Evaluating and predicting blastinduced ground vibration in opencast mine using ANN: a case study in Vietnam
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Abstract
Blasting is one of the cheapest and effective methods for breaking rock mass in openpit mines. However, its side effects are not small such as ground vibration (PPV), air overpressure, fly rock, back break, dust, and toxic. Of these side effects, blastinduced PPV is the most dangerous for the human and surrounding environment. Therefore, evaluating and accurately forecasting blastinduced PPV is one of the most challenging issues facing openpit mines today. In this paper, a series of artificial neural network models were applied to predict blastinduced PPV in an openpit coal mine of Vietnam; 68 blasting events were used in this study for development of the ANN models. Of the whole dataset, 80% (approximately 56 observations) were used for the training process, and the rest of 20% (12 observations) were used for the testing process. Five ANN models were developed in this study with the difference in the number of hidden layers. The ANN 251; ANN 2861; ANN 2531; ANN 28641; and ANN 210851 models were considered in this study. An empirical technique was also conducted to estimate blastinduced PPV and compared to the constructed ANN models. For evaluating the performance of the models, rootmeansquared error (RMSE) and determination coefficient (R^{2}) were used. The results indicated that the ANN 210851 model (10 neurons in the first hidden layer, 8 neurons in the second hidden layer, and 5 neurons for the third hidden layer) yielded a superior performance over the other models with an RMSE of 0.738 and R^{2} of 0.964. In contrast, the empirical performed poorest performance with an RMSE of 2.670 and R^{2} of 0.768. This study is a new approach to predict blastinduced PPV in opencast mines aim to minimize the adverse effects of blasting operations on the surrounding environment.
Keywords
ANN Machine learning Blasting Ground vibration Openpit mine1 Introduction
Blasting is one of the cheapest and most effective methods for hardrock fragmentation in openpit mines and civil engineering. However, many previous researchers have concluded that only 25–30% of the explosive energy was directly involved in breaking rock, the rest produces undesirable side effects such as ground vibration (PPV), air overpressure, fly rock, and back break [1, 2, 3, 4, 5, 6, 7]. Of these side effects, PPV is the most dangerous side effects for humans and the environment. Therefore, precise prediction of blastinduced PPV is an essential requirement in openpit mines.
To assess and predict blastinduced PPV, many scientists have access to empirical techniques based on mathematical statistics [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Empirical techniques were mostly based on mathematical statistical methods and used two input variables including explosive charge per delay/maximum explosive charge capacity (W) and monitoring distance (R). They were considered the two most influential factors for blastinduced PPV [19]. However, their performance was not high in some cases [20, 21, 22, 23, 24, 25].
Some studies of PPV prediction using soft computational models
References  Technique  No. of datasets  Performance 

Monjezi et al. [37]  MLPNN  269  R^{2} = 0.954; RMSE = 0.03 
Monjezi et al. [38]  ANN  182  R^{2} = 0.949 
Armaghani et al. [39]  PSOANN  44  R^{2} = 0.930; MSE = 10.71 
Saadat et al. [21]  ANN  69  R^{2} = 0.957; MSE = 0.000722 
Hasanipanah et al. [6]  SVM  80  R^{2} = 0.957; RMSE = 0.340 
Amiri et al. [40]  ANNKNN  75  R^{2} = 0.880; RMSE = 0.540 
Hasanipanah et al. [41]  PSO  80  R^{2} = 0.938; RMSE = 0.240 
Faradonbeh and Monjezi [42]  GEP  115  R^{2} = 0.874; RMSE = 6.732 
Taheri et al. [23]  ABCANN  89  R^{2} = 0.920; RMSE = 0.220 
Armaghani et al. [43]  ICA  73  R^{2} = 0.940; RMSE = 0.370 
Behzadafshar et al. [44]  ICA  76  R^{2} = 0.939; RMSE = 0.320 
Abbaszadeh Shahri and Asheghi [45]  ANN  37  R^{2} = 0.954; RMSE = 0.157 
Mokfi et al. [46]  GMDH  102  R^{2} = 0.911; RMSE = 0.889 
Torres et al. [47]  MLREmpirical  178  R^{2} = 0.898 
Although the studies of PPV predictions in openpit mines using artificial intelligence (AI) have been approached, no approach or model was optimal for every area. In addition, AI is an approach that needs to be continually evolving and diverse. Thus, several ANN models for predicting blastinduced PPV at an openpit mine in Vietnam were developed in this study. The USBM empirical technique was also developed in this study to predict and compare with the ANN technique.
The composition of the article includes four parts: Part 1 reviews a number of published studies and the reasons for this study; Sect. 2 summarizes the data used and the methodology used; the results of this study and discussion are presented in Sect. 3; Finally, the conclusions and recommendations are given in the last section.
2 Data used and methodologies
2.1 Summary of the data used
Characteristic of the datasets used
W  R  PPV 

