Wang et al 2021

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J. Cent. South Univ. (2021) 28: 527−542 
DOI: https://doi.org/10.1007/s11771-021-4619-8 
 
 
Rockburst prediction in hard rock mines developing bagging and 
boosting tree-based ensemble techniques 
 
WANG Shi-ming(王世鸣)1, ZHOU Jian(周健)2, LI Chuan-qi(李传奇)2, 
Danial Jahed ARMAGHANI3, LI Xi-bing(李夕兵)2, Hani S. MITRI4 
 
1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China; 
2. School of Resources and Safety Engineering, Central South University, Changsha 410083, China; 
3. Department of Civil Engineering, Faculty of Engineering, University of Malaya, 
50603 Kuala Lumpur, Malaysia; 
4. Department of Mining and Materials Engineering, McGill University, Montreal, Canada 
 
© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2021 
 
 
Abstract: Rockburst prediction is of vital significance to the design and construction of underground hard rock mines. 
A rockburst database consisting of 102 case histories, i.e., 1998−2011 period data from 14 hard rock mines was 
examined for rockburst prediction in burst-prone mines by three tree-based ensemble methods. The dataset was 
examined with six widely accepted indices which are: the maximum tangential stress around the excavation boundary 
(MTS), uniaxial compressive strength (UCS) and uniaxial tensile strength (UTS) of the intact rock, stress concentration 
factor (SCF), rock brittleness index (BI), and strain energy storage index (EEI). Two boosting (AdaBoost.M1, SAMME) 
and bagging algorithms with classification trees as baseline classifier on ability to learn rockburst were evaluated. The 
available dataset was randomly divided into training set (2/3 of whole datasets) and testing set (the remaining datasets). 
Repeated 10-fold cross validation (CV) was applied as the validation method for tuning the hyper-parameters. The 
margin analysis and the variable relative importance were employed to analyze some characteristics of the ensembles. 
According to 10-fold CV, the accuracy analysis of rockburst dataset demonstrated that the best prediction method for 
the potential of rockburst is bagging when compared to AdaBoost.M1, SAMME algorithms and empirical criteria 
methods. 
 
Key words: rockburst; hard rock; prediction; bagging; boosting; ensemble learning 
 
Cite this article as: WANG Shi-ming, ZHOU Jian, LI Chuan-qi, Danial Jahed ARMAGHANI, LI Xi-bing, Hani S. 
MITRI. Rockburst prediction in hard rock mines developing bagging and boosting tree-based ensemble techniques [J]. 
Journal of Central South University, 2021, 28(2): 527−542. DOI: https://doi.org/10.1007/s11771-021-4619-8. 
 
 
 
1 Introduction 
 
Rockburst as a common geological and 
dynamic hazard commonly occurs in the 
underground hard rock mines [1−3]. The 
occurrence of rockburst is caused by the release of 
accumulated energy in the rock in a violent way [4]. 
Rockbursts occurred suddenly and intensely which 
usually results in considerable damage to 
equipment/infrastructure and may even bring about 
injuries and fatalities [5−7]. Nowadays, with the 
scarcity of minerals in the shallower formations, 
mining must move farther from the surface and 
 
Foundation item: Projects(41807259, 51604109) supported by the National Natural Science Foundation of China; Project(2020CX040) 
supported by the Innovation-Driven Project of Central South University, China; Project(2018JJ3693) supported by the 
Natural Science Foundation of Hunan Province, China 
Received date: 2020-07-13; Accepted date: 2020-09-04 
Corresponding author: ZHOU Jian, PhD, Associate Professor; Tel: +86-18175162802; E-mail: csujzhou@hotmail.com; ORCID: https:// 
orcid.org/0000-0003-4769-4487 
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more widely, which could make the problem of 
rockburst worse [2, 8]. It is imperative to know 
whether rock excavations would burst or not. Thus, 
the rockburst prediction with high accuracy is 
crucial for reducing the risk of rockburst hazards 
and improving the level of mining safety in 
preliminary design. Although it is not easy to 
precisely forecast the rockburst during activies of 
mining, in the past several decades, extensive 
rockburst studies have been implemented in China, 
South Africa, Australia, Canada, and many other 
countries [2, 3, 9−13]. Many researchers have 
published a great deal of valuable results by ways 
of the electromagnetic radiation method, 
microseismicity monitoring, empirical criteria 
classification, in situ testing methods, as well as 
probabilistic methods on predicting rockbursts 
[1, 2, 5, 10, 13−15]. Moreover, various types of 
empirical methods and preliminary & qualitative 
judgment prediction methods investigated the 
mechanical characters of rockbursts through 
combining local monitoring data and laboratory 
tests, and are often applied in practice engineering 
design. These collective efforts have greatly 
improved the understanding of rockbursts. As 
pointed out by ZHOU et al [2], however, universal 
and practical rockburst criteria are rather difficult 
endorsed in hard rock mines. 
 Besides the abovementioned works, many 
statistical machine learning (ML)-based approaches 
for rockburst prediction have been investigated 
during recent decades. Most cited data-driven 
researches are reported in Figure 1 [2, 5, 13, 16−23]. 
Conventional discriminant analysis (DA)-based 
techniques such as Mahalanobis distance DA [18], 
Fisher DA [19], quadratic and partial least squares 
DA [13] are among the most commonly-used for 
rockburst classification based on real case histories. 
However, the disadvantage of the DA classifier is 
that it is suitable for a class of data with a unimodal 
Gaussian distribution and therefore, can only be 
successfully applied to such scenarios. Moreover, 
many supervised learning (SL) techniques including 
adaptive neural fuzzy inference system (ANFIS), 
artificial neural network (ANN), decision tree, 
random forest (RF), naive Bayes (NB), K-nearest 
neighbor (KNN), support vector machine (SVM), 
and gradient boosting machine (GBM) have been 
applied in this field. These models have been 
confirmed the ability to operate on sets of input and 
 
