Combination determination method for roof and side wall structure surface correlation and continuity based on unsupervised learning

Abstract

A method for determining the association and continuity combination of top-side-rock structural surfaces based on unsupervised learning is proposed. This method involves investigating the structural surfaces of the roof and side-rock masses in underground engineering projects to obtain geometric and statistical information. A unified encoding is performed to construct a joint feature set of roof-side-rock structural surfaces. An unsupervised density-based clustering algorithm is used for initial cluster analysis of the joint feature set. A swarm intelligence-based Lüperfox optimization algorithm is introduced to optimize key parameters of the DBSCAN clustering algorithm. A Latin hypercube sampling method is used to improve the population initialization process of the Lüperfox optimization algorithm, resulting in better DBSCAN hyperparameters and optimized structural surface clustering results. The method determines the structural surface system affiliation of structural surfaces in different locations, quantitatively calculates the spatial continuity and combination relationship of structural surfaces, and outputs the spatial association determination results and continuity levels of the roof-side-rock structural surfaces. This method enables intelligent identification and quantitative analysis of the spatial relationship between roof and side-rock rock structural surfaces.

Description

Technical Field

[0001] This invention belongs to the field of rock mass engineering and intelligent sensing technology, specifically relating to a method for determining the association and continuity combination of top edge and sidewall structural surfaces based on unsupervised learning. Background Technology

[0002] Under the long-term effects of stress, disturbance, and environmental evolution, primary and secondary structural planes within the surrounding rock of underground mines and engineering projects are continuously exposed and superimposed, forming a complex network system of structural planes. The roof and sidewalls, as two key components most easily exposed and subjected to significantly different stress conditions in underground space, directly influence the geometric integrity of the rock mass and its instability evolution path through the spatial extension, intersection, and combination of their structural planes. In engineering practice, roof and sidewall structural planes are often not isolated but rather spatial manifestations of the same source or group of structural planes in different locations. Their continuity and combination relationships across locations are crucial controlling factors for the formation and expansion of turquoise masses.

[0003] Currently, the analysis and judgment of structural surfaces in underground engineering still rely primarily on manual investigation and experience. This typically involves classifying and grouping structural surfaces by measuring their geometric parameters and statistical indicators on-site. While this method is feasible at small scales or when structural surfaces are relatively simple, it becomes susceptible to subjective human factors, differences in sampling scales, and limitations of the measurement environment in scenarios with dense structural surfaces, large spatial areas, or complex engineering conditions. This makes it difficult to arrive at a unified and stable judgment on the overall spatial relationship of structural surfaces in different locations. With the gradual application of automated structural surface identification methods based on image, point cloud, and statistical analysis, which extract feature parameters such as orientation, scale, density, and spacing of structural surfaces for digital description and analysis, a technical path has been provided to overcome the limitations of traditional methods. Furthermore, unsupervised learning methods can automatically group structural surface features to reduce human intervention. However, the application of commonly used unsupervised clustering algorithms in structural surface analysis generally relies on manually set or empirically selected key parameters. Structural surface data itself is characterized by uneven distribution, large scale differences, and numerous noise points; different parameter combinations often significantly affect the clustering results. This parameter sensitivity makes the clustering results unstable in different engineering scenarios, limiting its widespread application in practical engineering.

[0004] Furthermore, regarding the question of whether the roof and sidewall structural surfaces belong to the same structural surface system, existing technologies mostly rely on manual comparison of their directional characteristics or empirical judgment. There is a lack of a method that can jointly model and automatically identify the connections between structural surfaces of different locations within a unified feature space, and quantitatively characterize their spatial continuity and combination relationships. Achieving cross-location association identification and continuity level classification of roof and sidewall structural surfaces without requiring prior manual grouping remains a pressing technical problem in the field of underground engineering rock mass structural surface analysis. Therefore, there is an urgent need to provide a method for determining the association and continuity combination of roof and sidewall structural surfaces based on unsupervised learning, in order to achieve spatial association determination and continuity combination analysis of roof and sidewall structural surfaces across different locations. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for determining the association and continuity of top and side rock structural surfaces based on unsupervised learning. This method can intelligently identify and quantitatively analyze the spatial relationship between the structural surfaces of the roof and side rock mass, identify potential loose rock masses in the surrounding rock of underground mine roofs and classify the risk of rockfall, and provide a basis for on-site roof safety management and loose rock disposal decisions.

[0006] To achieve the above objectives, this invention provides a method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning, comprising the following steps: Step 1: Conduct a structural surface survey of the roof and side rock mass of the underground project, obtain geometric statistical information of the structural surface, and extract basic characteristic parameters; Step 2: Unify the feature parameters of the top plate and sidewall structural surfaces to construct a joint feature set of the top plate-sidewall structural surfaces, and normalize the feature parameters based on physical properties; Step 3: Use a density-based unsupervised clustering algorithm to perform initial clustering analysis on the constructed joint feature set to obtain the initial clustering results of the structural surface; Step 4: Introduce the Lüper Fox optimization algorithm based on swarm intelligence to optimize the key parameters of the DBSCAN clustering algorithm; Step 5: Improve the population initialization process of the Lüper Fox optimization algorithm by adopting the Latin hypercube sampling method, thereby enhancing the diversity and search uniformity of the initial population and obtaining better DBSCAN hyperparameters and optimized structural surface clustering results. Step Six: Based on the optimized structural surface clustering results, determine the structural surface system affiliation of different parts of the structural surface, quantify the spatial continuity and combination relationship of the structural surface, and finally output the spatial association determination result and continuity level of the top plate-side wall structural surface.

[0007] Furthermore, in order to achieve comprehensive collection of basic data, in step one, the structural surface geometric information includes the structural surface dip direction. ,inclination Joint group number Joint trace length Joint trace angle Joint trace density Joint trace intensity Spacing within joint groups Spacing between joint groups .

