1. Introduction
Rockburst is a deep underground rock construction process of hard and brittle surrounding rock due to excavation, mining, or other external disturbances, triggered by the rapid and violent release of the elastic properties gathered in the rock and leads to the production of surrounding rock fragments by bursting, rapid ejection, or throwing the dynamic destabilization phenomenon, which are sudden, random, and extremely hazardous geological hazards [
1,
2,
3]. In recent years, with the reduction of shallow mineral resources, more and more underground rock works are moving deeper at an unprecedented rate, and the rockburst hazards problem is becoming increasingly prominent. These hazards have been a pressing problem in deep underground rock engineering, often causing huge losses to construction personnel, equipment, and buildings, which in turn seriously affects the construction process, so it is particularly important to accurately predict the occurrence of rockburst hazards. Accurate and reliable prediction of rockburst hazards effectively avoids and controls rockbursts, and rockburst prediction has become a hot spot for research in the field of deep underground rock engineering [
4].
In order to accurately predict the intensity level of rockburst, many experts and scholars at home and abroad have carried out exploratory research on rockburst prediction methods, which can be classified into three categories: The first category is the acoustic emission technique [
5], microseismic observation technique [
6], and other methods of rockburst prediction based on field measurements; the second category is a single-factor prediction method, where the discrimination of rockburst intensity levels varies slightly with the criterion, such as Hoek criterion [
7], N-Jhelum criterion [
8], Erlang Mountain criterion [
9], and Lujiayou criterion [
10], etc. With the continuous research on the problem of rockburst prediction, a large number of scholars have gradually realized the complexity of the mechanism of rockburst and the many factors that induce rockburst [
11,
12,
13], but it is difficult to accurately predict rockburst using only single-factor prediction methods. At present, non-linear theory uses more than just the third category of rockburst prediction methods, that is, the multi-factor integrated prediction method and the multi-factor integrated prediction method, to integrate rock mechanics parameters and a variety of rockburst criterion to achieve rockburst intensity level prediction. The multi-factor integrated prediction method, according to the different non-linear theory, is divided into two subcategories. The former is mainly based on mathematical methods to predict the rockburst intensity level, which are representative of ideal point method [
14], cloud model theory [
15,
16], fuzzy comprehensive evaluation method [
17,
18,
19], uncertainty measurement theory [
20], gray system theory [
21], the TOPSIS method [
22], discriminant by distance method [
23], and the extenics theory [
3]. The latter is mainly based on intelligent algorithms to predict rockburst intensity levels, such as self-organizing feature mapping neural networks [
24], machine learning [
25,
26], deep neural networks [
27], generalized regression neural networks [
28], and sarticle swarm optimization [
29].
All of the above rockburst prediction methods have achieved some success, enriching the theory of rockburst prediction. However, there are still some shortcomings, for example, when ignoring the impact of correlation between rockburst prediction indicators on the prediction results, due to the diversity of factors affecting the occurrence of rockburst, there is a certain correlation between rockburst prediction indicators, which will not only lead to double calculation of indicators, increasing the workload in the prediction process, but will directly affect the accuracy and reliability of the prediction results. Therefore, the elimination of correlation between indicators is the key to accurate prediction of rockbursts, and research on the elimination of correlation between rockburst prediction indicators is necessary.
Factor analysis (FA) [
30] is the extension and development of principal component analysis, which regroups the information of the original variables to find out the common factors affecting the variables and can make the factor variables more interpretable and give high naming clarity by rotation. At present, the application of factor analysis method in rockburst intensity level prediction is relatively small in order to eliminate the correlation between rockburst prediction indicators. This paper uses the factor analysis method to extract the characteristics of rockburst prediction indicators, using the original rockburst prediction indicators with minimal loss of information, with comprehensive rockburst indicators, as much as possible to reflect the original rockburst prediction indicators information, which is a good solution to the problem of overlapping information indicators.
Probabilistic neural networks (PNNs) were proposed by Dr. D. F. Specht in 1988 and can implement the functions of nonlinear learning algorithms using linear learning algorithms, with the advantages of simple structure, good expansion performance, fast convergence, and high fault tolerance [
31]. However, when the probabilistic neural network is used, the problem of selecting the optimal smoothing factor is somewhat subjective and tedious. Therefore, this paper uses the sparrow search algorithm (SSA) to select the optimal smoothing factor, which has the advantages of being rapid and efficient when optimizing for a single objective and good merit-seeking ability and solves the problem of selecting the optimal smoothing factor very well.
Combining the above research, this paper selects 75 groups of typical rockburst case data, combines factor analysis method, sparrow search algorithm, and probabilistic neural network, and establishes a rockburst intensity level prediction method based on the FA-SSA-PNN model. The method has the advantages of simple logic, easy implementation, strong generalization ability of the model, high prediction accuracy, fast convergence, and applicability to small samples, which can be used as a new method for rockburst intensity level prediction. The present research results provide an important basis for predicting the rockburst intensity level in advance and provide preparation time for rockburst disaster prevention and control, and the method in this paper can also provide a reference for other geological hazard prediction problems similar to rockburst disasters.
