Quantitative characterization method for rock mass structure based on block shape clustering analysis
Through block shape clustering analysis, the problem of difficult to describe the block shape characteristics of rock mass is solved, and the refined quantitative characterization of rock mass structure is realized, providing a more accurate model basis for rockfall disaster prediction.
Patent Information
- Application Number
- CN202510402076.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-01
- Publication Date
- 2025-08-15
AI Technical Summary
The prior art is difficult to fully describe the shape characteristics of rock mass blocks, resulting in limited predictive capacity for falling rock disasters.
By collecting rock fracture data based on block shape clustering analysis, three-dimensional models are constructed, and the points, lines, surfaces and topological data processing of the block system are performed, the shape similarity is calculated and spectral clustering is performed to construct representative blocks to reflect the true shape and size characteristics.
A comprehensive quantitative characterization of the shape characteristics of rock mass block systems has been realized, and the ability to build refined models for rockfall disaster motion analysis has been improved.
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Figure CN120495504A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of rock mass structure characterization, and in particular to a rock mass structure quantitative characterization method based on block shape cluster analysis. Background Art
[0002] Rockfall is a globally distributed geological hazard. Rockfall motion analysis is a core component of this disaster prevention and control system. Its analysis object is essentially the rock mass structure, which consists of two major elements: structural surfaces (joints) and structural bodies (blocks). Structural surfaces are interfaces within the rock mass that can cut the rock mass into blocks of varying shapes. Rock mass stability primarily depends on the mechanical interactions between blocks, so the rock mass needs to be generalized as a block system. As an important branch of rock mass stability analysis, rockfall motion analysis studies the rock mass as a block system.
[0003] Constructing a rockfall geometry model is a prerequisite for rockfall motion analysis, and the geometric representation of the block system is the theoretical basis for model construction. This can be divided into two aspects: size representation and shape representation. In terms of block system size representation, scholars widely use the in situ block size distribution (IBSD) method to quantitatively analyze size distribution characteristics by constructing cumulative block volume curves. However, due to the complexity and variability of actual block shapes, the characterization of their shape characteristics remains at a qualitative stage. The current mainstream method is the block shape distribution (BSD) method. The BSD method is essentially a block shape classification method based on artificially assumed shape parameters. These shape parameters can only characterize a certain shape characteristic of the block, such as slenderness or flatness. The limited shape parameters make it difficult to fully describe the complexity of natural block morphology and cannot effectively characterize the shape characteristics of the block system. This limitation poses a major challenge to the construction of rockfall geometry models and seriously restricts the ability to predict rockfall disasters. Summary of the Invention
[0004] In response to the above technical deficiencies, the present invention provides a method for quantitatively characterizing rock mass structure based on block shape cluster analysis, which can more comprehensively describe the complexity of natural block morphology, more effectively characterize the shape characteristics of the block system, and solve the problem of quantitative characterization of the block system shape. The purpose of the present invention is achieved through the following technical solutions:
[0005] A method for quantitatively characterizing rock mass structure based on block shape cluster analysis includes the following steps:
[0006] 1) Data acquisition: Collect the fracture data of the rock mass to construct the three-dimensional fracture network model DFN of the rock mass, and obtain the points, lines, surfaces and geometric and topological data of all blocks in the block system through the three-dimensional block recognition algorithm.
[0007] 2) Normalization of blocks: All blocks in the block system are scaled to a uniform volume while maintaining their shape to obtain new block data.
[0008] 3) Constructing point cloud data for the new block: The new block is treated as a polyhedron, a cuboid bounding box is generated for the polyhedron, the bounding box volume is calculated, and a Monte Carlo method is used to generate a uniformly distributed point cloud inside the bounding box. Points located within the polyhedron are extracted from the point cloud within the bounding box to construct point cloud data. These point clouds can represent the shape of the corresponding polyhedron.
[0009] 4) Apply the point cloud registration method to align pairwise polyhedral point clouds: All pairs of polyhedral point clouds in the block system are divided into four cases, and the iterative closest point ICP algorithm is used for point cloud registration. The registered source set is called aligned point cloud; for any pair of polyhedral point clouds a and b, the four cases of point cloud registration are: the source set is polyhedral point cloud a, and the target set is polyhedral point cloud b; the source set is the mirror point cloud of polyhedral point cloud a, and the target set is polyhedral point cloud b; the source set is polyhedral point cloud b, and the target set is polyhedral point cloud a; the source set is the mirror point cloud of polyhedral point cloud b, and the target set is polyhedral point cloud a.