 
Figure 1 Most cited applications of data-driven approaches for rockburst prediction 
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output data from rockburst case histories. 
Compared with traditional prediction models, the 
greatest strength of SL modeling techniques is their 
high efficiency to capture the nonlinear 
relationships between features of the dataset instead 
of assuming a preconceived interaction between 
inputs and output (s). Although these methods are 
able to achieve satisfactory results, they have 
several identified shortcomings. For example, the 
potential shortcomings of ANN include slow 
learning rate and falls into local minima [24]. The 
modeling with ANFIS model and fining the best 
membership functions and rules of inputs is 
time-consuming [21, 25−27]. The SVM classifier is 
limited by the increase in the number of training 
vectors which lead to computation and storage 
requirements increased rapidly [28]. In large 
processingtime, kNN algorithm has some 
limitations to classify a new unknown observation 
and difficult to improve the classification accuracy 
when deal with the multidimensional data [29]. 
Unable to learn the interaction between two 
predictors/features under the conditional 
independence assumption is the main disadvantage 
of NB [2]. Although many rockburst estimation 
models have already been described and compared 
by previous researchers, developing the accurate 
and reliable rockburst predictive model still poses 
considerable challenge for burst-prone grounds 
[2, 5, 21, 30−36]. Moreover, many other models for 
forecasting the rockburst can be considered an 
efficient and valuable tool to be applied in other 
geological and mining engineering applications. 
Particularly, some engineers and scholars are 
increasingly interested in combining the output of 
several basic classification techniques into one 
integrated output using data mining technology, 
integrated learning and soft computing methods to 
improve classification accuracy [13, 37−40]. 
However, the integration method has less- 
contribution to the rockburst classification than 
other fields and requires more extensive 
experimental works. 
 In order to fill the research gap, this paper 
investigates a comparative study on the 
effectiveness of ensemble learning in rockburst 
classification developing two ensemble methods, 
i.e., bagging [41], and boosting [42, 43]. Above 
methods can be conducted by developing a series of 
predictive models which are based on a given 
algorithm named the base classifier and vote on all 
models in the set to make predictions on new 
observations. Classification and regression trees 
(CART) conduct by BREIMAN et al [44], is one of 
the most favoured algorithms for constructing 
classification trees and is usually used as a base 
classifier in a classification problem. According to 
above discussion, the objective of this investigation 
is the contribution to examine the ability of three 
CART-based ensemble algorithms for the potential 
of rockbursts prediction in hard rock mines. To 
accomplish this goal, a research methodology was 
developed for the comparison of the performance of 
different tree-based ensemble learning algorithms, 
including bagging, boosting and CART. These 
algorithms were particularly selected due to their 
attractions and attentions in various fields of 
science and engineering. However, to the best 
knowledge of the authors, they have not been 
carefully compared with each other for prediction 
of rockbursts in hard rock mines. The rest of this 
paper includes some explanations regarding 
established database and existing empirical models; 
then, rockburst prediction in burst-prone mines 
using boosting and bagging tree-based ensemble 
methods are developed and examined; margin 
analysis and the variable relative importance are 
also employed to analyze the performance of 
proposed models. 
 
