a neighborhood of P. pi The number of valid points within the cutoff radius of (x,y,z), ρ max For local density ρ i The maximum value;

[0022] Step 2: Use the fast decision density peak algorithm to find the density peak points. The total number of density peak points is the number of rock mass discontinuity groups. Then, automatically decide the optimal number of rock mass discontinuity groups.

[0023] The fast decision density peak algorithm includes two parameters: local density ρ. i and relative distance d i ;

[0024] Wherein, the local density ρ i As shown in the formula in step 1.4, the relative distance d i The specific formula is:

[0025]

[0026] Where, j:ρ j >ρ i For P pi Within the cutoff radius of (x,y,z), there exists a density higher than P. pi A point (x, y, z) with j: ρ j <ρ i P represents pi There are no densities higher than P within the cutoff radius of (x,y,z). pi The point in (x,y,z);

[0027] Step 3: Soft clustering is performed on the original 3D point cloud dataset D of the rock mass using a 3D Gaussian mixture model. The optimal 3D Gaussian mixture model is obtained by calculating the posterior probability of each point in the dataset D. The posterior probability of each point belonging to each 3D Gaussian mixture model is compared, and each point is assigned to the 3D Gaussian mixture model with the highest posterior probability. This achieves optimized soft clustering identification of the number of 3D Gaussian mixture models K, i.e., the optimal number of groups, thereby realizing statistical classification and identification of rock mass discontinuities using 3D Gaussian mixture models. This includes the following steps:

[0028] Step 3.1: Based on the extreme coordinates of each point in the original rock mass 3D point cloud dataset D, establish a 3D Gaussian mixture model P(X), with the specific formula as follows:

[0029]

[0030] Where, X = {P} p1 (x,y,z),P p2 (x,y,z),…,P pn (x,y,z)},P pn (x,y,z) are the coordinates of the pole of the nth point in X, π k ={π1,π2,…,π K},μ k ={μ1,μ2,…,μ K},Σ k ={Σ1,Σ2,…,Σ K}, where K is the number of 3D Gaussian mixture models, and π k The weight μ of each 3D Gaussian mixture model in the 3D Gaussian mixture model. k The mean of each 3D Gaussian mixture model, Σ k The covariance matrix for each 3D Gaussian mixture model;

[0031] Step 3.2: Establish the probability density function f(X) of the three-dimensional Gaussian mixture model. The specific formula is as follows:

[0032]

[0033] Step 3.3: Calculate the posterior probability γ(i,j) of each pole in X belonging to each 3D Gaussian model. The specific formula is as follows:

[0034]

[0035] Where γ(i,j) represents P pi (x,y,z) is the posterior probability of a three-dimensional Gaussian model j. For P pi(x,y,z) represents the total probability of all three-dimensional Gaussian models, and the total probability includes multiple posterior probabilities;

[0036] Step 3.4: Obtain the parameters of the 3D Gaussian mixture model. The specific formula is as follows:

[0037]

[0038] in, π k (t+1) Let μ be the weight after t iterations. k (t+1) Σ is the mean after iteration. k (t+1) The result is the covariance matrix after iteration;

[0039] This will proceed through t iterations until μ is reached. k (t+1) The iteration stops when no further changes occur, at which point the optimal three-dimensional Gaussian mixture model is obtained. Finally, the posterior probability γ(i,j) of each point belonging to each three-dimensional Gaussian model is compared, and each point is assigned to the three-dimensional Gaussian model with the largest posterior probability, thus realizing the statistical classification and identification of rock mass discontinuity three-dimensional Gaussian mixture model.

[0040] The beneficial effects of adopting the above technical solution are as follows: The present invention provides a statistical classification and identification method for three-dimensional Gaussian mixture models of rock mass discontinuities. Based on the calculation of the three-dimensional stereographic projection density mapping of the rock mass, the optimal number of discontinuities is automatically determined by a fast decision density peak method. Then, the posterior probability of each point belonging to each three-dimensional Gaussian mixture model is statistically analyzed using the three-dimensional Gaussian mixture model. Through a soft clustering method, each point is assigned to the three-dimensional Gaussian model with the largest posterior probability, thereby realizing the statistical classification and identification of three-dimensional Gaussian mixture models of rock mass discontinuities.