Min.: 136.0  Min.: 68.0  Min.: 17.80 
1st Qu.: 219.8  1st Qu.: 112.0  1st Qu.: 24.92 
Median: 305.5  Median: 134.5  Median: 27.30 
Mean: 316.5  Mean: 131.7  Mean: 27.47 
3rd Qu.: 405.0  3rd Qu.: 159.5  3rd Qu.: 29.61 
Max.: 670.0  Max.: 204.0  Max.: 35.63 
Before constructing the forecasting models, a data splitting procedure was performed for this study. Of the 68 observations, 80% of the whole data (56 observations) were used as the training dataset; the remaining 20% (12 observations) were used as the testing dataset. For the development of the PPV predictive models, the training dataset was used. For evaluating the performance of the models, the testing dataset was used as unseen data based on the developed models.
2.2 Empirical technique
2.3 Overview of ANN
ANN model works in the following manner: At the input layer, neurons receive input signals with weights. Then, they are processed and sent to the neurons of the first hidden layer via the transfer function. Here, the neurons will receive the results from the input and processing parameter classes, calculate the weights and send them to the second hidden layer via the transfer function. The process continues until the results are passed to the output layer and give the final output [53].
The results of the ANN model depend heavily on the learning process of the network, also known as the training process. The learning process of ANN includes two types of learning: supervised learning and unsupervised learning [54]. Input data for PPV prediction are numerical data and using regression algorithms, so most uses supervised learning based on input data and output requirements.
In this study, five ANN models with one, two, and three hidden layers were considered and developed to predict blastinduced PPV.
2.4 Establish the predictive models
Site factors and empirical equations for predicting PPV in this site study
No.  Site factors  Equation  

k  p  
1  9.520  − 0.359  \({\text{PPV}} = 9.520\left( {\frac{R}{{\sqrt[3]{W}}}} \right)^{0.359}\) 
2  6.640  − 0.480  \({\text{PPV}} = 6.640\left( {\frac{R}{{\sqrt[3]{W}}}} \right)^{0.480}\) 
3  9.427  − 0.362  \({\text{PPV}} = 9.427\left( {\frac{R}{{\sqrt[3]{W}}}} \right)^{0.362}\) 
4  6.602  − 0.482  \({\text{PPV}} = 6.602\left( {\frac{R}{{\sqrt[3]{W}}}} \right)^{0.482}\) 
5  9.378  − 0.364  \({\text{PPV}} = 9.378\left( {\frac{R}{{\sqrt[3]{W}}}} \right)^{0.364}\) 
In Fig. 3, I1 and I2 are input parameters corresponding to W and R; H1 to H10 is the number of neurons in each hidden layer; O1 is the output predicted value (PPV); B1 to B4 are biased layers that apply constant values to the nodes. The black line represents for positive weights, and the gray line represents for negative weights. Line thickness is in proportion to the magnitude of the weight relative to all others.
3 Results and discussion
3.1 Empirical models
Performance indices of the empirical models
No.  Training datasets  Testing datasets  

