Prediction of Rockburst Intensity Grade in Deep Underground Excavation Using Adaptive Boosting Classifier

its predictionat the early designstagesplays a signiﬁcant role in improving safety.The article describes a newlydeveloped model to predict rockburst intensity grade using Adaptive Boosting (AdaBoost) classiﬁer. A database including 165 rockburst case histories was collected from acrosstheworldtoachieve acomprehensiverepresentation,in whichfourkeyinﬂuencingfactorssuchasmaximumtangentialstress of the excavationboundary,uniaxial compressivestrengthof rock,tensile rock strength, andelasticenergy indexwere selectedasthe input variables, and the rockburst intensity grade was selected as the output. The output of the AdaBoost model is evaluated using statistical parameters including accuracy and Cohen’s kappa index. The applications for the aforementioned approach for predicting the rockburst intensity grade are compared and discussed. Finally, two real-world applications are used to verify the proposed AdaBoost model. It is found that the prediction results are consistent with the actual conditions of the subsequent construction.


Introduction
In underground rock engineering, a rockburst is a type of dynamic geological disaster. It is a dynamic instability phenomenon that occurs when a rock mass or geological structure is subjected to high stress or is in a state of limit equilibrium. A rockburst, which still draws a lot of interest today, has a significant impact on rock stability in deep underground conditions [1][2][3]. Because rockbursts occur suddenly and intensely, they frequently result in harm, including death of workers, equipment damage, and even significant interruption and loss of revenue in underground deep excavation. Various strategies for controlling rockbursts have been proposed, such as temporary and permanent rock support structures; however, these efforts are ineffective since the severity of rockbursts is difficult to predict precisely. To record and evaluate the rockburst occurrences, different monitoring systems, such as a microseismic system, were used [4]. e rockburst intensity is recorded by the microseismic monitoring system after the rockburst occurs and thus cannot predict the rockburst in advance. e tendency and intensity of rockburst were contrastively analyzed by Chen and Guo [5] using the strain energy index model of rockburst. As a result, estimating and predicting rockburst intensity is critical for a safe and cost-effective deep underground excavation or mining in burst-prone soils before it occurs.
Machine learning (ML) algorithms have been widely used to tackle real-world problems in the last ten years, particularly in civil engineering. ML algorithms have been successfully used to a variety of real situations, paving the way for several promising opportunities in civil engineering and other domains such as environmental [6], geotechnical and geological [7][8][9][10][11][12][13][14][15][16][17][18][19][20], and other sciences [21][22][23][24] including rockburst hazards prediction [25][26][27]. Furthermore, a variety of machine learning methods have been used, for example, Support Vector Machine (SVM) [28], Artificial Neural Networks (ANNs) [29], Distance Discriminant Analysis (DDA) [30], Bayes Discriminant Analysis (BDA) [31], and Fisher Linear Discriminant Analysis (LDA) [32], and some systems are based upon hybrid (Zhou et al. [33]; Adoko et al. [34]; Liu et al. [35]) or ensemble (Ge and Feng [36]; Dong et al. [37]) analyzing long-term prediction of rockburst. ese studies provided new concepts and ways for predicting rockbursts. However, each of the methods listed above has its own set of benefits and drawbacks. Understanding, predicting, and controlling rock bursts still pose a considerable challenge for underground engineering. Furthermore, the number of data and the type of ML algorithms have an influence on the accuracy of rockburst intensity prediction. As a result, developing a high-performing and time-saving ensemble classifier for a larger dataset is critical. Many researchers have increasingly implemented the AdaBoost-based method for prediction problems such as rock mass class and soil classification as a vital means in recent years [38,39]. For classification, prediction, and recognition issues, the AdaBoost methodology is widely regarded as the most successful and reliable artificial intelligence method. e article aims to add the following described contributions to this field: (1) A machine learning classifier for rockburst prediction based on case histories data is proposed. (2) e performance of AdaBoost is compared with other classifiers to confirm that the algorithm has superior or at par classification precision. (3) e effectiveness and feasibility in engineering practice applications and real-world examples are analyzed to predict rockburst intensity grade. e rest of this paper is arranged as follows. e second section introduces the selection of indicators and the data collection, AdaBoost algorithm, and performance measures. e establishment of the algorithm model is described in the third section. In the fourth section, results are discussed, and the proposed algorithm is compared with the developed empirical criteria, widely used models, and two real-world applications are used to verify the proposed model. Finally, the conclusions are drawn in the fifth section.

