Application of the k - Nearest neighbors algorithm for predicting blast - induced ground vibration in open - pit coal mines: a case study

22 Journal of Mining and Earth Sciences Vol. 61, Issue 6 (2020) 22 - 29 
Application of the k - nearest neighbors algorithm for 
predicting blast - induced ground vibration in open - 
pit coal mines: a case study 
Hoang Nguyen 1, 2, * 
1 Department of Surface Mining, Mining Faculty, Hanoi University of Mining and Geology, Vietnam 
2 Center for Mining, Electro - Mechanical Research, Hanoi University of Mining and Geology, Vietnam 
ARTICLE INFO 
ABSTRACT 
Article history: 
Received 15st Aug. 2020 
Accepted 05th Dec. 2020 
Available online 31st Dec. 2020 
 Blasting is considered as one of the most effective methods for rock 
fragmentation in open - pit mines. However, its side effects are significant, 
especially blast - induced ground vibration. Therefore, this study aims to 
develop and apply artificial intelligence in predicting blast - induced 
ground vibration in open - pit mines. Indeed, the k - nearest neighbors 
(KNN) algorithm was taken into account and developed for predicting 
blast - induced ground vibration at the Deo Nai open - pit coal mine 
(Vietnam) as a case study. An empirical model (i.e., USBM) was also 
developed to compare with the developed KNN model aiming to highlight 
the advantage of the KNN model. Accordingly, 194 blasting events were 
collected and analyzed for this aim. This database was then divided into 
two parts, 80% for training and 20% for testing. The MinMax scale and 
10 - fold cross - validation techniques were applied to improve the 
accuracy, as well as avoid overfitting of the KNN model. Root - mean - 
squared error (RMSE) and determination coefficient (R2) were used as the 
performance metrics for models’ evaluation and comparison purposes. 
The results indicated that the KNN model yielded better superior 
performance than those of the USBM empirical model with an RMSE of 
1,157 and R2 of 0,967. In contrast, the USBM model only provided a weak 
performance with an RMSE of 4,205 and R2 of 0,416. With the obtained 
results, the KNN can be introduced as a potential artificial intelligence 
model for predicting and controlling blast - induced ground vibration in 
practical engineering, especially at the Deo Nai open - pit coal mine. 
Copyright © 2020 Hanoi University of Mining and Geology. All rights reserved. 
Keywords: 
Artificial intelligence, 
Ground vibration, 
K - nearest neighbors, 
Machine learning, 
Peak particle velocity. 
1. Introduction 
Blasting is one of the most common methods 
for rock fragmentation in open - pit mines since its 
advantages in terms of economic and technical 
(Nguyen, 2019). However, according to scientists, 
_____________________ 
*Corresponding author 
E - mail: nguyenhoang@humg.edu.vn 
DOI: 10.46326/JMES.2020.61(6).03 
 Hoang Nguyen /Journal of Mining and Earth Sciences 61 (6), 22 - 29 23 
it is not the entire of the explosive energy that is 
useful for rock fragmentation. Only 25÷30% of the 
total explosive energy was used for this aim, and 
the remaining energy is wasted (Hasanipanah et 
al. 2017). It generated undesirable effects, such as 
ground vibration, air over - pressure, fly - rock, 
back - break, and air pollution (Monjezi et al. 
2010; Khandelwal, 2011; Armaghani et al. 2018; 
Fang et al. 2019a; Nguyen and Bui, 2019; Nguyen 
et al. 2020). Of those, blast - induced ground 
vibration is considered as the most hazardous 
phenomenon. It can make the vibration of 
buildings, bench/slope instability, and make 
discomposure for the residential (Bui et al. 2019; 
2020). Therefore, accurate prediction of blast - 
induced ground vibration is one of the efforts of 
researchers and engineers aiming to reduce the 
side effects on the surrounding environment. 
In order to evaluate the intensity of blast - 
induced ground vibration, peak particle velocity 
(PPV) is often used as a critical parameter in 
blasting operations. It can be estimated by 
empirical equations or artificial intelligence 
models (Armaghani et al. 2015; Ding et al. 2019; 
Fang et al. 2019a; Fang et al. 2019b; Nguyen et al. 
2019a). Indeed, in recent years, AI techniques 
have been widely applied in predicting PPV. Many 
researchers proposed and applied different AI 
techniques for this aim. Monjezi et al. (2013) 
developed an artificial neural network (ANN) to 