[0008] Furthermore, in order to achieve standardization and unification of multi-dimensional structural surface features and provide high-quality, highly adaptable feature data support for subsequent unsupervised clustering, the normalization process of feature parameters based on physical properties in step two is as follows: S21: Construction of original feature vectors; statistically analyze the geometric features of all structural surfaces, map these features to the same feature space, and form the original feature vectors of the structural surfaces; S22: Feature subgrouping based on physical properties; according to the physical meaning of the structural surface parameters, the feature parameters are divided into subgroups using formulas (1), (2), (3), and (4), respectively. , , , Four categories of feature subgroups based on physical attributes; (1); (2); (3); (4); In the formula, These are directional feature groups, representing the spatial attitude and trajectory of the structural surface; These are scale and quantity characteristic groups, representing the overall developmental scale and number of groups of structural surfaces; These are density and strength characteristic groups, representing the density of structural surface development and mechanical strength. This is a feature group representing the spatial spacing relationship between structural surfaces in the same and different groups; S23: Type-based normalization processing; For feature subgroups of different physical properties, a dedicated normalization method is used to eliminate the influence of dimensional differences and numerical ranges. For directional feature groups The angle parameters are converted into vector form using a vectorized mapping method. In the process of converting the orientation of the structural surface into a unit normal vector, the first normal vector is obtained according to formulas (5), (6), and (7). The unit normal vector of each structural surface is in , , Components of the axis , and During the transformation of joint trace angles into two-dimensional direction vectors, the first vector is obtained according to formula (8). Two-dimensional direction vector of each structural joint trace ; (5); (6); (7); (8); In the formula, For the first The inclination angle of each structural surface; For the first The tendency of each structural surface; For the first The joint trace angles of each structural surface; For size and quantity type feature groups Using logarithmic normalization, the results of the first step are obtained according to formulas (9) and (10), respectively. Normalized results of the number of joint groups and trace lengths for each sample , ; (9); (10); In the formula, For the first The number of joint groups in each sample; For the first The length of the joint trace in each sample; , These represent taking the minimum and maximum values ​​from the sample set, respectively. For density and intensity type feature groups Using a standardized processing method, the first step is obtained according to formula (11) and formula (12) respectively. Standardized results of joint trace density for each sample Standardized results of strength ; (11); (12); In the formula, For the first Joint trace density of each sample; For the first Joint trace intensity of each sample; , These are the mean values ​​of joint trace density and intensity, respectively, in the sample set; , These are the standard deviations of joint trace density and intensity in the sample set, respectively. For feature groups related to spacing and structure Using the maximum and minimum scale normalization method, the first number is obtained according to formula (13) and formula (14) respectively. Normalized results of intra- and inter-group intervals for each sample joint. , This maps the values ​​to the [0,1] interval; (13); (14); In the formula, , These are the minimum and maximum values ​​of the spacing within the joint group in the sample set, respectively. , These are the minimum and maximum values ​​of the spacing between joint groups in the sample set, respectively. S24: Joint feature vector construction; weighted fusion of the normalization results of various features, and construction of the first feature vector according to formula (15). The final joint feature vector of each structural surface sample used for unsupervised clustering analysis ; (15); In the formula, , , , , These are the weight coefficients for the direction normal vector, the trace direction vector, the scale quantity feature, the density intensity feature, and the spacing structure feature, respectively, and they satisfy the following conditions: =1; For the first The unit normal vector of the structural surface of each sample.

[0009] Furthermore, in order to provide a reasonable benchmark and quantitative basis for subsequent parameter optimization, the process of obtaining the initial clustering results of the structural surfaces in step three is as follows: S31: Clustering input data preparation; The obtained joint feature set of the top plate-side slope structural surface is used as the input data for unsupervised clustering analysis, where each structural surface or the first joint statistical unit is used as a cluster sample; S32: DBSCAN Algorithm Parameter Initialization; Set the key parameters of the DBSCAN clustering algorithm, including the neighborhood radius parameter and the minimum number of neighborhood samples parameter. In the initial stage, use engineering experience values ​​or algorithm default values. S33: Initial clustering execution; The DBSCAN unsupervised clustering algorithm is used to perform clustering analysis on the joint feature set. Based on the density reachability criterion, the top plate and side wall structural surfaces with similar structural surface features are automatically aggregated into the same cluster category, and the cluster category number corresponding to each structural surface sample is output. S34: Clustering effect evaluation; the initial clustering effect is evaluated using the contour validity index, wherein the sample is obtained according to formula (16). Contour effectiveness index ; (16); In the formula, For the sample The average distance to all other samples in the same cluster; For the sample The minimum average distance between samples and other clusters.

[0010] Furthermore, in order to balance the targeted nature of parameter optimization, algorithm adaptability, and result stability, in step four, the Lüper Fox optimization algorithm based on swarm intelligence is introduced to optimize the key parameters of the DBSCAN clustering algorithm. The process is as follows: S41: Determining the Optimization Object and Scope; Determine Eps and MinPts in the DBSCAN clustering algorithm as the optimization objects, and set the parameter value range based on the characteristics of underground engineering structural surface data and the applicable scope of the algorithm; S42: LFO Algorithm Parameter Settings; Set the core parameters of the Lüper Fox optimization algorithm, including the population size and number of iterations; S43: Population initialization; Initialize the individual positions of the population in the Lüper fox optimization algorithm according to the random distribution criterion. Each Lüper fox represents a set of candidate solutions, where the position of the first individual is obtained according to formula (17). Only the initial position of Lüper Fox ; (17); In the formula, and These represent the lower and upper boundary vectors of the search space; A vector of random numbers representing the interval [0,1]. S44: Fitness calculation and iterative optimization; establish a fitness function based on the SVI index, quantify the advantages of candidate parameter combinations, and output the first value according to formula (18). The fitness value of each candidate solution during the algorithm search and exploration phase. During the iteration process, the parameter combinations corresponding to the current position of each individual are applied sequentially to the DBSCAN clustering model to perform unsupervised clustering operations on the structural surface sample data. For each set of parameter configurations, the corresponding SVI value is calculated based on the clustering results, and this index is used as the fitness value to measure the quality of the current parameter combination. When the preset iteration termination condition is reached, the Lüper fox population with the largest fitness value that has remained stable for several consecutive iterations is selected from all iterations, and the parameter combination corresponding to the individual with the best position in this population is used as the optimal parameter configuration for the DBSCAN clustering model. (18); In the formula, This represents the maximum number of cross-validations. For the first The SVI value of the cross-validation.

[0011] Furthermore, to effectively improve the clustering accuracy, the process of obtaining better DBSCAN hyperparameters and optimized structural surface clustering results in step five is as follows: S51: Improved LHS population initialization; without changing the overall search mechanism of the Lüper Fox optimization algorithm, Latin hypercube sampling is used to generate a sampling matrix matching the population size and parameter dimensions in the interval [0, 1], so that each sub-interval is uniformly sampled once in each parameter dimension, thereby improving the representativeness and coverage of the initial population; among which, the first is obtained according to formula (19). Latin hypercube sampled values ​​of candidate solutions The initial population position, improved based on the Latin hypercube sampling matrix, is generated according to formula (20). ; (19); In the formula, This represents a random permutation of the integer set [1, 2, ..., N], used to ensure that each subinterval is sampled only once; Represented as the first The random perturbation term introduced by each candidate solution within the subinterval; Population size; (20); In the formula, This is a Latin hypercube sampling matrix. ; S52: Iterative optimization execution; repeat the fitness calculation and iterative optimization process of S44, execute the Lüper Fox optimization algorithm based on the improved initial population, and gradually approach the optimal parameter combination through the algorithm's search and update mechanism; S53: Population size sensitivity analysis; change the number of individuals in the population, repeat the optimization process, output the fitness value change curves of candidate solutions under various population sizes after all iterations are completed, analyze the impact of population size on optimization effect and efficiency, and determine the optimal population size that balances performance and efficiency. S54: Optimal hyperparameter selection; Based on the principle of maximizing fitness value, select the corresponding parameter combination from all candidate solutions as the optimal hyperparameters for the DBSCAN clustering algorithm; S55: Generation of optimized clustering results; Based on the optimal DBSCAN clustering algorithm under the best hyperparameters, S33 and S34 are re-executed to obtain the optimized structural surface clustering results.