[0010] 5) Calculate the maximum volume overlap ratio of each pair of polyhedrons: Calculate the maximum volume overlap ratio of all polyhedron pairs in the block system, and use the maximum volume overlap ratio to represent the shape similarity (SSI) of the polyhedrons. The maximum volume overlap ratio of two polyhedrons corresponding to the polyhedron point clouds a and b is expressed as:
[0011]
[0012] Where N bin Indicates: when the source set is a polyhedron point cloud a and the target set is a polyhedron point cloud b, the number of points of the aligned point cloud of the source set a that are inside the polyhedron b; N binm Indicates: when the source set is the mirror point cloud of polyhedron point cloud a and the target set is polyhedron point cloud b, the number of points of the aligned point cloud of the source set located within polyhedron b; N ain Indicates: when the source set is a polyhedron point cloud b and the target set is a polyhedron point cloud a, the number of points of the aligned point cloud of the source set b that are inside the polyhedron a; N ainm Indicates: when the source set is the mirror point cloud of polyhedron point cloud b and the target set is polyhedron point cloud a, the number of points of the aligned point cloud of the source set located within polyhedron a; N p The number of points inside the polyhedron is determined in advance.
[0013] 6) Constructing the shape similarity matrix: The SSI values of all pairs of blocks are stored in a matrix called the shape similarity matrix, as shown below:
[0014]
[0015] Where t is the total number of polyhedrons, SSI ij represents the SSI between the i-th and j-th blocks.
[0016] 7) Perform spectral clustering analysis on the shape similarity matrix: Use the MATLAB function "spectralcluster" to perform cluster analysis on the block shapes; this function requires two parameters: a similarity matrix and the number of clusters k; the shape similarity matrix obtained in step 6) is used as the similarity matrix, and the k value is determined by trial and error; the block grouping and clustering are completed based on the k value, and the random blocks are individually classified.
[0017] 8) Constructing representative shapes: In order to quantify the shape of each group of blocks, the block with the highest average similarity within the group is identified, and its shape is regarded as the representative shape of the group.
[0018] 9) Calculate the size distribution of each group of blocks: Apply the in situ block size distribution (IBSD) method to plot and analyze the volume probability distribution of the blocks; and use a histogram to approximate the probability density; the entire size distribution is classified into multiple parts; based on the cumulative probability curve intervals of different sizes, the main size indicators of the blocks in each group can be further determined; the main size indicators are identified from the ISBD diagram.
[0019] 10) Constructing a representative block: Combine steps 8) and 9) to construct a representative block for each group that combines representative shape and size information.
[0020] For further optimization, the specific operation of the block normalization in step 2) is as follows: treat the block as a polyhedron, first calculate the volume and centroid coordinates of the polyhedron; then, translate the polyhedron so that its centroid coincides with the origin of the coordinate system to obtain a normalized new polyhedron, and calculate the coordinates of all vertices of the new polyhedron; finally, the vertex coordinates of the normalized polyhedron are calculated using the following formula:
[0021]
[0022] Where V n is the predefined normalized volume, V p is the volume of the polyhedron, (x i ',y i ',z i ') represents the coordinate of the i-th vertex of the polyhedron after translation, and n is the total number of vertices of the polyhedron.
[0023] For further optimization, the number of bounding box points in step 3) is determined by the following formula:
[0024]
[0025] Where N boxis the number of point clouds within the bounding box, V box is the bounding box volume, N p is the number of points determined in advance inside the polyhedron, V p is the volume of the polyhedron; since the volumes of all polyhedrons are consistent, the number of points in the point cloud within the polyhedron is also consistent.
[0026] Furthermore, the trial-and-error method for determining the parameter k in step 7) is:
[0027] (a) Define the minimum average shape similarity threshold t m and the number threshold of random blocks t s There are some blocks with highly irregular shapes in the block system, called random blocks, which often exhibit two characteristics: (i) if they are clustered into clusters with regular shapes, their average similarity within the group is low; (ii) their number is much smaller than that of blocks with regular shapes. Therefore, when clustering results in a very small number of groups, the blocks within the group are considered random blocks. The threshold number of random block groups is expressed as t s , if the number of clustered block groups is less than or equal to t s , then the group of blocks is considered a random block. After removing these random blocks, the blocks remaining in the system are called grouped blocks. Clustering only grouped blocks can achieve better clustering results.
