# Study on Prediction of Coal-Gas Compound Dynamic Disaster Based on GRA-PCA-BP Model

Authors: Kai Wang; Kangnan Li; Feng Du
Journal: Geofluids
 (2021)

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## Abstract

The intensity and depth of China’s coal mining are increasing, and the risk of coal-gas compound dynamic disaster is prominent, which seriously restricts the green, safe, and efficient mining of China’s coal resources. How to accurately predict the risk of disasters is an important basis for disaster prevention and control. In this paper, the Pingdingshan No. 8 coal mine is taken as the research object, and the grey relational analysis (GRA), principal component analysis (PCA), and BP neural network are combined to predict the coal-gas compound dynamic disaster. First, the weights of 13 influencing factors are sorted and screened by grey relational analysis. Next, principal component analysis is carried out on the influencing factors with high weight value to extract common factors. Then, the common factor is used as the input parameter of BP neural network to train the previous data. Finally, the coal-gas compound dynamic disaster prediction model based on GRA-PCA-BP neural network is established. After verification, the model can effectively predict the occurrence of coal-gas compound dynamic disaster. The prediction results are consistent with the actual situation of the coal mine with high accuracy and practicality. This work is of great significance to ensure the safe and efficient production of deep mines.


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## Body

## 1. Introduction

With the increase of mining intensity and mining depth of China’s coal resources, when the coal under high ground stress and high gas pressure is disturbed by mining, the coupling effect of rockburst and coal-gas outburst becomes intense [1–3]. In particular, after entering deep mining, the interaction between rockburst and coal-gas outburst becomes serious, which no longer exists in the form of a single disaster. It shows the characteristics of compound disaster. It is called coal-gas compound dynamic disaster [4–6]. In the process of the occurrence of coal-gas compound dynamic disaster, many factors are intertwined with each other, which may be used as incentives and strengthen each other before, during, and after the accident. Compared with single dynamic disaster, the coupling of two disasters may make the coal-gas compound dynamic disaster more intense and violent, resulting in a large number of property losses and casualties. Coal-gas compound dynamic disaster has become a major disaster restricting the safe and efficient mining of coal resources in China. Therefore, how to accurately predict the occurrence of disasters has become a major scientific issue in the field of coal mine safety under the form of new disasters.Compared with rockburst and coal-gas outburst, the threshold of coal-gas compound dynamic disaster is lower, and the disaster mechanism is more complex [7–11]. The previous single disaster prediction method is no longer applicable, and the prediction difficulty of coal-gas compound dynamic disaster is greatly increased [12]. At present, the previous research on the prediction of rockburst and coal-gas outburst is quite fruitful [13–18]. However, the research on the prediction of coal-gas compound dynamic disaster is relatively less. Pan [19] put forward three kinds of integrated forecasting technologies, including multi-indexes integrated monitoring of drilling cutting method, real-time continuous monitoring of coal temperature, and real-time continuous monitoring of coal charge, and applied them in Pingdingshan and other mining areas. Luo et al. [20] used the analytic hierarchy process (AHP) to build a multiparameter risk assessment model of mine dynamic disasters and carried out classification early warning for rockburst, coal-gas outburst, and coal-gas compound dynamic disaster. The model is verified by some examples, and it is concluded that the model has strong applicability to the prediction of dynamic disasters in deep mines. Yuan [21] and Meng and Zhang [22] proposed that through the comprehensive detection method, the coal drilling cutting quantity, the initial gas emission velocity, and the gas desorption quantity should be used as the sensitive indexes for the risk assessment, prediction, and effective inspection of the coal-gas compound dynamic disaster. According to the multifactor coupling unified catastrophe characteristics of deep coal-gas dynamic disaster in Pingdingshan mining area, Yuan [23] proposed the unified prediction theory of deep coal-gas dynamic disaster based on geological dynamic zoning and the probability prediction method of pattern recognition and established the risk evaluation and prediction technical index system of deep coal-gas dynamic disaster in Pingdingshan mining area. By analyzing the correlation between “direction” and “mechanism” of the precursor of coal-gas compound dynamic disaster, Jiang et al. [24] put forward the multiparameter monitoring and joint early warning method of real-time danger. Through the construction of multiparameter joint warning platform, the test is carried out in many coal mines, and the preliminary results are obtained. Dou et al. [25] summarized the monitoring and early warning technologies of gas-earing coal rock dynamic disasters. They include zoning and grading monitoring and early warning, microseism monitoring method, electromagnetic radiation, elastic wave CT and vibration wave CT in the aspect of rock burst monitoring, drilling gas gushing initial velocity method, R-index method, and electromagnetic radiation method in the aspect of coal and gas outburst monitoring. They pointed out that for the monitoring and early warning of coal-gas compound dynamic disaster, we should focus on the establishment of multiparameter normalized dimensionless monitoring and early warning model and criteria for dynamic disaster risk, build the monitoring and early warning index system suitable for coal-gas compound dynamic disaster, and develop the corresponding monitoring technology and equipment.It can be seen that although relevant scholars have made some meaningful researches on the prediction of coal-gas compound dynamic disaster, most of them are still in the qualitative stage, and the application of quantitative mathematical methods in the prediction of coal-gas compound dynamic disaster is rarely reported. Therefore, combined with the application of mathematical method in the prediction of coal-gas outburst and rockburst [26–29], a method predicting the coal-gas compound dynamic disaster based on the GRA-PCA-BP model is put forward, and the model is verified, and good results are achieved.


