CN114118296A - Rock mass structural plane advantage and occurrence grouping method based on clustering integration - Google Patents
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Abstract
The invention relates to a rock mass structural plane advantage and occurrence grouping method based on clustering integration. The method converts the structural plane occurrence data acquired on site into a corresponding space unit normal vector n which is (x, y, z); calculating the distance D (n) between every two structural planes in the data seti，nj) Obtaining a distance matrix D of the structural surface data setN×N(ii) a Calculating M times of clustering on the data set by adjusting a clustering algorithm or a hyper-parameter to obtain M base clustering results pi with differencesm(ii) a Calculating a co-covariance matrix CA of the base clustering result; respectively setting the grouping number K as an integer not less than 2, and clustering the co-covariance matrix CA by adopting a coacervation hierarchical clustering algorithm; determining the optimal grouping number K according to the clustering performance measurement indexop(ii) a According to the optimal number of groups KopAnd (4) clustering and integrating the results, eliminating noise points and isolated values, and obtaining the grouping result of the structural surface superiority and occurrence. The invention can effectively identify the number of the structural plane occurrencesAnd obtaining a better and more stable clustering effect than a single clustering model according to the noise point and the isolated value.
Description
Technical Field
The invention relates to a clustering integration-based rock mass structural plane advantage occurrence grouping method, and belongs to the technical field of engineering geological exploration structural plane measurement and analysis.
Background
The structural plane is used as an important component of the rock mass, and the mechanical property and the engineering structure stability of the rock mass are influenced and controlled to a great extent. The rock mass structural plane under the natural state has the characteristic of grouping, and the accurate and reliable dominant occurrence grouping of the structural plane has very important practical significance for determining rock mass strength parameters, researching mechanical properties and evaluating engineering stability. In the process of structural surface measurement and statistical analysis, due to the existence of errors in measurement and recording and individual solitary value structural surfaces, the grouping result of the dominant occurrence of the rock structural surface is not ideal. At present, most of clustering analysis methods mainly use a single clustering model, certain assumptions made by the single clustering model on data do not necessarily accord with the real distribution situation of the data, the data are easy to fall into a local optimal solution, noise points and isolated values in the structural surface occurrence are difficult to identify, and accurate and effective clustering results are difficult to obtain. Therefore, a clustering integration technology is introduced, and by combining a plurality of base clustering results, essential characteristics of the data set are disclosed from different layers, structural plane noise points and isolated values are identified, and the defect of poor clustering effect of a single model is overcome.
Disclosure of Invention
The invention provides a rock mass structural plane advantage and occurrence grouping method based on clustering integration, aiming at the problems that a single clustering model has larger misjudgment risk and is difficult to identify noise points and isolated values.
A rock mass structural plane advantage and occurrence grouping method based on clustering integration comprises the following specific steps:
(1) converting the structural plane attitude data acquired on site into a corresponding space unit normal vector n which is (x, y, z);
(2) calculating the distance D (n) between every two structural planes in the data seti，nj) Obtaining a distance matrix D of the structural surface data setN×N；
(3) By adjusting clustering algorithm or hyper-parametersCalculating M times of clustering on the data set to obtain M base clustering results pi with differencesm；
(4) Calculating a co-covariance matrix CA of the base clustering result;
(5) respectively setting the grouping number K as an integer not less than 2, and clustering the co-covariance matrix CA by adopting a coacervation hierarchical clustering algorithm;
(6) determining the optimal grouping number K according to the clustering performance measurement indexop；
(7) According to the optimal number of groups KopAnd (4) clustering and integrating the results, eliminating noise points and isolated values, and obtaining the grouping result of the structural surface superiority and occurrence.