[0012] Furthermore, in order to automate and quantify the determination process of cross-part correlation and continuity of the top and side structural surfaces, the process of outputting the spatial correlation determination results and continuity level of the top plate-side structural surfaces in step six is ​​as follows: S61: Spatial mapping of clustering results; Map the optimized structural surface clustering results to the underground rock mass structural surface sampling space, mark the three-dimensional spatial coordinates of each structural surface sample and its corresponding location, and establish a three-dimensional association relationship between cluster category, spatial location and corresponding component. S62: Screening of cross-site candidate structural surfaces; statistically analyze the distribution of structural surface samples in the top plate and side plate regions in each cluster category, calculate the top plate coverage rate and side plate coverage rate, and screen the cluster categories whose top plate coverage rate and side plate coverage rate both meet the preset conditions as cross-site candidate structural surface systems. S63: Determination of spatial geometric relationship; compare the spatial geometric relationship and extension characteristics between the top plate and sidewall structural surfaces in the candidate structural surface system, and combine with the geological background analysis to determine whether the structural surfaces in different parts have the possibility of continuous extension, cross combination or homogeneous development in space. S64: Spatial continuity index calculation; Calculate the spatial continuity index by combining the minimum Euclidean distance, normal angle, number of interruptions and quantity of structural surfaces, and quantify the continuity of the structural surface system; S65: Continuity level classification and result output; Based on the magnitude of the spatial continuity index, classify the spatial continuity level of the structural surface system, and output the spatial correlation judgment result of the top plate-side wall structural surface and the corresponding continuity level.

[0013] This invention discloses a method for determining the association and continuity of top and sidewall structural surfaces based on unsupervised learning. First, the method collects geometric statistical information and basic characteristic parameters of the top and sidewall rock mass structural surfaces as the original basis for subsequent analysis, avoiding the problem of data being detached from the engineering site scenario. Simultaneously collecting data related to the top and sidewalls, rather than studying a single location, provides a reliable foundation for subsequent spatial association determination. Second, by using unified encoding, the structural surface characteristic parameters of the top and sidewalls are incorporated into the same framework, constructing a joint feature set to solve the problem that structural surface parameters in different locations are independent and cannot be directly compared and analyzed. Normalization based on physical properties effectively eliminates the influence of dimensional differences and numerical spans between different characteristic parameters, ensuring a balanced weight of each characteristic parameter in the subsequent unsupervised clustering algorithm, which is beneficial to ensuring the accuracy of the analysis. Next, the density-based unsupervised clustering algorithm DBSCAN is used to perform initial clustering analysis on the joint feature set. Adapting to the structural surface data characteristics, it can automatically aggregate top and sidewall structural surfaces with similar characteristics, truly reflecting the natural aggregation state of structural surfaces in space, and providing a reasonable initial clustering benchmark for subsequent optimization. Subsequently, addressing the sensitivity of the neighborhood radius parameter and minimum sample number parameter to the clustering results in the DBSCAN clustering algorithm, a multi-step hybrid optimization mechanism is introduced. First, a metaheuristic optimization algorithm is introduced to construct a global optimization framework for DBSCAN parameters. This framework can find the optimal parameter combination through intelligent iterative search, solving the problem of blind parameter selection and making the clustering results more closely match the actual distribution patterns of the structural surfaces. Then, the population initialization process of the metaheuristic optimization algorithm is updated and improved using the Latin hypercube sampling method. This not only improves the diversity and search uniformity of the initial population but also enhances the global search capability of the Lüper Fox optimization algorithm. It can traverse the parameter space more efficiently and find DBSCAN hyperparameters that are better than traditional optimization methods, thereby obtaining more accurate structural surface clustering results. As a result, the coverage uniformity and optimization convergence stability of the parameter search space can be significantly improved, significantly enhancing the clustering accuracy and stability. Then, based on the clustering results, the spatial geometric and topological relationships between the top plate and the sidewall structural surfaces are further combined to determine whether structural surfaces in different locations belong to the same structural surface system. The spatial continuity and combination relationship of the structural surfaces are calculated, and the spatial association judgment results and continuity levels of the top plate-sidewall structural surfaces are output. This achieves a quantitative judgment on the spatial continuity and combination characteristics of the structural surface system, which clarifies the grouping rules of the structural surfaces and provides quantitative indicators that can be directly used for engineering design. This provides a reliable data foundation and judgment basis for the identification of turquoise bodies and the analysis of rock mass stability.

[0014] This invention improves the stability and reliability of unsupervised clustering analysis by uniformly encoding and physically constraining the structural features of the roof and sidewall structures, and by introducing a parameter optimization mechanism. Furthermore, it combines the spatial geometric relationships and topological features of the structural surfaces to achieve spatial correlation determination and continuity combination analysis of cross-sections of the roof and sidewall structural surfaces without the need for manual prior grouping. This provides more objective and systematic basic data support for turquoise body identification and rock mass stability analysis. Compared with existing technologies, this invention has the following advantages: 1. A three-level feature processing workflow of "full data collection - classification coding - type-based normalization" was constructed to specifically address the core issues of inconsistent feature dimensions and mixed dimensions of structural surfaces in different parts. The workflow integrates core geometric parameters through multiple means, divides them into four feature subgroups according to physical attributes, and adopts a dedicated normalization method for each subgroup to eliminate dimensional interference and information distortion. Combined with the unified coding and joint analysis of the structural surface features of the top plate and side walls, the automatic determination of the spatial correlation and continuity level of structural surfaces in different parts is realized. This not only provides high-quality data for cross-part joint analysis, but also significantly improves the objectivity and consistency of the determination results, effectively eliminating the reliance on human experience.

