CN116842818A - Structural plane attitude grouping method based on pelican optimization algorithm - Google Patents
Structural plane attitude grouping method based on pelican optimization algorithm Download PDFInfo
- Publication number
- CN116842818A CN116842818A CN202310578613.2A CN202310578613A CN116842818A CN 116842818 A CN116842818 A CN 116842818A CN 202310578613 A CN202310578613 A CN 202310578613A CN 116842818 A CN116842818 A CN 116842818A
- Authority
- CN
- China
- Prior art keywords
- pelican
- structural plane
- objective function
- clustering
- initial
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 241000272194 Ciconiiformes Species 0.000 title claims abstract description 89
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 61
- 238000005457 optimization Methods 0.000 title claims abstract description 36
- 238000000034 method Methods 0.000 title claims abstract description 33
- 239000011435 rock Substances 0.000 claims abstract description 25
- 239000013598 vector Substances 0.000 claims abstract description 12
- 238000004364 calculation method Methods 0.000 claims description 13
- 238000005259 measurement Methods 0.000 claims description 5
- 241001061225 Arcos Species 0.000 claims description 3
- 238000011065 in-situ storage Methods 0.000 claims description 2
- 238000011156 evaluation Methods 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 9
- 239000006185 dispersion Substances 0.000 description 6
- 230000000694 effects Effects 0.000 description 5
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 5
- 230000001154 acute effect Effects 0.000 description 2
- 238000010408 sweeping Methods 0.000 description 2
- 241000577457 Lestidae Species 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000007621 cluster analysis Methods 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000000638 solvent extraction Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/23—Clustering techniques
- G06F18/232—Non-hierarchical techniques
- G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
- G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Evolutionary Computation (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Geometry (AREA)
- Artificial Intelligence (AREA)
- Life Sciences & Earth Sciences (AREA)
- Software Systems (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Computer Hardware Design (AREA)
- Mathematical Optimization (AREA)
- Health & Medical Sciences (AREA)
- Pure & Applied Mathematics (AREA)
- Probability & Statistics with Applications (AREA)
- Computational Mathematics (AREA)
- Medical Informatics (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Bioinformatics & Computational Biology (AREA)
- Evolutionary Biology (AREA)
- Mathematical Analysis (AREA)
- Biomedical Technology (AREA)
- Biophysics (AREA)
- Computational Linguistics (AREA)
- General Health & Medical Sciences (AREA)
- Molecular Biology (AREA)
- Computing Systems (AREA)
- Mathematical Physics (AREA)
- Image Analysis (AREA)
Abstract
The invention discloses a structural plane shape grouping method based on a pelicans optimization algorithm, which comprises the steps of converting rock structural plane shape sample data acquired on site into corresponding space unit normal vectors and randomly dividing the space unit normal vectors into a plurality of data groups to be clustered; adopting a pelican optimization algorithm POA to optimize an initial clustering center of a fuzzy C-means clustering algorithm; clustering each data group to be clustered by a fuzzy C-means clustering algorithm based on the optimized initial clustering center to obtain a final clustered data group; and carrying out validity check on the obtained final clustering data group to confirm the final clustering result. Based on the FMC algorithm, an initial clustering center is optimized through a pelicant optimization algorithm, and a simplified Xie Beini index is adopted as a grouping evaluation standard, so that compared with a traditional grouping method, the capacity of searching a global optimal solution is improved, structural plane data with unclear boundaries of occurrence poles can be precisely grouped, the application range of the grouping method is enlarged, and the capacity of solving the complex rock mass engineering problem of the grouping method is improved.
Description
Technical Field
The invention relates to the technical field of rock mass structural plane grouping, in particular to a structural plane shape grouping method based on a pelican optimization algorithm.
Background
The rock mass mainly comprises a structural surface and a structural body, and is a key factor influencing engineering stability. Among the widely distributed rock masses of structural plane, because the structural plane quantity is huge, be difficult to analyze one by one, consequently, realize the accurate grouping of rock mass structural plane, be the prerequisite that carries out rock mass engineering stability analysis and three-dimensional network computer simulation of structural plane. Because the field measurement environment is complex, a plurality of structural surface classification indexes are difficult to measure, and the yield index has a clear calculation method, so that the field measurement is convenient. Therefore, achieving structural plane dominant occurrence grouping through structural plane occurrence information remains the most efficient approach.