[0028] (b) Set an initial value for the number of clusters k, starting from 2.
[0029] (c) Based on the shape similarity matrix, spectral clustering analysis is performed using the MATLAB function "spectralcluster" to divide the blocks into k groups.
[0030] (d) Count the number of blocks in each group. If the number of blocks in a group is less than the threshold t s , then the group is determined to be a random block, and all relevant data need to be removed from the original similarity matrix to obtain a new similarity matrix; return to step (b) and start the process again, otherwise go to step (e).
[0031] (e) Construct a similarity matrix within each group of blocks and calculate the average similarity of each block in each group; if there is a block with an average similarity lower than t m , then add 1 to the k value and repeat steps (c) to (e) until the average similarity of all blocks exceeds t m .
[0032] (f) Complete block grouping and clustering, and classify random blocks into a separate category.
[0033] Furthermore, in step 9), the entire size distribution is classified into six parts according to the three-dimensional block volume classification index: "negligible", "very small", "small", "medium", "large" and "very large" blocks.
[0034] Furthermore, the number of bins in the histogram in step 9) is set to the square root of the total number of bins in the system.
[0035] Furthermore, in step 10), a representative shape of each group is obtained through step 8); for the representative size, the main size indicators are identified from step 9), and the weighted average of the box values in the main size of the distribution diagram is calculated as the representative size of the group; using the normalization method, a representative block is constructed by scaling the representative shape to the representative size.
[0036] Beneficial effects of the present invention:
[0037] 1. Compared with the traditional block shape chart method, the method for quantitative characterization of rock structure based on block shape cluster analysis disclosed in the present invention quantitatively characterizes the complex shape characteristics of blocks through representative shapes, and further constructs representative blocks to reflect the true shape and size characteristics of the block system, which can provide basic data for the construction of a refined model for rockfall disaster motion analysis.
[0038] 2. The method of the present invention uses the geometric data and topological relationships of points, lines, surfaces and bodies within the block system as the main input parameters. The operation is objective and simple, easy to program, and improves calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 This is a schematic diagram of polyhedron a in Example 1 being translated so that its centroid is aligned with the origin;
[0040] Figure 2 Schematic diagram of obtaining a new polyhedron a" by normalizing the volume of polyhedron a' in Example 1;
[0041] Figure 3 Schematic diagram of the construction of the bounding box of polyhedron A and the generation of its internal point cloud in Example 1;
[0042] Figure 4 Point cloud A of Example 1 pc Schematic diagram representing polyhedron A;
[0043] Figure 5 Schematic diagram of the spectral clustering analysis process of the shape similarity matrix in Example 1;
[0044] Figure 6 Construct a representative shape diagram for Example 1;
[0045] Figure 7 This is a schematic diagram of the size distribution of the block group in Example 1;
[0046] Figure 8 Schematic diagram of the block system in the DP unit of Experimental Example 1;
[0047] Figure 9 This is a schematic diagram of the quantitative characterization of the shape and size of the block system in an open-pit mine in the United States in Experimental Example 1;
[0048] Figure 10 Schematic diagram of the proportion of different shape types of blocks in different groups of Experimental Example 1 using the BSD method. DETAILED DESCRIPTION
[0049] The present invention will be further described in detail below with reference to the accompanying drawings. The following specific implementation steps may enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any form.
[0050] First, it should be noted that the use of computer simulation to generate a three-dimensional fracture network (DFN) model of a rock mass, three-dimensional block identification, iterative closest point (ICP), and spectral clustering analysis algorithms are all existing technologies and theoretical algorithms. The technical solution of the present invention quantitatively characterizes the block system based on the block geometry data obtained by three-dimensional block identification, which will involve a large amount of existing technology, the definitions or concepts of which are already well known or mastered in the art. Therefore, unless otherwise specifically explained in the present invention, other contents that are consistent with the existing known meanings will not be described one by one in the present invention.
[0051] Example 1
[0052] A quantitative characterization method for rock mass structure based on block shape cluster analysis
[0053] (1) Data collection:
[0054] The DFN model is constructed based on the existing field fracture data of the real rock mass. The point, line, surface and volume geometry and topology data of all blocks in the block system are obtained through the 3D block recognition algorithm.
