Investigation on Intelligent Early Warning of Rock Burst Disasters Using the PCA-PSO-ELM Model

Abstract

In order to conduct an intelligent early warning assessment of stope rock burst disasters in mining areas, and effectively prevent and control them, the principal component analysis (PCA) method was embraced to perform dimensionality reduction and feature information extraction from 10 main factors that affect the occurrence of rock bursts. On this basis, six principal component elements of the influencing factors of rock bursts have been obtained as the input vectors for an extreme learning machine (ELM). In the meantime, the parameter optimization ability of the PSO algorithm was adopted, the input weight values of the ELM and the threshold values of the hidden layer were optimized, and the functions of the three models were completely combined. Therefore, an early warning model of rock bursts based on the PCA-PSO-ELM combined algorithm was creatively proposed and the risk rank of rock bursts in the Yanshitai Coal Mine was predicted and evaluated. Consequently, the research results indicated that the prediction accuracy of the PCA-PSO-ELM model improved the prediction performance and generalization ability and reached a 100% contrast with the three models, namely the BP neural network, the radial basis function, and the extreme learning machine, which presented an updated method for the early warning investigation of rock burst disasters and had favorable engineering significance.

1. Introduction

Theoretically, a rock burst denotes a common nonlinear dynamic instability phenomenon that occurs during the mining process, which can seriously threaten mine production security [1,2,3]. At present, with the gradual increase in mining depths, the issue of mine dynamic force calamities in mines represented by rock bursts is becoming increasingly prominent. The early warning and evaluation of rock bursts is a problem that countries around the globe are attempting to solve [4,5,6]. Therefore, the research on intelligent warnings of rock bursts is of great significance for ensuring the safety of mining production.

In the present age, the main methods used for early warning and the evaluation of rock bursts include on-site monitoring techniques, numerical simulation methods, uncertainty theories, and intelligent algorithms. In general, on-site monitoring techniques signify one of the traditional methods for managing mine production and preventing accidents within mines, which have been widely applied in Chinese mines where rock bursts have occurred. The main on-site monitoring techniques involve the drilling cuttings method [7], the microseismic monitoring method [8,9], the acoustic emission monitoring method [10,11], and the electromagnetic radiation monitoring method [12,13]. However, due to the complexity, nonlinearity, and uncertainty of geological conditions in mining areas, on-site monitoring considering a single factor has significant limitations, such as difficulty in determining critical indicators [14]. In addition, the early warning assessment of rock bursts using numerical simulation is primarily based on the theoretical knowledge of elastoplastic mechanics, fracture mechanics, and damage theory. Afterwards, some complex cases that cannot explicitly express the analytical solution in theory are solved using numerical methods, and the mechanical response of surrounding rock under the influences of mining has been calculated [15]. Physical and mathematical models regarding the occurrence of rock bursts in mines, such as those presented by Vacek [16], were employed to investigate the mechanisms of occurrence for rock bursts using the PFC software. Chen et al. [17] evaluated the critical depth of rock bursts at different structural levels using extensive numerical simulations in light of the discontinuous deformation analysis (DDA) method. Since the occurrence processes of rock bursts can be analyzed using numerical simulation methods from the point of view of the mechanism, it is impossible to veritably simulate a rock burst in the mining environment with respect to the complexity and uncertainty of the stope rock mass. In other words, the simulation results often present relatively considerable errors in on-site situations. Therefore, inaccurate early warning cases would occur. Moreover, the uncertainty theories mainly include fuzzy mathematics [18,19], the rough set theory [20,21], the cloud model theory [22,23], the analytic hierarchy process (AHP) [24,25], the grey system theory [26], and the set pair analysis [27], which have been broadly applied to the prediction study of rock bursts. Although these methods introduce fuzzy and random characteristics to the influencing factors of rock bursts [28], the evaluation and analysis of the rock burst indicators mainly rely on experience and are relatively subjective, leading to a large gap between the prediction results and the actual situation.