Traditional structural plane grouping methods, such as: the pole diagram analysis and the isopycnic diagram analysis cannot give stable and accurate structure surface grouping results, and in places with inconspicuous boundaries of the occurrence poles, the pole diagram analysis and the isopycnic diagram analysis need to rely on professional knowledge of engineering personnel for identification, and the final grouping results have larger differences. Clustering algorithms based on partitioning, such as a K-means algorithm and an FCM algorithm, are local optimization algorithms, and are easy to fall into local optimal solutions, so that the obtained grouping result is unreliable. Based on the clustering algorithm, a plurality of optimization algorithms are introduced, the selection of an initial clustering center is improved, and the grouping result is improved. However, there are still problems in that the implementation process is cumbersome and the required input parameters are excessive.
Disclosure of Invention
The invention provides a structural face occurrence grouping method based on a pely optimization algorithm, which aims to overcome the technical problems.
In order to achieve the above object, the technical scheme of the present invention is as follows:
a structural face shape grouping method based on a pelican optimization algorithm, comprising the steps of:
step S1, converting rock mass structural plane attitude sample data acquired on site into corresponding space unit normal vectors n= (x, y, z) and randomly dividing the space unit normal vectors into a plurality of data sets to be clustered;
the rock mass structural plane attitude sample data includes a dip angle β (0 ° < β <90 °);
step S2: adopting a pelican optimization algorithm POA to optimize an initial clustering center of a fuzzy C-means clustering algorithm;
step S3: clustering each data group to be clustered by a fuzzy C-means clustering algorithm based on the optimized initial clustering center to obtain a final clustered data group;
step S4: and carrying out validity check on the obtained final clustering data packet to confirm a final clustering result.
Further, in step S1, the structural plane shape sample data collected in situ is converted into a corresponding spatial unit normal vector n= (x, y, z), where the calculation formula is
x 2 +y 2 +z 2 ＝1
Wherein x represents the component of the structure surface in the x-axis direction under a preset space rectangular coordinate system; y represents the component of the y-axis direction of the structural plane under a preset space rectangular coordinate system; z represents the component of the structure surface in the z-axis direction under a preset space rectangular coordinate system.
Further, in step S2, the initial clustering center adopting the pelican optimization algorithm POA to optimize the fuzzy C-means clustering algorithm is specifically
Step S2.1, setting a group size N of the pelicant, a maximum iteration number T and the number c of randomly divided data groups to be clustered; initializing an initial clustering center of a data set to be clustered;
the position of each pelican corresponds to the set of initial clustering centers of the data sets to be clustered;
step S2.2, based on the structural plane attitude sample data, the angle range of the inclination angle alpha and the inclination angle beta: alpha is more than 0 and less than 360 degrees; calculating the membership degree of a clustering center according to the initial clustering center, wherein beta is more than 0 degrees and less than 90 degrees, and acquiring a fuzzy objective function according to the membership degree; selecting the position of the pelicant with the minimum fuzzy objective function value as the global optimal solution;
step S2.3: randomly selecting c pieces of attitude data from the attitude sample data of the rock mass structural plane to update an initial clustering center, taking the updated initial clustering center as the position of the prey, and obtaining an objective function value of the position of the prey;
the position of the pelican is initially updated according to the position of the prey, and the membership degree and the objective function value of the position of the pelican after initial updating are calculated;
step S2.4, updating the position of the pelican again according to the initial updated objective function values of the position of the pelican and the position of the hunting object, and updating the global optimal solution;
step S2.5: and repeatedly executing the steps S2.3 to S2.4 until the maximum iteration times are reached, wherein the finally obtained pelican position is the initial clustering center with the global optimum.
