Mine water disaster risk dynamic prediction and risk evaluation method based on phase space support vector machine

Abstract

The invention discloses a mine water disaster risk dynamic prediction and risk evaluation method based on a phase space support vector machine, and the method comprises the steps: solving delay time tau and Cao from a one-dimensional time sequence of original data through an average mutual information method, and embedding the delay time tau and Cao into a dimension m to obtain a multi-dimensional time sequence; and dividing the multi-dimensional time series into training data and test data, and substituting the training data and the test data into a least square support vector machine regression algorithm to obtain a prediction effect. According to the method, one-dimensional time sequence data is converted into a multi-dimensional time sequence, the multi-dimensional time sequence is substituted into the support vector machine, the data is divided into training data and test data, and a prediction effect with high precision is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic prediction and analysis of mine water hazard risk, and more specifically to a method for dynamic prediction and risk assessment of mine water hazard risk based on a phase space support vector machine. Background Art

[0002] my country has abundant coal resources and a vast geographical distribution. The hydrogeological conditions vary significantly across coalfields, resulting in a diverse range of mine hazards. China is one of the countries with the most severe mining hazards in the world. Due to the high risk and uncertainty inherent in the coal mining industry, the domestic insurance industry has classified underground property and workers of coal mining enterprises as either cautiously covered or prohibited from coverage. Furthermore, with the continuous increase in the depth, scale, scope, and intensity of coal mining in recent years, the resulting waterlogged areas following the closure of numerous small coal mines have become increasingly complex. The hydrogeological conditions associated with coal mining are becoming increasingly complex, leading to a more severe degree of water hazards, an increase in the frequency and intensity of water inrush, and a greater challenge for mine water hazard prevention. Therefore, preventing coal mine accidents is essential for safe production in my country. How to effectively curb the occurrence of mine accidents is a major issue that urgently needs to be addressed. Using a dynamic risk assessment and early warning method based on a combination of phase space support vector machines to assess the comprehensive safety risk of early warning results for various types of coal mine hazards, and to reduce or avoid losses, is undoubtedly a key priority for coal safety efforts.

[0003] In order to solve this problem, a combination of phase space reconstruction and SVR support vector machine regression is used to evaluate and warn dynamic risks.

[0004] A time series is a collection of continuous random variables at different moments in time, each of which has a certain degree of correlation. Recording the evolution of events in chronological order constitutes a time series. If a time series is generated by a deterministic nonlinear dynamical system, recovering and characterizing the original dynamical system using the time series is called phase space reconstruction. The most common method for phase space reconstruction, or restoring the original system from a time series, is Takens' delayed embedding theorem. Reconstructing an equivalent state space requires examining only one component and using its measurements at fixed time delay points as new dimensions. This method preserves many properties of the original system.

[0005] Support vector machine is a machine learning method proposed based on statistical learning theory, which can solve practical problems such as small sample size, non-linearity, high dimensionality, and local minima. Moreover, support vector machine overcomes two drawbacks of neural networks, namely network structure determination and global optimal points. The main idea of support vector machine is to use the kernel function to perform non-linear mapping of data into a high-dimensional space, and find the optimal hyperplane in the high-dimensional feature space, which is a convex quadratic programming problem under linear constraint conditions. The optimal classification surface of the sample is obtained through quadratic programming. Least squares support vector machine regression can be used for classification and prediction. It learns the regression equation through training data and maps the independent variables into a higher-dimensional feature space. The optimization idea of the least squares support vector machine regression model is to minimize the distance between the sample with the largest distance from the regression plane and the regression plane.