Furthermore, intelligent algorithms essentially utilize enormous nonlinear capabilities, such as machine learning, to evaluate and provide early warnings of rock bursts. Zhang et al. [29] established an intelligent evaluation model for the risk of rock bursts in coal seams based on the BP neural network, which has been adequately validated in engineering. Zhou et al. [30] adopted the random gradient lifting method to classify and predict 254 data from rock bursts and assesses the model accuracy using the Kappa method. Chen et al. [31] constructed a data-driven model for rock bursts with regard to convolutional neural networks and deep learning and calculated the rock burst probability for each corresponding level. Ma et al. [32] used the LightGBM algorithm and correlation coefficient heat map to screen the characteristic variables of rock bursts and used the random forest classification model to classify and predict the rock burst risk level at the “t + 1” moment. Ji et al. [33] embraced the genetic algorithms to optimize the parameters of a support vector machine (SVM) and established a GA–SVM model to predict the rock burst using microseismic monitoring data. Although these algorithms offer certain advantages and have achieved certain results in the early warning research of rock bursts, multiple problems still need to be addressed, such as the slow model learning speed, the ability to easily fall into local optimization, the poor anti-interference ability, and the inaccurate early warning results.

In accordance with the insufficient results of the aforementioned methods, the model proposed in this paper has been verified in the risk rank prediction of rock bursts in the Yanshitai Coal Mine. To be more specific, the innovation points of the model predominantly included the use of the principal component analysis method to reduce the dimension of the 10 main factors affecting the occurrence of rock bursts, eliminating the influences of superimposed information and simplifying the network structure of the model. Meanwhile, the PSO algorithm was used to optimize the input weights and the thresholds of the hidden layer of the limit vector machine, which overcame the disadvantage of the randomness of the input weights and the thresholds of the hidden layer of the ELM. In contrast to the other methods, the prediction accuracy of the model has been tremendously enhanced, providing several advantages such as a good prediction performance, fast learning speed, strong generalization ability, and applicable robustness, and is of great significance in engineering practice.

Hence, this research firstly describes the basic principles and methods of the PCA–PSO–ELM model. Then, it explains how this model was applied to the risk rank prediction of rock bursts in the Yanshitai Coal Mine, and compares the accuracy to the other models. Lastly, it summarizes some conclusions concerning the existing research and the planned future work.

2. Model Principles and Methods

2.1. PCA

In practice, the principal component analysis (PCA) method represents a frequently used linear dimensionality reduction analysis, which converts a set of potentially correlated variables into a group of linearly unrelated variables through orthogonal transformation. Hence, the transformed set of variables can be defined as the principal component [34]. The principle can be presented as follows.

The original sample X is assumed to contain n indicators, namely,$X={[x_1,x_2,\dots ,x_n]}^T$. Among them, $x_1,x_2,\dots ,x_n$ signify the original sample data set, and $n$ denotes the dimensions of the variables. The new variable $Y,$ obtained after the dimensionality reduction, can be expressed as $Y={UX=[y_1,y_2,\dots ,y_m]}^T$. Meanwhile, $U$ depicts the coefficient matrix, where $U=\left(\begin{array}{ccc}{u}_{11}& \cdots & u_{1n}\\ ⋮& \ddots & ⋮\\ u_{m1}& \cdots & u_{mn}\end{array}\right)$, while $y_1,y_2,\dots ,y_m$ indicate the generated new variables, and $m$ refers to the dimensions of the new variables. Hence, the calculation formula for$y_1,y_2,\dots ,y_m$ can be realized as follows.

$$\left\{\begin{array}{c}{y}_1=u_{11} x_1+u_{12} x_1+\dots +u_{1n} x_n \\ y_2=u_{21} x_1+u_{22} x_1+\dots +u_{2n} x_n\\ ⋮\\ y_m=u_{m1} x_1+u_{m2} x_1+\dots +u_{mn} x_n\end{array}\right.$$

(1)

The major steps of the PCA method can be summarized as follows.

• Standardize the sample data and calculate the correlation matrix.
• Solve the eigenvalues and sort the principal components according to their magnitudes.
• Calculate the variance contribution rate of each principal component and select m (m < n) principal components based on the principle of the cumulative variance contribution rate reaching 85%.
• Calculate the correlation coefficient matrix and list the calculation formula of the principal components so that the dimensionality reduction of the original data can be achieved.