The attitude of the structural plane acquired in the step (1) on site is represented by a tendency alpha and an inclination angle beta, and a calculation formula for converting the attitude of the structural plane into a space unit normal vector n in a form of (x, y, z) is as follows:
the distance D (n) in the step (2)i，nj) Is the sine value of the included angle of the unit normal vectors of the two structural surfaces and the unit normal vector n of the two structural surfacesi(xi，yi，zi)、nj(xj，yj，zj) Distance D (n)i，nj)：
In the formula, niAnd njRespectively representing unit normal vectors of the structural surfaces i and j, theta represents an included angle of the unit normal vectors of the two structural surfaces, and T is a transposed symbol of the matrix.
The clustering algorithm in the step (3) is a K-means based on division, a level-based coacervation level clustering, a DBSCAN based on density or a spectral clustering algorithm based on a graph.
The super-parameters are parameters set by clustering algorithms in clustering analysis, each clustering algorithm comprises a plurality of super-parameters, for example, K-means, a coacervation hierarchical clustering algorithm and a spectral clustering algorithm comprise a group number K, and a DBSCAN algorithm comprises a radius eps and a minimum sample number min _ samples;
from the perspective of a clustering algorithm, a method for generating base clustering results with differentiation: using the same clustering algorithm, setting different hyper-parameters to cluster the data set to generate a base clustering result; for example, K-means, agglomerative hierarchical clustering and spectral clustering algorithms can set the K value to an integer no less than 2; the radius eps of the DBSCAN algorithm can be set to be 0.1-0.3, the minimum sample number min _ samples can be set to be 2-10, and the higher the density is, the larger the min _ samples is, the smaller the eps is according to the data set density setting;
from the perspective of a clustering algorithm, the method for generating differentiated base clustering results can also use different clustering algorithms to cluster the data set to generate base clustering results; the two methods can be combined to generate a base clustering result;
the co-ordination matrix CA in the step (4) is used for reorganizing the base clustering result, avoiding the corresponding problem of group labels in the base clustering result, and measuring the similarity between data points in a digitalized and accurate manner; the calculation expression of the co-ordination matrix CA is as follows:
CA＝{mij}N×N
in the formula, N is the quantity of the attitude data of the structural plane,
πm(xi) Is a sample xiClustering result in the basis pimThe group to which the (c) group belongs,
is whether sample i and sample j are present in the same group, if sample i and sample j are present in the same group, then
Otherwise
The larger the frequency of dividing a certain structural plane into the same group by the basis clustering result is, the larger the corresponding CA element value is.
The coacervation hierarchical clustering algorithm in the step (5) is
And taking each sample in the CA matrix as a separate group, and gradually combining two groups which are divided into the same group and have the highest frequency into one group in each iteration process until a termination condition is reached or finally grouping is realized.
The clustering performance measurement index in the step (6) is an index for measuring the clustering effect of the structural plane occurrence data, the contour coefficient SC is used as the clustering performance measurement index, and the SC expression is
Wherein s (i) represents a contour coefficient of one sample,
a (i) represents a sample xiAverage distance to other samples of the same group, b (i) denotes sample xiAverage distance between all samples of the adjacent nearest group;
the value range of SC is [ -1,1], and the larger the value of SC is, the better the clustering effect is;
the optimal number of packets K of the step (6)opThe value is the number of groups K with the maximum profile coefficient corresponding to the clustering performance metric index.
The noise point and the isolated value in the step (7) mean that the base clustering result in the clustering integration model is divided into the same group of structural planes with very low frequency.
The invention has the beneficial effects that:
(1) the invention introduces a clustering integration technology to realize the transition from a traditional structural plane single clustering model to an integration model;
(2) according to the invention, through integrating and complementing a plurality of base clustering results, the defects that the traditional single clustering model has misjudgment risks, is difficult to identify noise points and isolated values and is easy to fall into a local optimal solution are overcome, the clustering effect of the attitude of the structural surface is improved, the clustering result has global significance, an effective method is provided for the accurate grouping of the dominant attitude of the rock structural surface, and the method can be widely applied to the structural surface statistical analysis in the industries such as water conservancy and hydropower, mines, road construction and the like.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a spatial unit normal vector included angle of a structural plane;
FIG. 3 is a polar diagram of the attitude of a footwell structural plane of a turpentine hydropower station dam abutment;
FIG. 4 is a graph of clustering integrated model profile coefficients corresponding to different grouping numbers K;
FIG. 5 is a clustering integration result of structural plane occurrence;
fig. 6 shows the grouping result of the structural advantage occurrence.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments, but the scope of the present invention is not limited to the description.