2 Database of rockbursts and empirical 
models 
 
2.1 Calibration of database 
 The original database of rockbursts was 
reported in the study conducted by ZHOU et al [5] 
with 132 case histories and updated by ZHOU et al 
[13] with 246 case histories from many kinds of 
underground projects (i.e., underground 
powerhouse, cavern and tunnel of hydropower 
station, railway and road tunnel, coal and hard rock 
mines). These databases have been widely- 
employed in previous researches [1, 20, 21, 32, 
45−47]. With the aim of examining the performance 
of the developed tree-based ensemble approaches 
for estimating the potential of rockbursts in 
burst-prone ground, the data utilized in the present 
investigation consists of 102 cases of rockburst 
events collected from 14 underground hard rock 
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mines with published research works, and is part of 
previous database and all the data sources have 
been referenced [5, 13]. Field data obtained from 
Italian (Raibl lead zinc mine) mine and Russia mine 
(Soviet Rasvumchorr workings) besides China hard 
rock mines including Baima Iron Mine, Chengchao 
Iron Mine, Beiminghe Iron Mine, Maluping 
Phosphate Mine, Xincheng Gold Mine, Linlong 
Gold Mine, Fankou Lead-Zinc Mine, Jinchuan 
Nickel Mine, Tonglushan Copper Mine, 
Dongguashan Copper Mine and Hongtoushan 
Copper Mine. Out of all the parameters involved in 
formulating the present model, the values of 
parameters are used directly as available in the 
database. 
 
2.2 Data description 
 The boxplot of the initial dataset is provided in 
Figure 2(a). Obviously, the median is not in the 
center of the box for most of the data labels, which 
means that the distribution of most data labels is not 
symmetric (Figure 2(a)). Note that the circles with 
blue color indicating outliers. All dependent 
indicators have some outliers expect for the uniaxial 
compressive strength (UCS or σc) of the rock, the 
maximum tangential stress (σθ=MTS) around the 
opening and the stress concentration factor 
(SCF=σθ/σc) for H rockburst intensity and, the 
uniaxial tensile strength (UTS or σt) of the rock and 
BI (rock brittleness index (BI=σc/σt)) for L 
rockburst intensity, UCS, Wet or EEI (elastic strain 
energy index) and SCF for M rockburst intensity, 
UTS, SCF and MTS for N rockburst intensity. The 
distribution of the rockburst events used in this 
work after 1998 is shown in Figure 2(b) as a pie 
chart demonstrating the proportion of the four types 
of rockburst intensity in underground mines, 
categorized as none (N, 17 cases), low (L, 26 cases), 
moderate (M, 26 cases) and high (H, 33 cases). 
Obviously, this dataset contains a few class 
imbalance or sampling bias. The relevant input 
indicators used in the development of the rockburst 
prediction model with general statistical 
characteristics are shown in Figure 2(c) (i.e., range, 
mean, standard deviation, median, skew and 
kurtosis). Figure 3 shows the scatterplot matrix in 
the upper half whereby RPC is the rockburst 
prediction classification. The matrix shows 
bivariate scatterplots with LOWESS smooth curves 
and Pearson correlation values as a side effect [48], 
while the two-dimension kernel density estimates 
and contours are in the lower half, and the 
histograms for each parameter are depicted on the 
diagonal. From Figure 3, it is evident that the 
parameter MTS is correlated with SCF. In addition, 
the joint contours of the kernel density estimation 
between these paired indicators is obviously 
asymmetric under most circumstances. 
 
2.3 Results on rockburst full data by empirical 
criteria methods 
 Several conventional empirical criteria such as 
Russenes criterion [49]; EEI [2, 50], SCF [51], BI 
[51, 52], GB50487−2008 and measurable values of 
rockburst (MVR) [53] are applied to evaluating the 
rockburst potential of 102 case histories. The 
applied empirical criteria associated with their 
predictive performance on the whole dataset are 
presented in Table 1. The predictive accuracy of 
above methods is 25.4% (BI by ZHANG et al [52]) 
to 58.82% (MVR by ZHANG et al [53]) of the 
whole dataset and lower than 60% of the filtered 
 
 
Figure 2 Data description and visualization of combined rockburst database for tree-based ensemble modeling 
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Figure 3 Scatterplot matrix of rockburst samples for six parameters 
 
Table 1 Classification results of rockbursts with whole dataset using conventional empirical criteria 
Empirical method Equation 
Classification criterion Predictive 
accuracy/%None Low Moderate High 
Russenes criterion[49] SCF=σθ/σc ≤0.2 0.2−0.3 0.3−0.55 >0.55 43.14 
Strain energy storage index [50] EEI or Wet 5.0 58.82 
Strain energy storage index [2] EEI or Wet 10.0 49.04 
Stress concentration factor [2] SCF=σθ/σc 0.7 54.90 
GB50487−2008 [2] BI=σc/σt >40 40−26.7 26.7−14.5 7 4−7 2−4 22 25.49 
Measurable value of rockburst MVR [53] MVR 0.75 50.00 
Note: MVR=tanh{[0.1648 (σθ/σc)3.064 (BI)−0.4625 (Wet)2.672](1/3.6)}. 
 