2.2. PSO Method

The particle swarm optimization (PSO) method symbolizes a random search algorithm that simulates the bird foraging behavior [35,36]. Supposing there is a swam composed of M particles in the D-dimensional search space, the spatial position of the i-th particle can be expressed as $X_i=\left(x_{i1},x_{i2},\cdots ,x_{iD}\right)$. In the mean time, the particle movement speed can be signified as $v_i=\left(v_{i1},v_{i2},\dots ,v_{iD}\right)$, while the optimal position experienced by the particles refers to $P_i=\left(p_{i1},,\cdots ,p_{iD}\right)$ and the optimal position in history underwent by the swam can be denoted as $P_g=\left(p_{g1},p_{g2}\cdots ,p_{gD}\right)$. Thus, the updated formula for the velocity and position of the d-th dimension (1 ≤ d ≤ D) of each generation of particle i can be simplified as follows.

$$v_{id}^{\left(t+1\right)}=w{v}_{id}^{\left(t\right)}+c_1{r}_1\left(p_{id}-x_{id}^{\left(t\right)}\right)+c_2{r}_2\left(p_{gd}-x_{id}^{\left(t\right)}\right)$$

(2)

$$x_{id}^{\left(i+1\right)}=x_{id}^{\left(t\right)}+v_{id}^{\left(t+1\right)}$$

(3)

In the formula,$w$ represents the inertia weight; $c_1$ and $c_2$ indicate the learning factors, respectively; and ${ r}_1$ and $r_2$ depict the two random numbers that vary within [0, 1]. The flowchart of the PSO algorithm is exhibited in Figure 1.

2.3. ELM

As a matter of fact, the feedforward neural network algorithm that is in line with a single hidden layer can be denoted as the extreme learning machine (ELM). Compared to the traditional neural networks, the ELM is equipped with a faster learning speed and a more favorable generalization performance under the premise of ensuring a greater learning accuracy [37,38,39]. Therefore, its principle is as follows.

Assuming that there is a single hidden layer neural network with N arbitrary samples ($x_i,t_i$), $x_i={\left[x_{i1},x_{i2},\cdots ,x_{in}\right]}^TϵR^n$ and ${ t}_i={\left[t_{i1},t_{i2},\cdots ,t_{im}\right]}^TϵR^m$ signify the input and output data, respectively. Accordingly, the ELM network structure diagram is displayed in Figure 2.

A neural network with L neurons in a single hidden layer can be represented as follows.

$${\sum }_{i=1}^L{\beta }_{i}g({\omega }_i\times x_i+b_i)=o_j,j=1,\cdots ,N$$

(4)

In the formula, $g\left(x\right)$ depicts the activation function, $W_i={\left[{\omega }_{i1},{\omega }_{i2},\cdots ,{\omega }_{in}\right]}^T$ symbolizes the input weight value, ${\beta }_i$ indicates the output weight value, $b_i$ refers to the threshold of the ith neuron of the hidden layer, and $o_j$ denotes the calculated output value.

Admittedly, the purpose of training an ELM network is to minimize the errors between the calculated output values and the expected output values, which can be expressed as $\sum _{j=1}^N‖o_j-t_j‖=0$. Hence, Equation (4) can be simplified to the matrix form.

$$H\beta =T$$

(5)

In the formula, $H$ indicates the hidden layer output matrix, $\beta$ represents the output weight values, and $T$ symbolizes the expected output values.

Consequently, the definitions of $H$, $\beta$, and $T$ can be determined as the following.

$$H={\left(\begin{array}{ccc}g\left(w_1{x}_1+b_1\right)& \cdots & g\left(w_1{x}_1+b_L\right)\\ ⋮& \ddots & ⋮\\ g\left(w_1{x}_N+b_1\right)& \cdots & g\left(w_L{x}_N+b_L\right)\end{array}\right)}_{N\times L}$$

(6)

$$\beta ={\left(\begin{array}{c}{\beta }_1^T\\ ⋮\\ {\beta }_L^T\end{array}\right)}_{L\times m}$$

(7)

$$T={\left(\begin{array}{c}{t}_1^T\\ ⋮\\ t_L^T\end{array}\right)}_{L\times m}$$

(8)

$\widehat{\beta }=H^{+}T$. Among them,$H^{+}$ signifies the Moore–Penrose generalized inverse matrix of the output matrix $H$.