Further, the membership calculation formula is
Wherein u is ij Representing the membership degree of the jth structural surface belonging to the ith clustering center; c represents the number of randomly divided data sets; v i (i=1, 2, 3..c.) represents the cluster center of each group;
the calculation formula of the fuzzy objective function is that
Wherein d (v) i ，x j ) Representing v i And x j Distance between d (v) i ，x k ) Representing v i And x k The distance between the two points is measured by adopting the sine distance of the included angle as the distance measurement; m represents fuzzy weighting coefficient, m is [1 ], and is infinity]；u ij ∈[0,1]And is also provided withJ m (U, C) denotes a fuzzy objective function.
Further, in step S2.3, the position of the pelican is initially updated according to the position of the prey, and the update formula is as follows
Wherein:the position of the ith pelicant in the j-th dimension after initial updating; rand is [0,1]Random numbers within a range; i is a random integer of 1 or 2; p (P) j The position of the hunting object in the j-th dimension; f (F) p Objective function value for hunting; f (F) i The objective function value of the i-th pelican position; is->A new location for the i-th pelican; x is x i The objective function value of the i-th pel after initial updating at the new position is obtained.
Further, in step S2.4, the location of the pelican is updated again according to the initially updated location of the pelican and the objective function value of the location of the hunting object, where the update formula is
Wherein:the position of the ith pelicant in the j-th dimension after being updated again; rand is [0,1]Random numbers within a range; r is a random integer of 1 or 2; t is the current iteration number; t is the maximum iteration number; />A new location for the i-th pelican; f (F) i The objective function value of the i-th pelican position; />Is the objective function of the i-th pelican at the new position after updating again.
Further, in step S4, the validity check is performed on the obtained final cluster data packet, where the validity check is calculated by the formula
Wherein:representing the minimum distance between two cluster centers; u (U) ij Represents a Boolean value, and U ij The value is 0 or 1; v represents a simplified Xie Beini index; n (N) i Representing the ith occurrence pole; w (W) j Represents a j-th packet; d, d 2 (N i ,V j ) Representing the distance between the j-th grouping cluster centers; arcos (|N) i T V j I) represents the cosine of the angle between the ith occurrence pole and the jth cluster centerA value; />A cosine value of the minimum included angle between the occurrence pole and the jth clustering center is represented; k represents the number of clustering centers; v (V) j Represents V j Representing the j-th cluster center.
The beneficial effects are that: the invention provides a structural plane occurrence grouping method based on a pelican optimization algorithm, which is based on a fuzzy C-means clustering algorithm, optimizes an initial clustering center through the pelican optimization algorithm, adopts a simplified Xie Beini index as a grouping evaluation standard, and improves the capability of searching a global optimal solution compared with the traditional grouping method by introducing the pelican optimization algorithm, can accurately group structural plane data with unclear occurrence pole boundaries, expands the application range of the grouping method, and improves the capability of solving the complex rock mass engineering problem of the grouping method.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments or the description of the prior art will be briefly described below, it will be obvious that the drawings in the following description are some embodiments of the present invention, and that other drawings can be obtained according to these drawings without inventive effort to a person skilled in the art.
FIG. 1 is a block diagram of a structural plane shape grouping method based on a pely optimization algorithm of the present invention;
FIG. 2 is a flow chart of a method for structural face yield grouping based on the Rey optimization algorithm of the present invention;
FIG. 3 is a schematic view of the structural space of the rock mass structural plane in the present embodiment;
FIG. 4 is a pole diagram of the structure surface under the first dispersion in this embodiment;
FIG. 5 is a graph showing the clustering effect of the poles of the structural surface under the first dispersion in the present embodiment;
FIG. 6 is a pole diagram of the structure surface under the second dispersion in this embodiment;
FIG. 7 is a graph showing the clustering effect of the poles of the structural surface under the second dispersion in the present embodiment;
FIG. 8 is a pole diagram of the structure surface under the third dispersion in this embodiment;
FIG. 9 is a graph showing the clustering effect of the poles of the structural surface under the third dispersion in the present embodiment;
FIG. 10 is an isometric view of a rock mass structural plane in this embodiment;
fig. 11 is a structural plane cluster pole diagram of a density map of a rock mass structural plane in this embodiment.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment provides a structural plane shape grouping method based on a pelican optimization algorithm, which comprises the following steps as shown in fig. 1:
step S1, converting rock mass structural plane attitude sample data acquired on site into corresponding space unit normal vectors n= (x, y, z) and randomly dividing the space unit normal vectors into a plurality of data sets to be clustered;
the rock mass structural plane attitude sample data comprises a dip angle alpha, 0 DEG < alpha < 360 DEG and a dip angle beta, 0 DEG < beta <90 DEG;
step S2: adopting a pelican optimization algorithm POA to optimize an initial clustering center of a fuzzy C-means clustering algorithm;
step S3: clustering each data group to be clustered by a fuzzy C-means clustering algorithm based on the optimized initial clustering center to obtain a final clustered data group;
step S4: and carrying out validity check on the obtained final clustering data packet to confirm a final clustering result.