[0015] 2. Addressing the core issue of parameter sensitivity in the DBSCAN algorithm, an innovative two-stage hybrid optimization mechanism combining Lüper Fox Optimization (LFO) and Latin Hypercube Sampling (LHS) was adopted to construct a multi-step parameter adaptive optimization system. This mechanism uses SVI as the fitness function, achieving global parameter optimization through LFO, while combining LHS to improve the population initialization process, effectively enhancing search uniformity and convergence stability. Supplemented by population size sensitivity analysis, the algorithm can adaptively adapt to different geological data, significantly improving the accuracy and stability of structural surface clustering compared to manual parameter setting. This optimization mechanism not only strengthens the stability and reliability of unsupervised clustering analysis but also ensures that the judgment results can directly serve practical engineering applications such as turquoise body identification and rock mass stability analysis.

[0016] 3. A complete cross-site analysis chain was constructed, mapping clustering results to three-dimensional space, screening cross-site candidate systems, and quantifying and classifying the spatial continuity of structural surfaces through multiple indicators. The entire process requires no manual prior grouping, achieving data-driven automated quantitative judgment, solving the problem that traditional methods struggle to characterize cross-site relationships. The results can directly support surrounding rock stability evaluation, loose rock mass identification, and support optimization, reducing labor costs and adapting to complex engineering scenarios.

[0017] 4. Employing a fully unsupervised framework, it eliminates the need for numerous labeled samples and manual rules, and can adaptively process structural surface data of different geological and engineering types, overcoming the weakness of traditional supervised methods in terms of generalization. The fully automated design process enables integrated analysis, shortening the cycle time, improving efficiency, and possessing broad application value.

[0018] This method is simple to implement and has low implementation costs. Through feature engineering, algorithm optimization and spatial correlation quantitative analysis, it has constructed an efficient and accurate judgment method, which can realize the intelligent identification and quantitative analysis of the spatial relationship between the roof and side rock mass structural planes. It can also realize the identification of potential loose rock bodies in the roof surrounding rock of underground mines and the risk classification of collapse. It breaks through the limitations of traditional manual judgment and single algorithm, and can provide reliable technical support and decision-making basis for the safety management of underground engineering rock mass. Attached Figure Description

[0019] Figure 1 This is a flowchart of the present invention; Figure 2 This is a diagram showing the construction and normalization of the joint features of the top plate and sidewall structure surfaces in this invention; Figure 3 This is a diagram showing the initial clustering results of the structural surfaces in this invention; Figure 4 This is a graph showing the change in fitness values ​​of the improved Lüperfur fox optimization algorithm of this invention. Figure 5 This is a diagram showing the spatial relationship and continuity of the top plate-side wall structure surface in this invention. Detailed Implementation

[0020] The invention will now be further described with reference to the accompanying drawings.

[0021] like Figures 1 to 5 As shown, this invention provides a method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning, comprising the following steps: Step 1: Conduct a structural surface survey of the roof and side rock mass of the underground project, obtain geometric statistical information of the structural surface, and extract basic characteristic parameters; Common engineering methods such as manual measurement, photogrammetry, and point cloud inversion can be used to identify and number the structural surfaces of the exposed rock mass on the roof and sidewalls one by one, and measure or statistically analyze the geometric information of each structural surface. At the same time, each structural surface or joint statistical unit is stored as an independent sample in the original structural surface database to provide basic input data for subsequent unified analysis.

[0022] To achieve comprehensive acquisition of basic data, structural surface geometric information, including the structural surface dip direction, is required. ,inclination Joint group number Joint trace length Joint trace angle Joint trace density Joint trace intensity Spacing within joint groups Spacing between joint groups .

[0023] Step Two: As Figure 2 As shown, the feature parameters of the top plate and sidewall structural surfaces are uniformly encoded to construct a joint feature set of the top plate-sidewall structural surfaces, and the feature parameters are normalized based on physical properties. To achieve standardization and unification of multi-dimensional structural features, and to provide high-quality, highly adaptable feature data support for subsequent unsupervised clustering, the specific implementation process is as follows: S21: Construction of original feature vectors; After completing the collection of original structural surface data, the top plate structural surface sample and the side wall structural surface sample are merged and processed, all structural surface geometric features are statistically analyzed, these features are uniformly encoded and mapped to the same feature space to form the original feature vector of the structural surface, ensuring that features of different parts and different types are comparable; S22: Feature subgrouping based on physical properties; according to the physical meaning of the structural surface parameters, the feature parameters are divided into subgroups using formulas (1), (2), (3), and (4), respectively. , , , Four categories of feature subgroups based on physical attributes; (1); (2); (3); (4); In the formula, These are directional feature groups, representing the spatial attitude and trajectory of the structural surface; These are scale and quantity characteristic groups, representing the overall developmental scale and number of groups of structural surfaces; These are density and strength characteristic groups, representing the density of structural surface development and mechanical strength. This is a feature group representing the spatial spacing relationship between structural surfaces in the same and different groups; S23: Type-based normalization processing; For feature subgroups of different physical properties, a dedicated normalization method is used to eliminate the influence of dimensional differences and numerical ranges. For directional feature groups The angle parameters are converted into vector form using a vectorized mapping method, while retaining spatial orientation information. In the process of converting the structural surface attitude into a unit normal vector, the first normal vector is obtained according to formulas (5), (6), and (7). The unit normal vector of each structural surface is in , , Components of the axis , and During the transformation of joint trace angles into two-dimensional direction vectors, the first vector is obtained according to formula (8). Two-dimensional direction vector of each structural joint trace ; (5); (6); (7); (8); In the formula, For the first The inclination angle of each structural surface; For the first The tendency of each structural surface; For the first The joint trace angles of each structural surface; For size and quantity type feature groups Using logarithmic normalization, the results of the first step are obtained according to formulas (9) and (10), respectively. Normalized results of the number of joint groups and trace lengths for each sample , Compress the numerical range and weaken the influence of extreme values; (9); (10); In the formula, For the first The number of joint groups in each sample; For the first The length of the joint trace in each sample; , These represent taking the minimum and maximum values ​​from the sample set, respectively. For density and intensity type feature groups Using a standardized processing method, the first step is obtained according to formula (11) and formula (12) respectively. Standardized results of joint trace density for each sample Standardized results of strength This ensures that the features satisfy a zero-mean, unit-variance distribution. (11); (12); In the formula, For the first Joint trace density of each sample; For the first Joint trace intensity of each sample; , These are the mean values ​​of joint trace density and intensity, respectively, in the sample set; , These are the standard deviations of joint trace density and intensity in the sample set, respectively. For feature groups related to spacing and structure Using the maximum and minimum scale normalization method, the first number is obtained according to formula (13) and formula (14) respectively. Normalized results of intra- and inter-group intervals for each sample joint. , This maps the values ​​to the [0,1] interval; (13); (14); In the formula, , These are the minimum and maximum values ​​of the spacing within the joint group in the sample set, respectively. , These are the minimum and maximum values ​​of the spacing between joint groups in the sample set, respectively. S24: Joint feature vector construction; weighted fusion of the normalization results of various features, and construction of the first feature vector according to formula (15). The final joint feature vector of each structural surface sample used for unsupervised clustering analysis In order to take into account the importance of different features; (15); In the formula, , , , , These are the weight coefficients for the direction normal vector, the trace direction vector, the scale quantity feature, the density intensity feature, and the spacing structure feature, respectively, and they satisfy the following conditions: =1; For the first The unit normal vector of the structural surface of each sample.