3. Dataset Preparations
3.1. Selection of Rockburst Prediction Indicators
The rockburst mechanism is complex and has significant randomness and suddenness. The selection of indicators is the key to accurately predicting the rockburst. The selection of predictive indicators should meet the following conditions: (1) less influenced by external factors, so the actual measured values of indicators are easy to obtain; (2) has a good representative, so it can accurately reflect the main characteristics of the occurrence of rockbursts; (3) capable of reflecting comprehensive information on rockburst characteristics. This paper is based on a large number of rockburst case study analyses to determine the rockburst prediction evaluation indicators.
From the geological structure of the occurrence of rockbursts, rockbursts usually occur in the deeper buried underground works and higher structural stress in the rock mass. From the structural surface of the rock, rockburst often occurs near the hard structural surface, and the more irregular the structural surface, the more likely to occur rockburst. The maximum tangential stress in the surrounding rock can reflect the above factors well, so the maximum tangential stress in the surrounding rock (σθ) is selected as the rockburst prediction evaluation indicators.
The occurrence of rockburst section form of the surrounding rock is mainly tensile damage, and rockburst usually occurs in the structural integrity and hard rock. The hardness of the rock is usually expressed in terms of uniaxial compressive strength. Through reading a large amount of literature, we found that the actual rockburst case of uniaxial tensile strength and uniaxial compressive strength is more documented, and most of the rock projects need to obtain these two mechanical properties, so the uniaxial tensile strength (σt) and uniaxial compressive strength (σc) are rockburst prediction evaluation indicators.
From an energy point of view, rockburst is the rapid release of energy gathered in high-energy reservoirs. Under the same stress conditions, the elastic energy index, the performance of rock aggregation, and the release of energy is positively correlated, so the rock elastic energy index (Wet) is selected as the rockburst prediction indicators. A number of rockburst cases have shown that the occurrence of rockbursts is closely related to the brittleness of the rock, and the brittleness coefficient of the rock is often used as a rockburst criterion. The stress coefficient is also commonly used as a rockburst criterion; therefore, the brittleness index (σc/σt) and the stress coefficient (σθ/σc) are rockburst prediction evaluation indicators.
Comprehensive analysis of the above, according to the causes and characteristics of the occurrence of rockburst, six rockburst impact factors (σθ, σt, σc, σc/σt, σθ/σc, Wet) were selected as the rockburst prediction indicators in this paper.
3.2. Sample Library of Rockburst Case Data
Rockburst is currently a common geological hazard in many underground rock projects at home and abroad, and many engineering rockburst cases have been well documented. In this paper, through literature research [
35,
36,
37,
38], based on the rockburst prediction evaluation indicators selected by the study, 75 groups of typical rockburst cases at home and abroad were selected, and some of the raw data are shown in
Table 1, and the rockburst intensity level was divided into four levels, of which the actual distribution of rockburst levels is shown in
Figure 3.
The number of rockburst case data collected in the least number of I samples, 14; the number of II samples is 17; the number of III samples is the most, 29; the number of IV samples is 15; the ratio of various types of samples is 1.4:1.7:2.9:1.5; there is a certain imbalance in the characteristics of various types of samples. However, the ratio of the maximum sample size to the minimum sample size is only slightly greater than 2. The imbalance problem of rockburst samples is small.
Figure 4 shows the violin diagram of rockburst prediction evaluation indicators, whose horizontal coordinates indicate different rockburst levels, and vertical coordinates are rockburst prediction evaluation indicators. The violin chart is a combination of a box chart and a nuclear density chart, which gives a good indication of the shape of the distribution of the data. The white dot in the middle of the box line box indicates the median, the middle box line box indicates the interquartile range, the thin line extending from it represents the 95% confidence interval, and the outer shape is the nuclear density estimate.
4. Implementation Process of FA-SSA-PNN Model
4.1. Model Construction Steps
The 75 groups of rockburst case data collected show that there is variability in the dimensionality, which in turn leads to a decrease in the accuracy of the rockburst prediction model. In order to eliminate the impact of the difference in the dimensionality between the indicators and improve the accuracy of the rockburst prediction model, it is necessary to reduce the original rockburst prediction data, the dimensionality of the resulting comprehensive rockburst prediction data into the rockburst prediction model, and the prediction results of the model for analysis and discussion.
In this paper, Matlab software to program the calculation of the neural network algorithm to establish the FA-SSA-PNN rockburst prediction model process is shown in
Figure 5, and the main steps are as follows:
Step 1: Analysis of the impact of rockburst factors; the selection of rockburst prediction indicators.
