A comparative study of empirical and ensemble machine learning algorithms in predicting air over-pressure in open-pit coal mine

Abstract

This study aims to take into account the feasibility of three ensemble machine learning algorithms for predicting blast-induced air over-pressure (AOp) in open-pit mine, including gradient boosting machine (GBM), random forest (RF), and Cubist. An empirical technique was also applied to predict AOp and compared with those of the ensemble models. To employ this study, 146 events of blast were investigated with 80% of the total database (approximately 118 blasting events) being used for developing the models, whereas the rest (20% ~ 28 blasts) were used to validate the models’ accuracy. RMSE, MAE, and R2 were used as performance indices for evaluating the reliability of the models. The findings revealed that the ensemble models yielded more precise accuracy than those of the empirical model. Of the ensemble models, the Cubist model provided better performance than those of RF and GBM models with RMSE, MAE, and R2 of 2.483, 0.976, and 0.956, respectively, whereas the RF and GBM models provided poorer accuracy with an RMSE of 2.579, 2.721; R2 of 0.953, 0.950, and MAE of 1.103, 1.498, respectively. In contrast, the empirical model was interpreted as the poorest model with an RMSE of 4.448, R2 of 0.872, and MAE of 3.719. In addition, other findings indicated that explosive charge capacity, spacing, stemming, monitoring distance, and air humidity were the most important inputs for the AOp predictive models using artificial intelligence.

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Acta Geophysica
https://doi.org/10.1007/s11600-019-00396-x
RESEARCH ARTICLE - SOLID EARTH SCIENCES
A comparative study ofempirical andensemble machine learning
algorithms inpredicting air over‑pressure inopen‑pit coal mine
HoangNguyen1,2 · Xuan‑NamBui1,2· Quang‑HieuTran1· PhamVanHoa1· Dinh‑AnNguyen1· LeThiThuHoa1·
Qui‑ThaoLe1,2· Ngoc‑HoanDo1,3· TranDinhBao1· Hoang‑BacBui4,5· HosseinMoayedi6,7
Received: 9 April 2019 / Accepted: 26 December 2019
© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2020
Abstract
This study aims to take into account the feasibility of three ensemble machine learning algorithms for predicting blast-induced
air over-pressure (AOp) in open-pit mine, including gradient boosting machine (GBM), random forest (RF), and Cubist.
An empirical technique was also applied to predict AOp and compared with those of the ensemble models. To employ this
study, 146 events of blast were investigated with 80% of the total database (approximately 118 blasting events) being used
for developing the models, whereas the rest (20% ~ 28 blasts) were used to validate the models’ accuracy. RMSE, MAE, and
R2 were used as performance indices for evaluating the reliability of the models. The findings revealed that the ensemble
models yielded more precise accuracy than those of the empirical model. Of the ensemble models, the Cubist model provided
better performance than those of RF and GBM models with RMSE, MAE, and R2 of 2.483, 0.976, and 0.956, respectively,
whereas the RF and GBM models provided poorer accuracy with an RMSE of 2.579, 2.721; R2 of 0.953, 0.950, and MAE of
1.103, 1.498, respectively. In contrast, the empirical model was interpreted as the poorest model with an RMSE of 4.448, R2
of 0.872, and MAE of 3.719. In addition, other findings indicated that explosive charge capacity, spacing, stemming, moni-
toring distance, and air humidity were the most important inputs for the AOp predictive models using artificial intelligence.
Keywords Air over-pressure· Open-pit mine· Ensemble algorithm· Random forest· Gradient boosting machine· Cubist
* Xuan-Nam Bui
buixuannam@humg.edu.vn
1 Department ofSurface Mining, Hanoi University ofMining
andGeology, 18 Vien St., Duc Thang ward, Bac Tu Liem
Dist., Hanoi, Vietnam
2 Center forMining, Electro-Mechanical Research, Hanoi
University ofMining andGeology, 18 Vien St., Duc Thang
Ward, BacTuLiemDist.,Hanoi, Vietnam
3 Faculty ofMining, Saint-Petersburg Mining University,
SaintPetersburg, Russia
4 Faculty ofGeosciences andGeoengineering, Hanoi
University ofMining andGeology, 18 Vien St., Duc Thang
ward, Bac Tu Liem Dist., Hanoi, Vietnam
5 Center forExcellence inAnalysis andExperiment, Hanoi
University ofMining andGeology, 18 Vien St., Duc Thang
ward, Bac Tu Liem Dist., Hanoi, Vietnam
6 Department forManagement ofScience andTechnology
Development, Ton Duc Thang University, HoChiMinhCity,
Vietnam
7 Faculty ofCivil Engineering, Ton Duc Thang University,
HoChiMinhCity, Vietnam
Introduction
One of the most effective techniques for fragmenting rock
in open-pit mines is blasting because of its advantages from
technical and economical points of view. It can generate a
large amount of rock for the subsequent operations (e.g.,
loading, transporting) with low cost (Jhanwar etal. 1999).
However, its ill side influences are not negligible, includ-
ing air over-pressure (AOp), flyrock, ground vibration, dust,
and fumes (Nguyen etal. 2018; Zhang etal. 2019; Shang
etal. 2019) (Fig.1). Of those, AOp is considered as a dan-
gerous phenomenon, which is needed to control (Alel etal.
2018; Armaghani etal. 2015; Khandelwal and Kankar 2011;