## 2. Occurrence Law and Influencing Factors of Coal-Gas Compound Dynamic Disaster

### 2.1. Occurrence Law of Coal-Gas Compound Dynamic Disaster

Coal-gas compound dynamic disaster is an atypical dynamic disaster induced by mining activities. With the increase of mining depth and complex geological structure, a considerable number of mines are facing the double danger of coal-gas outburst and rockburst. Coal-gas compound dynamic disaster will occur under specific conditions. Based on the field investigation records and extensive literature review of coal-gas compound dynamic disaster in multitime period for multicoal mines, the occurrence laws and destructive characteristics of coal-gas compound dynamic disaster are summarized as follows:(1)
Compared with coal-gas outburst and rockburst, when coal-gas compound dynamic disaster occurs, the critical value of main controlling factors is lower, and the intensity and damage degree of disasters are obviously higher. Compared with the coal-gas outburst disaster, the gas pressure of coal-gas compound dynamic disaster is lower, and the coal strength is higher. Compared with rockburst disaster, when coal-gas compound dynamic disaster occurs, the gas pressure is higher, and the strength of coal seam roof strength is lower(2)
The damage type of coal-gas compound dynamic disaster is obviously different from coal-gas outburst and rockburst, which shows new disaster characteristics. The damage type of coal-gas compound dynamic disaster includes part of the damage characteristics of coal-gas outburst and rockburst disaster. When the coal-gas compound dynamic disaster occurs, the impact power is stronger, and gas emission is higher


### 2.2. Analysis of Factors Influencing Coal-Gas Compound Dynamic Disaster

To explore the influencing factors of coal-gas compound dynamic disaster, we need to understand the occurrence and development process of the disaster. Under the influence of mining disturbance, the coal-rock composite structure in critical state begins to deform and lose stability and release elastic strain energy. A large amount of gas expansion energy is accumulated in the pores of coal mass in coal-rock composite structure. The release of gas expansion energy has tensile damage to coal mass. Coal mass failure will further promote the release of elastic energy of coal mass and rock mass. At this time, the overall failure and instability of coal-rock composite structure induce the occurrence of coal-gas compound dynamic disaster. Combined with the influencing factors of coal-gas outburst disaster and rockburst disaster and the occurrence and development process of coal-gas compound dynamic disaster, the preliminary analysis is made to obtain the 13 influence factors of coal-gas compound dynamic disaster, which is buried depth (t1), fault number (t2), variation coefficient of coal thickness (t3), variation coefficient of coal seam dip angle (t4), soft stratification change (t5), surrounding rock combination (t6), type of coal mass failure (t7), coal thickness (t8), soft stratification thickness (t9), coal seam dip angle (t10), wrinkle coefficient (t11), initial velocity of gas emission (t12), and firmness coefficient (t13).


## 2.1. Occurrence Law of Coal-Gas Compound Dynamic Disaster

Coal-gas compound dynamic disaster is an atypical dynamic disaster induced by mining activities. With the increase of mining depth and complex geological structure, a considerable number of mines are facing the double danger of coal-gas outburst and rockburst. Coal-gas compound dynamic disaster will occur under specific conditions. Based on the field investigation records and extensive literature review of coal-gas compound dynamic disaster in multitime period for multicoal mines, the occurrence laws and destructive characteristics of coal-gas compound dynamic disaster are summarized as follows:(1)
Compared with coal-gas outburst and rockburst, when coal-gas compound dynamic disaster occurs, the critical value of main controlling factors is lower, and the intensity and damage degree of disasters are obviously higher. Compared with the coal-gas outburst disaster, the gas pressure of coal-gas compound dynamic disaster is lower, and the coal strength is higher. Compared with rockburst disaster, when coal-gas compound dynamic disaster occurs, the gas pressure is higher, and the strength of coal seam roof strength is lower(2)
The damage type of coal-gas compound dynamic disaster is obviously different from coal-gas outburst and rockburst, which shows new disaster characteristics. The damage type of coal-gas compound dynamic disaster includes part of the damage characteristics of coal-gas outburst and rockburst disaster. When the coal-gas compound dynamic disaster occurs, the impact power is stronger, and gas emission is higher


## 2.2. Analysis of Factors Influencing Coal-Gas Compound Dynamic Disaster

To explore the influencing factors of coal-gas compound dynamic disaster, we need to understand the occurrence and development process of the disaster. Under the influence of mining disturbance, the coal-rock composite structure in critical state begins to deform and lose stability and release elastic strain energy. A large amount of gas expansion energy is accumulated in the pores of coal mass in coal-rock composite structure. The release of gas expansion energy has tensile damage to coal mass. Coal mass failure will further promote the release of elastic energy of coal mass and rock mass. At this time, the overall failure and instability of coal-rock composite structure induce the occurrence of coal-gas compound dynamic disaster. Combined with the influencing factors of coal-gas outburst disaster and rockburst disaster and the occurrence and development process of coal-gas compound dynamic disaster, the preliminary analysis is made to obtain the 13 influence factors of coal-gas compound dynamic disaster, which is buried depth (t1), fault number (t2), variation coefficient of coal thickness (t3), variation coefficient of coal seam dip angle (t4), soft stratification change (t5), surrounding rock combination (t6), type of coal mass failure (t7), coal thickness (t8), soft stratification thickness (t9), coal seam dip angle (t10), wrinkle coefficient (t11), initial velocity of gas emission (t12), and firmness coefficient (t13).


