CN111027016B - Rock mass structural plane dominant occurrence cluster analysis method based on netting algorithm - Google Patents
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Abstract
A rock mass structural plane dominant occurrence cluster analysis method based on a net-work algorithm comprises the following steps: the method comprises the steps of (1) selecting an engineering rock slope to be analyzed in the wild; (2) Performing polar coordinate conversion on the structure surface shape and projecting the structure surface shape into a spherical space; (3) Calculating the similarity degree r between the output samples by adopting the square of the acute angle sine value clamped between normal vectors of structural surface units ij Constructing a fuzzy similar matrix R of the structural plane shape; (4) Modifying a fuzzy similar matrix R of the structural plane shape; (5) Constructing lambda section matrix R of structural plane shape of modified fuzzy similar matrix R λ The method comprises the steps of carrying out a first treatment on the surface of the (6) Cutting matrix R for structural plane shape λ Carrying out transformation; (7) For the modified truncated matrix R λ Clustering and grouping the structural plane shapes; (8) And calculating effectiveness evaluation indexes under different grouping numbers according to the clustering result of the structural face occurrence, and determining the optimal grouping number by combining engineering practice to obtain the structural face dominant occurrence. The invention makes grouping result more reasonable, and dominant output more in accordance with objective practice.
Description
Technical Field
The invention belongs to the technical field of engineering, relates to a clustering analysis method for grouping advantage of a rock mass structural plane by using a netting algorithm, and particularly provides a clustering analysis method for determining advantage production of the rock mass structural plane based on the netting algorithm by combining the advantage that the netting algorithm can quickly and effectively eliminate noise points of the structural plane from complexity and randomness of structural plane distribution.
Background
The rock mass forms a structural surface through long geological structures and complex geological actions, the distribution of the structural surface has complexity and randomness, the structural surface group is accurately identified, and the determination of the dominant occurrence of the structural surface is the basis for evaluating the stability of rock mass engineering. A large number of researches show that structural surfaces with the same construction period and formation cause have similarity in scale and development degree, can be classified into the same advantage group, and can be subjected to advantage grouping by using a statistical method. However, the internal and external dynamic factors for promoting the evolution of the structural surface are complex, some 'noise' data are inevitably acquired in field investigation, the 'noise' data and the dominant occurrence of the structural surface have overlarge deviation, the sample dispersion is higher, and the traditional structural surface cluster analysis method has the defect that the 'noise' cannot be eliminated. Therefore, the noise data is effectively eliminated, so that the structure surface clustering process and the clustering result are more reasonable and effective, and the method has important theoretical significance and practical value. At present, many scholars have conducted researches on structural face cluster analysis, wherein representative results are as follows:
in 2002, zhou and Maerz consider multivariate parameters such as structural plane occurrence, spacing, roughness and the like, and clustering grouping is carried out on the structural planes by adopting 4 methods of neighbor algorithm, K-means, fuzzy C-means and vector quantization.
In 2005, zhou Yuxin and the like provided a comprehensive clustering method of structural plane occurrence as an initial clustering center of a fuzzy soft clustering method by using a clustering result obtained by a fuzzy equivalent clustering method.
In 2013, xu and the like propose a rock mass structural plane multi-parameter advantage grouping method based on a variable-scale chaotic optimization algorithm, but the chaotic optimization algorithm has the defects of blind repetition, low search efficiency and long calculation time.
In 2015, song Tengjiao and the like propose a structural surface cluster analysis method based on a firefly algorithm, wherein a unit normal vector is used for representing the occurrence of structural surfaces, the distance between the structural surfaces is measured through an acute angle sine value clamped by the unit normal vector, a fuzzy objective function is established, and then an optimal cluster center is searched by using the firefly optimization algorithm to determine the boundary between groups.
In 2019, cui Xuejie and the like propose rock mass structural plane occurrence cluster analysis based on an improved genetic algorithm, and the method uses the genetic algorithm to select a proper cluster center for a K-means algorithm, so that the defect that the K-means algorithm is influenced by an initial cluster center and is easy to converge on a local optimal solution is overcome.
However, the above-mentioned research often requires a large amount of calculation work and takes much time, and the iteration condition is that all data points are clustered, so that the defect that "noise points" cannot be eliminated exists, the clustering process and the clustering result are affected, and the deviation of the dominant occurrence of the structural surface is caused.