[0041] This method is simple to implement, highly effective, and meets the application requirements. It can effectively achieve statistical classification and identification of rock mass discontinuities using a three-dimensional Gaussian mixture model, which is reflected in two aspects:

[0042] (1) It can automatically determine the optimal number of discontinuous groups using the fast decision density peak method;

[0043] (2) It can use the three-dimensional Gaussian mixture model to compare the posterior probability of each point belonging to each three-dimensional Gaussian model, and assign each point to the three-dimensional Gaussian model with the largest posterior probability, so as to realize the statistical classification and identification of rock mass discontinuity three-dimensional Gaussian mixture model. Attached Figure Description

[0044] Figure 1A flowchart of a statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity provided in this embodiment of the invention;

[0045] Figure 2 Density mapping diagram of three-dimensional stereoscopic projection provided in embodiments of the present invention;

[0046] Figure 3 The fast decision density peak decision map provided in this embodiment of the invention. Detailed Implementation

[0047] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0048] In this embodiment, a statistical classification and identification method for rock mass discontinuities using a three-dimensional Gaussian mixture model is described, such as... Figure 1 As shown, it includes the following steps:

[0049] Step 1: Generate the density mapping of the rock mass's 3D stereographic projection by calculating the local density of the original rock mass's 3D point cloud dataset, including the following steps:

[0050] The polar projection is an important basis for analyzing the spatial distribution of discontinuities in rock masses;

[0051] Step 1.1: Obtain the original 3D point cloud dataset D of the rock mass. The specific formula is as follows:

[0052] D={P1(x1,y1,z1),P2(x2,y2,z2),…,P n (x n ,y n ,z n )},n∈Z (1)

[0053] Among them, P n (x n ,y n ,z n Z represents the three-dimensional coordinates of the nth point in the original rock mass three-dimensional point cloud dataset D, where Z is a natural integer.

[0054] Step 1.2: Calculate the normal vector of the original rock mass 3D point cloud dataset D and normalize it;

[0055] Let A be the covariance matrix of the original 3D point cloud dataset D of the rock mass. The specific formula is as follows:

[0056]

[0057] Where, x' i ,y' i ,z' i xi ,y i ,z i The first derivative;

[0058] Find the eigenvalues ​​λ of the covariance matrix A i1 , λ i2 and λ i3 and the eigenvector V i1 V i2 and V i3 Among them, V i1 It is the normal vector of each point in the original 3D point cloud dataset D of the rock mass; then it is normalized and represented as V. i ;

[0059] Step 1.3: Calculate the density mapping coordinates P of the three-dimensional stereographic projection of the rock mass for each point in the original three-dimensional point cloud dataset D. pi (x, y, z) is called the pole, and the specific formula is:

[0060] P pi (x,y,z)=P pi (V i (x),V i (y),V i (z)) (3)

[0061] Among them, V i (x),V i (y),V i (z) represent V i Components in the x, y, and z directions;

[0062] Step 1.4: Calculate the local density ρ of each point in the 3D point cloud dataset D of the rock mass. i The specific formula is as follows:

[0063]

[0064] Where, d c For P pi The cutoff radius of (x,y,z), d ij For P pi Within the cutoff radius of (x,y,z) P pi (x,y,z) and P pj The distance P from (x,y,z) pj (x,y,z) is P pi The neighborhood of the cutoff radius of (x,y,z), where N is a neighborhood of P. pi The number of valid points within the cutoff radius of (x,y,z), ρ max For local density ρ i The maximum value;

[0065] The local density ρ i It is an important parameter that plays a crucial role in subsequent calculations;

[0066] Step 2: Use the fast decision density peak algorithm to find the density peak points. The total number of density peak points is the number of rock mass discontinuity groups. Then, automatically decide the optimal number of rock mass discontinuity groups.