[0055] (2) Normalization of blocks
[0056] These blocks are treated as polyhedrons and scaled to a uniform volume while maintaining their shape, resulting in new blocks with a uniform volume. Taking polyhedron a as an example, the normalization method is explained in detail.
[0057] Specifically in this embodiment Figure 1 As shown, the centroid coordinates of polyhedron a are: P aC (x ac ,y ac ,z ac ). The volume of polyhedron a is given by V apThen, translate the polyhedron a so that its center of mass coincides with the origin of the coordinate system, and obtain a new polyhedron a', as shown in Figure 1 shown.
[0058] Finally, the polyhedron a' is scaled to obtain a new polyhedron a", and the volume of the new polyhedron is the predefined normalized volume V n ,like Figure 2 As shown. The vertex coordinates of polyhedron a' are calculated by the following formula which is a concrete form of formula (3):
[0059]
[0060] In the formula, (x a'i ,y a'i ,z a'i ) represents the coordinates of the i-th vertex of polyhedron a'.
[0061] (3) Construct point cloud data for the new block
[0062] Generate a cuboid bounding box for the polyhedron, calculate the bounding box volume, and generate a uniformly distributed point cloud inside it using the Monte Carlo method.
[0063] In this embodiment, if the polyhedron A has been normalized, then its bounding box and the point cloud inside the box are as follows: Figure 3 The number of points in the box is determined by the following formula, which is a concrete form of formula (4):
[0064]
[0065] Where N Abox is the number of points in the bounding box, V Abox is the bounding box volume, N p is the number of points inside the polyhedron determined in advance, V Ap is the volume of polyhedron A. Since the volumes of all polyhedrons are consistent, the number of points in the point cloud within the polyhedron is also consistent.
[0066] Finally, the points inside the polyhedron are extracted from the point cloud inside the bounding box to construct the point cloud data. Figure 4 As shown, point cloud A pc As the internal point cloud of polyhedron A, the shape of polyhedron A can be reflected.
[0067] (4) Apply point cloud registration method to align pairwise polyhedron point clouds
[0068] The point cloud pair of any polyhedron A and B is represented as point cloud A pc and B pc For point cloud A pc and B pc There are four cases for point cloud registration between source set and target set: the source set is a polyhedral point cloud A pc, the target set is the polyhedron point cloud B pc ; The source set is the polyhedron point cloud A pc Mirror point cloud (A pcm ), the target set is the polyhedron point cloud B pc ; The source set is the polyhedron point cloud B pc , the target set is the polyhedron point cloud A pc ; The source set is the polyhedron point cloud B pc Mirror point cloud (B pcm ), the target set is the polyhedral point cloud A pc .
[0069] For polyhedron point cloud A pc and B pc The above four cases are registered using the Iterative Closest Point (ICP) algorithm. Finally, all the polyhedral point clouds in the block system are divided into the above four cases and point cloud registration is performed. The registered source set is called aligned point cloud.
[0070] (5) Calculating the Maximum Volume Overlap Ratio of Two Polyhedrons Specifically for this embodiment, for the polyhedron point cloud A pc and B pc There are four cases of point cloud registration. In each case, the number of points in the aligned point cloud that are inside the corresponding polyhedron of the target set is counted, and the proportion of internal points is further calculated. pc , the target set is the polyhedron point cloud B pc As an example of point cloud registration, after obtaining point cloud A pc Relative to the target set (polyhedron point cloud B pc )’s aligned point cloud A’ pc After that, the statistical point cloud A' pc The number of points N inside the polyhedron B Bin Number of points N Bin With N p The ratio of is the proportion of the number of internal points. After calculating the proportion of the number of internal points in the four cases, the maximum volume overlap of polyhedrons A and B can be expressed as the following formula, which is concretized by formula (1):
[0071]
[0072] Where N Bin Indicates: When the source set is a polyhedral point cloud A pc , the target set is the polyhedron point cloud B pc When the source set A pc The number of points of the aligned point cloud that are inside the polyhedron B; N Binm Indicates: When the source set is a polyhedral point cloud A pc Mirror point cloud A pcm , the target set is the polyhedron point cloud B pcWhen , the number of points of the source set’s aligned point cloud that are inside the polyhedron B; N Ain Indicates: When the source set is a polyhedral point cloud B pc , the target set is the polyhedron point cloud A pc When source set B pc The number of points of the aligned point cloud that are inside the polyhedron A; N Ainm Indicates: When the source set is a polyhedral point cloud B pc Mirror point cloud B pcm , the target set is the polyhedron point cloud A pc When , the number of points of the aligned point cloud of the source set lies within the polyhedron A.