## 3. Principles of the GRA-PCA-BP Model

### 3.1. Grey Relational Analysis (GRA)

Grey relational analysis is a method of quantitative description and comparison of the development and change situation of a system. By determining the geometric similarity between the reference data column and several comparison data columns, we can judge whether they are closely related, reflecting the degree of correlation between the curves. The grey relational analysis method has several characteristics: it does not need huge data. It can find the corresponding statistical law even in the case of less data. It has no requirement for whether the sample obeys the classical probability distribution function. It will not cause the problem that the qualitative analysis results and quantitative analysis results are inconsistent. The rules and relations of the studied system will not be misinterpreted [30–32].This method can be used to analyze the correlation degree between each influencing factor and the result when selecting the prediction index of coal-gas compound dynamic disaster. By evaluating the importance of each influencing factor, the main factors affecting the occurrence of coal-gas compound dynamic disaster are screened out from many parameters, and the interference of secondary factors on the prediction process and result is abandoned, which can improve the accuracy of the results and lay a good foundation for the operation of the model.The specific implementation steps of grey relational analysis are as follows:(1)
Suppose the parent sequence isY0, and each influencing factors be the comparison subfactors sequence Yii=1,2,⋯,n. The observed values of the parent factors are as follows:(1)Y0=y01,y02,⋯,y0nThe observed values of the subfactors are as follows:(2)Yi=yi1,yi2,⋯,yin.(2)
The original data of each sequence are dimensionless processed. Supposing thatX0,Xii=1,2,⋯,m are the observed values of parent factor and subfactor, respectively, after dimensionless treatment, then (the average method is used to process the data)(3)x0k=y0k1/n∑t=1ny0t,xik=yik1/n∑t=1nyit(3)
After dimensionless processing of original data, the correlation coefficientζ between x0 and xii=1,2,3,⋯,n at point k is(4)ζik=minimink∣x0k−xik∣+ρmaximaxk∣x0k−xik∣∣x0k−xik∣+ρmaximaxk∣x0k−xik∣In formula (4), the formula Δik=x0k−xik,i=1,2,3,⋯,n is called the absolute difference between x0 and xi at point k. The formula minimink∣x0k−xik∣ and the formula maximaxk∣x0k−xik∣ are two-level minimum difference and two-level maximum difference, respectively. The coefficient ρ is the resolution coefficient, generally ρ=0.5.
(4)
Calculation of the grey relational degreeri value(5)ri=1n∑k=1nζik


### 3.2. Principal Component Analysis (PCA)

Principal component analysis (PCA) is a statistical technique to extract common factors from variable groups. This technique can find out the hidden representative factors among many variables and classify the same essential variables into one new factor to effectively reduce the number of variables. This intelligent optimization algorithm has unique advantages in local and global optimization and robust performance.The advantages of principal component analysis are very suitable for the prediction of coal-gas compound dynamic disaster. The number of factors initially screened by GRA is large, and the correlation between the factors is high. There may be multicollinearity among the factors, which makes the model estimation distorted or difficult to estimate accurately due to the accurate correlation or high correlation between the factors, thus affecting the accuracy of BP neural network prediction. PCA simplification of influencing factors can effectively avoid the occurrence of this problem and can further reduce the dimension of influencing factors by obtaining new common factors [33–35].The specific implementation steps of principal component analysis are as follows:(1)
Standardized collection of original index dataThere arep-dimensional random vector x=x1,x2,⋯,xpT, n samples xi=xi1,xi2,⋯,xipT, i=1,2,⋯,n,n>p, constructing a sample matrix, performing the following standardized transformations on the sample matrix elements:
(6)Zij=xij−x¯jsj,i=1,2,⋯,n;j=1,2,⋯,p,wherex¯j=∑i=1nxij/n,sj2=∑i=1nxij−x¯j2/n−1. The normalized matrix Z is obtained.
(2)
The correlation coefficient matrix of standardized matrixZ is calculated(7)R=rijpxp=ZTZn−1,whererij=∑zkj·zkj/n−1,i,j=1,2,⋯,p.(3)
The characteristic equationR−λIp=0 is used to solve the sample correlation matrix R. Then, p characteristic roots are obtained to determine the principal component. Through equation ∑j=1mλj/∑j=1pλj≥t(t<1), the value of m is determined, which makes the utilization of information more than t. For each λj,j=1,2,⋯,m, the equation Rb=λjb is solved to get the unit eigenvector bjo(4)
The standardized index variables are transformed into main components(8)Uij=ziTbjo,j=1,2,⋯,mU1 is the first principal component, U2 is the second principal component, ..., and Up is the p principal component.


### 3.3. BP Neural Network

BP neural network is a kind of multilayer feedforward neural network trained according to the error back propagation algorithm, which is the most widely used neural network [36, 37]. The topological structure of BP neural network model is composed of three layers: input layer, hidden layer, and output layer. Gradient shrinkage technique is used to calculate the solution weight by iterative operation. The addition of hidden nodes makes the adjustable parameters increase and approach the accurate value. There is no uniform regulation on the number of neurons in the implied layer, which is generally determined by empirical formula. The empirical formula for determining the number of neurons N in the hidden layer is as follows:
(9)N=n×m,(10)N=n×m+a,(11)N=mn+1,(12)N=2m+1,wheren is the number of input layer nodes, m is the number of output layer nodes, and a is a constant between 1 and 10. From the input layer to the hidden layer and from the hidden layer to the output layer, the actual output value is obtained. When the output layer error exceeds the error tolerance range, it will be back propagation. By modifying the weights of the neural nodes, the mean square error of the expected output and the actual output is minimized. Therefore, the results meet the requirements. The structure diagram is shown in Figure 1.Figure 1
Error back propagation of three-layer network structure.


### 3.4. GRA-PCA-BP Model

In the GRA-PCA-BP model, firstly, the influencing factors with high weight are screened by grey relational analysis. Secondly, the influencing factors are integrated into representative common factors through principal component analysis, and the number of factors is further reduced. Finally, the common factor data is substituted into the input layer of BP neural network, and the training of prediction model is started to obtain a model that can accurately predict whether disasters occur. Grey relational analysis eliminates irrelevant or small influence factors. Principal component analysis eliminates multicollinearity between independent variables and further reduces the dimension of input data. The BP neural network has good predictability. The combination of the three methods can make full use of the advantages and avoid the disadvantages and can accurately and quickly predict the coal-gas compound dynamic disaster.