Step 2: Collect rockburst case data according to the selected rockburst prediction indicators.
Step 3: Use factor analysis to reduce the dimensionality of the collected rockburst case data to obtain the comprehensive rockburst prediction index CPI1, CPI2, CPI3.
Step 4: Partition the data set of the rockburst case data after dimensionality reduction processing; extract 80% of the overall rockburst prediction data samples as the training sets and 20% of the overall samples as the test sets.
Step 5: Imported the training samples into the SSA-PNN model and use the training for model training and updating parameters.
Step 6: After the training is completed, input the test samples to the model to test the network performance, get the rockburst intensity level prediction results, and calculate the accuracy of its rockburst intensity level prediction.
4.2. Test of Applicability of Factor Analysis
The rockburst cases at home and abroad were collected and organized, 75 groups of typical rockburst cases were selected as the sample data of the FA-SSA-PNN rockburst prediction model, the KMO test and Bartlett’s spherical test were used to test the applicability of factor analysis on the sample data, and the test results and applicability test criteria are shown in
Table 2 and
Table 3. It can be seen from
Table 2 and
Table 3 that it is feasible to conduct factor analysis on the selected rockburst case data.
4.3. Data Processing
The absolute value of the correlation coefficient
r reflects the degree of linear correlation between the two rockburst prediction evaluation indicators. When |
r| < 0.3, it means that the correlation between the two rockburst prediction evaluation indicators is extremely weak and can be regarded as uncorrelated; when 0.3 < |
r| < 0.5, the two rockburst prediction evaluation indicators are low correlated; when 0.5 < |
r| < 0.8, the two rockburst prediction evaluation indicators are significantly correlated; when 0.8 < |
r| < 1, the two rockburst prediction evaluation indicators are extremely correlated. Correlation analysis of rockburst prediction evaluation indicators and the correlation coefficient between predictors is shown in
Table 4. The absolute values of the correlation coefficients between
σθ and
σc,
σθ and
σt,
σθ and
σθ/
σc,
σc and
σt,
σc and
Wet, and
σt and
σc/
σt were all greater than 0.5, indicating that the rockburst prediction evaluation indicators were significantly correlated with each other and the sample data were suitable for factor analysis.
Factor analysis was used to reduce the dimensionality of the standardized 75 sets of rockburst data, and Mardia gave the correspondence between the original number of variables and the number of principal factors after dimensionality reduction in
Table 5. In this paper, 6 rockburst prediction evaluation indicators were selected as the original number of variables, so the number of principal factors after factor analysis was set to 3.
Table 6 shows the total variance interpretation of the rockburst prediction evaluation indicators, and we can see that the eigen values of the first three factor variables are all greater than 1 and the cumulative contribution of the first three principal factors is 85.538% > 85%, indicating that the first three principal factors retain 85.538% of the information carried by the original variables, so the extraction of the first three principal factors as influencing factors is consistent with the previous setting.
The changes in factor loadings before and after rotation are shown in
Table 7. Combining the positive and negative correlations and the composite rate, it can be seen that the principal factor
F1 is significantly positively correlated with the rockburst prediction evaluation indicators
σθ,
σc,
σt,
σθ/
σc, indicating that the principal factor
F1 concentrates on the maximum tangential stress, compressive strength, compressive strength, and the influence of the stress coefficient on the prediction results of rockburst. The principal factor
F2 is only positively correlated with the indicator
σc/
σt, indicating that the main factor
F2 combines the information of the indicators of the brittleness index, which can be referred to as the brittleness factor. The main factor
F3 is positively correlated with the indicator
Wet only and can be referred to as the energy factor.
Table 8 shows the factor score coefficient matrix. The factor analysis reallocated the weights of the impact of rockburst prediction evaluation indicators on the principal factor and reduced the impact of poorly correlated rockburst prediction evaluation indicators on the principal factor, resulting in a functional expression between the principal factors
Y1,
Y2,
Y3 and the six rockburst prediction evaluation indicators, as follows (
is the standardized data value of
).
Standardized data are substituted into Equations (17)–(19) to obtain partial principal factor data (
Table 1). The principal factor retains most of the information in the original data, so the three principal factors are comprehensive rockburst prediction evaluation indicators
CPI1,
CPI2,
CPI3.
4.4. Datasets Segmentation
The sample data of rockburst after factor analysis (see
Table 1) were divided into datasets, and 20% of the 75 sets of rockburst case data were taken as the test set, while 80% of the remaining data were used as the training set of the neural network model. After the division, there were 60 sets of sample data in the training set, and the training set was used to train the neural network model and update the parameters. There were 15 sets of sample data in the test set, and the test set was used to evaluate the generalization ability of the model and test the real prediction accuracy of the model.