[0073] Finally, the maximum volume overlap ratio of all polyhedron pairs within the block system is calculated. The greater the maximum volume overlap ratio of two polyhedrons, the closer their shapes are. Therefore, the maximum volume overlap ratio of polyhedrons is also called their shape similarity (SSI).
[0074] (6) Constructing shape similarity matrix
[0075] The SSI values of all block pairs are stored in a matrix called the shape similarity matrix, as shown in the following formula (2):
[0076]
[0077] Where t is the total number of blocks, SSI ij represents the SSI between the i-th and j-th blocks.
[0078] (7) Perform spectral clustering analysis on the shape similarity matrix
[0079] Cluster analysis of block shapes was performed using the MATLAB function "spectralcluster". This function requires two parameters: a similarity matrix and the number of clusters k. The shape similarity matrix obtained in step (6) was used as the similarity matrix, and the value of k was determined by trial and error.
[0080] The specific process of the trial-and-error method for determining the parameter k is:
[0081] (a) First define the minimum average shape similarity threshold t m and the number threshold of random blocks t s There are some blocks with highly irregular shapes in the block system, called random blocks, which often show two characteristics: (i) if they are clustered into clusters with regular shapes, their average similarity within the group is low; (ii) their number is much smaller than that of blocks with regular shapes. Therefore, when clustering results in a very small number of groups, the blocks within the group are regarded as random blocks. The threshold number of random block groups is expressed as t s , if the number of clustered block groups is less than or equal to ts , then the group of blocks is considered a random block. After removing these random blocks, the blocks remaining in the system are called grouped blocks. Clustering only grouped blocks can achieve better clustering results.
[0082] (b) Set an initial value for the number of clusters k, usually starting from 2.
[0083] (c) Based on the shape similarity matrix, spectral clustering analysis is performed using the MATLAB function "spectralcluster" to divide the blocks into k groups.
[0084] (d) Count the number of blocks in each group. If the number of blocks in a group is less than the threshold t s , then the group is determined to be a random block, and all relevant data must be removed from the original similarity matrix to obtain a new similarity matrix. Return to step (b) and restart the process, otherwise proceed to step (e).
[0085] (e) Construct a similarity matrix within each group of blocks and calculate the average similarity of each block in each group. If there is a block with an average similarity lower than t m , then add 1 to the k value and repeat steps (c) to (e) until the average similarity of all blocks exceeds t m .
[0086] (f) Complete block grouping and clustering, and classify random blocks into a separate category.
[0087] The flowchart of spectral clustering analysis of shape similarity matrix is shown in Figure 5 shown.
[0088] (8) Constructing representative shapes
[0089] In order to quantify the shape of each group of blocks, the block with the highest average similarity within the group is identified, and its shape is regarded as the representative shape of the group. Figure 6 As shown, the block information of a block system is represented by scattered points. These blocks are divided into two categories: grouped blocks and random blocks. The grouped blocks are clustered into three groups. Within each group, the block with the highest average SSI is selected as the representative shape of the group: Representative Shapes 1, 2, and 3. These representative shapes can be directly depicted, which offers advantages in visualization and refinement.
[0090] (9) Calculate the size distribution of each group of blocks
[0091] The in-situ block size distribution (IBSD) method was applied to plot and analyze the volume probability distribution of the blocks. Furthermore, a histogram was used to approximate the probability density, with the number of bins typically set to the square root of the total number of blocks in the system. Based on the three-dimensional block volume classification index, the entire size distribution was categorized into six parts: "negligible," "very small," "small," "medium," "large," and "very large" blocks. Based on the intervals between the cumulative probability curves for different sizes, the primary size index of the blocks in the system can be further determined. Figure 6 The size distribution of the third group of blocks in Figure 7 shown.
[0092] (10) Construction of representative blocks
[0093] For each group, a representative block combining representative shape and size information was constructed. First, the block with the highest average SSI within the group was identified; its corresponding shape data became the representative shape. For the representative size, the main dimensional indicators were first identified from the ISBD plot. The weighted average of the box values in the main dimensions of this distribution was then calculated as the representative size for the group. A normalization method was used to construct the representative block by scaling the representative shape to the representative size.