2.4. Combined Early Warning Model of PCA–PSO–ELM

Since the factors affecting the occurrence of rock bursts are not completely independent, this work performs dimension reduction and feature information extraction from the sample data before predicting the grade of the rock burst. The extracted principal components not only eliminate the correlation between the different factors, but also simplify the network structure and improve the model performance. Meanwhile, due to the randomness of the input weights and the thresholds of the hidden layer of the ELM neural network, it has a significant impact on the identification and generalization ability of the ELM. In order to enhance the performance of the ELM, this paper adopted the PSO algorithm to optimize the input weights and the hidden layer thresholds of the ELM, obtaining its optimal parameter combination, and finally established a rock burst prediction model in accordance with the PCA–PSO–ELM combined algorithm. The model flowchart is exhibited in Figure 3.

3. Example Analysis

3.1. Early Warning Indicator System for Rock Bursts

In the light of the dynamic phenomenon data of the Yanshitai Coal Mine for more than 30 years, and referring to the research results of Dai Gaofei and other scholars, this paper comprehensively selected 10 main factors that affect the occurrence of rock bursts in the Yanshitai Coal Mine as the risk assessment indicators of rock bursts, which can be presented as the coal thickness (X₁), dip angle (X₂), burial depth (X₃), structure (X₄), dip angle change (X₅), coal thickness change (X₆), gas concentration (X₇), roof management (X₈), pressure relief (X₉), and sound of the coal cannon (X₁₀). To facilitate model learning, it is necessary to quantify the non-quantitative indicators [40]. The quantification results are listed in

Table 1. Assignment of the qualitative indicators of the rock burst risk grade.

Assignment	Qualitative Index of Rock Bursts
	X4	X5	X6	X8	X9	X10
0	Simple	Unchanged	Unchanged	No support or poor support	No pressure relief measures	None
1	Average	Minor change	Minor change	Average	Average pressure relief effect	Less
2	Relatively complex	Relatively large changes	Relatively large changes	Relatively good	Relatively good pressure relief effect	Many
3	Complex	Severe change	Severe change	Good	Good pressure relief effect

.

According to the measured data [40] from 35 groups of hazardous mines of rock bursts in the Yanshitai Coal Mine, the rock bursts in the Yanshitai Coal Mine were divided into four grades: no rock burst (I), weak rock burst (II), medium rock burst (III), and strong rock burst (IV). The first 27 samples were used as the training set for the model (

Table 2. Rock burst training set sample.

Sample	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	Impact Level
1	1.3	29	530	0	0	0	0.07	3	3	0	Ι
2	1.2	25	542	0	0	0	0.24	3	3	0	Ι
3	1.4	44	560	0	0	0	0.09	3	3	0	Ι
4	3	24	573	0	0	1	0.36	2	3	0	Ι
5	0.8	34	553	1	0	0	0.15	0	2	1	Ⅱ
6	1.2	40	490	0	0	0	0.2	2	0	1	Ⅱ
7	1.4	35	480	0	0	1	0.36	2	0	1	Ⅱ
8	1.2	27	490	0	0	0	0.64	2	2	1	Ⅱ
9	2.6	48	752	2	0	2	0.48	1	1	1	Ⅲ
10	2.8	52	733	0	1	1	0.54	2	2	1	Ⅲ
11	3	78	560	1	3	2	1.14	2	3	1	Ⅲ
12	6	30	465	1	1	3	1.3	1	0	2	Ⅲ
13	1.5	65	570	1	3	1	0.28	1	2	2	Ⅲ
14	3	35	612	2	0	2	0.56	2	0	2	Ⅲ
15	2	35	614	1	0	2	0.56	1	0	2	Ⅲ
16	3	55	855	3	2	3	0.075	1	1	2	Ⅳ
17	4	52	675	3	2	3	1.88	0	0	2	Ⅳ
18	1.3	73	486	3	3	3	0.43	1	0	2	Ⅳ
19	2.1	67	498	3	3	3	1.89	0	0	2	Ⅳ
20	2.5	65	450	3	2	3	0.67	1	1	2	Ⅳ
21	1.7	60	314	3	3	1	1.3	0	0	2	Ⅳ
22	1.1	47	485	3	3	3	0.43	1	0	2	Ⅳ
23	1.8	54	238	3	1	3	1	0	0	2	Ⅳ
24	1.6	35	583	2	0	3	1.5	3	3	1	Ⅱ
25	1.5	35	530	0	0	0	0.56	3	3	0	Ⅰ
26	1.6	62	307	3	2	2	1	0	0	2	Ⅳ
27	1.9	59	542	1	2	3	0.25	0	0	1	Ⅲ