## 3.1. Grey Relational Analysis (GRA)

Grey relational analysis is a method of quantitative description and comparison of the development and change situation of a system. By determining the geometric similarity between the reference data column and several comparison data columns, we can judge whether they are closely related, reflecting the degree of correlation between the curves. The grey relational analysis method has several characteristics: it does not need huge data. It can find the corresponding statistical law even in the case of less data. It has no requirement for whether the sample obeys the classical probability distribution function. It will not cause the problem that the qualitative analysis results and quantitative analysis results are inconsistent. The rules and relations of the studied system will not be misinterpreted [30–32].This method can be used to analyze the correlation degree between each influencing factor and the result when selecting the prediction index of coal-gas compound dynamic disaster. By evaluating the importance of each influencing factor, the main factors affecting the occurrence of coal-gas compound dynamic disaster are screened out from many parameters, and the interference of secondary factors on the prediction process and result is abandoned, which can improve the accuracy of the results and lay a good foundation for the operation of the model.The specific implementation steps of grey relational analysis are as follows:(1)
Suppose the parent sequence isY0, and each influencing factors be the comparison subfactors sequence Yii=1,2,⋯,n. The observed values of the parent factors are as follows:(1)Y0=y01,y02,⋯,y0nThe observed values of the subfactors are as follows:(2)Yi=yi1,yi2,⋯,yin.(2)
The original data of each sequence are dimensionless processed. Supposing thatX0,Xii=1,2,⋯,m are the observed values of parent factor and subfactor, respectively, after dimensionless treatment, then (the average method is used to process the data)(3)x0k=y0k1/n∑t=1ny0t,xik=yik1/n∑t=1nyit(3)
After dimensionless processing of original data, the correlation coefficientζ between x0 and xii=1,2,3,⋯,n at point k is(4)ζik=minimink∣x0k−xik∣+ρmaximaxk∣x0k−xik∣∣x0k−xik∣+ρmaximaxk∣x0k−xik∣In formula (4), the formula Δik=x0k−xik,i=1,2,3,⋯,n is called the absolute difference between x0 and xi at point k. The formula minimink∣x0k−xik∣ and the formula maximaxk∣x0k−xik∣ are two-level minimum difference and two-level maximum difference, respectively. The coefficient ρ is the resolution coefficient, generally ρ=0.5.
(4)
Calculation of the grey relational degreeri value(5)ri=1n∑k=1nζik


## 3.2. Principal Component Analysis (PCA)

Principal component analysis (PCA) is a statistical technique to extract common factors from variable groups. This technique can find out the hidden representative factors among many variables and classify the same essential variables into one new factor to effectively reduce the number of variables. This intelligent optimization algorithm has unique advantages in local and global optimization and robust performance.The advantages of principal component analysis are very suitable for the prediction of coal-gas compound dynamic disaster. The number of factors initially screened by GRA is large, and the correlation between the factors is high. There may be multicollinearity among the factors, which makes the model estimation distorted or difficult to estimate accurately due to the accurate correlation or high correlation between the factors, thus affecting the accuracy of BP neural network prediction. PCA simplification of influencing factors can effectively avoid the occurrence of this problem and can further reduce the dimension of influencing factors by obtaining new common factors [33–35].The specific implementation steps of principal component analysis are as follows:(1)
Standardized collection of original index dataThere arep-dimensional random vector x=x1,x2,⋯,xpT, n samples xi=xi1,xi2,⋯,xipT, i=1,2,⋯,n,n>p, constructing a sample matrix, performing the following standardized transformations on the sample matrix elements:
(6)Zij=xij−x¯jsj,i=1,2,⋯,n;j=1,2,⋯,p,wherex¯j=∑i=1nxij/n,sj2=∑i=1nxij−x¯j2/n−1. The normalized matrix Z is obtained.
(2)
The correlation coefficient matrix of standardized matrixZ is calculated(7)R=rijpxp=ZTZn−1,whererij=∑zkj·zkj/n−1,i,j=1,2,⋯,p.(3)
The characteristic equationR−λIp=0 is used to solve the sample correlation matrix R. Then, p characteristic roots are obtained to determine the principal component. Through equation ∑j=1mλj/∑j=1pλj≥t(t<1), the value of m is determined, which makes the utilization of information more than t. For each λj,j=1,2,⋯,m, the equation Rb=λjb is solved to get the unit eigenvector bjo(4)
The standardized index variables are transformed into main components(8)Uij=ziTbjo,j=1,2,⋯,mU1 is the first principal component, U2 is the second principal component, ..., and Up is the p principal component.


## 3.3. BP Neural Network

BP neural network is a kind of multilayer feedforward neural network trained according to the error back propagation algorithm, which is the most widely used neural network [36, 37]. The topological structure of BP neural network model is composed of three layers: input layer, hidden layer, and output layer. Gradient shrinkage technique is used to calculate the solution weight by iterative operation. The addition of hidden nodes makes the adjustable parameters increase and approach the accurate value. There is no uniform regulation on the number of neurons in the implied layer, which is generally determined by empirical formula. The empirical formula for determining the number of neurons N in the hidden layer is as follows:
(9)N=n×m,(10)N=n×m+a,(11)N=mn+1,(12)N=2m+1,wheren is the number of input layer nodes, m is the number of output layer nodes, and a is a constant between 1 and 10. From the input layer to the hidden layer and from the hidden layer to the output layer, the actual output value is obtained. When the output layer error exceeds the error tolerance range, it will be back propagation. By modifying the weights of the neural nodes, the mean square error of the expected output and the actual output is minimized. Therefore, the results meet the requirements. The structure diagram is shown in Figure 1.Figure 1
Error back propagation of three-layer network structure.


## 3.4. GRA-PCA-BP Model

In the GRA-PCA-BP model, firstly, the influencing factors with high weight are screened by grey relational analysis. Secondly, the influencing factors are integrated into representative common factors through principal component analysis, and the number of factors is further reduced. Finally, the common factor data is substituted into the input layer of BP neural network, and the training of prediction model is started to obtain a model that can accurately predict whether disasters occur. Grey relational analysis eliminates irrelevant or small influence factors. Principal component analysis eliminates multicollinearity between independent variables and further reduces the dimension of input data. The BP neural network has good predictability. The combination of the three methods can make full use of the advantages and avoid the disadvantages and can accurately and quickly predict the coal-gas compound dynamic disaster.