Example 1: as shown in fig. 1, a rock mass structural plane advantage occurrence grouping method based on cluster integration specifically comprises the following steps:
(1) converting the structural plane attitude data acquired on site into a corresponding space unit normal vector n which is (x, y, z);
the attitude of the structural plane acquired on site is expressed by inclination alpha and inclination angle beta, and the calculation formula for converting the attitude of the structural plane into a space unit normal vector n in a form of (x, y, z) is as follows:
(2) calculating the distance D (n) between every two structural planes in the data seti，nj) Obtaining a distance matrix D of the structural surface data setN×N；
Distance D (n)i，nj) The schematic diagram of the unit normal vector included angle of the two structural surfaces is shown in FIG. 2, and the unit normal vectors n of the two structural surfaces are sine valuesi(xi，yi，zi)、nj(xj，yj，zj) Distance D (n)i，nj)：
In the formula, niAnd njRespectively representing unit normal vectors of the structural surfaces i and j, theta represents an included angle of the unit normal vectors of the two structural surfaces, and T is a transposed symbol of the matrix;
(3) calculating M times of clustering on the data set by adjusting a clustering algorithm or a hyper-parameter to obtain M base clustering results pi with differencesm；
The clustering algorithm is a K-means based on division, a level-based coacervation level clustering, a DBSCAN based on density or a spectral clustering algorithm based on a graph; the super-parameters are parameters set by clustering algorithms in clustering analysis, each clustering algorithm comprises a plurality of super-parameters, for example, K-means, the aggregation level clustering and the spectral clustering algorithms comprise the group number K, and the DBSCAN algorithm comprises the radius eps and the minimum sample number min _ samples;
from the perspective of a clustering algorithm, a method for generating base clustering results with differentiation: using the same clustering algorithm, setting different hyper-parameters to cluster the data set to generate a base clustering result; for example, K-means, agglomerative hierarchical clustering and spectral clustering algorithms can set the K value to an integer no less than 2; the radius eps of the DBSCAN algorithm can be set to be 0.1-0.3, the minimum sample number min _ samples can be set to be 2-10, and the higher the density is, the larger the min _ samples is, the smaller the eps is according to the data set density setting;
from the perspective of a clustering algorithm, the method for generating differentiated base clustering results can also use different clustering algorithms to cluster the data set to generate base clustering results; the two methods can be combined to generate a base clustering result;
(4) calculating a co-covariance matrix CA of the base clustering result;
the co-ordination matrix CA is used for reorganizing the base clustering result, avoiding the corresponding problem of group labels in the base clustering result, and measuring the similarity between data points in a digitalized and accurate manner; the calculation expression of the co-ordination matrix CA is as follows:
CA＝{mij}N×N
in the formula, N is the quantity of the attitude data of the structural plane,
πm(xi) Is a sample xiClustering result in the basis pimThe group to which the (c) group belongs,
is whether sample i and sample j are present in the same group, if sample i and sample j are present in the same group, then
Otherwise
The larger the frequency of dividing a certain structural plane into the same group by the basis clustering result is, the larger the corresponding CA element value is;
(5) respectively setting the grouping number K as an integer not less than 2, and clustering the co-covariance matrix CA by adopting a coacervation hierarchical clustering algorithm;
the coacervation hierarchical clustering algorithm is
Taking each sample in the CA matrix as a separate group, and gradually combining two groups which are divided into the same group and have the highest frequency into one group in each iteration process until a termination condition is reached or the two groups are finally grouped into one group;
(6) determining the optimal grouping number K according to the clustering performance measurement indexop；
The clustering performance measurement index is an index for measuring the clustering effect of the occurrence data of the structural plane, the contour coefficient SC is used as the clustering performance measurement index, and the SC expression is
Wherein s (i) represents a contour coefficient of one sample,
a (i) represents a sample xiAverage distance to other samples of the same group, b (i) denotes sample xiAverage distance between all samples of the adjacent nearest group;
the value range of SC is [ -1,1], and the larger the value of SC is, the better the clustering effect is;
optimal number of packets KopThe value is the grouping number K with the maximum profile coefficient corresponding to the clustering performance measurement index;
(7) according to the optimal number of groups KopThe clustering integration result is obtained, noise points and isolated values are removed, and the structure surface advantage and occurrence grouping result is obtained; the noise and the isolated value mean that the base clustering result in the clustering integration model is divided into the same group of structural surfaces with very low frequency.