According to the invention, structural face dominant bearing grouping is realized aiming at rock structural face bearing sample data, a fuzzy C-means clustering algorithm is adopted, an initial clustering center is optimized through a pelican optimization algorithm, and finally, a simplified Xie Beini index is adopted as a grouping evaluation standard to qualitatively analyze the superiority and inferiority of a division result.
In a specific embodiment, as shown in fig. 3, the structure plane's occurrence is described by two sets of data, trend α (0 ° < α < 360 °) and tilt angle β (0 ° < β <90 °), the occurrence being an important basis for structure plane grouping. Trend α refers to the azimuth angle of the projection on the horizontal plane perpendicular to the straight line drawn by the structure facing downward; the inclination angle beta is an acute angle between the structural surface and the horizontal plane. In mathematical modeling analysis of structural surface morphology, the morphology data is typically normalized: assuming that the rock structural plane is a space plane without thickness, the method can be represented by unit normal vector, a space rectangular coordinate system is established according to the rock structural plane, a pair of straight lines which are mutually perpendicular to each other are searched in the space plane, a straight line perpendicular to the plane is searched, the right-hand spiral rule is followed, the intersection point O of the three intersecting lines is determined, and in step S1, the on-site collected structural plane shape sample data is converted into a corresponding space unit normal vector n= (x, y, z), and the calculation formula is that
x 2 +y 2 +z 2 ＝1 (2)
Wherein x represents the component of the structure surface in the x-axis direction under a preset space rectangular coordinate system; y represents the component of the y-axis direction of the structural plane under a preset space rectangular coordinate system; z represents the component of the structure surface in the z-axis direction under a preset space rectangular coordinate system.
In a specific embodiment, as shown in fig. 2, the main principle of the fuzzy C-means clustering algorithm FCM based on the pelican optimization algorithm POA is to continuously correct the pelican position (i.e. the clustering center) by calculating and adjusting the objective function value F of the pelican position, thereby obtaining a global ideal solution (i.e. an optimal clustering result), and in step S2, the initial clustering center of the fuzzy C-means clustering algorithm is optimized by adopting the pelican optimization algorithm POA, specifically
Step S2.1, setting a group size N of the pelicant, a maximum iteration number T and the number c of randomly divided data groups to be clustered; randomly selecting an initial clustering center of a data set to be clustered; and the larger N and T are, the higher the searching precision is, and after trial calculation is carried out for many times through experiments, N is set to be 30, and T is set to be 100;
the position of each pelican corresponds to the set of initial clustering centers of the data sets to be clustered; initializing the pelican positions, repeating the process N times, generating N pelican positions,
step S2.2, based on the structural plane attitude sample data, the angle range of the inclination angle alpha and the inclination angle beta: alpha is more than 0 and less than 360 degrees; calculating the membership degree of a clustering center according to the initial clustering center, wherein beta is more than 0 degrees and less than 90 degrees, and acquiring a fuzzy objective function according to the membership degree; selecting the position of the pelicant with the minimum fuzzy objective function value as the global optimal solution;
step S2.3: randomly selecting c pieces of attitude data from the attitude sample data of the rock mass structural plane to update an initial clustering center, taking the updated initial clustering center as the position of the prey, and obtaining an objective function value of the position of the prey;
the position of the pelican is initially updated according to the position of the prey, and the membership degree and the objective function value of the position of the pelican after initial updating are calculated;
step S2.4, updating the position of the pelican again according to the initial updated objective function values of the position of the pelican and the position of the hunting object, and updating the global optimal solution;
step S2.5: and repeatedly executing the steps S2.3 to S2.4 until the maximum iteration times are reached, wherein the finally obtained pelican position is the initial clustering center with the global optimum.