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Khandelwal and Singh 2005; Nguyen and Bui 2018; Nguyen
etal. 2017, 2018).
For predicting blast-induced AOp, several scholars pro-
posed empirical equations, as listed in Table1. Accordingly,
the relationship between monitoring distance (D) and explo-
sive charge per delay/maximum explosive charge capacity
(W) was established through empirical equations.
Of the empirical equations in Table1, the equation No.1
(USBM empirical equation) has been widely used to pre-
dict blast-induced AOp (Siskind etal. 1980; Hustrulid 1999;
Walter 1990; Kuzu etal. 2009; Hasanipanah etal. 2016;
Mahdiyar etal. 2018). However, the accuracy of empiri-
cal models was often not high due to some drawbacks of
them, as discussed by Hasanipanah etal. (Hasanipanah etal.
2016), Mahdiyar etal. (Mahdiyar etal. 2018).
Recently, artificial intelligence (AI) became more appro-
priate and highly used in different fields, especially min-
ing technology (Pierini etal. 2013; Rahmani and Farnood
Ahmadi 2018; Montahaei and Oskooi 2014; Wiszniowski
2016; Naganna and Deka 2019; Piasecki etal. 2018; Nguyen
etal. 2019a, b, c, d; Zhou etal. 2019; Asteris etal. 2016;
Asteris and Nikoo 2019). In order to estimate blast-induced
AOp, Hajihassani etal. (Hajihassani etal. 2014) trained
an artificial neural network (ANN) by an evolutionary
algorithm (Particle Swarm Optimization—PSO), namely
ANN-based PSO model, using 62 AOp datasets. Their
results showed that the ANN-based PSO model performed
properly in forecasting blast-caused AOp with the correla-
tion coefficient (CC) of 0.94. In another study, Mohamad
etal. (Mohamad etal. 2016) predicted blast-induced AOp
by an ANN-based genetic algorithm (GA), abbreviated as
GA-ANN, using 76 blasting events. Empirical and ANN
models were also provided to predict AOp and compared
them to those of the GA-ANN model. Their results inter-
preted that the GA-ANN model performed better than those
of empirical and ANN models. Hasanipanah etal. (2016)
used ANFIS, ANN, fuzzy system (FS) techniques, and an
empirical equation for estimating blast-induced AOp. For
developing these models, a group of 77 blasting events was
used in their study. Their findings revealed that the ANFIS
system was the most superior approach in forecasting AOp.
Amiri etal. (2016) also introduced a new combination of
k-nearest neighbors (KNN) and ANN models to predict AOp
using 75 blasting events. Their results indicated that the
KNN-ANN model predicted better than those of ANN and
empirical models. Mahdiyar etal. (2018) also proposed three
AI models to estimate AOp based on PSO algorithm and 80
blasting events. The results indicated that the PSO model
estimated AOp very well with a promising result. Nguyen
etal. (2019) also discovered a hybrid model based on clus-
tering technique and backpropagation neural networks. In
another study, Nguyen etal. (2018) performed a comparative
study of MLP neural nets, BRNN, and HYFIS in estimating
AOp. Their results showed that the MLP neural nets were
the most superior model than those of the other models.
They also developed another AI model based on ensemble
of ANN and RF (i.e., ANNs-RF) for predicting AOp with
an excellent result (Nguyen and Bui 2018). By the use of
optimization algorithm, AminShokravi etal. (2018) dem-
onstrated the potential of the PSO algorithm in predicting
AOp with high accuracy. Bui etal. (2019) also evaluated the
Fig. 1 Illustration of the
undesirable effects of blasting
operations
Table 1 Several empirical equations for predicting blast-induced AOp
k and β are the coefficients of the study site; SD denotes the scaled
distance (mkg0.33)
No. References Empirical model
1 Siskind etal. (1980)
AOp =
k
(SD)−𝛽
2 Loder (1985)
AOp
=
140 3
√
W
200
D
3 McKenzie (1990)
AOp =165 −24 log (
R
∕
D
1∕3)