[0024] Step 3: Use density-based unsupervised clustering algorithm (DBSCAN) to perform initial clustering analysis on the constructed joint feature set, automatically aggregating top plate and sidewall structural surfaces with similar features to obtain the initial clustering results of the structural surfaces; In order to provide a reasonable benchmark and quantitative basis for subsequent parameter optimization, the specific implementation process is as follows: S31: Clustering input data preparation; The obtained joint feature set of the top plate-side slope structural surface is used as the input data for DBSCAN unsupervised clustering analysis. The initial clustering analysis process is performed, and each structural surface or the first joint statistical unit is taken as a cluster sample. S32: DBSCAN Algorithm Parameter Initialization; Set the key parameters of the DBSCAN clustering algorithm, including the neighborhood radius parameter (Eps) and the minimum number of neighborhood samples (MinPts). In the initial stage, use engineering experience values ​​or algorithm default values. Preferably, the initial values ​​of Eps and MinPts are given to the range of [0.05, 0.5] and [6, 12], respectively, to provide an initial benchmark for subsequent parameter optimization. S33: Initial clustering execution; Six sets of parameter combinations are randomly set to start clustering analysis. The DBSCAN unsupervised clustering algorithm is used to perform clustering analysis on the joint feature set. Based on the density reachability criterion of the DBSCAN algorithm, the top plate and side wall structural surfaces with similar structural surface features are automatically aggregated into the same cluster category. The cluster category number corresponding to each structural surface sample is output to achieve the initial grouping of structural surfaces. S34: Evaluation of clustering performance; such as Figure 3 As shown, the effectiveness of the initial clustering effect is quantitatively evaluated using the Profile Validity Index (SVI), where the sample is obtained according to formula (16). Contour effectiveness index ; (16); In the formula, For the sample The average distance to all other samples in the same cluster; For the sample The minimum average distance between samples in other clusters, where the number of clusters varies from 2 to K. The larger the SVI value, the more sample points are likely to be assigned to the correct clusters, and the better the clustering effect.

[0025] Step 4: Introduce the Lüper Fox optimization algorithm based on swarm intelligence to optimize the key parameters of the DBSCAN clustering algorithm, so as to improve the clustering accuracy and stability; To balance the specificity of parameter optimization, algorithm adaptability, and the stability of results, the specific implementation process is as follows: S41: Determining the Optimization Object and Scope; Determine Eps and MinPts in the DBSCAN clustering algorithm as the optimization objects, and set the parameter value range based on the characteristics of underground engineering structural surface data and the applicable scope of the algorithm, where a set of Eps and MinPts values ​​is a candidate solution; S42: LFO Algorithm Parameter Settings; Set the core parameters of the Lüper Fox optimization algorithm, including the population size and number of iterations, to balance the algorithm's search efficiency and global optimality; As a preferred option, the population size is set to 15, 30, 45 and 60, respectively, and the maximum number of iterations is set to 100; S43: Population initialization; Initialize the individual positions of the population in the Lüper fox optimization algorithm according to the random distribution criterion. Each Lüper fox represents a set of candidate solutions, where the position of the first individual is obtained according to formula (17). Only the initial position of Lüper Fox ; (17); In the formula, and These represent the lower and upper boundary vectors of the search space; A vector of random numbers representing the interval [0,1]. S44: Fitness calculation and iterative optimization; establish a fitness function based on the SVI index, quantify the advantages of candidate parameter combinations, and output the first value according to formula (18). The fitness value of each candidate solution during the algorithm search and exploration phase. In each iteration, the candidate parameter combinations corresponding to the current position of each individual are applied sequentially to the DBSCAN clustering model to perform cluster analysis. For each parameter configuration, the corresponding SVI value is calculated based on the clustering results, and this index is used as the fitness value to measure the quality of the current parameter combination. When the preset iteration termination condition is reached, the Lüper fox population with the largest fitness value that has remained stable for several consecutive iterations is selected from all iterations, and the parameter combination corresponding to the individual with the best position in this population is used as the optimal parameter configuration of the DBSCAN clustering model. (18); In the formula, This represents the maximum number of cross-validations. For the first The SVI value of the cross-validation.

[0026] Step 5: As Figure 4 As shown, the population initialization process of the Lüper Fox optimization algorithm is improved by adopting the Latin hypercube sampling method, which enhances the initial population diversity and search uniformity, and obtains better DBSCAN hyperparameters and optimized structure surface clustering results. To effectively improve the accuracy of clustering, the specific implementation process is as follows: S51: LHS Improved Population Initialization; Without changing the overall search mechanism of the Lüper Fox optimization algorithm, the initial population of the optimization algorithm is constructed using the Latin hypercube sampling method. This method generates a sampling matrix matching the population size and parameter dimension in the interval [0, 1]. By uniformly generating new candidate solutions in the parameter search space, it ensures that each sub-interval in each parameter dimension is sampled uniformly once, and also improves the uniformity of the search space coverage and the convergence stability of the optimization process, thereby improving the representativeness and coverage of the initial population; where, according to formula (19), the first Latin hypercube sampled values ​​of candidate solutions The initial population position, improved based on the Latin hypercube sampling matrix, is generated according to formula (20). ; (19); In the formula, This represents a random permutation of the integer set [1, 2, ..., N], used to ensure that each subinterval is sampled only once; Represented as the first The random perturbation term introduced by each candidate solution within the subinterval; Population size; (20); In the formula, This is a Latin hypercube sampling matrix. ; S52: Iterative optimization execution; repeat the fitness calculation and iterative optimization process of S44, execute the Lüper Fox optimization algorithm based on the improved initial population, and gradually approach the optimal parameter combination through the algorithm's search and update mechanism; S53: Population size sensitivity analysis; change the number of individuals in the population, repeat the optimization process, and repeatedly execute the DBSCAN clustering analysis and SVI calculation process in multiple iterations to generate and output the fitness value change curves of candidate solutions under various population sizes after all iterations are completed. Analyze the impact of population size on optimization effect and efficiency, and determine the optimal population size that balances performance and efficiency. S54: Optimal Hyperparameter Selection; Based on the principle of maximizing fitness value, select the parameter combination with stable performance and the largest fitness value, and determine it as the optimal hyperparameter configuration for the DBSCAN clustering algorithm; S55: Optimized clustering results are generated; based on the optimal hyperparameter configuration, S33 and S34 are re-executed to obtain structural surface clustering results with optimized accuracy and stability, providing a reliable basis for subsequent spatial association determination.