data. Apparently, the accuracy of rockburst 
estimates from empirical criteria is often not 
satisfactory due to the influence of various 
conditions on rockburst and its complexity of the 
features. Fundamentally, these empirical methods 
come from their own specific engineering practice, 
which leads to the strong dependence of these 
methods on the specific engineering background. In 
this paper, 102 rockburst cases in 14 mines were 
collected, and thus the case engineering types were 
extensive, and the locations were quite different. 
Moreover, the characteristics of the empirical 
method itself determine that it is not a universal 
method. Therefore, it can be concluded that the 
abovementioned empirical criteria cannot achieve 
desirable prediction results from the predictive 
accuracy on these rockburst cases. 
 
3 Methodology 
 
3.1 Classification and regression trees (CART) 
 Recursive partitioning [55] is one of the 
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typical decision tree methods. Herein we used 
CART which is a form of binary recursive 
partitioning [44]. The developing of CART model 
comes from the recursive partitioning of dataset: the 
constitutive model is defined as a tree structure 
whose nodes are associated with data splitting along 
one variable [56, 57]. 
 
3.2 Bagging 
 BREIMAN [41] introduced bagging 
(Bootstrap aggregating for short) ensemble learning 
technology, which can improve classification 
accuracy and generalize data patterns. Based on the 
training set (Sn), Q bootstrap samples (Sq) are 
obtained, where q=1, 2, … , Q. Getting these 
bootstrap samples requires drawing the same 
number of elements as the original set (n in this 
case) to replace. Partial guidance samples may 
reject or at least filter partial noise observations, 
which means that the classifiers in these sets behave 
better than the classifiers constructed in the original 
sets. Therefore, bagging is conducive to the 
establishment of a better classifier for training sets 
with noisy observations. Bagging follows three 
simple steps (see Figure 4(a)) [37, 58]: 
 1) m samples were randomly created from the 
training data set. Some slightly different data sets 
are allowed to be created in the bootstrapped 
samples, but the distribution should be the same as 
the entire training set; 
 2) The classifier built for each bootstrap 
sample comes from training an unpruned and single 
regression tree; 
 3) The average prediction value is obtained 
before the average individual predictions of these 
multiple classifiers. 
 
3.3 Boosting 
 FREUND and SCHAPIRE [42] imposed a 
boosting ensemble learning technology to improve 
classification accuracy by transforming a set of 
weak classifiers into strong classifiers. Boosting 
provides sequential learning of the predictors, and 
the major procedure of boosting algorithm is 
illustrated in Figure 4(b). In the proposed boosting 
algorithm for multi-class classification problems, 
two typical boosting algorithms, called 
AdaBoost.M1 [37, 42] and SAMME [43, 58], have 
been chosen due to their simplicity and natural 
extensions. 
 1) AdaBoost.M1 algorithm 
 AdaBoost.M1 is based on AdaBoost which 
was first tried on multiple classification problems 
and has been widely-used [37, 42, 58]. Given a 
training set Sn={(x1; y1), …, (xi, yi), …, (xn, yn)} 
where y i t akes va lues in 1 , 2 , … , k . Each 
 
 
Figure 4 Approach to bagging and boosting-based ensemble methodologies: (a) Bagging; (b) Boosting 
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observation xi gets the corresponding weight wq(i) 
and the initial value is set to 1/n, and then the initial 
value is updated with the number of steps. 
Constructing a basic classifier Cq(xi) on this new 
training set (Sq) and apply it to each training 
example. The eq indicates the error of the classifiers 
and is calculated as follows [42]: 
 
1
( ) ( ( ) )
n
q q q i i
i
e w i I C x y

  (1) 
 
where I(•) is the indicator function which outputs 1 
indicating that the internal expression is true, 
whereas an output of 0 indicates that the internal 
expression is false. 
 The update of weights requires a constant q to 
be calculated by the error of the classifier in the qth 
iteration. According to FREUND and SCHAPIRE 
[42], q=ln[(1–eq)/eq]. However, BREIMAN [59] 
used q=0.5ln[(1–eq)/eq]. Thus, the new weight for 
the (q+1)th iteration will be as follows: 
 
wq+1(i)=wq(i)exp[αqI(Cq(xi)≠yi)] (2) 
 
 The process step is repeated with the change of 
q, q=1, 2, …, Q. The ensemble classifier calculates 
the voting weights and values of each class. Then, 
the class with the highest vote is assigned. 
Specifically, 
 
1
( ) argmax ( ( ) )
Q
f i j Y q q i
q
C x I C x j

  (3) 
 