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performance of different AI techniques for estimating AOp
in an open-pit coal mine, including RF, boosted regression
trees, KNN, SVR, GP (Gaussian process), BART (Bayes-
ian additive regression trees), and ANN. They claimed the
feasibility of the mentioned AI techniques. ANN model was
recommended as the best model in their study for estimating
AOp. Zhou etal. (2019) also developed a novel AI model
for forecasting AOp based on FS and firefly algorithm (FA),
namely FS-FA model. A high prediction level was confirmed
in their study for the proposed FS-FA model. Gao etal.
(2019) also took into account the performance of the GA
and group method of data handling (GMDH) for forecasting
AOp. Eventually, their GA-GMDH model was proposed as
a robust technique with an excellent agreement.
A review of the literature shows that blast-induced AOp
predictive models were developed and proposed quite well.
Nevertheless, they cannot apply and represent other loca-
tions/regions, whereas the effects of blast-induced AOp
are different from country to country. In this study, blast-
induced AOp was assessed and predicted by three ensemble
machine learning algorithms, including RF, GBM (gradient
boosting machine), and Cubist. An empirical model was also
developed to predict and compare with those of ensemble
models herein.
The rest of the present work is arranged as follows:
“Study area and data used” section presents the study site
and characteristics of the dataset; “Methods” section pro-
vides the principle of the approaches used; the preparation of
the dataset is introduced in “Preparing the dataset” section;
the development of the models is shown in “Establishing the
AOp predictive models” section; some performance indices
are presented in “Performance indices” section; and “Results
and discussion” section reports the results and discussion.
Finally, “Conclusions and remarks” section presents our
conclusions of this work.
Study area anddata used
Study area
Herein, the Deo Nai open-pit coal mine, which is located
in Quang Ninh Province, Vietnam, was selected as a spe-
cial study area. It lies within latitudes 21°001′00″N and
21°020′00″N and between longitudes 107°018′15″E and
107°019′20″E (Fig.2). The coal store is 42.5Mt, and pro-
duction capacity is 2.5Mt/year; overburden is 20–30 Mt/
year. (Vinacomin 2015). With a large amount of overburden
per year and the hardness of rock being high (from 10 to
14 according to Protodiakonov’s classification (Bach etal.
2012)), blasting was selected as a proper technique for frag-
menting rock in the mine. ANFO is the main explosive used
in this mine, with the amount being up to 20 tons. The non-
electric delay blasting method was applied to fragment rock
with the diameter of borehole of 105mm. The nearest dis-
tance from blasts to the residential area is about 400–500m.
Hence, the ill side effects of blasts are substantial.
Data collection andits characteristics
In this study, 146 events of blasting were investigated,
with ten parameters being measured. Of the ten parame-
ters, nine first variables were used as the inputs to predict
the outcome of AOp, including powder factor (q), maxi-
mum explosive charge capacity (W), burden (B), length of
stemming (T), spacing (S), number of rows per blast (N),
Fig. 2 Location of the study site