In a specific embodiment, in a fuzzy C-means clustering algorithm (FCM), an initial clustering center is required to be given, and after the initial clustering center is obtained, the membership degree of all sample data to the clustering center is calculated according to the initial clustering center; after the clustering center and the membership degree are obtained, a fuzzy objective function can be calculated, wherein the fuzzy objective function value is an important index for evaluating the quality of the clustering result, and the lower the fuzzy objective function value is, the better the clustering result is; re-selecting a clustering center according to the fuzzy objective function value, updating membership according to the new clustering center, and finally calculating a new fuzzy objective function according to the updated membership; repeating the steps until the obtained fuzzy objective function value is the minimum value and the clustering center and membership degree are optimal;
given N rock mass structural plane attitude sample data x j (j=1, 2, 3..n.) it is divided into C groups of data sets to be clustered, each group of data sets to be clustered having a clustering center v i (i=1, 2, 3C); definition u ij If the j-th structural surface belongs to the membership degree of the i-th clustering center, the membership degree calculation formula in the step S2.2 is as follows
Wherein u is ij Representing the membership degree of the jth structural surface belonging to the ith clustering center; c represents the number of randomly divided data sets; v i (i=1, 2, 3..c.) represents the cluster center of each group;
the calculation formula of the fuzzy objective function is that
Wherein d (v) i ，x j ) Representing v i And x j Distance between d (v) i ，x k ) Representing v i And x k The distance between the two points is measured by adopting the sine distance of the included angle as the distance measurement; m represents fuzzy weighting coefficient, m is [1 ], and is infinity]The method comprises the steps of carrying out a first treatment on the surface of the The method is used for controlling the distribution of membership degrees and the fuzzy degree of clustering, and is analyzed from the angle of clustering effectiveness, the value of m is between 1.5 and 2.5, and in the normal case, the value of m=2; u (u) ij ∈[0,1]AndJ m (U, C) denotes a fuzzy objective function.
In a specific embodiment, the pelican optimization algorithm (Pelican Optimization Algorithm, POA) is a new meta-heuristic optimization algorithm, inspiration comes from the hunting behavior of the pelican. And (3) establishing a mathematical model of an algorithm by simulating the whole pelican hunting process, and finding out an optimal solution for solving the problem. The method has the advantages of few input parameters, high convergence speed, combination of global optimization and local search, simple algorithm operation flow and the like. In the POA algorithm, the objective function is used to evaluate the merits of the candidate solutions, the smaller the objective function value, the better the candidate solution, and the closer the candidate solution to the optimal solution. The method comprises the steps of grouping and cluster analysis on a rock mass structural plane, selecting a fuzzy objective function as an objective function, and obtaining a cluster center combination with the minimum objective function value as the dominant yield of the structural plane; defining an objective function in the pelican optimization algorithm POA algorithm as
F＝J m (U,C) (5)
The initialization stage assumes that n pelicans exist in m-dimensional space, and the position of the ith pelican in m-dimensional space is X i ＝[X i1 ,X i2 ,…,X in ]The position X of n-pelicans in m-dimensional space is expressed as
The pelican position initialization formula is as follows
x ij ＝l j +rand(u j -l j )i＝1,2,3,...,n；j＝1,2,3...,m (7)
Wherein: x is x ij The position of the ith pelican in the j-th dimension; n is the population number of pelicans; m is the dimension of the solution problem; rand is [0,1]Random numbers within a range; u (u) j To solve the problem in the j-th dimension, l j A lower boundary in the j-th dimension for solving the problem;
moving to the prey stage: at this stage, the pelicans recognizes the position of the prey and moves toward the prey; the feature of random distribution of the hunting objects in the search space enhances the global optimizing capability of the algorithm; in step S2.3, the position of the pelican is initially updated according to the position of the prey, and the initial updated position formula is as follows
And updating the location if the objective function value improves at the location
Wherein:the position of the ith pelican in the jth dimension after updating for moving to the prey stage; rand is [0,1]Random numbers within a range; i is a random integer of 1 or 2; p (P) j The position of the hunting object in the j-th dimension; f (F) p Objective function value for hunting; f (F) i The objective function value of the i-th pelican position; is->A new location for the i-th pelican; x is x i The objective function value at the new position for the i-th pelican after the update for moving to the prey stage.