## 4. Case Analysis

### 4.1. Grey Relational Analysis of Influencing Factors

The influencing factors of 13 kinds of coal-gas compound dynamic disasters were analyzed. In this paper, we need to compare the 13 factors with whether the occurrence of compound disasters and calculate the correlation degree, so the parent sequenceY0 is whether the occurrence of compound disasters. The 46 groups of data of Pingdingshan No. 8 coal mine are selected and analyzed by the SPSS software. Some initial data are shown in Table 1, some dimensionless data are shown in Table 2, and correlation coefficient and correlation degree are shown in Table 3.Table 1
Partial initial data of coal-gas compound dynamic disaster in No. 8 coal mine.
Numbert1/mt2t3t4t5t6t7t8/mt9/mt10/°t11t12/mmHgt13Disaster or not15350000.51.4735.40.8110.0611.230.321255400.08011.4735.40.7110.0515.470.281115661000.51.7823.501607.930.571125661000.51.7823.501609.000.811204840000.52.1333.5010012.560.2912153030011.7234.30.65240.1111.480.67129540000.130.52.0334.71.2110.1012.050.27130457000.140.51.0743.50.4310.065.090.150385100000.51.5434.51.5200.1312.740.2613980010.170.390.52.0333.0011015.890.180Note: In the column “Disaster or not”, the “1” represents that the disaster occurs, and the “0” represents the disaster does not occur.Table 2
Partial dimensionless data of coal-gas compound dynamic disaster in No. 8 coal mine.
Numbert1t2t3t4t5t6t7t8t9t10t11t12t13Disaster or not10.93970000.93310.85671.04551.34311.2370.78630.78630.89550.8746120.973102.725901.86610.85671.04551.34311.08240.78630.65531.23360.76531110.99421.3529000.93311.03740.6970.870501.143700.63231.55791120.99421.3529000.93311.03740.6970.870501.143700.71772.21391200.85010000.93311.24141.04550.870500.714801.00150.79261210.93094.0588001.86611.00241.04551.06951.0051.71561.44160.91541.83131290.9485001.11780.93311.18311.04551.1691.85550.78631.310.96090.7381300.8027001.20370.93310.62361.39390.87050.61852.2160.78630.40590.410380.89580000.93310.89751.04551.11922.31931.42971.70371.01590.71061391.40521.35295.79263.35330.93311.18311.04550.746100.786301.26710.4920Table 3
Partial correlation coefficient and correlation degree.
Correlation coefficientNumbert1t2t3t4t5t6t7t8t9t10t11t12t1310.90460.74330.74330.74330.90320.88760.92720.99750.97130.87370.87370.89550.891220.91160.74330.74050.74330.88420.88760.92720.99750.93540.87370.84890.97040.8696110.916110.74330.74330.90320.92550.85660.89040.74330.94930.74330.84470.9503120.916110.74330.74330.90320.92550.85660.89040.74330.94930.74330.86050.8199200.88630.74330.74330.74330.90320.97230.92720.89040.74330.860.74330.91770.8749210.90280.59150.74330.74330.88420.91790.92720.93250.91850.91530.97790.89960.8912290.90640.74330.74330.94340.90320.95850.92720.95520.88630.87370.98930.9090.8643300.83110.7650.80770.86270.73760.81820.86370.63880.83290.90610.9053380.89550.74330.74330.74330.90320.89590.92720.94370.80220.98080.91780.92080.8592390.73610.74330.40350.53890.80770.76810.78940.8410.832910.75570.8885Correlation degreet1t2t3t4t5t6t7t8t9t10t11t12t130.88040.83170.73460.75560.87170.89230.87120.89880.81970.87170.81170.85310.9077Correlation degree ranking49131263721051181Through the process of grey relational analysis, the order of 13 factors affecting the strength of coal-gas compound dynamic disaster is obtained: coal firmness coefficientt13>coal thickness t8>surrounding rock combination t6>buried depth t1>coal seam dip angle t10>change of soft stratification t5>coal failure type t7>initial velocity of gas emission t12>number of faults t2>thickness of soft stratification t9>wrinkle coefficient t11>variation coefficient of coal seam dip angle t4>variation coefficient of coal thickness t3. Some of the influencing factors with a small degree of relevance (less than 0.85) are deduced, and the first eight influencing factors are kept.