), whereas the last eight were chosen as the model test set (

Table 3. Samples of the rock burst test set.

Sample	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	Impact Level
1	1.8	62	283	3	2	3	1	0	0	2	Ⅳ
2	1.3	44	570	0	0	0	0.66	3	3	0	Ι
3	2.2	54	290	3	2	2	1	0	0	2	Ⅳ
4	3	34	475	2	2	1	0.42	0	0	2	Ⅲ
5	3.2	42	574	3	0	0	0.29	0	0	2	Ⅲ
6	1.8	62	283	3	2	3	1	0	0	2	Ⅳ
7	1.3	44	656	2	1	3	0.24	1	1	2	Ⅲ
8	1.2	40	553	2	2	2	0.49	1	2	2	Ⅲ

).

3.2. Principal Component Data Analysis

3.2.1. KMO Inspection and Bartlett Sphericity Test

Before performing the principal component analysis, it was essential to test the suitability of using this method among various factors. This study conducted the Bartlett sphericity test and KMO inspection, and the inspection results are listed in

Table 4. KMO and Bartlett sphericity test results.

Fitness Quantity of KMO Sampling		0.753
	Approximate chi square	302.168
Bartlett sphericity test	Degree of freedom	45
	Significance	0.000

.

With respect to the test results, the fitness of the KMO sampling referred to 0.753, which was greater than 0.600 with a significance of 0.000 and less than 0.05, indicating a correlation between the original indicators. Therefore, the PCA method was suitable for the dimensionality reduction of the original data.

3.2.2. Principal Component Extraction

In particular, the SPSS software was adopted in this paper to conduct the principal component analysis on the data. First, the original data was normalized to eliminate the significant differences. Afterwards, the correlation analysis was conducted on the 10 influencing factors of rock burst disasters. The thermodynamic diagram of the correlation coefficient is exhibited in Figure 4.

After the principal component analysis, the variance contribution rates of the first six selected principal components were 48.142%, 14.054%, 12.678%, 9.751%, 4.259%, and 3.776%, respectively. Remarkably, the cumulative variance contribution rate reached 92.659%, which was greater than 85% and reflected the original information of the indicators to the greatest possible extent. The variance contribution rate and its cumulative contribution rate are exhibited in Figure 5.

Eventually, a subsequent analysis was performed on the last six principal components to obtain the principal component coefficient matrix. In relation to Formula (9) to Formula (14), the training and testing samples obtained from the principal component analysis are shown in

Table 5. Training set samples after the PCA analysis.