 2) SAMME algorithm 
 SAMME (short for stagewise additive 
modeling with loss function of multi-class 
exponential), is the second boosting algorithm 
implemented herein. Its theoretical development is 
first introduced by ZHU et al [43]. Note that, there 
is no difference between the SAMME algorithm 
and AdaBoost.M1 except for the calculation of the 
alpha constant based on the number of classes. 
 Because of this modification, the SAMME 
algorithm only requires that (1−eq)>1/k in order for 
the alpha constant to be positive and the weight will 
update to follow the right direction [58], that is 
αq=ln(k−1)+ln[(1−eq)/eq]. Therefore, the accuracy 
of any weak classifier should be higher than the 
accuracy of random guess (1/k) rather than the fixed 
value 0.5, which is an appropriate requirement for 
the two-class case but very demanding for the 
multi-class one. 
3.4 Margin analysis 
 The margin of an object is closely related to 
the certainty of its classification and is determined 
according to the difference between the support of 
the true label and the maximum support of the false 
label [38, 58, 60]. For the k class, the margin of 
each sample xi is obtained by the votes of each class 
j in the final ensemble, which are called the support 
degree or posterior probability of different classes 
μj(xi), j=1, 2, …, k as: 
 
( ) ( ) max ( )i c i j i
j c
m x x x 

  (4) 
where c is the correct class of xi and 
1
( ) 1.
k
j i
j
x

 
 Once the data distribution D is determined, the 
margin distribution graph (MDG) is defined as the 
fraction of instances whose margin is at most λ as a 
function of λ∈[−1, 1] [60]. 
 
R(λ)=|Dλ|/|D| (5) 
 
where Dλ={x:margin(x)≤λ}, λ∈[−1, 1], |•| 
represents size operation, and R(λ)∈[0, 1]. 
 Therefore, negative classified examples could 
only appear in all misclassified examples, while 
positive classified examples only exist in correctly 
classified examples [61]. The margin value for 
positive classified observations with high 
confidence will approach 1. On the other hand, the 
sample margin value with uncertain classification is 
small. 
 
3.5 Evaluation criteria 
 Accuracy is a major concern metric in ML and 
the classification accuracy rate (CAR) is taken as 
the evaluation criterion of the prediction ability of 
the ensemble tree-based ensemble algorithm for 
rockburst data [62], which is defined as the 
percentage of the amount of casestruly predicted in 
the classification model to the total amount of cases, 
the main evaluation criterion. The CAR expression 
is as follows: 
1
1
CAR 100%
C
ii
i
x
n 
 
  
 
 (6) 
 
4 Tree-based ensemble methods for 
rockburst classification 
 
4.1 Indicator analysis 
 By evaluating the occurring rockburst cases 
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and considering their main results and theoretical 
methods, a series of single indices or standards for 
evaluating the occurrence and intensity of 
rockbursts have been put forward to analyze the 
rockburst phenomena from multiple angles [2, 5, 
13]. Empirical criterion method for rockburst 
estimation is primarily used stress/strength, 
brittleness, energy and critical depth-based 
approaches [2, 5]. The index characteristic of rock 
often guides and decides the planning and design of 
civil engineering and mining excavation and is also 
closely related to the rockburst phenomenon in hard 
rock mines [60, 61]. Therefore, it is generally 
accepted in many mines to use appropriate rock 
index to identify rockburst tendency [62] 
particularly UCS and UTS of intact rock are 
commonly taken as rockburst potential indicator 
[5, 20]. In addition, MTS is another rockburst 
indicator because it can reflect the effect of 
hydrologic conditions (mainly groundwater), rock 
stress environment, opening shape and diameter 
factors on rockbursts around the opening [13, 49, 
63−67]. Meanwhile, the EEI index defined by 
KIDYBINSKIA [51] is another key indicator of 
inducing rockburst in hard rock mine. MARTIN 
et al [68] mentioned that rockbursts in brittle 
hardrock may occur when the SCF reached at some 
values. Additionally, the rock brittleness, BI, as 
inherent physicomechanical property of rocks 
usually, is applied to estimating the potential of 
rockbursts [2, 69, 70]. Besides, other engineers 
considered the microseismic events for degree of 
clustering is proportional with the decrease of 
fractal dimension [70]. However, data are needed 
on the microseismic event distribution and the 
proximity of the events to the seismic source 
(hypocenter) which is difficult to be available in our 
dataset. Based on these considerations, the input 
parameters studied in this paper are the six 
indicators (MTS, UCS, UTS, SCF, BI and EEI), 
which are also the main indicators for quantitative 
assessment of rockburst activities hard rock mines. 
Additionally, in previous data-driven researches 
equal widely used these indicators [5, 13, 20, 21, 
32, 46, 62]. Meanwhile, the potential of rockbursts 
is defined using four intensities: none (N), low (L), 
medium (M) and high (H). RUSSENES [49] and 
ZHOU et al [5, 13] described the classification of 
rockbursts in the combined database. In addition, 
three different input models are studied which 
combine the above indices with the tree-based 
ensemble method to evaluate rock burst, and the 
traditional parameters of rock burst classification 
are selected and labeled ‘√’ in Table 2. Model I of 
traditional variables includes MTS, UCS, UTS and 
EEI. Model II of traditional variables includes SCF, 
BI and EEI. Model III of traditional variables 
includes MTS, UCS, UTS, SCF, BI and EEI. 
 