Dataset.
A total of 165 cases of rockburst events reported in the literature were collected to build a dataset [33,40]. e maximum tangential stress of the excavation boundary (σ θ ), the uniaxial compressive strength of rock (σ c ), the tensile rock strength (σ t ), and the elastic energy index (Wet) are selected as input parameters in this study by referring to the previous research [41,42] and rockburst intensity as the output. ese input variables are commonly applied in rockburst classification and can provide fundamental understandings about rockburst occurrence in underground conditions. σ c , σ t , and Wet were obtained by rock mechanics experiments, and σ θ was calculated according to the stress of the surrounding rock. rough field observation and evaluation, the rockburst grade was obtained. According to rock failure properties, the output parameter, i.e., rockburst intensity, contains four different classes, namely, no, moderate, strong, and violent, which are indicated by 1, 2, 3, and 4, respectively, as shown in Table 1 [40]. Figure 1 shows a boxplot of each affecting parameter for the four rockburst levels. As shown in Figure 1, the rockburst hazard intensity grades are associated with each attribute. Table 2 contains an overview of the case histories, as well as parameter statistics. e following is a brief summary of various input parameters.

Maximum Tangential Stress of the Surrounding Rock.
e maximum tangential stress is frequently used to determine the angle at which a rock fractures [43]. For example, Ryder [44] determined that the fault-slip and shear fracture modes had a significant role in African metal mines in his investigation of the influence of excess shear stress on rockburst-prone circumstances, whereas Qian et al. [45] proposed two rock burst dynamic failure modes: one strain mode resulting from the rock failure and one sliding mode caused by the fault-slip and shear fracture events. Qian et al. [45] also analyzed two rockburst accidents in coal mines in China, stating that the instability due to rockburst occurrence could also be classified as fault-slip and shear fracture modes. As a result, past studies show that the maximum tangential stress has a significant impact on the incidence of shear fracture instabilities in tunnels, making it an important parameter for rockburst prediction. It is also an often used parameter in the data set.

Uniaxial Compressive and Tensile Strength.
Other characteristics that can influence rockburst include uniaxial compressive strength (UCS) and uniaxial tensile strength (UTS), both of which have been used in the past. UCS and UTS values are widely known parameters for rockburst hazards prediction modeling.

Elastic Energy Index.
e proportion of residual strain energy that dissipated during a single loading-unloading cycle under uniaxial compression is defined by the elastic energy index, Wet [46,47]. is parameter is related to the rockburst hazards, and Wang et al. [48] developed a rockburst prediction criterion based on Wet. e Wet values can be easily obtained through laboratory tests and direct (double-hole method) or indirect (rebound method) in situ evaluations.

AdaBoost Algorithm.
e AdaBoost algorithm, short for Adaptive Boosting, is a boosting approach used in machine learning as an ensemble method that uses decision trees as 2 Complexity the main classifier. It is called Adaptive Boosting as the weights are reassigned to each instance, with higher weights assigned to incorrectly classified instances. Freund and Schapire's AdaBoost is the most widely used version of the boosting algorithm [49], making maximum use of a classifier by improving its accuracy. It is a simple learning approach that creates a strong classifier from a small number of efficient but weak classifiers (see Figure 2). e goal is to combine the weak classifiers to improve their performance. As a result, the final robust classifier generated a data set for a model that can predict the class of a new observation. AdaBoost improves the classification efficiency of a simple learning algorithm by combining sets of weak classifiers to build a more robust classifier. In the language of boosting algorithms, the simple learning algorithm is known as a weak learner, and it selects a small, effective set of weak   classifiers with the lowest classification error from a wide number of potential features. e weak learner does not categorise the training data well even using the best classification function. To enhance the weak learner, it is necessary to solve a series of learning challenges. After the first learning cycle, the instances are reweighted to highlight those that were inaccurately categorised by the previous weak classifier. e final robust classifier uses a weighted combination of the weak classifiers to determine the best threshold classification function for each feature.
Algorithm 1 [50] shows the AdaBoost technique used to solve a prediction problem.

Performance Metric.
In this study, the classical methods for model evaluation are used. e accuracy (ACC) and Cohen's kappa index were used to evaluate rockburst classification. A confusion matrix is commonly used as a standard for evaluating the performance of a classification model on training and testing datasets with known true values.
X � where m represents the number of rockburst levels, ×11 is the number of features accurately predicted for the class m, and xmm denotes the number of class features categorised to class n. Based on the confusion matrix, ACC and Cohen's kappa index are determined by (2) and (3), respectively.
A kappa value of less than 0.4 indicates poor agreement, while a value of 0.4 and above indicates good agreement [51,52]. e ideal condition of a good model should have high ACC and kappa values simultaneously.