Sample	Principal Component						Impact Level
	Y1	Y2	Y3	Y4	Y5	Y6
1	−4.13	−0.52	0.22	0.38	0.23	0.13	Ⅰ
2	−4.15	−0.38	0.17	0.55	0.38	−0.09	Ⅰ
3	−3.84	−0.73	0.80	0.24	0.05	0.23	Ⅰ
4	−3.22	0.99	0.37	0.73	−0.23	−0.2	Ⅰ
5	−1.85	−0.83	−1.1	−0.77	−0.59	−1.5	Ⅱ
6	−2.12	−0.56	−1.35	−0.17	−0.30	0.7	Ⅱ
7	−1.79	−0.13	−1.32	0.11	0.2	0.83	Ⅱ
8	−2.67	−0.29	−0.79	0.71	0	−0.35	Ⅱ
9	−0.49	1.15	0.43	−1.07	0.33	−0.63	Ⅲ
10	−1.63	0.74	1.42	−0.3	−0.68	0.17	Ⅲ
11	0.31	−0.61	3.04	1.19	−0.63	0.38	Ⅲ
12	1.39	3.2	−0.65	1.65	−0.81	0.99	Ⅲ
13	0.27	−1.48	1.15	−0.82	−1.12	0.24	Ⅲ
14	−0.06	1.57	−0.78	−0.53	0.64	0.56	Ⅲ
15	−0.17	0.94	−1.15	−0.74	0.35	0.08	Ⅲ
16	1.17	1.16	1.43	−2.5	0.17	0.03	Ⅳ
17	2.96	1.96	0.66	0.65	−0.06	−1.04	Ⅳ
18	2.34	−1.54	0.55	−0.89	0.44	0.86	Ⅳ
19	3.44	−0.4	0.62	1.04	0.26	−0.73	Ⅳ
20	1.96	−0.5	0.51	−0.05	0.36	0.47	Ⅳ
21	2.48	−1.62	−0.7	1.06	−0.70	−0.52	Ⅳ
22	1.80	−1.02	−0.29	−0.84	0.80	0.55	Ⅳ
23	2.34	−0.94	−1.54	0.95	0.67	0.02	Ⅳ
24	−1.14	0.75	1.15	1.42	2.49	−0.62	Ⅱ
25	−3.74	−0.37	0.56	1.06	0.25	−0.14	Ⅰ
26	2.39	−1.44	−0.92	0.62	−0.05	−0.18	Ⅳ
27	0.87	−0.54	0.03	−0.78	−0.37	0.54	Ⅲ

and

Table 6. Test set samples after the PCA analysis.

Sample	Principal Component						Impact Level
	Y1	Y2	Y3	Y4	Y5	Y6
1	2.74	−1.24	−0.83	0.73	0.34	0.16	Ⅳ
2	−3.57	−0.55	0.98	0.95	0.28	−0.25	Ⅰ
3	2.33	−0.94	−1.16	0.83	−0.22	−0.1	Ⅳ
4	0.94	0.31	−1.36	−0.38	−1.24	−0.08	Ⅲ
5	0.42	0.81	−1.59	−1.1	−1.11	−0.9	Ⅲ
6	2.74	−1.24	−0.83	0.73	0.34	0.16	Ⅳ
7	0.37	0.09	−0.03	−1.56	0.96	0.01	Ⅲ
8	0.21	−0.64	0.15	−0.61	0.37	−0.4	Ⅲ

.

$$\begin{array}{cc}\hfill { Y}_1=0.1560X_1& + 0.2946X_2-0.1189X_3+0.4008X_4+0.3432X_5+0.3711X_6+0.2649X_7-0.3637X_8\hfill \\ & - 0.3133X_9+0.3976X_{10}\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill Y_2=0.6887X_1& - 0.3720X_2+0.4412X_3-0.0413X_4-0.3005X_5+0.1984X_6+0.1854X_7+0.0604X_8\hfill \\ & - 0.1288X_9+0.0834X_{10}\hfill \end{array}$$

(10)

$$\begin{array}{cc}\hfill Y_3=0.13903X_1& + 0.4668X_2+0.4434X_3-0.0191X_4+0.3815X_5+0.1785X_6+0.1370X_7+0.2727X_8\hfill \\ & + 0.51121X_9-0.1837X_{10}\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill Y_4=0.2109X_1& - 0.04976X_2-0.5881X_3-0.1678X_4+0.0106X_5-0.0370X_6+0.6918X_7+0.1534X_8\hfill \\ & + 0.1461X_9-0.2327X_{10}\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill Y_5=-0.4653X_1& - 0.1623X_2+0.0352X_3+0.3573X_4-0.3092X_5+0.5730X_6+0.1732X_7+0.4145X_8\hfill \\ & + 0.0033X_9-0.0485X_{10}\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill { Y}_6=0.2292X_1& \hfill + 0.1601X_2-0.2970X_3-0.3435X_4+0.1813X_5+0.2904X_6-0.3921X_7+0.5549X_8\\ & - 0.3503X_9+0.1141X_{10}\hfill \end{array}$$

(14)

3.3. Combined Early Warning Model of PCA–PSO–ELM for Rock Bursts

The principal components Y₁, Y₂, Y₃, Y₄, Y₅, and Y₆ after the dimensionality reduction were taken as the input factors for the model, and the risk level of the rock burst was chosen as the output factor for the model. The training set samples were trained and the PSO algorithm was used to optimize the initial weight values of the ELM. The threshold values of the hidden layer were used to obtain the optimal parameter combination, which was input into the super parameters of the ELM model to predict the rock burst grade of the test set. Eventually, the rock burst prediction model with regard to the PCA–PSO–ELM combination algorithm was established.