[0094] Test Example 1
[0095] Taking the Devonian Popovich (DP) unit in the slope of an open-pit mine in the United States as an example, the application of the quantitative characterization method of rock mass structure based on block shape cluster analysis in the present invention is further explained. For the slope geometric parameters, according to the data reported by the mining company, the inclination of the cutting slope is set to 230°, and the existing step surface angle is set to 75°. The overall shape of the study area is similar to an inverted right-angled trapezoidal prism, with the upper depth, upper width and slope height of 3 meters, 3 meters and 4 meters respectively. A three-dimensional fracture network (DFN) model was generated in this study area. The structural surfaces are assumed to be equivalent disks, and their geometric characteristic data are summarized in Table 1. Using the three-dimensional block recognition algorithm, the block system geometric data in the DP unit are further identified, such as Figure 8 shown.
[0096] Table 1. Summary of characteristic parameters of DP structure face groups
[0097]
[0098] Set the normalized volume of all blocks to 100m 3 The number of random points generated in each block is set to 10,000, and the minimum average shape similarity t m Set to 40%, the random block number threshold t sSet to 2% of the total number of block clusters. Using the method of Example 1, this test example quantitatively characterized 617 finite blocks in the slope, which were divided into 608 grouped blocks and 9 random blocks. Spectral clustering further classified the grouped blocks into 8 groups. For each group of blocks, the representative shape was determined by selecting the block with the highest average similarity within the group, and the size distribution of each group of blocks was calculated. The relevant data are summarized in Figure 9 middle.
[0099] The method of Example 1 was compared with the currently widely used block shape distribution (BSD) method, and the proportions of different groups of blocks in different shape types of the BSD method were calculated, such as Figure 10 As shown. Although the shape characteristics of each representative block can be partially inferred by the proportion of the shape area to which it belongs. However, the two shape parameters and six shape categories of the BSD method are difficult to fully capture the other morphological characteristics of the block, and fail to fully reflect the multidimensional characteristics of shape evaluation. In contrast, the method of Example 1 can intuitively capture the morphological characteristics of each group of blocks by defining representative shapes rather than limited qualitative shape characteristics. In addition, although the slender shape can characterize the characteristics of five to eight groups of blocks to a certain extent, the method of the present invention can further refine the characterization of its shape to obtain a more refined expression effect. It can be seen that this method is effective and feasible.
[0100] The actual scope of the invention encompasses not only the specific embodiments disclosed above, but also all equivalent arrangements that can practice or implement the invention under the claims.
Claims
1. A method for quantitative characterization of rock mass structure based on block shape cluster analysis, characterized in that: The following steps are involved: 1) Data acquisition: Collect rock mass fracture data to construct a three-dimensional fracture network (DFN) model of the rock mass, and obtain the points, lines, surfaces, and geometric and topological data of all blocks in the block system through a three-dimensional block recognition algorithm; 2) Block normalization: scaling all blocks in the block system to a uniform volume while maintaining their shape to obtain new block data; 3) Constructing point cloud data for the new block: Treat the new block as a polyhedron, generate a cuboid bounding box for the polyhedron, calculate the volume of the bounding box, and use the Monte Carlo method to generate a uniformly distributed point cloud inside the bounding box. Extract the points inside the polyhedron from the point cloud inside the bounding box to construct the point cloud data; 4) Apply point cloud registration method to align pairwise polyhedral point clouds: All pairs of polyhedral point clouds in the block system are divided into four cases, and the iterative closest point ICP algorithm is used for point cloud registration. The registered source set is called aligned point cloud; for any pair of polyhedral point clouds a and b, the four cases of point cloud registration are as follows: the source set is polyhedral point cloud a and the target set is polyhedral point cloud b; the source set is the mirror point cloud of polyhedral point cloud a and the target set is polyhedral point cloud b; the source set is polyhedral point cloud b and the target set is polyhedral point cloud a; the source set is the mirror point cloud of polyhedral point cloud b and the target set is polyhedral point cloud a; 5) Calculate the maximum volume overlap ratio of each pair of polyhedrons: Calculate the maximum volume overlap ratio of all polyhedron pairs in the block system, and use the maximum volume overlap ratio to represent the shape similarity (SSI) of the polyhedrons. The maximum volume overlap ratio of two polyhedrons corresponding to the polyhedron point clouds a and b is expressed as: Where N bin Indicates: when the source set is a polyhedron point cloud a and the target set is a polyhedron point cloud b, the number of points of the aligned point cloud of the source set a that are inside