Disclosure of Invention
In order to overcome the defects of the traditional structural surface clustering analysis method, the invention provides a clustering analysis method for reasonably determining the dominant occurrence of the rock structural surface based on a network algorithm, the method eliminates the influence of structural surface noise on the clustering process and the clustering result, and self-organizing clustering is carried out on the premise of not needing to designate the initial grouping number and the initial clustering center, so that the reliability of the structural surface clustering process is ensured, the grouping result is more reasonable, and the dominant occurrence accords with objective reality.
The technical scheme adopted for solving the technical problems is as follows:
a rock mass structural plane dominant occurrence cluster analysis method based on a screening algorithm comprises the following steps:
(1) Selecting an engineering rock slope to be analyzed in the field, and systematically measuring as many engineering rock slopes as possible by a measuring means to obtain enough structural surface attitude data;
(2) The structure plane shape is transformed into polar coordinates, projected into spherical space, and expressed in three-dimensional Cartesian coordinates by adopting unit normal vector, and the unit normal vector of any structure plane is expressed as N= (x) 1 ，x 2 ，x 3 ) Wherein x is 1 ＝cosα·sinβ，x 2 ＝sinα·sinβ，x 3 =cos β, α represents the tendency of the structural plane, β represents the inclination angle of the structural plane;
(3) Calculating the similarity degree r between the output samples by adopting the square of the acute angle sine value clamped between normal vectors of structural surface units ij ，i＝1，2..n; j=1, 2,. -%, n; n is the total number of samples of the structural plane shape, and a fuzzy similarity matrix R of the structural plane shape is constructed, wherein R= (R) ij ) n×n ；
(4) Modifying fuzzy similar matrix R of structural plane shape, deleting all elements above diagonal line due to symmetry, and using sequence number O of classified object i Replacing elements on the diagonal;
(5) Selecting a confidence level lambda of the structural plane shape, and constructing a lambda section matrix R of the structural plane shape for the modified fuzzy similar matrix R λ Wherein R is λ ＝(r λ ij ) n×n ；
(6) Cutting matrix R for structural plane shape λ Modifications are made below the diagonal, replacing "1" with the node number ". Substituted" 1", and omitting R λ All "0" s in (3);
(7) For the modified truncated matrix R λ Clustering and grouping the structural plane shapes, namely leading warps and wefts to diagonal lines by nodes 'x', and grouping the shape samples connected together by the warps and the wefts through the same node into a group, so as to realize classification;
(8) According to the clustering result of the structural plane occurrence, calculating the effectiveness evaluation index V under different grouping numbers XB And combining engineering to actually determine the optimal grouping number, thereby obtaining the dominant yield of the structural surface.
Further, in the step (3), the degree of similarity r between the occurrence samples ij The expression is as follows:
r ij ＝sin 2 θ＝1-(N i ·N j T ) 2
wherein N is i A unit normal vector for the i-th sample; n (N) j A unit normal vector for the j-th sample; θ is any two unit normal vectors N i 、N j The acute angle is clamped.
Still further, in the step (3), the fuzzy similarity matrix R of the structural plane shape is expressed as:
wherein r is 11 A degree of similarity between the 1 st sample and the 1 st sample; r is (r) 12 A degree of similarity between sample 1 and sample 2; r is (r) 1n A degree of similarity between the 1 st sample and the nth sample; r is (r) 21 A degree of similarity between sample 2 and sample 1; r is (r) 22 A degree of similarity between the 2 nd sample and the 2 nd sample; r is (r) 2n A degree of similarity between the 2 nd sample and the nth sample; r is (r) n1 A degree of similarity between the nth sample and the 1 st sample; r is (r) n2 A degree of similarity between the nth sample and the 2 nd sample; r is (r) nn Is the degree of similarity of the nth sample to the nth sample.
Still further, in the step (5), r is in a cross-sectional matrix of the structural plane shape λ ij The expression is as follows:
wherein r is λ ij The membership of the structural plane shape sample at the confidence level λ.