[0067] The fast decision density peak algorithm includes two important parameters: local density ρ. i and relative distance d i ;

[0068] Wherein, the local density ρ i As shown in the formula in step 1.4, the relative distance d i The specific formula is:

[0069]

[0070] Where, j:ρ j >ρ i For P pi Within the cutoff radius of (x,y,z), there exists a density higher than P. pi A point (x, y, z) with j: ρ j <ρ i P represents pi There are no densities higher than P within the cutoff radius of (x,y,z). pi The point in (x,y,z);

[0071] Analysis of the density mapping diagram of the three-dimensional stereographic projection of the rock mass reveals that, as Figure 2 As shown, the number of discontinuous groups is determined by the number of density peaks at the poles in the density mapping of the three-dimensional stereographic projection. The characteristics of density peaks are high local density and large relative distance. This is because density peaks are surrounded by neighboring points with lower local density than their local density, and they are relatively far away from any point with higher local density than their local density. Using this decision criterion, density peaks can be accurately identified, and the total number of density peaks is the number of discontinuous groups.

[0072] The fast decision density peak decision graph is as follows: Figure 3 As shown, by Figure 3 It can be seen that point P1 has high local density and large relative distance, so it is determined to be the density peak point; Figure 3 Point P2 in the figure has low local density and large relative distance. Obviously, there are points around it with higher local density. These points are not density peak points. Point P3 in the figure has high local density and small relative distance. It belongs to the cluster where P1 is located. Point P4 in the figure has low local density and small relative distance. These points are isolated and belong to discrete points.

[0073] Step 3: Soft clustering is performed on the original 3D point cloud dataset D of the rock mass using a 3D Gaussian mixture model. The optimal 3D Gaussian mixture model is obtained by calculating the posterior probability of each point in the dataset D. The posterior probability of each point belonging to each 3D Gaussian mixture model is compared, and each point is assigned to the 3D Gaussian mixture model with the highest posterior probability. This achieves optimized soft clustering identification of the number of 3D Gaussian mixture models K, i.e., the optimal number of groups, thereby realizing statistical classification and identification of rock mass discontinuities using 3D Gaussian mixture models. This includes the following steps:

[0074] Step 3.1: Based on the extreme coordinates of each point in the original rock mass 3D point cloud dataset D, establish a 3D Gaussian mixture model P(X), with the specific formula as follows:

[0075]

[0076] Where, X = {P} p1 (x,y,z),P p2 (x,y,z),…,P pn (x,y,z)},P pn (x,y,z) are the coordinates of the pole of the nth point in X, π k ={π1,π2,…,π K},μ k ={μ1,μ2,…,μ K},Σ k ={Σ1,Σ2,…,Σ K}, where K is the number of 3D Gaussian mixture models, and π k The weight μ of each 3D Gaussian mixture model in the 3D Gaussian mixture model. k The mean of each 3D Gaussian mixture model, Σ k The covariance matrix for each 3D Gaussian mixture model;

[0077] Special attention should be paid to μ k ={V i (x),V i (y),V i (z)},V i As expressed by formula (2), μ k It is a three-dimensional vector, used to represent a three-dimensional Gaussian mixture model;

[0078] Step 3.2: Establish the probability density function f(X) of the three-dimensional Gaussian mixture model. The specific formula is as follows:

[0079]

[0080] Step 3.3: Calculate the posterior probability γ(i,j) of each pole in X belonging to each 3D Gaussian model. The specific formula is as follows:

[0081]

[0082] Where γ(i,j) represents P pi (x,y,z) is the posterior probability of a three-dimensional Gaussian model j. For P pi (x,y,z) represents the total probability of all three-dimensional Gaussian models, and the total probability includes multiple posterior probabilities;

[0083] Step 3.4: Obtain the parameters of the 3D Gaussian mixture model. The specific formula is as follows:

[0084]

[0085] in, π k (t+1) Let μ be the weight after t iterations. k (t+1) Σ is the mean after iteration. k (t+1) The result is the covariance matrix after iteration;