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monitoring distance (D), bench height (H), and air humidity
(RH) (Fig.3). For monitoring blast-induced AOp, an instru-
ment of Instantel (Canada) was utilized with a microphone.
According to the guideline of the producer, the microphone
should be placed at the sensitive locations and straightfor-
ward with the direction of blasts (Fig.4). Also, a handheld
GPS was used to define D. RH was measured by Kanomax
2212 air quality meter (Japan). It is one of the most influ-
ential parameters for estimating AOp, which was recom-
mended by Nguyen etal. (2018). The remaining inputs were
extracted from the design of blasts. Table2 shows the char-
acteristics of inputs and output in this work.
Methods
Empirical
Empirical is one of the methods which is utilized to predict
blast-produced AOp in open-cast mine. Of the empirical
methods (as shown in Table1), USBM empirical formula
was widely applied to predict AOp in open-pit mines (Haji-
hassani etal. 2014; Armaghani etal. 2016). For example,
Kuzu etal. (2009) used the empirical equation of the USBM
to forecast AOp with a promising result. In the USBM
equation, the scaled distance was illustrated through W and
D as follows:
Subsequently, the USBM empirical equation can be com-
puted according to Eq.2:
where
𝛾
and
𝛼
are the site factors.
Random forest
Decision tree (DT) is one of the branches of AI, and RF
belongs to the DT branch, which was developed by Brei-
man (2001). As a robust DT model, RF can solve both
classification and regression cases. Based on the differ-
ent results of the trees, this method has been suggested
as a suitable method for achieving predictive precision
(Vigneau etal. 2018). In addition, this method used the
results of the exclusive tree in the forest to present the best
outcome. As a voter, each tree contributes its predictions
for the final decision of RF (Gao etal. 2018). On the other
hand, RF ensembles the predictions of the tree and making
a final decision based on the obtained results. The key of
(1)
SD =DW −0.33
(2)
AOp =𝛾(SD)−𝛼
Fig. 3 Structure of the borehole
and its parameters. a Parameters
of blast design and b a combi-
nation plan of blasting

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the RF for regression is presented in three steps: (i) pro-
ducing bootstrap instances as the tree number in the for-
est (ntree) according to the database, (ii) expand a suitable
regression tree for any bootstrap instance using random
sampling of the estimators (mtry) (Dou etal. 2019). Of
those variables, choose the most appropriate split and (iii)
estimate recent perception using ensemble the estimated
amounts of the trees (ntree). For the regression issue (i.e.,
estimating AOp), the mean amount of the estimated values
in the single tree is applied.
According to the training dataset, a prediction of the
error rate may be calculated according to the two follow-
ing steps:
1 At any iteration of bootstrap, estimate the non-informa-
tion in the instance of bootstrap using the tree grown
with the bootstrap instance, named “out-of-bag” (OOB).
2 Collect the OOB estimations and predict the error.
More details of the RF algorithm can be explained in
(Nguyen and Bui 2018; Breiman 2001; Bui etal. 2019).
Gradient boosting machine
GBM is an ensemble approach that is suggested by Fried-
man (2002). It is an improved boosting algorithm and can
be applied for regression, as well as classification problems
(Friedman 2001). The boosting algorithm can be described
according to the pseudocode in Fig.5 (Friedman 2002).
Subsequently, Friedman (Friedman 1999) provided a par-
ticular algorithm based on the platform of boosting algo-
rithm for various loss criteria like least squares:
Least absolute deviation:
(3)
𝜓
(y
AOp
,T)=(y
AOp
−T)
2
Fig. 4 Data collection for predicting AOp in this work
Table 2 Inputs, output, and their properties
Categories W H B S T
Minimum 1376 13.00 7.500 7.400 6.200
Mean 13183 14.37 8.064 7.814 6.879
Maximum 24171 16.00 8.500 8.200 7.500
Standard deviation 4685.73 0.937 0.332 0.213 0.362
Categories q N RH DAOp
Minimum 0.3500 2.000 76.00 180 92.26
Mean 0.4178 3.486 85.16 469 123.19
Maximum 0.4800 5.000 94.00 726 147.00
Standard deviation 0.035 1.216 4.817 159.896 11.912