Model Development
e proposed model for predicting rockburst intensity grade was developed using Orange software. e model structure was based on an input matrix (x) defined by x � {σ θ , σ c , σ t , W et } that provided the predictor variables, while the target variable (y) is rockburst intensity grade. During every modeling step, the most critical task is to identify the appropriate size of the training and testing datasets. e way data is split into training and research sets has a substantial impact on data mining results [53]. e main goal of the statistical analysis was to ensure that the statistical properties of the subsets were as similar as possible, and thus they represented the same statistical population. e dataset was divided into 137 (83%) training cases and 28 (17%) test cases and was kept the same as that of Zhao and Chen [41] owing to fairly evaluating the predictive performance of the proposed AdaBoost model in this work. e AdaBoost model was tuned to optimize the rockburst intensity grade prediction using a trial and error method. Figure 3 depicts the prediction model's construction.
Most ML algorithms have hyperparameters that need to be tuned [54]. e optimization method attempts to find the appropriate parameters for the AdaBoost model in order to achieve the best prediction accuracy. Some critical hyperparameters in the AdaBoost model are tuned in this study, as shown in Table 3. e definitions of these hyperparameters are also clarified in Table 3. First, the search range of different hyperparameters values is specified randomly and then adjusted throughout the trials until the best fitness metrics shown in Table 3 were reached.

Results and Discussion
% Update the distribution, where Z t is a normalized factor with enables D t+1 to be a distribution end.

Applications in Real-World Rockburst Prediction.
Two real-world examples are analyzed using our proposed AdaBoost-based rockburst prediction model to study the effectiveness and feasibility in engineering practice applications. Five rockburst events in two different tunnel projects were predicted by the AdaBoost model. e field data were collected from available literature, including the Duoxiongla tunnel [58] and Anlu tunnel [59]. e prediction outcomes are summarized in Table 6, indicating that the rock burst intensity was predicted correctly for all cases. e prediction results in the real-world rockburst prediction cases are basically consistent with this strong-to-moderate intensity grading.
is study proves that the AdaBoost model is a robust alternative tool for the rockburst intensity grade assessment, and it can be successfully applied in various geotechnical engineering projects.

Limitations and Future Works
e proposed approach obtains desirable prediction results, although some limitations should be addressed in the future.
(1) e dataset is relatively small and unbalanced. e prediction performance of ML algorithms is heavily affected by the number and quality of dataset. Generally, if the dataset is small, the generalization and reliability of model would be influenced, although AdaBoost algorithm works well with small datasets. Furthermore, the suggested model is open to further development, and the accumulation of more data will lead to a much better prediction capacity. It is important to note that the validity of the proposed model is limited by the data ranges used to train the model. (2) Other variables may have an effect on the prediction outcomes. Numerous factors influence the risk of a rockburst, including rock properties, energy, excavation depth, and support structure, among others.
Although the four indicators used in this study can define the required conditions for rockburst hazard assessment to some degree, some other indicators, such as the buried depth of the tunnel, failure duration time, and energy-based burst potential index, may also have an impact on rockburst hazard. As a consequence, it is crucial to look into the effects of these variables on the prediction outcomes.

Conclusions
In this paper, the AdaBoost classifier's application was investigated to evaluate the rockburst phenomenon. e predictive variables for the AdaBoost model included the main effective parameters on rockburst, i.e., σ θ , σ c , σ t , and W et .
e model was developed and tested using Orange software based on a database including 165 rockburst case histories. e main conclusion points are summarized below: (1) e comparison of proposed model efficiency and previously developed empirical criteria revealed that the AdaBoost model is remarkably better than empirical criteria with accuracy and kappa value obtained as 100% and 1.00, respectively. (2) e proposed approach was compared with other machine learning-based models in the literature. e comparison results have shown that the prediction accuracy of the proposed model is as adequate as other techniques such as CNN and RT models. (3) Two real-world rockburst examples are used to verify the proposed model's accuracy and effectiveness. It can be concluded that the AdaBoost classifier is a feasible and efficient tool for the classification of rockburst intensity grades. e proposed model can be applied in the initial stages of underground projects and the rockburst phenomenon can be assessed by an acceptable accuracy, which can reduce casualties due to rockburst. Data Availability e data that support the findings of this study are openly available in [33,40].