Stage of skimming water: after pelicans reach the water surface, they spread wings on the water surface, collect the hunting object in the laryngeal bag, this process enhances the local search capability of the algorithm; according to the initial update position of the pelican, optimizing and updating the pelican position in each iteration, and in step S2.4, updating the pelican position again according to the initial update position of the pelican and the objective function value of the position of the hunting object, wherein the optimizing and updating formula of the pelican position is as follows
If the objective function value is improved at the location, the location is updated
Wherein:updating the position of the ith pelican in the jth dimension after the water surface sweeping stage; rand is [0,1]Random numbers within a range; r is a random integer of 1 or 2; t is the current iteration number; t is the maximum iteration number; />A new location for the i-th pelican; f (F) i The objective function value of the i-th pelican position; />The objective function of the ith pelican at the new position after updating for the water surface sweeping stage.
In a specific embodiment, as shown in fig. 4 to 11, the validity of the obtained final clustered data packet is checked in step S4, and the key of the evaluation of the cluster validity is to determine the rationality of the number of divisions of the sample data and how to qualitatively analyze the superiority and inferiority of the division result, where a simplified Xie Beini index is used, and the distance between the structural planes is represented by an acute angle, and the simplified index has high precision and strong practicability. The calculation formula of the validity check is
Wherein:representing the minimum distance between two cluster centers; u (U) ij Representing a boolean value, if the structural plane is in the current packet, then it is 1; otherwise, 0; the smaller the Xie Beini index is, the better the clustering effect is; otherwise, the worse the clustering effect. And U is ij The value is 0 or 1; v represents a simplified Xie Beini index; n (N) i Representing the ith occurrence pole; w (W) j Represents a j-th packet; d, d 2 (N i ,V j ) Representing the distance between the j-th grouping cluster centers; arcos (|N) i T V j I) represents the cosine value of the included angle between the ith occurrence pole and the jth cluster center; />A cosine value of the minimum included angle between the occurrence pole and the jth clustering center is represented; k represents the number of clustering centers; v (V) j Represents V j Representing the j-th cluster center.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (7)
1. A structural face shape grouping method based on a pelican optimization algorithm, comprising the steps of:
step S1, converting rock mass structural plane attitude sample data acquired on site into corresponding space unit normal vectors n= (x, y, z) and randomly dividing the space unit normal vectors into a plurality of data sets to be clustered;
the rock mass structural plane attitude sample data comprises a dip angle alpha, 0 DEG < alpha < 360 DEG and a dip angle beta, 0 DEG < beta <90 DEG;
step S2: adopting a pelican optimization algorithm POA to optimize an initial clustering center of a fuzzy C-means clustering algorithm;
step S3: clustering each data group to be clustered by a fuzzy C-means clustering algorithm based on the optimized initial clustering center to obtain a final clustered data group;
step S4: and carrying out validity check on the obtained final clustering data packet to confirm a final clustering result.
2. The structural plane shape grouping method based on pelican optimization algorithm as claimed in claim 1, wherein in step S1, the structural plane shape sample data collected in situ is converted into corresponding space unit normal vector n= (x, y, z), and the calculation formula is
x 2 +y 2 +z 2 ＝1
Wherein x represents the component of the structure surface in the x-axis direction under a preset space rectangular coordinate system; y represents the component of the y-axis direction of the structural plane under a preset space rectangular coordinate system; z represents the component of the structure surface in the z-axis direction under a preset space rectangular coordinate system.