4.5. Model Parameter Setting and Implementation
The traditional PNN model uses the original rockburst prediction evaluation indicators (
σθ,
σt,
σc,
σc/
σt,
σθ/
σc,
Wet) as the input vectors of the model. The FA-SAA-PNN rockburst prediction model developed in this paper used factor analysis to preprocess the original rockburst prediction evaluation indicators, and the comprehensive rockburst prediction indicators
CPI1,
CPI2,
CPI3 obtained after factor analysis were used as the prediction input vectors of the model. The selection of the smoothing factor is the key to the performance of PNN networks, and when the value of the smoothing factor is too small, it tends to cause the network to be overfitted and in essence a nearest neighbor classifier; when the value of the smoothing factor is too large, the details cannot be fully distinguished so close to a linear classifier [
39]. This paper makes use of the good global search ability of the SSA algorithm to optimize the smooth factor of PNN neural network. The algorithm has the advantages of being rapid and efficient when optimizing for a single objective, as well as good merit-seeking ability, which solves the problem of selecting the optimal smoothing factor and improves the accuracy of the prediction model.
At present, there is no uniform standard for rockburst intensity grading, and scholars have recognized the rockburst intensity level in four classes, respectively: no rockburst (I), minor rockburst (II), medium rockburst (III), and strong rockburst (IV). This paper uses the PNN network model output vector set to 1 × 4 line vector, the i class in the line vector of the i neuron output value of 1, and the rest of the neuron output value of 0, such as the output vector is (0, 0, 1, 0), which means that the prediction model predicts the sample data as a medium rockburst (III).
The main parameters of the FA-SSA-PNN model are shown in
Table 9, and the rockburst prediction model is programmed and calculated in this paper using Matlab software version 2018b, and the code implementation is based on M language.
6. Conclusions
As more and more underground rock projects move deeper at an unprecedented rate, the geological environment in which the rock masses are embedded is more complex, and the problem of rockburst hazards is becoming increasingly prominent. In this paper, based on 75 sets of typical rockburst case data collected, a rockburst intensity level prediction model based on FA-SSA-PNN is established, and F1 value, macro-averaged F1 value, and accuracy rate are introduced as the evaluation indexes of rockburst prediction model classification performance. This study proposes a new method for predicting the intensity level of rockbursts, which provides better guidance for the problem of predicting rockbursts in deep underground rock projects and can provide a reference for other geological hazard prediction problems similar to rockburst hazards, with the following main conclusions:
- (1)
The maximum tangentialstress of surrounding rock (σθ), uniaxial tensile strength (σt), uniaxial compressive strength (σc), brittleness index (σc/σt), stress coefficient (σθ/σc), and elastic energy index (Wet) of surrounding rock are selected to form a rockburst prediction index system. The characteristic information of the original rockburst prediction indexes was compressed and extracted by the factor analysis method, and three comprehensive rockburst prediction indexes, CPI1,CPI2, and CPI3, were obtained. The introduction of factor analysis into the rockburst intensity level prediction eliminates the correlation between indicators and solves the problem of overlapping information of indicators, so that the comprehensive prediction index of rockburst after dimensionality reduction has a broader mathematical expression of Gaussian function in the PNN model.
- (2)
Fifteen sets of rockburst case data were sampled as test data, and the prediction results of the FA-PNN model were analyzed and compared with those of the original PNN model. It was found that the macro-average F1 value and accuracy of the FA-PNN model were improved, with the macro-average F1 value reaching 88.1% (from 69.6% to 88.1%) and the accuracy rate reaching 80% (from 66.7% to 80%).
- (3)
The SSA algorithm was used to select the smoothing factors in PNN to avoid the subjectivity and contingency of the existence of artificial preset smoothing factors. The comparison between the prediction results of FA-SSA-PNN rockburst prediction model and those of FA-PNN rockburst prediction model shows that, after the introduction of SSA algorithm, the accuracy of FA-SSA-PNN rockburst prediction model significantly improved, reaching 93.3% (increased from 80% to 93.3%), and the macro-average F1 value is 93.1% (increased from 88.1% to 93.1%). Moreover, the SSA algorithm has good optimization ability and can complete the optimization of smoothing factors in a few seconds. It greatly reduces the operation time of the model and improves the prediction efficiency of the model.
- (4)
The prediction results of the FA-SSA-PNN model were compared and analyzed with those of the FA-PNN model, PNN model, RF model, SVM model, and ANN model, and the results showed that the macro-averaged F1 values and the prediction accuracy of the FA-SSA-PNN model were significantly higher than those of the other five models, which verified the feasibility and effectiveness of the FA-SSA-PNN rockburst prediction model.
The complexity of the rockburst mechanism and the many factors that induce rockburst, such as the traditional rockburst prediction methods, have not been able to make accurate and efficient predictions of the rockburst intensity level. Therefore, it will become more and more important to propose new methods for predicting rockburst intensity levels.