[0006] According to regulations and rules such as the Coal Mine Safety Regulations and the Detailed Rules for Preventing Coal and Gas Outbursts, on the basis of comprehensively collecting the major disaster records, general information, and daily measurement parameters of each coal mine, the whole process of the disaster prevention and control management mode of each coal mine is analyzed in detail. Combining a large number of coal mine disaster accident cases, through on-site observation, statistics, fitting, calculation, and analysis, prevention and control evaluation models for spontaneous combustion risk, rock burst risk, gas outburst risk, and carbon dioxide outburst risk in goaf are established respectively. Based on this, specific warning indicators and rules are determined, and they are applied to the real-time data of various disaster monitoring systems for dynamic calculation and analysis to generate warning results in a timely manner. Finally, a comprehensive safety risk assessment of the warning results of various disasters is carried out. Based on the predicted results, the practicability of the model is discussed and corresponding warning methods are given. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to provide a method for dynamic prediction and risk assessment of mine water disaster risk based on phase space support vector machine with good stability and good prediction effect.

[0008] To solve the above technical problem, the present invention provides the following technical solutions:

[0009] A method for dynamic prediction and risk assessment of mine water disaster risk based on phase space support vector machine includes the following steps:

[0010] (1) For the one-dimensional water level time series of the original data, obtain the delay time τ and Cao embedding dimension m through the average mutual information method, and substitute them into the Takens embedding theorem to obtain a multi-dimensional time series;

[0011] (2) Divide the multi-dimensional time series into training data and test data, and substitute them into the least squares support vector machine regression algorithm to obtain the prediction effect.

[0012] The above dynamic prediction and risk assessment method for mine water disaster risk based on phase space support vector machine, in step (1), the original data includes mine water inflow, L / (s·m), and water level, m.

[0013] The above dynamic prediction and risk assessment method for mine water disaster risk based on phase space support vector machine, in step (1), let the one-dimensional time series of the original water level data be {x(i), i = 1, 2,..., n}, where n is a positive integer greater than 1, and n is the data length of the time series; first, the delay time τ is determined by using the method of taking the first minimum value of the average mutual information. The specific method is as follows: The original one-dimensional water level time series takes

[0014] x*(i) = x(i), i = 1, 2,..., n - τ.

[0015] y*(j) = x(i), i = τ + 1,..., n. j = i - τ, j = 1,..., n - τ.

[0016] Average mutual information function

[0017] Among them, for the probability in the mutual information function, the grid method is used. x* and y* are divided into a number of equally spaced grids in a two-dimensional space, and then the probability is calculated through the number of points in the grids; x* is divided into M equally spaced grids, and the grids are marked with serial numbers s = 1, 2,..., M; y* is divided into M equally spaced grids, and the grids are marked with serial numbers t = 1, 2,..., M;

[0018] is the number of x* data in the s-th grid,

[0019] is the number of y* data in the t-th grid,

[0020] N st is the number of two-dimensional data (x*, y*) in the two-dimensional (s, t) grid,

[0021] When I(x * , y * ) = 0, it means that the two time series have no correlation at all, and when I(x * , y * ) takes the minimum value, it means that the two time series are most likely uncorrelated, and the optimal delay time τ will be selected when I(x * , y *) For the first minimum value, the delay time τ cannot be too large. If the delay time τ is too large, the information compressed during phase space reconstruction will be excessive, resulting in poor simulation results. Therefore, to prevent the delay time τ from being too large, a maximum delay time τ* is set such that τ ≤ τ*; take τ = 1, 2…τ*, until the τ when I(x * , y * ) reaches the first minimum value is the optimal delay time.

[0022] For the above dynamic prediction and risk assessment method of mine water disaster risk based on phase space support vector machine, in step (1), based on the known determined delay time τ, the Cao method is used to calculate the embedding dimension m; the specific method is as follows: for the one-dimensional time series of the original water level data {x(i), i = 1, 2,..., n}, the time delay reconstruction is carried out by applying the Takens embedding theorem to establish a Takens reconstructed phase space, where τ is the delay time; m is the embedding dimension of the system, unknown:

[0023]

[0024] Among them, τ is the delay time; m is the embedding dimension of the system; N = n - (m - 1)τ, which is the number of phase points;

[0025] Use the Cao method to calculate the embedding dimension m;

[0026]