3. The structural plane shape grouping method based on pelican optimization algorithm as claimed in claim 1, wherein the initial clustering center adopting pelican optimization algorithm POA optimization fuzzy C-means clustering algorithm in step S2 is specifically
Step S2.1, setting a group size N of the pelicant, a maximum iteration number T and the number c of randomly divided data groups to be clustered; initializing an initial clustering center of a data set to be clustered;
the position of each pelican corresponds to the set of initial clustering centers of the data sets to be clustered;
step S2.2, based on the structural plane attitude sample data, the angle range of the inclination angle alpha and the inclination angle beta: alpha is more than 0 and less than 360 degrees; calculating the membership degree of a clustering center according to the initial clustering center, wherein beta is more than 0 degrees and less than 90 degrees, and acquiring a fuzzy objective function according to the membership degree; selecting the position of the pelicant with the minimum fuzzy objective function value as the global optimal solution;
step S2.3: randomly selecting c pieces of attitude data from the attitude sample data of the rock mass structural plane to update an initial clustering center, taking the updated initial clustering center as the position of the prey, and obtaining an objective function value of the position of the prey;
the position of the pelican is initially updated according to the position of the prey, and the membership degree and the objective function value of the position of the pelican after initial updating are calculated;
step S2.4, updating the position of the pelican again according to the initial updated objective function values of the position of the pelican and the position of the hunting object, and updating the global optimal solution;
step S2.5: and repeatedly executing the steps S2.3 to S2.4 until the maximum iteration times are reached, wherein the finally obtained pelican position is the initial clustering center with the global optimum.
4. The structural plane shape grouping method based on pelican optimization algorithm according to claim 3, wherein the membership calculation formula is
Wherein u is ij Representing the membership degree of the jth structural surface belonging to the ith clustering center; c represents the number of randomly divided data sets; v i (i=1, 2, 3..c.) represents the cluster center of each group;
the calculation formula of the fuzzy objective function is that
Wherein d (v) i ，x j ) Representing v i And x j Distance between d (v) i ，x k ) Representing v i And x k The distance between the two points is measured by adopting the sine distance of the included angle as the distance measurement; m represents fuzzy weighting coefficient, m is [1 ], and is infinity]；u ij ∈[0,1]And is also provided withJ m (U, C) denotes a fuzzy objective function.
5. A structural plane shape grouping method based on pelican optimizing algorithm as recited in claim 3, wherein said initial update of pelican position according to the position of said game in step S2.3 is given by the following formula
Wherein:the position of the ith pelicant in the j-th dimension after initial updating; rand is [0,1]Random numbers within a range; i is a random integer of 1 or 2; p (P) j The position of the hunting object in the j-th dimension; f (F) p Objective function value for hunting; f (F) i The objective function value of the i-th pelican position; is->A new location for the i-th pelican; x is x i The objective function value of the i-th pel after initial updating at the new position is obtained.
6. The structural plane shape grouping method based on pelican optimization algorithm of claim 3, wherein in step S2.4, the pelican position is updated again according to the initial updated pelican position and the objective function value of the position of the prey, and the update formula is
Wherein:the position of the ith pelicant in the j-th dimension after being updated again; rand is [0,1]Random numbers within a range; r is a random integer of 1 or 2; t is the current iteration number; t is the maximum iteration number; />A new location for the i-th pelican; f (F) i The objective function value of the i-th pelican position; />Is the objective function of the i-th pelican at the new position after updating again.