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Huber M:
(4)
𝜓
(yAOp ,T)=
|
|
|
yAOp −T
|
|
|
(5)
𝜓
(yAOp ,T)=(yAOp −T)21(
|
|
|
yAOp −T
|
|
|
≤𝛿)+2𝛿(
|
|
|
yAOp −T
|
|
|
−𝛿∕2)1(
|
|
|
yAOp −T
|
|
|
>𝛿
)
Let
{
y
i.AOp
,x
i.AOp }N
1
as the entire training information
instance and
{
𝜋(i)}
N
i
stands for random permutation for
integers
{1, …,N}
. Then, a random subsample of size
̃
N<N
is predicted by
{
y𝜋
(
i
.AOp)
,x𝜋
(
i
.AOp)}̃
N
1
. The pseudoc-
ode of the GBM algorithm is described in Fig.6 (Fried-
man 2002).
Cubist
Cubist algorithm (Rulequest 2016a, b) is one of the rule-
based algorithms, which is utilized to make predictive mod-
els according to the input information analysis, whereas the
See5/C5.0 method that is able to solve classification prob-
lems (Quinlan 2004), the Cubist can solve regression issues
very well. The outcomes from the Cubist model are more
priority than those of linear regression models. In addition,
it is simpler than the ANN model (Rulequest 2016a, b).
The Cubist model is expanded based on Quinlan’s M5
model tree (Quinlan 1992) with the capability to apply for
thousands of input characteristics (Rulequest 2016a, b). In
the Cubist model, the targets depend on the inputs, and it
is computed based on the rule(s). A combination of differ-
ent conditions with a linear function is conducted for these
rules. The related linear function is used to estimate the
outputproperly if a rule takes into consideration the whole
requirements. The Cubist algorithm can perform multiple
situations at the same time and then detect various distinct
linear functions for estimating output. Therefore, Cubist can
generate various models and mixes them based on the rules
which are determined before. Developing multiple models
with different rules and their combinations can assist Cubist
model in attaining much higher levels of precision. More
details of Cubist can be found in Refs. (Nguyen etal. 2019;
Kuhn etal. 2012; Drzewiecki 2016; Kuhn etal. 2018; Bernat
and Drzewiecki 2015).
Preparing thedataset
In this section, the AOp dataset is prepared as a geospatial
database by the ArcGIS software; 146 records of blast were
divided into two sections according to the recommendations
of previous researchers (Nguyen etal. 2019a, b); 80% of the
total datasets (approximate 118 events of blast) are selected
by randomly and applied as the training dataset to build the
AOp predictive models. The rest (28 records of the blast)
were utilized as the testing dataset for evaluating the AOp
models’ performance. Summary of training and testing data-
sets is shown in Tables3 and 4, respectively.
Fig. 5 Pseudocode of the boosting algorithm
Fig. 6 Pseudocode of the GBM algorithm

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Establishing theAOp predictive models
For the empirical model, 118 blasting events (training data-
set) were used to compute the site factors k and β. Microsoft
Excel 2016 was used to define k and β by the use of a multi-
variate regression analysis technique. As a result, k = 208.26
and β = 0.183 are the optimal values of the USBM model
for predicting AOp. The USBM model (in this case) can be
described as:
For the development of the ensemble models, the ten-
fold cross-validation method, along with three repetitions,
is utilized to avoid overfitting. Furthermore, the ensemble
models used the same training as those used for the devel-
opment of the USBM model. To develop the RF model, the
number of trees was set equal to 2000 to meet the diversity
of the forest (Nguyen etal. 2017). Then, the random pre-
dictor (mtry) was tuned to get the optimal performance of
the RF model. Herein, mtry was set in the range of 1–50 as
a trial and error procedure. Ultimately, an optimal value
of mtry was determined for the RF model with mtry = 41.
Figure7 shows the efficiency of the RF model for estimat-
ing AOp.
Unlike the RF model, the GBM model used four
parameters to control the model’s performance, such
as the number of trees, max tree depth, shrinkage, and
n.minobsinnode. A grid search method was also applied
to define the optimal parameters for the GBM model. As
a result, number of trees =500, max tree depth =4, shrink-
age =0.1, and n.minobsinnode =5 were the best values for
the GBM model in this case. GBM’s performance is illus-
trated in Fig.8.
To develop the Cubist model, committees and neighbors
were used as the key parameters. The results indicated
that the Cubist model reached optimal performance with
committees of 80 and neighbors of 0, as shown in Fig.9.
Performance indices
For evaluating the efficiency of the AOp predictive mod-
els, three performance indices were computed, including
mean absolute error (MAE), coefficient of determination
(R2), and root mean square error (RMSE).
(6)
AOp =208.026(SD)−0.183
Table 3 Summary of the training dataset
Categories W H B S T
Minimum 1376 13.00 7.500 7.400 6.200
Mean 13036 14.36 8.054 7.807 6.877
Maximum 24171 16.00 8.500 8.200 7.500
Standard deviation 4735.744 0.949 0.332 0.209 0.367
Categories q N RH DAOp
Minimum 0.350 2.000 76.00 180 92.26
Mean 0.417 3.466 85.22 473.4 122.98
Maximum 0.480 5.000 94.00 726 147.00
Standard deviation 0.035 1.217 4.665 158.747 11.999
Table 4 Summary of the testing dataset
Categories W H B S T
Minimum 1376 13.00 7.500 7.400 6.200
Mean 13183 14.37 8.064 7.814 6.879
Maximum 24171 16.00 8.500 8.200 7.500
Standard deviation 4497.849 0.903 0.330 0.233 0.349
Categories q N RH DAOp
Minimum 0.3500 2.000 76.00 180 92.26
Mean 0.4178 3.486 85.16 469 123.19
Maximum 0.4800 5.000 94.00 726 147.00
Standard deviation 0.034 1.230 5.497 166.333 11.712
Fig. 7 RF modeling for predic-
tion of AOp