predict PPV with a promising result. In another 
study, Armaghani et al. (2014) developed a hybrid 
model based on ANN and an optimization 
algorithm (i.e., particle swarm optimization - PSO) 
for predicting PPV, called PSO - ANN model. Their 
results are positive, and the PSO - ANN model was 
proposed as a potential model in blasting 
operations. In another study, they applied the 
imperialist competitive algorithm (ICA) for 
predicting PPV, and the positive results were 
reported as well (Armaghani et al. 2018). In 
another study, Ding et al. (2019) proposed a novel 
hybrid model, namely ICA - XGBoost, for 
predicting PPV. They claimed that this model 
could predict PPV with high accuracy. Hajihassani 
et al. (2015) also proposed a potential model for 
predicting PPV in open - pit mines, namely ICA - 
ANN. Finally, they introduced that this model can 
predict PPV with high reliability, and it can be 
used instead of empirical models. In addition, 
many other studies were developed or proposed 
AI techniques for predicting PPV with high 
performance (Nguyen et al. 2019b; Shang et al. 
2019; Yang et al. 2019; Zhang et al. 2019). 
A review of the literature shows that AI 
techniques have been successfully applied in 
predicting PPV in open - pit mines. Nonetheless, 
they have not been applied anywhere. In this 
study, the k - nearest neighbors (KNN) algorithm 
was investigated and applied to predict PPV at the 
Deo Nai open - pit coal mines (Vietnam). An 
empirical model was also taken into account and 
compared with the KNN model to have a 
comprehensive assessment of PPV predi ... holes with the 
diameters in the range of 105 mm to 250 mm 
were applied in this mine for blasting, and the 
millisecond - delay blasting method was applied. 
For the data collection, this study collected 
eight parameters, including maximum explosive 
charge per delay (Q), the hole depth (L), burden 
(W), spacing (B), stemming (LB), powder factor 
(q), monitoring distance (D), and PPV. Of those, 
the first seven parameters were used as the input 
parameters, and the last one (i.e., PPV) was used 
as the output parameter. Herein, the PPV was 
Figure 1. Location and a view of the Deo Nai open - pit coal mine (Vietnam). 
 Hoang Nguyen /Journal of Mining and Earth Sciences 61 (6), 22 - 29 25 
measured by the blastmate III or micromate 
(Instantel - Canada), D was calculated based on 
the locations of blast sites and measurement 
points that were pointed by a GPS receiver. The 
remaining parameters were extracted from blast 
patterns. Finally, 194 blasting events were 
recorded, and the dataset was summarized in 
Figure 2. 
4. Development of the models 
In this section, the details of the models’ 
development are presented. As mentioned in the 
introduction section, this study aims at applying 
the KNN algorithm for predicting PPV at the Deo 
Nai open - pit coal mine. Also, an empirical model 
was developed to compare with the KNN model. 
Before developing the models, the dataset 
was divided into two sections: 80% of the whole 
dataset was used for training the models, and the 
remaining 20% of the dataset was used for testing
 the developed models. It is worth noting that this 
task was performed randomly. 
For the development of the KNN model, the 
number of “k nearest neighbors” (k) and their 
distance (d) were used as the main parameter to 
control the accuracy of the KNN model. Also, 
different kernel functions were applied during 
training the KNN model aiming to map the dataset 
to higher feature space, such as inv, rectangular, 
triangular, triweight, biweight, cos, epanechnikov, 
and gaussian. In order to avoid overfitting of the 
KNN model, 10 - fold cross - validation technique, 
and the MinMax scale [0,1] were applied. A trial 
and error procedure with the maximum 
neighbors in the range of 1 to 52, their distance in 
the range of 0 to 3, was applied to find out the best 
KNN model. Finally, one hundred KNN models 
were developed, as shown in Figure 3. The best 
KNN model was then defined with k = 35, d = 
0,215, and the inv kernel function (Figure 3).
Figure 2. Summary of the dataset used in this study. 
26 Hoang Nguyen /Journal of Mining and Earth Sciences 61 (6), 22 - 29 
For the empirical model, the U.S Bureau of 
Mines (USBM) empirical equation (Duvall and 
Petkof 1958) was applied for estimating PPV, as 
follows: 
Q
PPV
D