Table 2 Three different models for rockburst assessment 
with respect to different input attributes combination 
Model number MTS UCS UTS SCF BI Wet
Model I √ √ √ √ 
Model II √ √ √ 
Model III √ √ √ √ √ √ 
 
4.2 Model development and analysis 
 This section examines the feasibility of the two 
boosting (AdaBoost.M1 and SAMME) and bagging 
classification algorithms using the rockburst dataset, 
where the CART method is taken as baseline 
classifier. Figure 5 demonstrates the basic ML 
terms and procedures for building a tree-based 
ensemble system. In ML, classifier is used to 
predict class of new items which must be tested 
after performance in a given dataset. In this regard, 
two validation methods were used to guarantee the 
comparability and to verify the proposed models 
[13, 71]: (a) Train-test split, which means that the 
rockburst dataset D is split into two disjointed sets 
Dtrain (for training) and Dtest (for testing), and (b) 
k-fold cross-validation (CV) which can effectively 
avoid over-learning, and the final result is more 
convincing than other forms [13]. The original 
dataset is randomly classified for a known category 
rockburst into two subsets: Dtrain, which is required 
to estimate model parameters and construct the each 
rockburst classifier model. In this regard, 2/3 of the 
available data (68 datasets of all 102 data sets) were 
considered to form a training dataset; and Dtest is an 
external validation set that tests the performance 
and predictive capabilities of each final model. The 
test data set contains the remaining 34 data. 
Meanwhile, the adabag package [58] is applied and 
implemented BREIMAN’s [41] bagging algorithm, 
FREUND and SCHAPIRE’s [42] Adaboost.M1 
algorithm and ZHU’s [43] Adaboost-SAMME 
algori thm with classi f icat ion t rees as base 
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Figure 5 Research architectures of tree-based ensemble approach for rockburst prediction 
 
classifiers using the rpart package [72] within the R 
environment [73]. Thus, many experiments were 
performed in R environment associated with 
rockburst data and tree-based ensemble methods. 
These algorithms typically use parameter settings 
based on default or recommended values. 
Furthermore, variable relative importance and 
margins analysis are implemented to explain some 
characteristics of the ensembles. With the aim of 
showing the advantages of using ensembles, results 
from a single CART tree as the baseline classifier 
are compared to those obtained with two Boostings 
and bagging approaches. Considering the number of 
rockbursts classes, trees with the maximum depth 
of 5 and complexity parameter of −1 are used both 
in the single and the ensemble cases, and the 
ensembles consist of 250 trees. 
 With the aim of comparing the error of the four 
methods (CART, Bagging, Adaboost.M1 and 
SAMME), the mean result is calculated after 
10 runs, as described in Table 3. For instance, it can 
be seen that the single CART tree model II with a 
mean test error of 33.82% is outperformed by 
Adaboost.M1 and SAMME, 29.41% and 29.41%, 
respectively, and particularly by bagging with a 
much lower error (26.47%) maybe because bagging 
can reduce the variance error. Similarly, results can 
be found in model I and model III. Apparently, 
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Table 3 Testing error for 250 iterations with tree models 
Method 
Model I Model II Model III 
Train 
set 
Test 
set 
 
Train 
set 
Test 
set 
 
Train 
set 
Test
set 
CART 0.2794 0.3235 0.2611 0.3382 0.2819 0.3382
Bagging 0 0.2647 0.0312 0.2647 0.0514 0.0882
AdaBoost.M1 0 0.3235 0 0.2941 0 0.1176
SAMME 0 0.3235 0 0.2941 0 0.0882
 
there is not a significant difference between the 
Adaboost.M1 and SAMME methods for the three 
models. Taking model III as an example, Figure 6 
shows the error development process of training set 
and testing set. It is obvious from the figure that the 
error values of training set and testing set are 
positively correlated with the number of iterations, 
and the final error of the test set is less than half of 
the error at the beginning of the iteration. In 
particular, after the number of iterations reaches the 
range 50−100, the error between the training set and 
the testing set tends to stabilize. The performance 
(CAR) of the test set fell within the range of 
67.65% to 91.18% across the twelve models. For 
tree-based ensemble classifiers, the confusion 
matrix is also a common way to assess theeffectiveness of the proposed models with 
independent test set (see Figure 7) [13, 74]. 
 As mentioned above, margin distribution 
 