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Fig. 8 GBM modeling for
prediction of AOp
Fig. 9 Cubist modeling for
prediction of AOp

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n is the total number of observations.
yAOp
is recorded val-
ues,
̂yAOp
is predicted values, and
̄yAOp
is the average of
recorded values.
Results anddiscussion
Once the models were well established, their performance
is evaluated and checked through the performance indices
according to Eqs.(7–9). Table5 shows the results, as well
as the performance of the ensemble and empirical models
on training/testing datasets.
(7)
RMSE
=




1
n
n

i=1
(yAOp −̂yAOp )
2
(8)
R
2=1−
∑
i(yAOp −̂yAOp )
2
∑i
(y
AOp
−̄y
AOp
)2
(9)
MAE
=1
n
n
∑
i=1|
|
|
yAOp −̂yAOp
|
|
|
It can be easy to recognize that the ensemble models
performed very well in this study. On the training data-
set, the ensemble models obtained high performance with
RMSE of 1.739–2.199; R2 of 0.968–0.970; and MAE of
0.980–1.451. The similar results were also observed on
the testing dataset for the ensemble models with RMSE of
2.483–2.721, R2 of 0.950–0.956, and MAE of 0.976–1.498.
In contrast to the ensemble models, the empirical model
provided the poorest efficiency (i.e., RMSE = 4.838, 4.448;
Table 5 Performance indices
of the ensemble and empirical
models
Method Training dataset Testing dataset
RMSE R2MAE RMSE R2MAE
Empirical 4.838 0.871 4.101 4.448 0.872 3.719
RF 2.030 0.968 1.143 2.592 0.953 1.103
GBM 2.199 0.970 1.451 2.721 0.950 1.498
Cubist 1.739 0.969 0.980 2.483 0.956 0.976
Fig. 10 Relationship of meas-
ured and predicted AOp on the
ensemble and empirical models
Fig. 11 Sensitivity analysis of the parameters

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R2 = 0.871, 0.872; and MAE = 4.101, 3.719, on the training
and testing datasets, respectively). Among three ensemble
models (RF, GBM, Cubist), the Cubist model was the most
dominant model with an RMSE of 2.483, R2 of 0.956, and
MAE of 0.976 on the testing database. Figure10 shows the
efficiency of the AOp predictive models in testing process.
Although the efficiency of the ensemble models is better
than the empirical model in this study, however, the practi-
cal technique used only two input parameters (W and D) to
estimate blast-induced AOp, whereas the ensemble models
used nine input parameters for predicting the same objective.
Therefore, a sensitivity analysis procedure was conducted to
assess the effect of the inputs on the AOp predictive model
(Tarantola etal. 2007; Saltelli etal. 2010). The results
showed that W, S, T, RH, and D were the most influential
parameters on the AOp predictive model, as illustrated in
Fig.11.
Conclusions andremarks
Based on the obtained results of this study, some conclusions
and remarks are withdrawn as follows:
• Ensemble machine learning algorithms are good can-
didates for predicting blast-induced AOp than those of
empirical methods, especially RF, GBM, and Cubist
models. They should be considered to control the unde-
sirable effects of blasting in practical engineering.
• Cubist is a robust ensemble AI model for predicting AOp
in this study. Its accuracy can ensure safety for the sur-
rounding environment. However, it should be reconsid-
ered in other locations/areas.
• RF and GBM are also good AI techniques for predict-
ing AOp. However, its performance seems not to satisfy.
Therefore, they need to improve and further research.
• For predicting AOp, it is not only W and D, but also S,
T, and RH are the important inputs for the development
of the AOp predictive models. They should be carefully
collected to ensure the accuracy level of the models.
Acknowledgements This research was supported by Hanoi University
of Mining and Geology (HUMG), Hanoi, Vietnam; Duy Tan Univer-
sity, Da Nang, Vietnam; and the Center for Mining, Electro-Mechanical
research of HUMG.
Compliance with ethical standards
Conflict of interest Authors declare that they have no conflict of inter-
est
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