### 4.2. Using PCA to Simplify the Main Influencing Factors

The first eight retained factors were simplified by PCA using the SPSS software. After the process of inspection, extraction, and calculation, four common factor data were finally obtained. The following are the specific steps.KMO (Kaiser-Meyer-Olkin) and Bartlett test results are shown in Table4. KMO test statistics show whether the partial correlation between variables is strong enough. Bartlett sphericity test is used to judge whether the correlation matrix is the identity matrix. It can be seen from Table 4 that the value of KMO test statistic is 0.543, which indicates that the degree of information overlap among the variables is acceptable and can be used for principal component analysis. In Bartlett’s sphericity test, the value of significance is 0, which indicates that the hypothesis that each variable is independent is rejected and there is a strong correlation between variables.Table 4
Kaiser-Meyer-Olkin and Bartlett tests.
Kaiser-Meyer-Olkin0.543Bartlett sphericity testApproximate chi-square91.012Degree of freedom28Significance0Figure2 is the gravel diagram, and Table 5 shows the explanation of total variance. The horizontal axis of the gravel diagram is the number of each common factor, and the vertical axis represents the size of its characteristic value. The diagram can intuitively get the importance of each common factor. The detailed information of each common factor is listed on the left side of the total variance explanation table, and the information of extracting the common factor is on the right side. It can be seen from Figure 2 and Table 5 that the eigenvalues of the first four common factors are close to or greater than 1, and the sum of the variance percentages reaches 77.7%, that is, the first four common factors can represent eight influencing factors.Figure 2
Gravel diagram.Table 5
Total variance explained.
Total variance explainedInitial eigenvalueExtract the sum of squares of the loadCommon factorTotalVariance percentageCumulative percentageTotalVariance percentageCumulative percentage12.55131.88631.8862.55131.88631.88621.37117.14349.0291.37117.14349.02931.31116.38665.4151.31116.38665.41540.98312.28977.7030.98312.28977.70350.7158.93686.63960.5797.24393.88270.2563.20397.08680.2332.914100Table6 is the component matrix, and Table 7 shows part of the calculated common factor data. Component matrix, also known as factor load matrix, is the coefficient of the factor expression of each original variable, which expresses the influence degree of the extracted common factor on the original variable. Through the factor load matrix, we can get the linear combination of the original index variables, such as X1=a11×F1+a12×F1+a13×F1+⋯+a18×F1, where X1 is the common factor data 1. a11、a12、a13⋯a18 are the factor loads on the same line as component F1. F1 is the extracted component.Table 6
Composition matrix.
ComponentF1F2F3F4Buried deptht10.5760.009-0.661-0.05Change of soft stratificationt90.2020.2860.6170.518Surrounding rock combinationt6-0.2140.235-0.490.762Coal failure typet70.844-0.1980.1450.119Coal thicknesst80.1040.7170.346-0.19Coal seam dip anglet10-0.098-0.8160.3280.17Initial velocity of gas emissiont120.8920.082-0.022-0.133Coal firmness coefficientt13-0.7780.095-0.057-0.183Table 7
Some common factor data after calculation.
NumberX1X2X3X411.609697370.747495360.3394179280.81290003522.2040367981.031989240.8918519591.269598519110.4577727060.2722977740.0849382370.966876527120.023533260.3416113890.0456707990.835486048201.5920374850.5574927090.0255422121.189012618210.9159416840.1865603041.0047110861.439935842291.6914538770.6918186140.1198060841.110542908301.610308877-0.9672546210.9374214561.166563328381.7243341780.0655057570.488723121.012079589392.3750378210.394508286-0.3210692441.172335713


### 4.3. Construction of BP Neural Network

As shown in Figure3, this paper uses the MATLAB software to build a neural network model, repeatedly trains and verifies the common factor data, and finally obtains a model that can effectively predict coal-gas compound dynamic disaster.Figure 3
BP neural network model.The MATLAB software includes input layer, hidden layer, and output layer. The common factor data in Table7 takes the output type of numerical matrix as the input data of BP neural network, and the output type of numerical matrix is taken as the output data of BP neural network in the column of “Disaster or not” in Table 1.The 32 sets (70%) of data are randomly selected as the training set. The 7 sets (15%) of data are selected as the validation set. The other 7 sets (15%) of data are selected as the test set. For the number of neurons in the hidden layer, formula (9) is used for calculation, a=8. Thus, the prediction model structure is set as a 3-layer 4-10-1 structure.During the model training, the parameters are set as follows: the maximum number of network training is set to 1000 times, the training accuracy is set to 0.0001, and the learning rate is set to 0.01.Figure4 shows the performance of the neural network. The ordinate is the mean square error, and the abscissa is the number of iterations. It can be seen from the figure that after training the neural network using the Levenberg-Marquardt method, the number of iterations of the neural network is very small, and the network training is completed in only 10 steps. And the best verification of the neural network is obtained when the number of iteration steps is 4. The square error value is 0.04572.Figure 4
Working performance of neural network.Figure5 shows the visualization of gradient, Mu factor, and generalization ability transformation in the network training process. It can be seen from the figure that the actual gradient of the network is 0.036, and the actual value of the damping factor Mu in the Levenberg-Marquardt algorithm used by the network is 1e-4. Validation checks indicate the generalization ability check standard of the network. If the training error cannot be reduced for 6 consecutive times, the training task will be ended.Figure 5
Training status diagram.Figure6 shows the error histogram. In the figure, the abscissa represents the median of the error interval, and the ordinate represents the number of samples located in the error interval. From this figure, the error between the output value of the neural network and the original target value of the sample can be obtained.Figure 6
Error histogram.Figure7 shows the fitting results of the linear regression analysis of the test set, training set, and validation set. From the figure, the regression fitting situation of the data can be obtained. The regression R value measures the correlation between the output and the target. An R value of 1 indicates a close relationship, and 0 indicates a random relationship. The overall R value of the three sets is 0.90224, indicating that the regression fitting effect is good.Figure 7
Linear regression analysis.


### 4.4. Test of GRA-PCA-BP Model

The last three groups of data are selected to input the model for prediction, testing whether the model constructed in this paper meets the target requirements. The prediction results are shown in Table8. From the prediction results, it can be seen that the prediction results of GRA-PCA-BP model are completely consistent with the actual situation, which indicates that this method is feasible to predict the risk of coal-gas compound dynamic disaster and has good promotion value in practice.Table 8
Prediction results of common factor test set of coal-gas compound dynamic disaster.
NumberX1X2X3X4Forecast resultsExpected results441.3990424950.785939655-0.118102081.14111180311451.1904273250.760470516-0.2190589631.09174389211462.44822473-0.2275218770.2871812631.0312151800