 
 
 
Figure 7 Confusion matrices and associated rockburst classifier accuracies for tree-based ensemble prediction models 
based on independent test set 
Figure 6 Models error vs number of trees 
for model III: (a) Bagging; (b) Adaboost. 
M1; (c) SAMME 
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information can be reflected to provide useful 
insights and suggestions for ensemble learning 
methods with the help of margin analysis [60], and 
the margins of these ensemble classifiers were 
obtained by the margin () function in the adabag R 
package [58]. With the aiming of achiveing the 
visualization of results, KUNCHEVA [75] 
introduced MDG model to demonstrate the 
cumulative distribution of the margins under a 
given dataset. Hence, the x-axis is the margin (m) as 
defined in Eq. (4) and the y-axis represents the 
amount of points where the margin is not greater 
than m based on Eq. (5). If the cumulative graph is 
a vertical line at m=1, it means that all points are 
truly classified and have the greatest possible 
certainty. The purpose of MDGs of the training set 
(coloured in orange) and the test set (coloured in 
blue) is to perform a more detailed margin analysis 
of the three ensemble learning methods as described 
above. Figure 8 presents the cumulative distribution 
of margins for the bagging and two boosting 
(AdaBoost.M1 and SAMME) classifiers developed 
on the rockburst datasets in this application. In 
particular, the cumulative distribution of marginal 
value 0 (y-axis) in the MDG represents the 
classification error rate. Obvirously, AdaBoost.M1 
and SAMME are always positive due to the null 
training error as illustrated by the dotted line in 
Figure 8(a). It should also be indicated that almost 
13% and 8% of the observations in bagging, for 
training set and testing set, respectively, achieve a 
maximum margin of 1, which is outstanding 
considering the large number of classes. This 
observation is also true for the results reported in 
Table 3. It is hoped that the analysis presented 
in this study will provide some interesting 
observations and unique insights into the ensemble 
learning of marginal analysis. 
 Overall, the following observations are made 
from Table 3 and Figure 8: 1) for the three 
tree-based ensemble techniques, the performance 
(CAR) of testing set performance fell within the 
range of 67.65% to 91.18% across the twelve 
models; 2) model III with six input indicators is the 
best one when compared with the results from the 
two other models with the subsets of attributes; and 
3) in the context of determination of rockburst 
occurrence and the potential of rockburst, these 
methods can be trained to learn the relationships 
between the stress condition, rock brittleness and 
 
 
Figure 8 Margin distribution graph for three models with 
bagging, Adaboost.M1 and SAMME methods over 
rockburst dataset: (a) Model I; (b) Model II; (c) Model 
III 
 
strain energy characteristics with the rockburst 
activity, requiring no need to know in advance of 
the form of the relationship between them. It is 
important to note that these observations are only 
based on the dataset used in this work. Whether or 
not such observations can be made to other 
rockburst datasets is a question that would 
necessitate that the new dataset be reanalyzed. 
 
4.3 Relative importance of discriminating 
features 
 Unlike unascertained mathematics, fuzzy 
mathematics, extension theory and cloud model, the 
developing bagging and boosting tree-based 
ensemble techniques do not need to determine the 
weight of each index via analytic hierarchy process 
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538
 
and/or information entropy. It is worth noting that 
bagging and boosting ensemble learning methods 
can provide relative importance of predictive 
variables based on their predictability of rockbursts 
potential. For this goal, the measure of importance 
considers not only the Gini yield given by a feature 
in each tree, but also the weights of trees in the 
bagging, AdaBoost.M1 and SAMME cases. 
Figure 9 shows the variables ranked by its relative 
importance value for each rockburst model with 
 
 
Figure 9 Variables relative importance for each model: 
(a) Model I; (b) Model II; (c) Model III 
bagging and the two boosting ensemble classifiers. 
In terms of model I (Figure 9(a)), the most sensitive 
factor in the indicators is EEI, followed by the 
indicators MTS, UTS, UCS; In terms of model II 
(Figure 9(b)), EEI has the greatest impact on results 
when making the same changes compared to other 
indicators, followed by the indicators SCF, BI; In 
terms of model III (Figure 9(c)), EEI is still the 
most sensitive factor among the indicators, 
followed by the indicators MTS, SCF, UTS, UCS, 
and BI. Findings demonstrate that among the 
rockburst classification prediction indicators, EEI is 
also the most relevant predictor. Destress blasting 
techniques commonly used to avoid high-stress 
concentrations around underground openings have 
been proven very effective to mitigate the risks of 
rockburst [76]. 
 