Still further, in the step (5), a lambda-cut matrix R of the structural plane shape is generated λ The expression is as follows:
wherein r is λ 21 Membership of sample 2 and sample 1 at confidence level λ; r is (r) λ n1 Membership of the nth sample and the 1 st sample at a confidence level λ; r is (r) λ n2 Is the membership of the nth sample to the 2 nd sample at the confidence level λ.
Further, in the step (8), the validity evaluation index V XB The expression is as follows:
wherein c is the clustering grouping number; n is the total number of samples; x is x j A j-th structural plane shape sample; v i The clustering center of the i group; the sum of the values of the two values is the standard of the measurement distance in the classification space, and sine square measurement is needed for fuzzy clustering of the occurrence; u (u) ij Is fuzzy membership, representing x j Belonging to the cluster center v i The extent of (3); m is a fuzzy weighted index, and general research takes m=2.
The beneficial effects of the invention are mainly shown in the following steps: the influence of the structural plane noise on the clustering process and the clustering result can be effectively eliminated.
Drawings
FIG. 1 is a polar diagram of a slot mouth slope structure surface;
FIG. 2 is a diagram of a tiger mouth slope structural face going to a rose;
FIG. 3 is an isometric view of a slot side slope structural surface;
FIG. 4 is a schematic view of the structural plane shape;
fig. 5 is a grouping result of the slot side slope at λ=0.980;
fig. 6 is a grouping result of the slot side slope at λ=0.975;
fig. 7 shows the grouping result of the slot side slope at λ=0.970.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 7, a rock mass structural plane dominant occurrence cluster analysis method based on a netting algorithm, the method comprises the following steps:
(1) Selecting an engineering rock slope to be analyzed in the field, and systematically measuring as many engineering rock slopes as possible by a measuring means to obtain enough structural surface attitude data;
(2) The structure plane shape is transformed into polar coordinates, projected into spherical space, and expressed in three-dimensional Cartesian coordinates by adopting unit normal vector, and the unit normal vector of any structure plane is expressed as N= (x) 1 ，x 2 ，x 3 ) Wherein x is 1 ＝cosα·sinβ，x 2 ＝sinα·sinβ，x 3 =cos β, α represents the tendency of the structural plane, β represents the inclination angle of the structural plane;
(3) Calculating the similarity degree r between the output samples by adopting the square of the acute angle sine value clamped between normal vectors of structural surface units ij I=1, 2, n; j=1, 2,. -%, n; n is the total number of samples of the structural plane shape, and a fuzzy similarity matrix R of the structural plane shape is constructed, wherein R= (R) ij ) n×n ；
(4) Modifying fuzzy similar matrix R of structural plane shape, deleting all elements above diagonal line due to symmetry, and using sequence number O of classified object i Replacing elements on the diagonal;
(5) Selecting a confidence level lambda of the structural plane shape, and constructing a lambda section matrix R of the structural plane shape for the modified fuzzy similar matrix R λ Wherein R is λ ＝(r λ ij ) n×n ；
(6) Cutting matrix R for structural plane shape λ Modifications are made below the diagonal, replacing "1" with the node number ". Substituted" 1", and omitting R λ All "0" s in (3);
(7) For the modified truncated matrix R λ Clustering and grouping the structural plane shapes, namely leading warps and wefts to diagonal lines by nodes 'x', and grouping the shape samples connected together by the warps and the wefts through the same node into a group, so as to realize classification;
(8) According to the clustering result of the structural plane occurrence, calculating the effectiveness evaluation index V under different grouping numbers XB And combining engineering to actually determine the optimal grouping number, thereby obtaining the dominant yield of the structural surface.