RMSE  R ^{2}  RMSE  R ^{2}  
Empirical 1  2.480  0.603  2.670  0.768 
Empirical 2  2.329  0.616  2.814  0.677 
Empirical 3  2.468  0.599  2.705  0.599 
Empirical 4  2.266  0.618  3.042  0.663 
Empirical 5  2.631  0.573  1.823  0.761 
Performance indices of the empirical models and their ranking
Method  Model  RMSE  R ^{2}  Rank for RMSE  Rank for R^{2}  Total rank 

Empirical  Training 1  2.48  0.603  2  3  5 
Training 2  2.329  0.616  4  4  8  
Training 3  2.468  0.599  3  2  5  
Training 4  2.266  0.618  5  5  10  
Training 5  2.631  0.573  1  1  2  
Testing 1  2.67  0.768  4  5  9  
Testing 2  2.814  0.677  2  3  5  
Testing 3  2.705  0.599  3  1  4  
Testing 4  3.042  0.663  1  2  3  
Testing 5  1.823  0.761  5  4  9 
Total rank of the empirical models
Method  Model no.  Total rank 

Empirical  1  14 
2  13  
3  9  
4  13  
5  11 
3.2 The ANN models
Performance indices of the ANN models
Model  Training datasets  Testing datasets  

RMSE  R ^{2}  RMSE  R ^{2}  
ANN 251  1.007  0.933  1.035  0.936 
ANN 2531  0.903  0.946  0.831  0.958 
ANN 2861  0.842  0.953  0.806  0.96 
ANN 28641  0.856  0.952  0.648  0.973 
ANN 210851  0.821  0.956  0.738  0.964 
Performance indices of the ANN models and their ranking
Method  Model  RMSE  R ^{2}  Rank for RMSE  Rank for R^{2}  Total rank 

ANN  Training 1  1.007  0.933  1  1  2 
Training 2  0.903  0.946  2  2  4  
Training 3  0.842  0.953  4  4  8  
Training 4  0.856  0.952  3  3  6  
Training 5  0.821  0.956  5  5  10  
Testing 1  1.035  0.936  1  1  2  
Testing 2  0.831  0.958  2  2  4  
Testing 3  0.806  0.96  3  3  6  
Testing 4  0.648  0.973  5  5  10  
Testing 5  0.738  0.964  4  4  8 
Total rank of the ANN models
Method  Model no.  Total rank 

ANN  1  4 
2  8  
3  14  
4  16  
5  18 
3.3 Performance evaluation between the ANN model and empirical model
Comparisons of performance between the empirical and ANN selected
Method  Training datasets  Testing datasets  

RMSE  R ^{2}  RMSE  R ^{2}  
Empirical  2.480  0.603  2.670  0.768 
ANN  0.821  0.956  0.738  0.964 
4 Conclusion and remarks

ANN is an advanced and robust technique that should be used to predict blastinduced PPV in openpit mines. This study has developed a robust ANN model with high accuracy (RMSE = 0.738, R^{2} = 0.964). It should be applied in practical engineering to control the undesirable effects on the surrounding environment. However, the development of the ANN models in openpit mine is often complicated, requiring the user to have an understanding of mathematics and programming.

The ANN model with a hidden layer should not be used to predict PPVs because it does not reflect all the characteristics of the data that lead to the inaccuracy of the forecasting model. The ANN model with three hidden layers has been proposed for predicting blastinduced PPV in practical engineering based on the results of this study. ANN models with many hidden layers should be considered in the future for predicting blastinduced PPV.

The empirical technique is a rapid and straightforward method of estimating blastinduced PPV, but further research is needed to improve the accuracy of empirical models.

The other influence parameters should be considered and supplemented to improve the accuracy of PPV predictive models, especially for empirical methods.
The results of this study are the basis for the development of blastinduced PPV predictive models for other openpit mines with similar conditions. At the same time, it is useful for managers, engineers, and blasters in optimizing blasting efficiency and minimizing the negative impacts caused by blasting operations in openpit mines.
Notes
Acknowledgements
We thank Hanoi University of Mining and Geology (HUMG), and the Center for Mining, ElectroMechanical research of HUMG.
Compliance with ethical standards
Conflict of interest
The author declares that there is no conflict of interests regarding the publication of this paper.
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