[0027] Specifically, after determining the upper and lower bounds of the search space for DBSCAN clustering parameters, the initial population of the Lüper Fox optimization algorithm is constructed using the Latin hypercube sampling method. After the population initialization is completed, the SVI is used as the fitness evaluation criterion. The parameters corresponding to the current position of each individual in the initial population are combined and applied to the DBSCAN clustering model. The corresponding SVI value is calculated based on the clustering results, and the best candidate solution is output through iterative optimization.

[0028] Step Six: As Figure 5 As shown, based on the optimized structural surface clustering results, the structural surface system of different parts (top plate and side plate) is determined, the spatial continuity and combination relationship of the structural surfaces are quantitatively calculated, and the spatial association determination result and continuity level of the top plate-side plate structural surface are finally output.

[0029] To automate and quantify the determination of the cross-part correlation and continuity of the top edge structural surface, the specific implementation process is as follows: S61: Spatial mapping of clustering results; After obtaining the optimized structural surface clustering results, the clustering results are mapped back to the actual underground rock mass structural surface sampling space, and the three-dimensional spatial coordinates of each structural surface sample and its corresponding part (top plate or sidewall) are marked. The three-dimensional relationship between cluster category, spatial location and corresponding component is established to lay the spatial foundation for subsequent analysis. S62: Screening of cross-part candidate structural surfaces; statistically analyze the distribution of structural surface samples in the top plate and side plate regions in each cluster category, calculate the top plate coverage rate and side plate coverage rate, screen the cluster categories whose top plate coverage rate and side plate coverage rate both meet the preset conditions, and use them as cross-part candidate structural surface systems, excluding structural surface categories that only have a single component developed. S63: Determination of spatial geometric relationship; compare the spatial geometric relationship and extension characteristics between the top plate and sidewall structural surfaces in the candidate structural surface system, and combine with the geological background analysis to determine whether the structural surfaces in different parts have the possibility of continuous extension, cross combination or homogeneous development in space. S64: Spatial continuity index calculation; calculate the minimum Euclidean distance, normal angle, number of interruptions, and other indices between the top plate and sidewall structural surfaces within the candidate structural surface system. Based on the minimum Euclidean distance, normal angle, number of interruptions, and other indices of the structural surfaces, calculate the spatial continuity index to quantify the continuity of the structural surface system. S65: Continuity level classification and result output; Based on the magnitude of the spatial continuity index, the spatial continuity level of the structural surface system is classified, and the spatial correlation judgment result of the top plate-side wall structural surface and the corresponding continuity level are output, providing core basis for the evaluation of surrounding rock stability and optimization of support schemes in underground engineering.

[0030] Figure 5(a) illustrates the practical application of this method in an underground tunnel. The tunnel roof and adjacent sidewalls exhibit diverse structural surface types, with different joint groups showing a spatially interwoven and partially interconnected pattern. Furthermore, the roof and sidewall structural surfaces differ significantly in spatial location and exposure conditions, making it difficult to comprehensively determine the structural surface system through analysis of a single location. To address the issues of unclear cross-location relationships and difficulty in quantifying the continuity of such roof-sidewall structural surfaces, this method is employed to jointly determine and analyze the spatial correlation and continuity between the tunnel roof and sidewall structural surfaces.

[0031] First, this invention collects and processes structural surface information of the roof and adjacent sidewalls of the roadway. The acquired geometrical statistical parameters, such as dip direction, dip angle, trace length, trace angle, trace density, number of joint groups, and spacing, are uniformly encoded and physically normalized, and a joint feature set of the roof-sidewall structural surfaces is constructed. Subsequently, the DBSCAN unsupervised clustering algorithm is used to perform initial clustering analysis on the structural surface samples, and SVI is used to evaluate the clustering results, resulting in the following... Figure 5 (b) shows the initial clustering and evaluation results. Based on this, the Lüpertz optimization algorithm is introduced, combined with the Latin hypercube sampling method, to optimize the Eps and MinPts parameters in the DBSCAN clustering algorithm. Through multiple rounds of iteration, the parameter combination with the largest fitness value is selected to obtain a more stable structure surface optimized clustering result, such as... Figure 5 (c) shows the process; finally, the optimized clustering results are mapped back to the structural surface sampling space, and the location of each structural surface sample is labeled as either the top plate or the side plate. The distribution of different cluster categories in the top plate and side plate is statistically analyzed. Cross-location structural surface systems that meet the preset coverage conditions are selected. Furthermore, the spatial continuity index of the structural surface is calculated by comprehensively considering indicators such as minimum Euclidean distance, normal angle, and interruption characteristics. Based on this, the continuity level is divided, and the spatial association judgment result of the top plate-side plate structural surface is output, such as... Figure 5 As shown in (d).

[0032] This invention discloses a method for determining the association and continuity of top and sidewall structural surfaces based on unsupervised learning. First, the method collects geometric statistical information and basic characteristic parameters of the top and sidewall rock mass structural surfaces as the original basis for subsequent analysis, avoiding the problem of data being detached from the engineering site scenario. Simultaneously collecting data related to the top and sidewalls, rather than studying a single location, provides a reliable foundation for subsequent spatial association determination. Second, by using unified encoding, the structural surface characteristic parameters of the top and sidewalls are incorporated into the same framework, constructing a joint feature set to solve the problem that structural surface parameters in different locations are independent and cannot be directly compared and analyzed. Normalization based on physical properties effectively eliminates the influence of dimensional differences and numerical spans between different characteristic parameters, ensuring a balanced weight of each characteristic parameter in the subsequent unsupervised clustering algorithm, which is beneficial to ensuring the accuracy of the analysis. Next, the density-based unsupervised clustering algorithm DBSCAN is used to perform initial clustering analysis on the joint feature set. Adapting to the structural surface data characteristics, it can automatically aggregate top and sidewall structural surfaces with similar characteristics, truly reflecting the natural aggregation state of structural surfaces in space, and providing a reasonable initial clustering benchmark for subsequent optimization. Subsequently, addressing the sensitivity of the neighborhood radius parameter and minimum sample number parameter to the clustering results in the DBSCAN clustering algorithm, a multi-step hybrid optimization mechanism is introduced. First, a metaheuristic optimization algorithm is introduced to construct a global optimization framework for DBSCAN parameters. This framework can find the optimal parameter combination through intelligent iterative search, solving the problem of blind parameter selection and making the clustering results more closely match the actual distribution patterns of the structural surfaces. Then, the population initialization process of the metaheuristic optimization algorithm is updated and improved using the Latin hypercube sampling method. This not only improves the diversity and search uniformity of the initial population but also enhances the global search capability of the Lüper Fox optimization algorithm. It can traverse the parameter space more efficiently and find DBSCAN hyperparameters that are better than traditional optimization methods, thereby obtaining more accurate structural surface clustering results. As a result, the coverage uniformity and optimization convergence stability of the parameter search space can be significantly improved, significantly enhancing the clustering accuracy and stability. Then, based on the clustering results, the spatial geometric and topological relationships between the top plate and the sidewall structural surfaces are further combined to determine whether structural surfaces in different locations belong to the same structural surface system. The spatial continuity and combination relationship of the structural surfaces are calculated, and the spatial association judgment results and continuity levels of the top plate-sidewall structural surfaces are output. This achieves a quantitative judgment on the spatial continuity and combination characteristics of the structural surface system, which clarifies the grouping rules of the structural surfaces and provides quantitative indicators that can be directly used for engineering design. This provides a reliable data foundation and judgment basis for the identification of turquoise bodies and the analysis of rock mass stability.