## 4.1. Grey Relational Analysis of Influencing Factors

The influencing factors of 13 kinds of coal-gas compound dynamic disasters were analyzed. In this paper, we need to compare the 13 factors with whether the occurrence of compound disasters and calculate the correlation degree, so the parent sequenceY0 is whether the occurrence of compound disasters. The 46 groups of data of Pingdingshan No. 8 coal mine are selected and analyzed by the SPSS software. Some initial data are shown in Table 1, some dimensionless data are shown in Table 2, and correlation coefficient and correlation degree are shown in Table 3.Table 1
Partial initial data of coal-gas compound dynamic disaster in No. 8 coal mine.
Numbert1/mt2t3t4t5t6t7t8/mt9/mt10/°t11t12/mmHgt13Disaster or not15350000.51.4735.40.8110.0611.230.321255400.08011.4735.40.7110.0515.470.281115661000.51.7823.501607.930.571125661000.51.7823.501609.000.811204840000.52.1333.5010012.560.2912153030011.7234.30.65240.1111.480.67129540000.130.52.0334.71.2110.1012.050.27130457000.140.51.0743.50.4310.065.090.150385100000.51.5434.51.5200.1312.740.2613980010.170.390.52.0333.0011015.890.180Note: In the column “Disaster or not”, the “1” represents that the disaster occurs, and the “0” represents the disaster does not occur.Table 2
Partial dimensionless data of coal-gas compound dynamic disaster in No. 8 coal mine.
Numbert1t2t3t4t5t6t7t8t9t10t11t12t13Disaster or not10.93970000.93310.85671.04551.34311.2370.78630.78630.89550.8746120.973102.725901.86610.85671.04551.34311.08240.78630.65531.23360.76531110.99421.3529000.93311.03740.6970.870501.143700.63231.55791120.99421.3529000.93311.03740.6970.870501.143700.71772.21391200.85010000.93311.24141.04550.870500.714801.00150.79261210.93094.0588001.86611.00241.04551.06951.0051.71561.44160.91541.83131290.9485001.11780.93311.18311.04551.1691.85550.78631.310.96090.7381300.8027001.20370.93310.62361.39390.87050.61852.2160.78630.40590.410380.89580000.93310.89751.04551.11922.31931.42971.70371.01590.71061391.40521.35295.79263.35330.93311.18311.04550.746100.786301.26710.4920Table 3
Partial correlation coefficient and correlation degree.
Correlation coefficientNumbert1t2t3t4t5t6t7t8t9t10t11t12t1310.90460.74330.74330.74330.90320.88760.92720.99750.97130.87370.87370.89550.891220.91160.74330.74050.74330.88420.88760.92720.99750.93540.87370.84890.97040.8696110.916110.74330.74330.90320.92550.85660.89040.74330.94930.74330.84470.9503120.916110.74330.74330.90320.92550.85660.89040.74330.94930.74330.86050.8199200.88630.74330.74330.74330.90320.97230.92720.89040.74330.860.74330.91770.8749210.90280.59150.74330.74330.88420.91790.92720.93250.91850.91530.97790.89960.8912290.90640.74330.74330.94340.90320.95850.92720.95520.88630.87370.98930.9090.8643300.83110.7650.80770.86270.73760.81820.86370.63880.83290.90610.9053380.89550.74330.74330.74330.90320.89590.92720.94370.80220.98080.91780.92080.8592390.73610.74330.40350.53890.80770.76810.78940.8410.832910.75570.8885Correlation degreet1t2t3t4t5t6t7t8t9t10t11t12t130.88040.83170.73460.75560.87170.89230.87120.89880.81970.87170.81170.85310.9077Correlation degree ranking49131263721051181Through the process of grey relational analysis, the order of 13 factors affecting the strength of coal-gas compound dynamic disaster is obtained: coal firmness coefficientt13>coal thickness t8>surrounding rock combination t6>buried depth t1>coal seam dip angle t10>change of soft stratification t5>coal failure type t7>initial velocity of gas emission t12>number of faults t2>thickness of soft stratification t9>wrinkle coefficient t11>variation coefficient of coal seam dip angle t4>variation coefficient of coal thickness t3. Some of the influencing factors with a small degree of relevance (less than 0.85) are deduced, and the first eight influencing factors are kept.


## 4.2. Using PCA to Simplify the Main Influencing Factors

The first eight retained factors were simplified by PCA using the SPSS software. After the process of inspection, extraction, and calculation, four common factor data were finally obtained. The following are the specific steps.KMO (Kaiser-Meyer-Olkin) and Bartlett test results are shown in Table4. KMO test statistics show whether the partial correlation between variables is strong enough. Bartlett sphericity test is used to judge whether the correlation matrix is the identity matrix. It can be seen from Table 4 that the value of KMO test statistic is 0.543, which indicates that the degree of information overlap among the variables is acceptable and can be used for principal component analysis. In Bartlett’s sphericity test, the value of significance is 0, which indicates that the hypothesis that each variable is independent is rejected and there is a strong correlation between variables.Table 4
Kaiser-Meyer-Olkin and Bartlett tests.
Kaiser-Meyer-Olkin0.543Bartlett sphericity testApproximate chi-square91.012Degree of freedom28Significance0Figure2 is the gravel diagram, and Table 5 shows the explanation of total variance. The horizontal axis of the gravel diagram is the number of each common factor, and the vertical axis represents the size of its characteristic value. The diagram can intuitively get the importance of each common factor. The detailed information of each common factor is listed on the left side of the total variance explanation table, and the information of extracting the common factor is on the right side. It can be seen from Figure 2 and Table 5 that the eigenvalues of the first four common factors are close to or greater than 1, and the sum of the variance percentages reaches 77.7%, that is, the first four common factors can represent eight influencing factors.Figure 2
Gravel diagram.Table 5
Total variance explained.
Total variance explainedInitial eigenvalueExtract the sum of squares of the loadCommon factorTotalVariance percentageCumulative percentageTotalVariance percentageCumulative percentage12.55131.88631.8862.55131.88631.88621.37117.14349.0291.37117.14349.02931.31116.38665.4151.31116.38665.41540.98312.28977.7030.98312.28977.70350.7158.93686.63960.5797.24393.88270.2563.20397.08680.2332.914100Table6 is the component matrix, and Table 7 shows part of the calculated common factor data. Component matrix, also known as factor load matrix, is the coefficient of the factor expression of each original variable, which expresses the influence degree of the extracted common factor on the original variable. Through the factor load matrix, we can get the linear combination of the original index variables, such as X1=a11×F1+a12×F1+a13×F1+⋯+a18×F1, where X1 is the common factor data 1. a11、a12、a13⋯a18 are the factor loads on the same line as component F1. F1 is the extracted component.Table 6
Composition matrix.
ComponentF1F2F3F4Buried deptht10.5760.009-0.661-0.05Change of soft stratificationt90.2020.2860.6170.518Surrounding rock combinationt6-0.2140.235-0.490.762Coal failure typet70.844-0.1980.1450.119Coal thicknesst80.1040.7170.346-0.19Coal seam dip anglet10-0.098-0.8160.3280.17Initial velocity of gas emissiont120.8920.082-0.022-0.133Coal firmness coefficientt13-0.7780.095-0.057-0.183Table 7
Some common factor data after calculation.
NumberX1X2X3X411.609697370.747495360.3394179280.81290003522.2040367981.031989240.8918519591.269598519110.4577727060.2722977740.0849382370.966876527120.023533260.3416113890.0456707990.835486048201.5920374850.5574927090.0255422121.189012618210.9159416840.1865603041.0047110861.439935842291.6914538770.6918186140.1198060841.110542908301.610308877-0.9672546210.9374214561.166563328381.7243341780.0655057570.488723121.012079589392.3750378210.394508286-0.3210692441.172335713