(4) 
where Q stands for the maximum explosive 
charge per delay (in Kg); D stands for the 
monitoring distance (m); 𝜆 and 𝛼 were the site 
parameters and were considered using the 
multivariate regression analysis. Finally, the 
USBM empirical equation was defined as follows: 
0.524
Q
PPV 1.493
D
(5) 
5. Assessment of the models 
Once the KNN and empirical models were 
well - developed based on the training dataset, the 
testing dataset was used to validate the 
performance of the models. To evaluate the 
performance as well as the accuracy of the 
models, root - mean - squared error (RMSE), 
determination coefficient (R2) and mean absolute 
error (MAE) were used as the performance 
metrics, and they are calculated as follow: 
2
1
1
ˆRMSE ( )
n
PPVi PPVi
i
y y
n 
 
(6) 
Figure 3. Performance of the KNN models with different parameters and kernel functions. 
 Hoang Nguyen /Journal of Mining and Earth Sciences 61 (6), 22 - 29 27 
2
2 1
2
1
ˆ
R 1
n
PPVi PPVi
i
n
PPVi PPVi
i
y y
y y


(7) 
2
1
1
R
n
PPVi PPVi
i
y y
n 
 
(8) 
where n stands for a total number of 
observations; 𝛾𝑃𝑃𝑉𝑖 is the measured PPV, 𝛾𝑃𝑃𝑉𝑖 is 
predicted PPV, and 𝛾𝑃𝑃𝑉𝑖 is the mean of 𝛾𝑃𝑃𝑉𝑖 . The 
results of the KNN and USBM empirical models 
are shown in Table 1. 
From the results in Table 1, it can be seen that 
the KNN model provided much better 
performance than those of the USBM model with 
an RMSE of 0,759 and R2 of 0,974 on the training 
dataset, and RMSE of 1,157 and R2 of 0,967 on the 
testing dataset. In contrast, the USBM empirical 
model yielded a bad performance with an RMSE 
of 3,619; R2 of 0,461; and MAE of 2,794 on the 
training dataset and RMSE of 4,205; R2 of 0,416, 
and MAE of 3,361 on the testing dataset. For 
further assessment of the models, the chart of the 
correlation between measured and predicted 
PPVs by the KNN and USBM empirical models was 
used, as shown in Figure 4. 
Based on the observations in Figure 4, it is 
clear that the correlation between measured and 
predicted PPVs by the KNN model is much better 
than those of the USBM model. On the other hand, 
most of the predicted PPVs are inside of the 80% 
confidence level of the KNN model. Whereas, most 
of the predicted PPVs of the USBM are outside of 
the 80% confidence level. This finding indicated 
that the USBM empirical model is not suitable for 
predicting PPV in this case study. In contrast, the 
KNN model is a robust AI model for predicting 
PPV at the Deo Nai open - pit coal mine with a 
promising result (i.e., RMSE = 1,157, R2 = 0,967, 
and MAE = 0,602). 
6. Conclusion 
Blasting is an effective method for 
fragmenting rock; however, its side effects are 
significant for the surrounding environment, 
especially blast - induced ground vibration. This 
study investigated and developed a KNN model 
for predicting blast - induced ground vibration in 
open - pit mines, and it was applied to the Deo Nai 
open - pit coal mine (Vietnam) as a case study. 
Model 
Training dataset Testing dataset 
RMSE R2 MAE RMSE R2 MAE 
KNN 0,759 0,974 0,467 1,157 0,967 0,602 
USBM 3,619 0,461 2,794 4,205 0,416 3,361 
Table 1. Results of the KNN and USBM models based on both training and testing datasets. 
Figure 4. Correlation between measured and predicted PPVs by the KNN and USBM models. 
28 Hoang Nguyen /Journal of Mining and Earth Sciences 61 (6), 22 - 29 
The results revealed that the KNN model 
could predict PPV with high reliability, and it can 
be used in practical engineering to predict and 
control blast - induced ground vibration. The 
USBM empirical model or other empirical 
equations should be further studied in the future 
to improve the accuracy in predicting PPV in open 
- pit mines. 
Acknowledgments 
This paper was supported by the Ministry of 
Education and Training (MOET) in Viet Nam 
under grant number B2020 - MDA - 16. The 
authors also thank the Center for Mining, Electro - 
Mechanical research of Hanoi University of 
Mining and Geology (HUMG), Hanoi, Vietnam, and 
the research team of Innovations for Sustainable 
and Responsible Mining (ISRM) of HUMG. 
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