[0033] This invention improves the stability and reliability of unsupervised clustering analysis by uniformly encoding and physically constraining the structural features of the roof and sidewall structures, and by introducing a parameter optimization mechanism. Furthermore, by combining the spatial geometric relationships and topological features of the structural surfaces, it achieves spatial correlation determination and continuity combination analysis of the roof and sidewall structural surfaces across different parts without the need for manual prior grouping. This provides more objective and systematic basic data support for the identification of loose rock bodies and the analysis of rock mass stability.

[0034] This method is simple to implement and has low implementation costs. Through feature engineering, algorithm optimization and spatial correlation quantitative analysis, it has constructed an efficient and accurate judgment method, which can realize the intelligent identification and quantitative analysis of the spatial relationship between the roof and side rock mass structural planes. It can also realize the identification of potential loose rock bodies in the roof surrounding rock of underground mines and the risk classification of collapse. It breaks through the limitations of traditional manual judgment and single algorithm, and can provide reliable technical support and decision-making basis for the safety management of underground engineering rock mass.

Claims

1. A method for determining the association and continuity combination of top-edge-support structure surfaces based on unsupervised learning, characterized in that, Includes the following steps: Step 1: Conduct a structural surface survey of the roof and side rock mass of the underground project, obtain geometric statistical information of the structural surface, and extract basic characteristic parameters; Step 2: Unify the feature parameters of the top plate and sidewall structural surfaces to construct a joint feature set of the top plate-sidewall structural surfaces, and normalize the feature parameters based on physical properties; Step 3: Use a density-based unsupervised clustering algorithm to perform initial clustering analysis on the constructed joint feature set to obtain the initial clustering results of the structural surface; Step 4: Introduce the Lüper Fox optimization algorithm based on swarm intelligence to optimize the key parameters of the DBSCAN clustering algorithm; Step 5: Improve the population initialization process of the Lüper Fox optimization algorithm by adopting the Latin hypercube sampling method, thereby enhancing the diversity and search uniformity of the initial population and obtaining better DBSCAN hyperparameters and optimized structural surface clustering results. Step Six: Based on the optimized structural surface clustering results, determine the structural surface system affiliation of different parts of the structural surface, quantify the spatial continuity and combination relationship of the structural surface, and finally output the spatial association determination result and continuity level of the top plate-side wall structural surface.

2. The method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning according to claim 1, characterized in that, In step one, the structural surface geometry information includes the structural surface dip direction. ,inclination Joint group number Joint trace length Joint trace angle Joint trace density Joint trace intensity Spacing within joint groups Spacing between joint groups .

3. The method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning according to claim 2, characterized in that, In step two, the process of normalizing the feature parameters based on physical properties is as follows: S21: Construction of original feature vectors; statistically analyze the geometric features of all structural surfaces, map these features to the same feature space, and form the original feature vectors of the structural surfaces; S22: Feature subgrouping based on physical properties; according to the physical meaning of the structural surface parameters, the feature parameters are divided into subgroups using formulas (1), (2), (3), and (4), respectively. , , , Four categories of feature subgroups based on physical attributes; （1）； （2）； （3）； （4）； In the formula, These are directional feature groups, representing the spatial attitude and trajectory of the structural surface; These are scale and quantity characteristic groups, representing the overall developmental scale and number of groups of structural surfaces; These are density and strength characteristic groups, representing the density of structural surface development and mechanical strength. This is a feature group representing the spatial spacing relationship between structural surfaces in the same and different groups; S23: Type-based normalization processing; For feature subgroups of different physical properties, a dedicated normalization method is used to eliminate the influence of dimensional differences and numerical ranges. For directional feature groups The angle parameters are transformed into vector form using a vectorized mapping method. In the process of transforming the orientation of the structural surface into the unit normal vector, the first normal vector is obtained according to formulas (5), (6) and (7). The unit normal vector of each structural surface is in , , Components of the axis , and During the transformation of joint trace angles into two-dimensional direction vectors, the first vector is obtained according to formula (8). Two-dimensional direction vector of each structural joint trace ; （5）； （6）； （7）； （8）； In the formula, For the first The inclination angle of each structural surface; For the first The tendency of each structural surface; For the first The joint trace angles of each structural surface; For size and quantity type feature groups Using logarithmic normalization, the results of the first step are obtained according to formulas (9) and (10), respectively. Normalized results of the number of joint groups and trace lengths for each sample , ; （9）； （10）； In the formula, For the first The number of joint groups in each sample; For the first The length of the joint trace in each sample; , These represent taking the minimum and maximum values ​​from the sample set, respectively. For density and intensity type feature groups Using a standardized processing method, the first step is obtained according to formula (11) and formula (12) respectively. Standardized results of joint trace density for each sample Standardized results of strength ; （11）； （12）； In the formula, For the first Joint trace density of each sample; For the first Joint trace intensity of each sample; , These are the mean values ​​of joint trace density and intensity, respectively, in the sample set; , These are the standard deviations of joint trace density and intensity in the sample set, respectively. For feature groups related to spacing and structure Using the maximum and minimum scale normalization method, the first number is obtained according to formula (13) and formula (14) respectively. Normalized results of intra- and inter-group intervals for each sample joint. , This maps the values ​​to the [0,1] interval; （13）； （14）； In the formula, , These are the minimum and maximum values ​​of the spacing within the joint group in the sample set, respectively. , These are the minimum and maximum values ​​of the spacing between joint groups in the sample set, respectively. S24: Joint feature vector construction; weighted fusion of the normalization results of various features, and construction of the first feature vector according to formula (15). The final joint feature vector of each structural surface sample used for unsupervised clustering analysis ; （15）； In the formula, , , , , These are the weight coefficients for the direction normal vector, the trace direction vector, the scale quantity feature, the density intensity feature, and the spacing structure feature, respectively, and they satisfy the following conditions: =1; For the first The unit normal vector of the structural surface of each sample.

4. The method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning according to claim 3, characterized in that, In step three, the process of obtaining the initial clustering results of the structural surfaces is as follows: S31: Clustering input data preparation; The obtained joint feature set of the top plate-side slope structural surface is used as the input data for unsupervised clustering analysis, where each structural surface or the first joint statistical unit is used as a cluster sample; S32: DBSCAN Algorithm Parameter Initialization; Set the key parameters of the DBSCAN clustering algorithm, including the neighborhood radius parameter. In the initial stage, use engineering experience values ​​or algorithm default values. S33: Initial clustering execution; The DBSCAN unsupervised clustering algorithm is used to perform clustering analysis on the joint feature set. Based on the density reachability criterion, the top plate and side wall structural surfaces with similar structural surface features are automatically aggregated into the same cluster category, and the cluster category number corresponding to each structural surface sample is output. S34: Clustering effect evaluation; the initial clustering effect is evaluated using the contour validity index, wherein the sample is obtained according to formula (16). Contour effectiveness index ; （16）； In the formula, For the sample The average distance to all other samples in the same cluster; For the sample The minimum average distance between samples and other clusters.

5. The method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning according to claim 4, characterized in that, In step four, the process of introducing the Lüper Fox optimization algorithm based on swarm intelligence to optimize the key parameters of the DBSCAN clustering algorithm is as follows: S41: Determining the Optimization Object and Scope; Determine Eps and MinPts in the DBSCAN clustering algorithm as the optimization objects, and set the parameter value range based on the characteristics of underground engineering structural surface data and the applicable scope of the algorithm; S42: LFO Algorithm Parameter Settings; Set the core parameters of the Lüper Fox optimization algorithm, including the population size and number of iterations; S43: Population initialization; Initialize the individual positions of the population in the Lüper fox optimization algorithm according to the random distribution criterion. Each Lüper fox represents a set of candidate solutions, where the position of the first individual is obtained according to formula (17). Only the initial position of Lüper Fox ; （17）； In the formula, and These represent the lower and upper boundary vectors of the search space; A vector of random numbers representing the interval [0,1]. S44: Fitness calculation and iterative optimization; establish a fitness function based on the SVI index, quantify the advantages of candidate parameter combinations, and output the first value according to formula (18). The fitness value of each candidate solution during the algorithm search and exploration phase. During the iteration process, the parameter combinations corresponding to the current position of each individual are applied sequentially to the DBSCAN clustering model to perform unsupervised clustering operations on the structural surface sample data. For each set of parameter configurations, the corresponding SVI value is calculated based on the clustering results, and this index is used as the fitness value to measure the quality of the current parameter combination. When the preset iteration termination condition is reached, the Lüper fox population with the largest fitness value that has remained stable for several consecutive iterations is selected from all iterations, and the parameter combination corresponding to the individual with the best position in this population is used as the optimal parameter configuration for the DBSCAN clustering model. （18）； In the formula, This represents the maximum number of cross-validations. For the first The SVI value of the cross-validation.

6. The method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning according to claim 5, characterized in that, In step five, the process of obtaining better DBSCAN hyperparameters and optimized structural surface clustering results is as follows: S51: Improved LHS population initialization; without changing the overall search mechanism of the Lüper Fox optimization algorithm, Latin hypercube sampling is used to generate a sampling matrix matching the population size and parameter dimensions in the interval [0, 1], so that each sub-interval is uniformly sampled once in each parameter dimension, thereby improving the representativeness and coverage of the initial population; among which, the first is obtained according to formula (19). Latin hypercube sampled values ​​of candidate solutions The initial population position, improved based on the Latin hypercube sampling matrix, is generated according to formula (20). ; （19）； In the formula, This represents a random permutation of the integer set [1, 2, ..., N], used to ensure that each subinterval is sampled only once; Represented as the first The random perturbation term introduced by each candidate solution within the subinterval; Population size; （20）； In the formula, This is a Latin hypercube sampling matrix. ; S52: Iterative optimization execution; repeat the fitness calculation and iterative optimization process of S44, execute the Lüper Fox optimization algorithm based on the improved initial population, and gradually approach the optimal parameter combination through the algorithm's search and update mechanism; S53: Population size sensitivity analysis; change the number of individuals in the population, repeat the optimization process, output the fitness value change curves of candidate solutions under various population sizes after all iterations are completed, analyze the impact of population size on optimization effect and efficiency, and determine the optimal population size that balances performance and efficiency. S54: Optimal hyperparameter selection; Based on the principle of maximizing fitness value, select the corresponding parameter combination from all candidate solutions as the optimal hyperparameters for the DBSCAN clustering algorithm; S55: Generation of optimized clustering results; Based on the optimal DBSCAN clustering algorithm under the best hyperparameters, S33 and S34 are re-executed to obtain the optimized structural surface clustering results.

7. The method for determining the association and continuity combination of top-edge-side structural surfaces based on unsupervised learning according to claim 6, characterized in that, In step six, the process of outputting the spatial association determination result and continuity level of the top plate-side wall structural surface is as follows: S61: Spatial mapping of clustering results; Map the optimized structural surface clustering results to the underground rock mass structural surface sampling space, mark the three-dimensional spatial coordinates of each structural surface sample and its corresponding location, and establish a three-dimensional association relationship between cluster category, spatial location and corresponding component. S62: Cross-site candidate structural plane screening; The distribution of structural surface samples in the top plate and side plate regions of each cluster category is statistically analyzed. The top plate coverage rate and side plate coverage rate are calculated. Cluster categories that meet the preset conditions for both top plate coverage rate and side plate coverage rate are selected as cross-regional candidate structural surface systems. S63: Determination of spatial geometric relationships; By comparing the spatial geometric relationships and extension characteristics between the top plate and sidewall structural surfaces within the candidate structural surface system, and combining the geological background analysis, it is determined whether the structural surfaces in different locations have the potential for continuous extension, cross combination, or homogeneous development in space. S64: Spatial continuity index calculation; Calculate the spatial continuity index by combining the minimum Euclidean distance, normal angle, number of interruptions and quantity of structural surfaces, and quantify the continuity of the structural surface system; S65: Continuity level classification and result output; Based on the magnitude of the spatial continuity index, classify the spatial continuity level of the structural surface system, and output the spatial correlation judgment result of the top plate-side wall structural surface and the corresponding continuity level.

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