[0086] This will proceed through t iterations until μ is reached. k (t+1) The iteration stops when no further changes occur, at which point the optimal three-dimensional Gaussian mixture model is obtained. Finally, the posterior probability γ(i,j) of each point belonging to each three-dimensional Gaussian model is compared, and each point is assigned to the three-dimensional Gaussian model with the largest posterior probability, thus realizing the statistical classification and identification of rock mass discontinuity three-dimensional Gaussian mixture model.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuities, characterized in that: Includes the following steps: Step 1: Generate the density mapping of the three-dimensional stereographic projection of the rock mass by calculating the local density of the original three-dimensional point cloud dataset of the rock mass; Step 2: Use the fast decision density peak algorithm to find the density peak points. The total number of density peak points is the number of rock mass discontinuity groups. Then, automatically decide the optimal number of rock mass discontinuity groups. Step 3: Use a 3D Gaussian mixture model to process the original 3D point cloud dataset of the rock mass. Soft clustering is performed by calculating the original 3D point cloud dataset of the rock mass. The posterior probability of each point is calculated to obtain the optimal 3D Gaussian mixture model. The posterior probability of each point belonging to each 3D Gaussian mixture model is compared, and each point is assigned to the 3D Gaussian mixture model with the highest posterior probability, thus achieving the desired number of 3D Gaussian mixture models. That is, the optimal soft clustering identification with the best number of groups, thereby realizing the statistical classification and identification of rock mass discontinuity three-dimensional Gaussian mixture model; Step 3.1: Based on the original rock mass 3D point cloud dataset A three-dimensional Gaussian mixture model is established using the pole coordinates of each point. The specific formula is as follows: （6） in, , for The coordinates of the pole of the nth point in the equation. , The number of 3D Gaussian mixture models. The weight of each 3D Gaussian mixture model in the 3D Gaussian mixture model. The mean of each 3D Gaussian mixture model, The covariance matrix for each 3D Gaussian mixture model; Step 3.2: Establish the probability density function of the three-dimensional Gaussian mixture model The specific formula is as follows: （7） Step 3.3: Calculation The posterior probability of each pole belonging to each 3D Gaussian model The specific formula is as follows: （8） in, express Belongs to the three-dimensional Gaussian model The posterior probability, for The total probability belonging to all three-dimensional Gaussian models, wherein the total probability includes multiple posterior probabilities; Step 3.4: Obtain the parameters of the 3D Gaussian mixture model. The specific formula is as follows: （9） （10） （11） in, , For iteration t The subsequent weights, The mean after iteration. The result is the covariance matrix after iteration; Will pass t The iteration continues until... The iteration stops when no further changes occur, at which point the optimal 3D Gaussian mixture model is obtained; finally, the posterior probability of each point belonging to each 3D Gaussian is compared. The size is determined by assigning each point to the three-dimensional Gaussian model with the highest posterior probability, thereby achieving statistical classification and identification of rock mass discontinuities using a three-dimensional Gaussian mixture model.

2. The statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity according to claim 1, characterized in that: The specific method for step 1 is as follows: Step 1.1: Obtain the original 3D point cloud dataset of the rock mass : （1） in, Original rock mass 3D point cloud dataset The three-dimensional coordinates of the nth point in the equation are: It is a natural integer; Step 1.2: Calculate the original rock mass 3D point cloud dataset The normal vector and normalize it to a vector ; Step 1.3: Calculate the original rock mass 3D point cloud dataset Density mapping coordinates of the three-dimensional stereographic projection of the rock mass This is called the pole, and the specific formula is: （3） in, They are respectively exist Components in three directions; Step 1.4: Calculate the 3D point cloud dataset of the rock mass Local density at each point .

3. The statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity according to claim 2, characterized in that: The specific method for step 1.2 is as follows: Establish the original three-dimensional point cloud dataset of the rock mass. The covariance matrix is The specific formula is as follows: （2） in, They are respectively The first derivative; Solve the covariance matrix eigenvalues and eigenvectors ;in It is a dataset of original rock mass 3D point clouds. The normal vector of each point in the vector; then normalize it, and represent it as... .

4. The statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity according to claim 3, characterized in that: The local density described in step 1.4 The specific formula is: （4） in, for Cut-off radius, for Within the cutoff radius and distance, for The neighborhood points of the cutoff radius, for The number of valid points within the cutoff radius. For local density The maximum value.

5. The statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity according to claim 4, characterized in that: Step 2 describes a fast decision density peak algorithm that includes two parameters: local density. and relative distance .

6. The statistical classification and identification method for three-dimensional Gaussian mixture model of rock mass discontinuity according to claim 5, characterized in that: The relative distance The specific formula is: （5） in for Within the cutoff radius, there exists a density higher than point, express There is no density higher than [a certain value] within the cutoff radius. point.

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