Examples: a rock mass structural plane dominant occurrence cluster analysis method based on a net-work algorithm comprises the following steps:
(1) In the field, selecting a Wenchun county-Yinchun gecko mouth rock high slope of Sichuan province to perform cluster analysis of structural face dominant occurrence, and performing systematic measurement on the slope by a survey line method to obtain 200 structural face occurrence data;
(2) And carrying out statistical analysis on the structure surface occurrence to generate a structure surface pole diagram (see figure 1), a trend rose diagram (see figure 2) and an isocenter diagram (see figure 3). Preliminary grouping is carried out on the structural faces of the tiger mouth side slopes through field judgment of structural face statistical geologic causes and analysis of a polar diagram, a trend rose diagram and an equal density diagram, the grouping results are 3 groups, and table 1 is the preliminary grouping result of the structural faces of the tiger mouth side slopes;
table 1 (3) converts the polar coordinates of the structural plane shape, projects the structural plane shape into a spherical space, and uses the unit normal vector to represent the structural plane shape in three-dimensional cartesian coordinates, wherein the unit normal vector of any structural plane can be represented as n= (x) 1 ，x 2 ，x 3 ) Wherein x is 1 ＝cosα·sinβ，x 2 ＝sinα·sinβ，x 3 =cos β. FIG. 4 is a schematic view of the structural plane shape;
(4) Calculating the similarity degree r between the output samples by adopting the square of the acute angle sine value clamped between normal vectors of structural surface units ij I=1, 2, 200; j=1, 2,..200. Constructing a fuzzy similarity matrix R of the structural plane shape, wherein R= (R) ij ) 200×200 The expression is:
(4) Modifying fuzzy similar matrix R of structural plane shape, deleting all elements above diagonal line due to symmetry, and using sequence number O of classified object i Replacing elements on the diagonal;
(5) When square of acute angle sine values clamped between normal vectors of structural surface units is used as a calculation formula of similarity degree between output samples, the probability of best clustering results between 0.995 and 0.970 of lambda values is generally greatest, so that lambda values of 0.995 are preferentially selected for trial calculation, and accuracy of 0.005 is sequentially reduced to respectively verify grouping results. After transformation according to the confidence level lambda of the selected structural surfaceIs used for constructing lambda section matrix R of structural plane shape of fuzzy similar matrix R λ Wherein R is λ ＝(r λ ij ) 200×200 The expression is:
(6) Cutting matrix R for structural plane shape λ Modifications are made below the diagonal, replacing "1" with the node number ". Substituted" 1", and omitting R λ Is "0" in the above-mentioned formula. Leading warps and wefts to diagonal lines by nodes, and grouping the output samples connected together by the warps and the wefts through the same node into a group;
(7) The trial calculation of different confidence levels of the structural plane shows that the structural plane presents a better clustering result when the lambda value takes 0.980, 0.975 and 0.970. Table 2 is the clustering result of the network algorithm when λ=0.980, and the corresponding grouping result is shown in fig. 5; table 3 is the clustering result of the network algorithm at λ=0.975, and the corresponding grouping result is shown in fig. 6; table 4 shows the clustering results of the network algorithm at λ=0.970, and the corresponding grouping results are shown in fig. 7.
TABLE 2
TABLE 3 Table 3
As can be seen from tables 2 to 4, table 4 (8) shows that when λ=0.980, the clustering result is 4 groups; when λ=0.975, the clustering result is 3 groups; when λ=0.970, the clustering result is 2 groups. On the basis, the effectiveness evaluation is carried out on the clustering results obtained by different groups, and when the grouping results are 4 groupsEffectiveness evaluation index V XB =0.20; when the grouping result is 3 groups, the effectiveness evaluation index V XB =0.12; when the grouping result is 2 groups, the effectiveness evaluation index V XB =0.23. According to V XB The smaller the index is, the better the cluster quality is, as can be seen from the validity judgment of the index. Comparison of the three groups of indexes shows that the grouping result is V when the grouping result is 3 groups XB The index is minimum, the group number is the optimal group number of the structural surface, the result is the same as the initial group result of the slope, and the dominant yield is consistent with the initial group. Therefore, the clustering result of the network algorithm when λ=0.975 can be determined to be an optimal classification scheme, the side slope mainly develops 3 groups of structural surfaces, and the dominant occurrence of the side slope is 105 degrees, 38 degrees, 200 degrees, 60 degrees and 288 degrees, 66 degrees respectively.