the polyhedron b; N binm Indicates: when the source set is the mirror point cloud of polyhedron point cloud a and the target set is polyhedron point cloud b, the number of points of the aligned point cloud of the source set located within polyhedron b; N ain Indicates: when the source set is a polyhedron point cloud b and the target set is a polyhedron point cloud a, the number of points of the aligned point cloud of the source set b that are inside the polyhedron a; N ainm Indicates: when the source set is the mirror point cloud of polyhedron point cloud b and the target set is polyhedron point cloud a, the number of points of the aligned point cloud of the source set located within polyhedron a; N p The number of points inside the polyhedron is determined in advance; 6) Constructing the shape similarity matrix: The SSI values of all pairs of blocks are stored in a matrix called the shape similarity matrix, as shown below: Where t is the total number of polyhedrons, SSI ij represents the SSI between the i-th and j-th blocks; 7) Performing spectral clustering analysis on the shape similarity matrix: Performing cluster analysis on the block shapes using the MATLAB function "spectralcluster"; this function requires two parameters: a similarity matrix and the number of clusters k; the shape similarity matrix obtained in step 6) is used as the similarity matrix, and the k value is determined by trial and error; the blocks are grouped and clustered based on the k value, and random blocks are individually classified into one category; 8) Constructing representative shapes: To quantify the shape of each group of blocks, the block with the highest average similarity within the group is identified, and its shape is considered to be the representative shape of the group; 9) Calculate the size distribution of each group of blocks: Apply the in situ block size distribution (IBSD) method to plot and analyze the volume probability distribution of the blocks; use a histogram to approximate the probability density; and identify the main size indicators from the ISBD plot; 10) Constructing a representative block: Combine steps 8) and 9) to construct a representative block for each group that combines representative shape and size information.
2. The processing method according to claim 1, characterized in that: The specific operation of the block normalization in step 2) is as follows: the block is regarded as a polyhedron, and the volume and centroid coordinates of the polyhedron are first calculated; then, the polyhedron is translated so that its centroid coincides with the origin of the coordinate system to obtain a normalized new polyhedron, and the coordinates of all vertices of the new polyhedron are calculated; finally, the vertex coordinates of the normalized polyhedron are calculated using the following formula: Where V n is the predefined normalized volume, V p is the volume of the polyhedron, (x i ',y i ',z i ') represents the coordinate of the i-th vertex of the polyhedron after translation, and n is the total number of vertices of the polyhedron.
3. The processing method according to claim 1, characterized in that: The number of bounding box points in step 3) is determined by the following formula: Where N box is the number of point clouds within the bounding box, V box is the bounding box volume, N p is the number of points determined in advance inside the polyhedron, V p is the volume of the polyhedron.
4. The processing method according to claim 1, characterized in that: The trial and error method for determining the parameter k in step 7) is: (a) Define the minimum average shape similarity threshold t m and the number threshold of random blocks t s ; (b) Set an initial value for the number of clusters k, starting from 2; (c) Based on the shape similarity matrix, spectral clustering analysis was performed using the MATLAB function "spectralcluster" to divide the blocks into k groups; (d) Count the number of blocks in each group. If the number of blocks in a group is less than the threshold t s , then the group is determined to be a random block, and all relevant data need to be removed from the original similarity matrix to obtain a new similarity matrix; Return to step (b) and restart the process, otherwise go to step (e); (e) Construct a similarity matrix within each group of blocks and calculate the average similarity of each block in each group; if there is a block with an average similarity lower than t m , then add 1 to the k value and repeat steps (c) to (e) until the average similarity of all blocks exceeds t m ; (f) Complete block grouping and clustering, and classify random blocks into a separate category.
5. The processing method according to claim 1, characterized in that: In step 9), the entire size distribution is classified into six parts according to the three-dimensional block volume classification index: "negligible", "very small", "small", "medium", "large" and "very large" blocks.
6. The processing method according to claim 1, characterized in that: The number of bins in the histogram in step 9) is set to the square root of the total number of bins in the system.
7. The processing method according to claim 1, characterized in that: In step 10), the representative shape of each group is obtained through step 8); for the representative size, the main size indicators are identified from step 9), and the weighted average of the box values in the main size of the distribution diagram is calculated as the representative size of the group; using the normalization method, the representative block is constructed by scaling the representative shape to the representative size.
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