[0027] Among them: X i (m + 1) = {x(i), x(i + τ),..., x(i + (m)τ)} is the i-th reconstructed phase space vector with an embedding dimension of m + 1; X n(i,m) (m + 1) is the vector closest to X i (m + 1); α(i, m) is the distance formula containing the parameter m; X i (m) = {x(i), x(i + τ),..., x(i + (m - 1)τ)}, which is the i-th reconstructed phase space vector with an embedding dimension of m, and X n(i,m) (m) is represented as the vector closest to X i (m); the average value of a(i, m) is defined as follows:

[0028]

[0029] Among them: the magnitude of the parameter E(m) depends on the delay time τ and the embedding dimension m;

[0030] To study the change from m to m + 1, define

[0031] E * (m) = E(m + 1) / E(m)

[0032] m = 1, 2, … When m starts from a certain value such that E * (m) stops changing, then m + 1 is the minimum embedding dimension.

[0033] For the above dynamic prediction and risk assessment method of mine water disaster risk based on the phase space support vector machine, the delay time τ and the embedding dimension m are calculated. Applying the Takens embedding theorem, multi-dimensional data is obtained as follows:

[0034]

[0035] N = n - (m - 1)τ, where (X T ) N×m = (X1, X2, …, X N-1 , X N ) T N×m = (XX1, XX2, …, XX m ) N×m .

[0036] XX = (XX1, XX2, …, XX m-1 ), Y = XX m ;

[0037] Among them, X is an m × N matrix, and (X T ) N×m is the transpose of X, which is an N × m matrix. Therefore, there are m columns of Y; T represents the vector transpose, Y is the last column of the transpose of X, and XX is the first m - 1 columns of the transpose of X.

[0038] For the above dynamic prediction and risk assessment method of mine water disaster risk based on the phase space support vector machine, in step (2), for the data (X) after phase space reconstruction m×N , the first m - 1 columns of its transpose matrix are used as independent variables, and the mth column is used as the dependent variable. Take the first s rows as training data and the last N - s rows as the training set, and substitute them into the support vector machine regression model for prediction; the support vector machine (SVR) is a non-linear regression prediction method that uses the kernel function to map the multi-dimensional data to the dot product operation in the high-dimensional phase space, thereby obtaining the global optimal solution:

[0039] The SVM regression prediction function is:

[0040]

[0041] In the formula: a i, b are unknown coefficients and can be calculated according to the above equation; K(g) is the kernel function of the support vector machine; kernel functions can be divided into five types: linear kernel function, radial basis kernel function, RBF, polynomial kernel function, sigmoid kernel function and composite kernel function; the penalty coefficient range in the support vector machine regression model is [-4, 4], and the kernel parameter value range is [-4, 4], and their values are determined by cross-validation method.

[0042] The technical solution of the present invention achieves the following beneficial technical effects:

[0043] This method uses the mutual information method and the CAO method to calculate the delay time and embedding dimension of one-dimensional time series such as mine water inflow and water level, and then reconstructs the phase space. This method converts the one-dimensional time series data into a multidimensional time series and inserts it into a support vector machine. The data is divided into training data and test data, resulting in highly accurate prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Flowchart of the method for dynamic prediction and risk assessment of mine water hazard risk based on phase space support vector machine of the present invention;

[0045] Figure 2 Schematic diagram of prediction results of the method for dynamic prediction and risk assessment of mine water hazard risk based on phase space support vector machine of the present invention. DETAILED DESCRIPTION

[0046] like Figure 1 The process shown specifically includes the following methods:

[0047] 1. The one-dimensional water level time series of the original data is used to obtain the delay time τ and the Cao embedding dimension m through the average mutual information method and then brought into the takens embedding theorem to obtain a multidimensional time series;

[0048] (1) In this embodiment, the data of the water level change in Fangezhuang from July 11, 2009 to April 23, 2020 is used as the original data, with a total of 3,500 data.