7. The structural plane shape grouping method based on pelican optimization algorithm as in claim 1, wherein the step S4 performs validity check on the obtained final clustered data group, and the validity check has a calculation formula of
Wherein:representing the minimum distance between two cluster centers; u (U) ij Represents a Boolean value, and U ij The value is 0 or 1; v represents a simplified Xie Beini index; n (N) i Representing the ith occurrence pole; w (W) j Represents a j-th packet; d, d 2 (N i ,V j ) Representing the distance between the j-th grouping cluster centers; arcos (|N) i T V j I) represents the cosine value of the included angle between the ith occurrence pole and the jth cluster center; />A cosine value of the minimum included angle between the occurrence pole and the jth clustering center is represented; k represents the number of clustering centers; v (V) j Represents V j Representing the j-th cluster center.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310578613.2A CN116842818A (en) | 2023-05-22 | 2023-05-22 | Structural plane attitude grouping method based on pelican optimization algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310578613.2A CN116842818A (en) | 2023-05-22 | 2023-05-22 | Structural plane attitude grouping method based on pelican optimization algorithm |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116842818A true CN116842818A (en) | 2023-10-03 |
Family
ID=88160672
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310578613.2A Pending CN116842818A (en) | 2023-05-22 | 2023-05-22 | Structural plane attitude grouping method based on pelican optimization algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116842818A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117170250A (en) * | 2023-10-31 | 2023-12-05 | 山东舜水信息科技有限公司 | Water conservancy monitoring equipment control optimization method based on meta heuristic algorithm |
-
2023
- 2023-05-22 CN CN202310578613.2A patent/CN116842818A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117170250A (en) * | 2023-10-31 | 2023-12-05 | 山东舜水信息科技有限公司 | Water conservancy monitoring equipment control optimization method based on meta heuristic algorithm |
| CN117170250B (en) * | 2023-10-31 | 2024-01-30 | 山东舜水信息科技有限公司 | Water conservancy monitoring equipment control optimization method based on meta heuristic algorithm |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Robles-Kelly et al. | Graph edit distance from spectral seriation | |
| CN105223546B (en) | Indoor orientation method based on received signal strength and reference point locations double focusing class | |
| CN112101430B (en) | Anchor frame generation method for image target detection processing and lightweight target detection method | |
| CN110533722A (en) | A kind of the robot fast relocation method and system of view-based access control model dictionary | |
| CN108984785B (en) | Historical data and increment-based fingerprint database updating method and device | |
| CN107948930A (en) | Indoor positioning optimization method based on location fingerprint algorithm | |
| CN111027140B (en) | Airplane standard part model rapid reconstruction method based on multi-view point cloud data | |
| CN108627798B (en) | WLAN indoor positioning algorithm based on linear discriminant analysis and gradient lifting tree | |
| CN113344019A (en) | K-means algorithm for improving decision value selection initial clustering center | |
| CN112396133B (en) | Multi-scale space-based urban area air-ground integrated fusion point cloud classification method | |
| CN109034231A (en) | The deficiency of data fuzzy clustering method of information feedback RBF network valuation | |
| CN108882172A (en) | A kind of prediction technique of the indoor moving track data based on HMM model | |
| CN108764157B (en) | Building laser foot point extraction method and system based on normal vector Gaussian distribution | |
| CN116842818A (en) | Structural plane attitude grouping method based on pelican optimization algorithm | |
| CN108810799B (en) | Multi-floor indoor positioning method and system based on linear discriminant analysis | |
| CN117274339A (en) | Point cloud registration method based on improved ISS-3DSC characteristics combined with ICP | |
| CN116520281A (en) | DDPG-based extended target tracking optimization method and device | |
| CN114997366B (en) | Protein structure model quality assessment method based on graph neural network | |
| Xing et al. | Fuzzy c-means algorithm automatically determining optimal number of clusters | |
| CN116008671A (en) | Lightning positioning method based on time difference and clustering | |
| CN113707213B (en) | Protein structure rapid classification method based on contrast graph neural network | |
| CN110310322A (en) | Method for detecting assembly surface of 10-micron-level high-precision device | |
| CN109241628B (en) | Three-dimensional CAD model segmentation method based on graph theory and clustering | |
| CN111639712A (en) | Positioning method and system based on density peak clustering and gradient lifting algorithm | |
| CN108614889B (en) | Moving object continuous k nearest neighbor query method and system based on Gaussian mixture model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |