Label collaborative rockburst prediction method based on kernel perception and global manifold particle constraint

Abstract

The invention discloses a label collaborative rockburst prediction method based on kernel perception and global manifold particle constraint, and solves the problem of low rockburst prediction accuracy caused by nonlinearity and weak separability among rockburst index data. The method specifically comprises the following steps: (1) mapping rockburst data to a high-dimensional feature set through kernel mapping to realize feature perception, and constructing a global manifold particle constraint graph for a sample set after kernel perception; (2) constructing a kernel perception and global manifold particle constrained label collaboration model by means of class label information and a consistency analysis theory, and performing optimization solution on a target function of the model to obtain an analytical solution in a kernel label collaboration projection direction; and (3) directly obtaining kernel label collaborative characteristics with good discrimination from the randomly extracted rock burst test sample through the kernel label collaborative projection direction, and obtaining a rock burst prediction result. Compared with the prior art, the rockburst prediction method provided by the invention has higher accuracy and robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to a label collaborative rock burst prediction method based on kernel perception and global manifold particle constraint, and belongs to the field of data mining and pattern recognition. BACKGROUND

[0002] Rock burst is a sudden and destructive dynamic disaster phenomenon in the field of engineering, and its prediction and prevention are crucial to engineering safety. In actual engineering data, rock burst related indicators often show nonlinear distribution characteristics, and there is a multiple collinearity problem between various characteristic variables, which leads to mixed distribution of data in the original feature set, blurred class boundary, and typical "weakly separable" situation, so that traditional linear models cannot achieve effective classification. Although the kernel method can solve the problem of linear inseparability by mapping data to a high-dimensional set, the bandwidth parameter setting of the conventional kernel function is easily affected by the data distribution. If the bandwidth is not set properly, it is easy to cause overfitting or underfitting, and the traditional kernel mapping often lacks sufficient mining of the intrinsic geometric structure of the data, making it difficult to capture the global distribution trend and local manifold structure, limiting the generalization ability and classification accuracy of the model on complex rock burst data. Therefore, the present application realizes feature perception through kernel mapping, kernelizes rock burst data, and introduces an adaptive parameter optimization mechanism to dynamically adjust the kernel parameters according to the data distribution characteristics. Secondly, a global manifold particle constraint graph is constructed for the kernel perceived sample set through data granulation to mine the global geometric structure and local manifold relationship of the data. Finally, the objective function of the label collaborative model based on kernel perception and global manifold particle constraint is constructed with the help of class label information and consistent analysis theory, and the model objective function is optimized and solved to obtain the analytical solution of the kernel particle label collaborative projection direction. The kernel particle label collaborative feature with good discriminability is obtained directly according to the projection direction, and the accurate prediction of rock burst is realized. SUMMARY

[0003] In order to solve the problem of low rock burst prediction accuracy caused by nonlinearity and weak separability between rock burst index data, the present application combines kernel perception and data granulation under the framework of related learning theory, uses class label information and consistent analysis theory to construct a label collaborative model based on kernel perception and global manifold particle constraint, and obtains the analytical solution of the kernel particle label collaborative projection direction through theoretical derivation. The kernel particle label collaborative feature with good discriminability is obtained directly according to the kernel particle label collaborative projection direction. The specific implementation steps of the present application are as follows: 1. Convert the original rock burst index data into a column vector to form rock burst data , wherein represents the dimension of the rock burst data, represents the number of samples, represents the th rock burst data, and maps the rock burst data to a high-dimensional feature set to realize feature perception through kernel mapping, and obtain a kernel perceived sample set wherein represents the sample dimension after kernel perception, represents the first dimension of the sample, represents the number of samples in the same dimension , represents the first data in a single dimension, represents the first sample in .

[0004] The high-dimensional feature set mapping process of rockburst data is as follows: Calculate the Euclidean distance between rockburst data: wherein represents the sample in the data set , and is a symmetric matrix of which satisfies . The distance between rockburst data is further processed by nearest neighbors, and the formula is as follows: wherein represents the nearest neighbor sample set of the sample . The adaptive kernel based on rockburst data is calculated by : An intervention adjustment value is introduced to obtain the final kernel parameter: .

[0005] Based on the kernel parameter, the rockburst data is kernelized to obtain: In order to eliminate the constant bias in the feature set, the kernel matrix is centralized to obtain the sample set after kernel perception: Through the kernel function, the information in the rockburst data is implicitly mapped to a high-dimensional set, thereby solving the linearly inseparable problem of rockburst data.

[0006] 2. Construct a global manifold particle constraint graph for the sample set after kernel perception.

[0007] The specific construction steps of the global manifold particle constraint graph are as follows: For the sample set after kernel perception , for in a single dimension , the normalized result is: wherein denotes the dimension , denotes the maximum value of the data , denotes the minimum value of all data in the same dimension , , and satisfies . The neighborhood parameter is set, and the function of determining whether different data in the same dimension are adjacent points is defined as: wherein denotes and are adjacent points in the same dimension , and vice versa. According to the discrimination information of , the global manifold particle is constructed: wherein denotes the adjacency relationship of with all . On the basis of the global manifold particle, the global manifold particle vector is further constructed: wherein denotes the global manifold particle constructed by the data in the dimension . Through the constructed global manifold particle and global manifold particle vector, the global manifold particle vector distance is defined as: wherein , , denotes the difference bit number of the manifold particles of the two samples in the dimension , and satisfies: . The global manifold particle constraint graph is defined as: wherein when , .

[0008] The global manifold particle constraint graph considers the absolute difference of all samples, distinguishes the manifold structure from the global level, captures the nonlinear granulation relationship and complex patterns in high-dimensional sets, and reduces the interference of local noise.

[0009] 3. Constructing a label collaborative model with kernel perception and global manifold particle constraint by means of class label information and consistent analysis theory.

[0010] The specific construction steps of the label collaborative model with kernel perception and global manifold particle constraint are as follows: By means of class label information and consistent analysis theory, the single class label information is converted into a class label vector by means of one-hot encoding , wherein , represents the class label of the i-th sample, represents the number of classes of rockburst risk levels. The main idea of the model is to find a basis vector for the rockburst sample in combination with the label information, so as to maximize the correlation between variables, that is, to minimize the loss of association between the projection and the label under the premise of preserving the geometric structure, and the objective function of the model is as follows: , wherein , represents the i-th column of the matrix , representing the i-th sample feature after local structure constraint, is the i-th sample of the label modal . is the Laplacian matrix calculated by the global manifold particle constraint graph, specifically, . , wherein is the global manifold particle constraint graph of X, represents the operator. For the matrix , , . is a diagonal matrix, and the diagonal line is the row sum of . The function measures the overall difference between the projection result of after global manifold particle constraint and the label Y, and expands it as follows: Since is a symmetric matrix, i.e. , then ​​​​​​​​​Meanwhile is a constant term irrelevant to the projection vector , which can be omitted in optimization, then the objective function can be expressed as: where is a constant.

[0011] Since minimizing the correlation loss is equivalent to maximizing the correlation of both, the logical derivation of its equivalent goal is as follows: Maximizing the correlation under the constraint of preserving geometric structure, the geometric structure regularization of is introduced, which is realized by the within-class scatter matrix, which is: To avoid the scale of the projection vector being infinite, the geometric structure constraint of is introduced: Under the above constraints, maximize the projection and the correlation strength of the label , and the optimized objective function is: Let , and the final objective function can be simplified as: The objective function forces the projection direction of to be closer to the label information while avoiding the simple structure dilution of the optimization target due to the one-hot encoding of modal.

[0012] 4. Optimize the objective function of the model to obtain the analytical solution of the kernel particle label collaborative direction, directly obtain the kernel particle label collaborative features with good discriminability according to the projection direction, and obtain the rock burst prediction result.

[0013] The optimization solving process is as follows: Optimize the objective function, which can be expressed as: Where the numerator reflects the square of the cross-correlation between and , and the denominator reflects the within-class scatter of .

[0014] Convert the maximization objective function into a generalized eigenvalue problem: Two sides same ride , get: Let , substitute the above formula equation into: . The eigenvalue decomposition is carried out on the matrix : , wherein is the eigenvector matrix, is the eigenvalue diagonal matrix, and . The eigenvectors corresponding to the first maximum eigenvalues are selected , wherein is the rank of . Each eigenvector is normalized: The analytical solution of the kernel particle label collaborative projection direction is: The method has the following advantages: (1) the original rock burst index data is converted into a column vector to form rock burst data, and the feature perception is realized through kernel mapping, the sample set after kernel perception is obtained, the risk of overfitting and underfitting is avoided, and the depth of the nonlinear characteristics of the data is realized. (2) the global manifold particle constraint graph is constructed by data granulation for the sample set after kernel perception, the manifold relationship between samples in a single dimension is integrated, and the multi-dimensional global information is structured and fused to capture the nonlinear granulation relationship and complex pattern in high-dimensional set, reduce the interference of local noise, on the one hand, the global topological structure of the data is deeply integrated, and the control of the overall law of rock burst is ensured, on the other hand, the local adjacency relationship of the data is accurately associated, and the subtle feature change is captured, so that the complex manifold characteristics hidden in the rock burst data are efficiently extracted. (3) the label collaborative model of kernel perception and global manifold particle constraint is constructed by means of class label information and consistent analysis theory, so that the discriminative information contained in the label is directly utilized to optimize and solve the model, and the analytical solution of the kernel particle label collaborative projection direction is obtained, the kernel particle label collaborative feature with good discriminability is directly obtained according to the projection direction, and more accurate rock burst prediction is realized. BRIEF DESCRIPTION OF DRAWINGS

[0015] The present application will be further described below in combination with the drawings and examples.

[0016] Figure 1 is the flow chart of the present application, wherein is the number of indexes, is the number of rock burst grades.

[0017] Figure 2 It represents the prediction accuracy under different training samples. Detailed Implementation

[0018] The specific implementation steps of this invention are as follows: 1. Convert the raw rockburst index data into column vectors to form rockburst data. ,in The dimension representing rockburst data, Indicates the number of samples. Indicates the first Each set of rockburst data is processed and mapped to a high-dimensional feature set. Feature perception is then achieved through kernel mapping, resulting in a kernel-perceived sample set. ,in This represents the dimension of the sample after kernel sensing. Represents the sample's first dimension, Representing the same dimension The number of samples below Represents the first dimension in a single dimension One data point, express The first in One sample.

[0019] 2. Based on the tag collaboration model of kernel sensing and global manifold particle constraints, the model is as follows: The analytical solution of the model is transformed into a generalized eigenvalue problem, which is solved by constructing the Lagrange equation. (Selecting the previous...) The eigenvectors corresponding to the largest eigenvalues ,in for The rank of the eigenvector. Normalizing each eigenvector, the final analytical solution for the nucleo-particle label co-projection direction. .

[0020] 3. A low-dimensional training sample feature set is obtained from high-dimensional samples of rockburst data through nucleo-particle label co-projection direction; by randomly sampling test samples, the sampled test samples are directly used to obtain nucleo-particle label co-projection direction to obtain nucleo-particle label co-features with good discriminative power, thereby realizing rockburst prediction.

[0021] The effectiveness of this invention was further verified through the following experiments: The collected rockburst index data were divided into four rockburst levels: no rockburst, weak rockburst, moderate rockburst, and strong rockburst, for experimental verification. In this experiment, 3, 6, and 9 rockburst data points from each category were selected to perform predictions under three different training samples. Figure 2 This visually demonstrates the prediction accuracy across different training samples. Figure 2 As can be seen, the accuracy of the method of this invention increases with the increase of the number of training samples, and the stability is good. Experimental results show that the method disclosed in this invention is an accurate and effective rockburst method.