[0049] Assume that the original one-dimensional time series of water level data is {x(i), i=1,2,...,n}, where n is a positive integer greater than 1 and n is the data length of the time series. First, the delay time τ is determined by taking the first minimum value of the average mutual information. The specific method is as follows: the original one-dimensional water level time series is taken

[0050] x*(i)=x(i), i=1,2,…,n-τ.,

[0051] y*(j) = x(i), i = τ + 1, …, n. j = i - τ, j = 1, …, n - τ.;

[0052] Average mutual information function

[0053] Among them, for the probabilities in the mutual information function, the grid method is used. The x* and y* are divided into several equally spaced grids in the two-dimensional space, and then the probabilities are calculated by the number of points in the grids; x* is divided into M equally spaced grids, and the grids are marked with serial numbers s = 1, 2, …, M; y* is divided into M equally spaced grids, and the grids are marked with serial numbers t = 1, 2, …, M;

[0054] is the number of x* data in the s-th grid,

[0055] is the number of y* data in the t-th grid,

[0056] N st is the number of two-dimensional data (x*, y*) in the two-dimensional (s, t) grid,

[0057] When I(x * , y * ) = 0, it means that the two time series have no correlation at all. And when I(x * , y * ) takes the minimum value, it indicates the maximum possible lack of correlation between the two time series. Generally, the optimal delay time τ will choose the first minimum value of I(x * , y * ). The delay time τ cannot be too large. If the delay time τ is too large, the information compressed during the phase space reconstruction will be too large, resulting in poor simulation results. Therefore, in order not to let the delay time τ be too large, a maximum delay time τ* will be set so that τ ≤ τ*; take τ = 1, 2 … τ*, until the τ that makes I(x * , y * ) reach the first minimum value is the optimal delay time.

[0058] The maximum delay time is set to 15 s, and the average mutual information function is used to calculate the optimal delay time as 4 by substituting the previous water level data.

[0059] (2) On the basis of having determined the delay time τ, the Cao method is applied to calculate the embedding dimension; the specific method is as follows: the one-dimensional time series of the original water level data {x(i), i = 1, 2,..., n}, the Takens embedding theorem is applied for time-delay reconstruction to establish a Takens reconstructed phase space, where τ is the delay time; m is the embedding dimension of the system, unknown:

[0060]

[0061] Among them, τ is the delay time; m is the embedding dimension of the system; N = n - (m - 1)τ, which is the number of phase points.

[0062] Calculate the embedding dimension m using the Cao method;

[0063]

[0064] Among them: X i (m + 1) = {x(i), x(i + τ),..., x(i + (m)τ)} is the i-th reconstructed phase space vector with an embedding dimension of m + 1; X n(i,m) (m + 1) is the vector closest to X i (m + 1); α(i, m) is the distance formula containing the parameter m; X i (m) = {x(i), x(i + τ),..., x(i + (m - 1)τ)}, which is the i-th reconstructed phase space vector with an embedding dimension of m, X n(i,m) (m) is denoted as the vector closest to X i (m); define the average value of a(i, m) as follows:

[0065]

[0066] Among them: The magnitude of the parameter E(m) depends on the delay time τ and the embedding dimension m;

[0067] To study the change from m to m + 1, define

[0068] E * (m) = E(m + 1) / E(m)

[0069] m = 1, 2,... When m starts from a certain value and makes E * (m) stop changing, then m + 1 is the minimum embedding dimension.

[0070] When the optimal delay time is 4, the embedding dimension is calculated using the cao algorithm, and the embedding dimension is obtained as 7.

[0071] (3) Use the calculated delay time and embedding dimension to perform phase space reconstruction.

[0072] The delay time τ and the embedding dimension m are calculated. Apply the Takens embedding theorem to obtain multi-dimensional data as follows:

[0073]

[0074] N = n - (m - 1)τ, where (X T ) N×m=(X1,X2,…,X N-1 ,X N ) T N×m =(XX1,XX2,…,XX m ) N×m .

[0075] XX=(XX1,XX2,…,XX m-1 ), Y = XX m . Among them, X is an m×N matrix, (X T ) N×m is the transpose of X, which is an N×m matrix. T represents the vector transpose. Y is the last column of the transpose of X, and XX is the first m - 1 columns of the transpose of X.

[0076] Construct the Takens matrix X with 3500 water level data, which is 7*3476. (3476 = N = n - (m - 1)τ = 3500 - (7 - 1)×4) to transform the one-dimensional 3500 water level data into a multi-dimensional matrix.

[0077] 2. Divide the multi-dimensional time series into training data and test data, and substitute them into the least squares support vector machine regression algorithm to obtain the prediction effect.

[0078] For the data (X) after phase space reconstruction m×N , the first m - 1 columns of its transpose matrix are independent variables, and the mth column is the dependent variable. Take the first s rows as training data and the last N - s rows as the training set, and substitute them into the support vector machine regression model for prediction; Support Vector Machine (SVR) is a non-linear regression prediction method that uses the kernel function to map multi-dimensional data to the dot product operation in a high-dimensional phase space, thereby obtaining the global optimal solution:

[0079] The SVM regression prediction function is:

[0080] <00>

[0081] In the formula: a i , b are unknown coefficients, which can be obtained according to the above equation; K(g) is the kernel function of the support vector machine; the kernel function can be divided into 5 types: linear kernel function, radial basis kernel function (RBF), polynomial kernel function, Sigmoid kernel function, and composite kernel function; the penalty coefficient range in the support vector machine regression model is [-4, 4], and the kernel parameter value range is [-4, 4]. Use the cross-validation method to determine their values.

[0082] Transpose the Takens matrix to obtain XX as a 3476×7 matrix. The first six columns of the matrix are the independent variables for support vector machine regression, and the seventh column is the dependent variable. Use the first 3000 water level data to train the support vector machine model. Among them, the kernel function is the radial basis function, the penalty coefficient is 1, and the kernel parameter is 1.5.

[0083] Make predictions.

[0084] Start testing the data from the 3001st data, predict 7 data backward each time, and predict 60 groups backward in total. The relative errors of the 60 groups of tests are as Figure 2 shown. The average value of the relative errors of the 60 groups of tests is 0.0498. Thus, it can be concluded that the model has stability and good prediction effect, as Figure 2 shown.

[0085] Obviously, the above embodiments are merely examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the claims of this patent application.

Claims

1. A dynamic prediction and risk assessment method for mine water disaster risk based on a phase space support vector machine, characterized in that, It includes the following steps: (1) For the one-dimensional water level time series of the original data, obtain the delay time τ and the Cao embedding dimension m through the average mutual information method, and substitute them into the Takens embedding theorem to obtain a multi-dimensional time series; (2) Divide the multi-dimensional time series into training data and test data, and substitute them into the least squares support vector machine regression algorithm to obtain the prediction effect.

2. The dynamic prediction and risk assessment method for mine water disaster risk based on phase space support vector machine according to claim 1, characterized in that, In step (1), the original data includes the mine water inflow, L / (s·m), and the water level, m.

3. The dynamic prediction and risk assessment method for mine water disaster risk based on the phase space support vector machine according to claim 1, characterized in that, In step (1), let the one-dimensional time series of the original water level data be {x(i), i = 1, 2,..., n}, where n is a positive integer greater than 1 and n is the data length of the time series; first, use the average mutual information to take the first minimum value method to determine the delay time τ. The specific method is as follows: for the original one-dimensional water level time series, take x*(i) = x(i), i = 1, 2,..., n - τ., y*(j) = x(i), i = τ + 1,..., n.j = i - τ, j = 1,…, n - τ.; Average mutual information function Among them, for the probabilities in the mutual information function, the grid method is used. For x * , y * They are divided into several equally spaced grids in the two-dimensional space, and then the probabilities are calculated by the number of points in the grids; for x * It is divided into M equally spaced grids, and the grids are marked with serial numbers s = 1, 2, …, M; for y * It is divided into M equally spaced grids, and the grids are marked with serial numbers t = 1, 2, …, M; is the number of x * data in the s-th cell, is the number of y * data in the t-th cell, N st is the number of two-dimensional data (x * , y * ) in the two-dimensional (s, t) grid, When I(x * , y * ) = 0, it indicates that the two time series have no correlation at all. When I(x * , y * ) takes the minimum value, it means the maximum possible lack of correlation between the two time series. The optimal delay time τ will select the first minimum value of I(x * , y * ). The delay time τ cannot be too large. If the delay time τ is too large, the information compressed in the phase space reconstruction will be excessive, resulting in poor simulation results. Therefore, to prevent the delay time τ from being too large, a maximum delay time τ * is set such that τ ≤ τ * ; take τ = 1, 2... τ * , until the τ that makes I(x * , y * ) reach the first minimum value is the optimal delay time.

4. The dynamic prediction and risk assessment method for mine water disaster risk based on phase space support vector machine according to claim 3, characterized in that, In step (1), on the basis of having determined the delay time τ, apply the Cao method to calculate the embedding dimension m; the specific method is as follows: for the one-dimensional time series of the original water level data {x(i), i = 1, 2,..., n}, apply the Takens embedding theorem for time-delay reconstruction to establish a Takens reconstructed phase space. Given that τ is the delay time; m is the embedding dimension of the system, which is unknown: Among them, τ is the delay time; m is the embedding dimension of the system; N = n - (m - 1)τ, which is the number of phase points; Use the Cao method to calculate the embedding dimension m; Where: X i (m + 1) = {x(i), x(i + τ),..., x(i + (m)τ)} is the i-th reconstructed phase space vector with an embedding dimension of m + 1; X n(i,m) (m + 1) is the vector closest to X i (m + 1); α(i, m) is a distance formula containing the parameter m; X i (m) = {x(i), x(i + τ),..., x(i + (m - 1)τ)}, which is the i-th reconstructed phase space vector with an embedding dimension of m, X n(i,m) (m) is denoted as the vector closest to X i (m); the average value of a(i, m) is defined as follows: Among them: the magnitude of the parameter E(m) depends on the delay time τ and the embedding dimension m; To study the change from m to m + 1, define E * E(m) = E(m + 1) / E(m) m = 1, 2, … When m starts from a certain value such that E * (m) stops changing, then m + 1 is the minimum embedding dimension.

5. The dynamic prediction and risk assessment method for mine water disaster risk based on the phase space support vector machine according to claim 4, characterized in that, The delay time τ and the embedding dimension m are calculated, and the Takens embedding theorem is applied to obtain multi-dimensional data as follows: N = n - (m - 1)τ, where (X T ) N×m = (X1, X2, …, X N-1 , X N ) T N×m = (XX1, XX2, …, XX m ) N×m . XX = (XX1, XX2, …, XX m-1 ), Y = XX m ; where X is an m×N matrix, (X T ) N×m is the transpose of X, which is an N×m matrix, T represents the vector transpose, Y is the last column of the transpose of X, and XX is the first m - 1 columns of the transpose of X.

6. The dynamic prediction and risk assessment method for mine water disaster risk based on phase space support vector machine according to claim 5, characterized in that, Step (2), the data (X) after phase space reconstruction m×N , where the first m - 1 columns of its transposed matrix are independent variables, the mth column is the dependent variable, the first s rows are taken as training data, and the last N - s rows are taken as the training set, and then substituted into the support vector machine regression model for prediction; Support Vector Machine (SVR) is a non - linear regression prediction method that uses a kernel function to map multi - dimensional data to the dot - product operation in a high - dimensional phase space, thereby obtaining the global optimal solution: The SVM regression prediction function is: Where: a i , b are unknown coefficients, which can be obtained according to the above equations; K(g) is the kernel function of the support vector machine; the kernel function can be divided into 5 types: linear kernel function, Radial Basic Function (RBF), polynomial kernel function, Sigmoid kernel function, and composite kernel function; the penalty coefficient range in the support vector machine regression model is [-4, 4], and the kernel parameter value range is [-4, 4], and their values are determined by the cross-validation method.

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