Example 2: as shown in fig. 1, a rock mass structural plane advantage occurrence grouping method based on cluster integration specifically comprises the following steps:
(1) structural surface attitude data which is obtained by surveying a turpentine hydropower station dam abutment-adit is used as test data, and a structural surface attitude polar diagram is shown in figure 3 and comprises 305 structural surfaces in total; converting the occurrence into a space unit normal vector n which is (x, y, z):
(2) calculating the distance D (n) between every two structural surfaces by using the sine value of the included angle of the normal vector of the space uniti，nj) The schematic diagram of the unit normal vector included angle of the structural surface is shown in fig. 2, and a distance matrix D of the structural surface data set is constructedN×N；
In the formula, niAnd njRespectively representing unit normal vectors of the structural surfaces i and j, theta represents an included angle of the unit normal vectors of the two structural surfaces, and T is a transposed symbol of the matrix;
(3) taking K-means as an example, and aiming at a structural plane occurrence data set, carrying out disturbance by adjusting a hyper-parameter K value of the K-means, wherein the value of K is an integer of 2-11, and obtaining 10 base clustering results with difference;
(4) reorganizing 10 base clustering results, calculating a co-ordination matrix CA of the base clustering results, avoiding the corresponding problem of group labels in the base clustering results, and measuring the similarity between data points in a digitalized and accurate manner;
the CA calculation expression is:
CA＝{mij}N×N
wherein, N represents the number of structural plane attitude data, N is 305,
πm(xi) Represents a sample xiClustering result in the basis pimThe group to which the (c) group belongs,
indicating whether sample i and sample j are present in the same group, and if a pair of samples i, j is present in the same group,
otherwise
The larger the frequency of dividing a certain structural plane into the same group by the basis clustering result is, the larger the corresponding CA element value is;
(5) and respectively setting the grouping number K as an integer of 2-10, and clustering the co-covariance matrix CA by adopting a coacervation hierarchical clustering algorithm.
Taking each sample in the CA matrix as a separate group, and gradually combining two groups which are divided into the same group and have the highest frequency into one group in each iteration process until a termination condition is reached or the two groups are finally grouped into one group;
(6) calculating the clustering performance metric index contour coefficient SC of the CA matrix of each algorithm in the grouping number K belongs to [2, 10], as shown in FIG. 4, the SC expression is:
where s (i) represents the contour coefficient of one of the samples,
a (i) represents a sample xiAverage distance to other samples of the same group; b (i) represents a sample xiAverage distance between all samples of the adjacent nearest group;
as can be seen from fig. 4, the clustering performance metric index SC is the largest and the clustering effect is the best when K is 4 in the 4 clustering algorithms, so that the optimal grouping number K of the structural plane data set is determinedopIs 4;
(7) according to the optimal number of groups KopObtaining a final clustering integration result, as shown in fig. 5, it can be seen from the figure that the structural surfaces with the identification symbols of "x" are very dispersed and do not appear in groups, so the structural surfaces in the groups are noise points and isolated values;
(8) after noise points and isolated values are removed, the structure surface data dominance occurrence grouping result is shown in fig. 6, and it can be known that the adit has 3 groups of dominance structure surfaces, and the grouping result conforms to the actual situation;
comparing the clustering effects before and after integration, wherein the SC maximum value is 0.16 in 10K-means clustering models before clustering integration; after the noise points and the isolated values are clustered and removed, the SC is 0.60, the clustering effect is remarkably improved, and the clustering integration technology is feasible and effective when being applied to structural plane occurrence advantage grouping, so that not only is a clear intergroup boundary given, but also the noise points and the isolated value structural planes are effectively identified, which is difficult to realize by a common structural plane advantage occurrence grouping method.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit and scope of the present invention.