## 4.3. Construction of BP Neural Network

As shown in Figure3, this paper uses the MATLAB software to build a neural network model, repeatedly trains and verifies the common factor data, and finally obtains a model that can effectively predict coal-gas compound dynamic disaster.Figure 3
BP neural network model.The MATLAB software includes input layer, hidden layer, and output layer. The common factor data in Table7 takes the output type of numerical matrix as the input data of BP neural network, and the output type of numerical matrix is taken as the output data of BP neural network in the column of “Disaster or not” in Table 1.The 32 sets (70%) of data are randomly selected as the training set. The 7 sets (15%) of data are selected as the validation set. The other 7 sets (15%) of data are selected as the test set. For the number of neurons in the hidden layer, formula (9) is used for calculation, a=8. Thus, the prediction model structure is set as a 3-layer 4-10-1 structure.During the model training, the parameters are set as follows: the maximum number of network training is set to 1000 times, the training accuracy is set to 0.0001, and the learning rate is set to 0.01.Figure4 shows the performance of the neural network. The ordinate is the mean square error, and the abscissa is the number of iterations. It can be seen from the figure that after training the neural network using the Levenberg-Marquardt method, the number of iterations of the neural network is very small, and the network training is completed in only 10 steps. And the best verification of the neural network is obtained when the number of iteration steps is 4. The square error value is 0.04572.Figure 4
Working performance of neural network.Figure5 shows the visualization of gradient, Mu factor, and generalization ability transformation in the network training process. It can be seen from the figure that the actual gradient of the network is 0.036, and the actual value of the damping factor Mu in the Levenberg-Marquardt algorithm used by the network is 1e-4. Validation checks indicate the generalization ability check standard of the network. If the training error cannot be reduced for 6 consecutive times, the training task will be ended.Figure 5
Training status diagram.Figure6 shows the error histogram. In the figure, the abscissa represents the median of the error interval, and the ordinate represents the number of samples located in the error interval. From this figure, the error between the output value of the neural network and the original target value of the sample can be obtained.Figure 6
Error histogram.Figure7 shows the fitting results of the linear regression analysis of the test set, training set, and validation set. From the figure, the regression fitting situation of the data can be obtained. The regression R value measures the correlation between the output and the target. An R value of 1 indicates a close relationship, and 0 indicates a random relationship. The overall R value of the three sets is 0.90224, indicating that the regression fitting effect is good.Figure 7
Linear regression analysis.


## 4.4. Test of GRA-PCA-BP Model

The last three groups of data are selected to input the model for prediction, testing whether the model constructed in this paper meets the target requirements. The prediction results are shown in Table8. From the prediction results, it can be seen that the prediction results of GRA-PCA-BP model are completely consistent with the actual situation, which indicates that this method is feasible to predict the risk of coal-gas compound dynamic disaster and has good promotion value in practice.Table 8
Prediction results of common factor test set of coal-gas compound dynamic disaster.
NumberX1X2X3X4Forecast resultsExpected results441.3990424950.785939655-0.118102081.14111180311451.1904273250.760470516-0.2190589631.09174389211462.44822473-0.2275218770.2871812631.0312151800


## 5. Conclusion

The prediction of coal-gas compound dynamic disaster is of great significance for the safe and efficient mining of coal mine. Firstly, the grey relational analysis method is used to eliminate irrelevant or small influential factors, and then, the principal component analysis method is used to eliminate the multicollinearity between the independent variables. Moreover, the input data dimension is further reduced. Combined with the good prediction effect of BP neural network, the coal-gas compound dynamic disaster prediction model based on GRA-PCA-BP is finally obtained. The model has high prediction accuracy and convenient operation.Model verification of the disaster case of Pingdingshan No. 8 mine shows that the coal-gas compound dynamic disaster prediction model based on GRA-PCA-BP neural network has high accuracy and practicability, which provides a new method for the disaster prediction of the coal mines with coal-gas compound dynamic disaster risk, and provides a theoretical basis for the safe and efficient mining of coal resources in deep mining areas in China.To the best of our knowledge, this is the first work using mathematical methods to predict coal-gas compound dynamic disaster. But only relying on the limited data of Pingdingshan No. 8 mine for research, the accuracy still needs to be verified by using more data of the coal mine. Meanwhile, the model used in this article is relatively simple. It is necessary to continue to study more accurate mathematical models to accurately predict coal-gas compound dynamic disaster. This is our focus in the future.



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*Source: 3508806-2021-10-14.xml*