4.4 Limitations 
 There are some limitations regarding this work 
that will be perfected in future research. First, the 
proposed ensemble method is designed for general 
purpose but is only validated on 102 datasets. 
Additional datasets can be used for further 
validation. Secondly, class imbalance and sampling 
bias are two representative important factors of 
model uncertainty that have an impact on the 
predictive probability of rockburst classification 
models and should be addressed in future studies. 
Thirdly, tuning hyper-parameters of ensemble 
models and combining more baseline classifier 
models are not addressed for further improvement 
on the performance of ensemble techniques in this 
work. Meanwhile, the rockburst is associated with 
in-situ stress, rock property, structure of rock mass, 
and dynamic disturbance effect on rockbursts [2, 4, 
63, 64]. Thus it is very difficult to predict time- 
space distribution of rockburst exactly. Moreover, 
note that only strainburst type in hard rock mines is 
developed in this work, other types of rockburst 
such as fault-slip are not addressed due to data 
limitation. Also, other additional indicators such as 
peak particle velocity (PPV) [60, 61] at the time of 
rockburst and local geological joint or fractures 
[62, 77] may be applied to improving the 
performance of rockburst potential prediction; 
however, collecting such data can be cumbersome. 
Finally, the “black box” feature of the ensemble 
algorithm is a dark cloud that hangs over the 
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complex relationship between the interpreted 
response and the predictor variable. 
 
5 Conclusions 
 
 Models for forecasting rockburst with high 
accuracy can be beneficial tools for mitigating the 
risk of rockburst hazards and strengthening mine 
safety in burst-prone grounds. In this work, six 
traditional rockburst indicators were measured and 
three CART-based models for ensemble approaches 
were presented and compared for the prediction of 
rockburst in hard rock mines can be beneficial tools 
for work in burst-prone grounds. A data set of 102 
rockburst cases compiled from 14 hard rock mines 
is applied to developing the proposed models. 
Findings reveal that the performance of the 
proposed models with combination of the indicators 
with ensemble methods works much better than that 
with eight empirical criteria. Bagging was 
particularly found to be the best model among all 
three ensemble methods, while thereis not a big 
difference between the two boosting methods from 
the aspect of accurancy. These results illustrated 
that ensemble learning approaches can be taken as a 
viable tool for identifying rockburst. Meanwhile, 
bagging and two boosting methods demonstrate that 
the EEI index is the most relevant indicator among 
the features for the task of rockburst classification 
prediction. In summary, the main work of this paper 
was to provide a relatively reliable model for 
rockburst prediction. To further enhance the 
accuracy of prediction models, the authors hope to 
fuse the results obtained from different empirical 
criteria and ML methods in future work with more 
rockburst case histories. 
 
Contributors 
 WANG Shi-ming and ZHOU Jian provided the 
concept and wrote the original draft of manuscript. 
ZHOU Jian, LI Chuan-qi and Danial Jahed 
ARMAGHANI collected, visualized and analyzed 
dataset, conducted the models. LI Xi-bing and Hani 
S. MITRI edited the draft of manuscript. 
 
Conflict of interest 
 The authors declare that they have no conflicts 
of interest. 
 
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(Edited by YANG Hua) 
 
 
中文导读 
 
用基于树的 Bagging 和 Boosting 集成技术预测硬岩矿山岩爆 
 
摘要：岩爆预测对地下硬岩矿山的设计和施工至关重要。使用三种基于树的集成方法，对由 102 个历
史案例(即 1998—2011 年期间 14 个硬岩矿山数据)组成的岩爆数据库进行了检查，以用于有岩爆倾向
矿井的岩爆预测。该岩爆数据集包含六个广泛接受的倾向性指标，即：开挖边界周围的最大切向应力
(MTS)、完整岩石的单轴抗压强度(UCS)和单轴抗拉强度(UTS)、应力集中系数(SCF)、岩石脆性指数(BI)
和应变能储存指数(EEI)。以分类树作为基准分类器的两种 Boosting 算法(AdaBoost.M1，SAMME)和
Bagging 算法进行了评估，评估了它们学习岩爆的能力。将可用数据集随机分为训练集(整个数据集的
2/3)和测试集(其余数据集)。采用重复 10 倍交叉验证(CV)作为调整模型超参数的验证方法，并利用边
际分析和变量相对重要性分析了各集成学习模型特征。根据重复 10 倍交叉验证结果，对岩爆数据集
的精度分析表明，与 AdaBoost.M1、SAMME 算法和岩爆经验判据相比，Bagging 方法是预测硬岩矿
山岩爆的最佳方法。 
 
关键词：岩爆；硬岩；预测；Bagging 方法；Boosting 方法；集成学习