Claims (6)
1. The rock mass structural plane dominant occurrence cluster analysis method based on the netting algorithm is characterized by comprising the following steps of:
(1) Selecting an engineering rock slope to be analyzed in the field, and systematically measuring as many engineering rock slopes as possible by a measuring means to obtain enough structural surface attitude data;
(2) The structure plane shape is transformed into polar coordinates, projected into spherical space, and expressed in three-dimensional Cartesian coordinates by adopting unit normal vector, and the unit normal vector of any structure plane is expressed as N= (x) 1 ，x 2 ，x 3 ) Wherein x is 1 ＝cosα·sinβ，x 2 ＝sinα·sinβ，x 3 =cos β, α represents the tendency of the structural plane, β represents the inclination angle of the structural plane;
(3) Calculating the similarity degree r between the output samples by adopting the square of the acute angle sine value clamped between normal vectors of structural surface units ij I=1, 2, n; j=1, 2,. -%, n; n is the total number of samples of the structural plane shape, and a fuzzy similarity matrix R of the structural plane shape is constructed, wherein R= (R) ij ) n×n ；
(4) Modifying fuzzy similar matrix R of structural plane shape, deleting all elements above diagonal line due to symmetry, and using sequence number O of classified object i Replacing on diagonalAn element;
(5) Selecting a confidence level lambda of the structural plane shape, and constructing a lambda section matrix R of the structural plane shape for the modified fuzzy similar matrix R λ Wherein R is λ ＝(r λ ij ) n×n ；
(6) Cutting matrix R for structural plane shape λ Modifications are made below the diagonal, replacing "1" with the node number ". Substituted" 1", and omitting R λ All "0" s in (3);
(7) For the modified truncated matrix R λ Clustering and grouping the structural plane shapes, namely leading warps and wefts to diagonal lines by nodes 'x', and grouping the shape samples connected together by the warps and the wefts through the same node into a group, so as to realize classification;
(8) According to the clustering result of the structural plane occurrence, calculating the effectiveness evaluation index V under different grouping numbers XB And combining engineering to actually determine the optimal grouping number, thereby obtaining the dominant yield of the structural surface.
2. The method for clustering dominant bearing capacity of structural face of rock mass based on network algorithm as claimed in claim 1, wherein in said step (3), the degree of similarity r between bearing capacity samples is ij The expression is as follows:
r ij ＝sin 2 θ＝1-(N i ·N j T ) 2
wherein N is i A unit normal vector for the i-th sample; n (N) j A unit normal vector for the j-th sample; θ is any two unit normal vectors N i 、N j The acute angle is clamped.
3. The method for clustering dominant occurrence of structural faces of rock mass according to claim 1 or 2, wherein in the step (3), the fuzzy similarity matrix R of occurrence of structural faces is expressed as:
wherein r is 11 A degree of similarity between the 1 st sample and the 1 st sample; r is (r) 12 A degree of similarity between sample 1 and sample 2; r is (r) 1n A degree of similarity between the 1 st sample and the nth sample; r is (r) 21 A degree of similarity between sample 2 and sample 1; r is (r) 22 A degree of similarity between the 2 nd sample and the 2 nd sample; r is (r) 2n A degree of similarity between the 2 nd sample and the nth sample; r is (r) n1 A degree of similarity between the nth sample and the 1 st sample; r is (r) n2 A degree of similarity between the nth sample and the 2 nd sample; r is (r) nn Is the degree of similarity of the nth sample to the nth sample.
4. The method for clustering dominant bearing capacity of structural plane of rock mass based on network algorithm according to claim 1 or 2, wherein in said step (5), r is in the truncated matrix of bearing capacity of structural plane λ ij The expression is as follows:
wherein r is λ ij The membership of the structural plane shape sample at the confidence level λ.
5. The method for clustering dominant facies of a rock mass structure according to claim 1 or 2, wherein in the step (5), a lambda-cut matrix R of facies morphology λ The expression is as follows:
wherein r is λ 21 Membership of sample 2 and sample 1 at confidence level λ; r is (r) λ n1 Membership of the nth sample and the 1 st sample at a confidence level λ; r is (r) λ n2 Membership of nth sample and 2 nd sample at confidence level λ。
6. The method for clustering dominant bearing capacity of structural face of rock mass according to claim 1 or 2, wherein in the step (8), the effectiveness evaluation index V XB The expression is as follows:
wherein c is the clustering grouping number; n is the total number of samples; x is x j A j-th structural plane shape sample; v i The clustering center of the i group; the sum of the values of the two values is the standard of the measurement distance in the classification space, and sine square measurement is needed for fuzzy clustering of the occurrence; u (u) ij Is fuzzy membership, representing x j Belonging to the cluster center v i The extent of (3); m is a fuzzy weighted index.
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