3.4. Results Analysis

After training the PSO–ELM model, the obtained curve of the variation of the model iteration error was achieved, as shown in Figure 6, indicating that the fitness value did not change after 35 iterations, i.e., the algorithm converged and the optimal parameter combination was identified.

The parameter combination obtained through optimization was input into the ELM super parameter so that the rock burst grade could be predicted. The prediction results of the model for the test set are displayed in Figure 7.

Notably, it was evidently discovered from the analysis in Figure 7 that the prediction accuracy of the PSO–ELM model reached 100%. In order to further investigate the performance for predicting the rock burst model of the PSO–ELM algorithm, this paper employed the BP neural network, the radial basis function, and the extreme learning machine to learn the training set samples and predict the rock burst grade of the test set. The prediction results are exhibited in Figure 8, Figure 9, and Figure 10, respectively.

Comparing the prediction results of the PSO–ELM neural network with those of the BP neural network, the radial basis function, and the ELM, as shown in Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 and

Table 7. Comparison of the prediction results of the different models.

Test Sample	Actual Grade	BP	RBF	ELM	PSO–ELM
1	Ⅳ	Ⅳ	Ⅳ	Ⅳ	Ⅳ
2	Ⅰ	Ⅰ	Ⅰ	Ⅰ	Ⅰ
3	Ⅳ	Ⅳ	Ⅳ	Ⅳ	Ⅳ
4	Ⅲ	Ⅲ	Ⅲ	Ⅲ	Ⅲ
5	Ⅲ	Ⅳ	Ⅳ	Ⅲ	Ⅲ
6	Ⅳ	Ⅳ	Ⅳ	Ⅳ	Ⅳ
7	Ⅲ	Ⅲ	Ⅲ	Ⅳ	Ⅲ
8	Ⅲ	Ⅳ	Ⅱ	Ⅲ	Ⅲ

, the prediction accuracy of the BP neural network, RBF, and traditional ELM referred to 75%, 75%, and 87.5%, respectively. The ELM rock burst prediction model optimized using PSO reached 100%, which overcame the shortcomings of randomness of the ELM input weights and the hidden layer thresholds so that the prediction accuracy of the combined PCA–PSO–ELM model could be tremendously improved and a novel idea for the early warning exploration of rock burst in mines could be evidently provided.

4. Conclusions

• Taking the 10 factors that affected the occurrence of rock bursts in the Yanshitai Coal Mine as the main influencing factors, the PCA method was used to extract the dimension reduction feature information of the evaluation index, from which six principal components were extracted as the input vectors for extreme learning machine, eliminating the interaction between the various factors and simplifying the network structure of the model.
• Using the PSO algorithm, the initial weights and hidden layer neuron thresholds of the ELM were optimized. Therefore, a combined early warning PSO–ELM model for rock bursts was ultimately established, which overcame the disadvantage of randomness of the input weights and hidden layer thresholds of the ELM and enhanced the accuracy of the model prediction.
• Through the precision analysis and comparison between the prediction results of the BP neural network, radial basis function, and ELM, the research findings indicated that the prediction accuracy of the PSO–ELM model on the test set was as high as 100%, and the prediction accuracy was far better than the other three models.
• In summary, the rock burst PCA–PSO–ELM prediction model had the advantages for good prediction performance, fast learning speed, firm generalization ability, and satisfied robustness, which provided an idea for the early warning research of rock burst disasters and exhibited favorable engineering significance.
• It is worth noting that rock bursts are not only affected by the conditions of geology and mining technology, but also influenced by the hidden factors of Class II mining technology and so on during the prediction process of rock burst, such as the progress degree of the working face or the expansion and repair of roadway walls, prompting the risk rank assessment of rock bursts to become a difficult subject. Consequently, the investigation on intelligent early warning for rock bursts requires further research and discussion.