Claims

1. A label collaborative rockburst prediction method based on nuclear perception and global manifold particle constraint, characterized in that, The method comprises the following steps: (1) Convert the original rockburst index data into column vectors to form rockburst data. ,in The dimension representing rockburst data, Indicates the number of samples. Indicates the first Each set of rockburst data is processed and mapped to a high-dimensional feature set. Feature perception is then achieved through kernel mapping, resulting in a kernel-perceived sample set. ,in This represents the dimension of the sample after kernel sensing. Represents the sample's first dimension, Representing the same dimension The number of samples below Represents the first dimension in a single dimension One data point, express The first in One sample; (2) constructing a global manifold particle constraint graph for the sample set after kernel perception; (3) constructing a label collaborative model of kernel perception and global manifold particle constraint by means of class label information and consistent analysis theory; (4) optimizing and solving the objective function to obtain an analytical solution of the kernel particle label collaborative projection direction, directly obtaining a kernel particle label collaborative feature with good discriminability according to the projection direction, and obtaining a rock burst prediction result.

2. The label collaborative rockburst prediction method based on kernel perception and global manifold particle constraint according to claim 1, characterized in that The feature perception is realized by kernel mapping, and the steps are as follows: For the original rockburst sample set The rockburst data is mapped to a high-dimensional feature set by kernel mapping, and the sample set after kernel perception is obtained: wherein is a centered matrix, denotes the cored rockburst data, is defined as: wherein is the Euclidean distance between rockburst data, is the kernel parameter, is defined as: wherein is an intervention adjustment value, in rounding up the integer value, denotes an adaptive kernel based on rockburst data, is defined as: wherein represents the number of the neighbor data of is the distance matrix after the neighbor screening process, is defined as: wherein represents the first sample, represents the set of neighboring data of sample .

3. The label collaborative rockburst prediction method based on kernel perception and global manifold particle constraint according to claim 1, characterized in that The global manifold particle constraint graph is constructed for the sample set after kernel perception, and the steps are as follows: The set of samples after nucleic acid perception , constructing a global manifold graph constraint , is defined as: wherein is a neighborhood parameter, is a global manifold particle vector distance, and satisfies , is defined as: wherein , , represents the difference in the number of global manifold particles in dimension between two samples, is the global manifold particle vector of sample , is defined as: wherein representing data In the dimension Global manifold particles constructed under, defined as: wherein represents all adjacent relationship, is a function of judging whether different data in the same dimension are adjacent points, is defined as: wherein represents and are adjacent points in the same dimension, represents and are not adjacent points in the same dimension, represents a radial basis function of different data in the same dimension, is defined as: wherein represents a single dimension in the normalized result of satisfies , is defined as: wherein represents the dimension the lower data of the maximum value, represents the dimension the lower data of the minimum value.

4. The label collaborative rockburst prediction method based on kernel perception and global manifold particle constraint according to claim 1, characterized in that The label collaborative model of kernel perception and global manifold particle constraint is constructed by means of class label information and consistent analysis theory, and the steps are as follows: With the help of class label information and consistency analysis theory, the single class label information is converted into class label vector by using one-hot encoding wherein , represents the class label, represents the number of categories of rock burst risk level, and the model objective function is constructed as follows, which takes maximizing the correlation between kernel perception samples and label modal as the core: where is the analytical solution of the kernel particle tag colocalization direction, the constraint condition is used to avoid projection vectors with infinite scale, , is the within-class scatter matrix of the geometric regularization introduced , is defined as: wherein is a Laplacian matrix computed from the global manifold graph, in particular, , is a diagonal matrix with diagonal of the rows of , , denotes an operator satisfying .

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