Claims (8)
1. A rock mass structural plane advantage and occurrence grouping method based on cluster integration is characterized by comprising the following specific steps:
(1) converting the structural plane attitude data acquired on site into a corresponding space unit normal vector n which is (x, y, z);
(2) calculating the distance D (n) between every two structural planes in the data seti，nj) Obtaining a distance matrix D of the structural surface data setN×N；
(3) Calculating M times of clustering on the data set by adjusting a clustering algorithm or a hyper-parameter to obtain M base clustering results pi with differencesm；
(4) Calculating a co-covariance matrix CA of the base clustering result;
(5) respectively setting the grouping number K as an integer not less than 2, and clustering the co-covariance matrix CA by adopting a coacervation hierarchical clustering algorithm;
(6) determining the optimal grouping number K according to the clustering performance measurement indexop；
(7) According to the optimal number of groups KopAnd (4) clustering and integrating the results, eliminating noise points and isolated values, and obtaining the grouping result of the structural surface superiority and occurrence.
2. The clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 1, wherein: the attitude of the structural plane acquired on site in the step (1) is expressed by a tendency alpha and an inclination angle beta, and a calculation formula for converting the attitude of the structural plane into a space unit normal vector n in a (x, y, z) form is as follows:
3. the clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 1, wherein: step (2) distance D (n)i，nj) Is the sine value of the included angle of the unit normal vectors of the two structural surfaces and the unit normal vector n of the two structural surfacesi(xi，yi，zi)、nj(xj，yj，zj) Distance D (n)i，nj)：
In the formula, niAnd njRespectively representing unit normal vectors of the structural surfaces i and j, theta represents an included angle of the unit normal vectors of the two structural surfaces, and T is a transposed symbol of the matrix.
4. The clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 1, wherein: and (3) the clustering algorithm is a K-means based on division, a level-based coacervation level clustering, a DBSCAN based on density or a spectral clustering algorithm based on a graph.
5. The clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 4, wherein: the hyper-parameters are parameters set by a clustering algorithm in clustering analysis.
6. The clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 1, wherein: and (4) calculating an expression of the co-covariance matrix CA as follows:
CA＝{mij}N×N
in the formula, N is the quantity of the attitude data of the structural plane,
πm(xi) Is a sample xiClustering result in the basis pimThe group to which the (c) group belongs,
is whether sample i and sample j are present in the same group, if sample i and sample j are present in the same group, then
Otherwise
7. The clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 1, wherein: the coacervation hierarchical clustering algorithm in the step (5) is
And taking each sample in the CA matrix as a separate group, and gradually combining two groups which are divided into the same group and have the highest frequency into one group in each iteration process until a termination condition is reached or finally grouping is realized.
8. The clustering integration-based rock mass structural plane dominance occurrence grouping method according to claim 1, wherein: the clustering performance measurement index in the step (6) adopts a contour coefficient SC, and the SC expression is
Wherein s (i) represents a contour coefficient of one sample,
a (i) represents a sample xiAverage distance to other samples of the same group, b (i) denotes sample xiAverage distance between all samples of the nearest neighboring group.
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