Artificial Intelligence Models for Predicting Ground Vibrations in Deep Underground Mines to Ensure the Safety of Their Surroundings

Abstract

Ground vibrations induced by underground mining blasting has a significant impact on the stability and safety of surface buildings near mines. Due to the thick rock layers overlying underground mines, there is presently limited accuracy in regard to predicting ground vibrations induced by underground mine blasting. Therefore, this study aims to improve the accuracy of predicting ground vibrations induced by underground blasting by comprehensively measuring the peak particle velocity (PPV) in all three directions and independently considering on the impact of vertical distance. Random forest regression (RFR), bagging regression (BR), and gradient boosting regression (GBR) were used to regress the X-axis PPV (X-PPV), Y-axis PPV (Y-PPV), and Z-axis PPV (Z-PPV) based on blasting records measured at an iron mine. In addition, a genetic algorithm, gray wolf optimizer (GWO), and a particle swarm optimization were used to optimize the parameters of the RFR, BR, and GBR. The comparison results show that GWO-GBR is the optimal model for the prediction of the X-PPV (R² = 0.8072), Y-PPV (R² = 0.9147), and Z-PPV (R² = 0.9265), respectively. Thus, the GWO-GBR model proposed in this study is considered a highly reliable model for predicting ground vibrations induced by underground mine blasting to ensure the safety of the mines’ surroundings.

1. Introduction

The blasting technique is known for its superior efficacy in rock fragmentation and its economic benefits, and it has become the preferred strategy for metal mines and tunnel engineering [1]. However, the energy distributed during explosive blasting is imbalanced, and the remaining energy inevitably generates ground vibrations, loud noises, and environmental pollution. This poses a potential threat to surrounding structures around the working area. Among these hazard factors, blast-induced ground vibration (BIGV) is a major hazard to residential buildings around mines. At present, the evaluation of BIGV mainly relies on seismic monitoring equipment, geological exploration, and seismic dynamic analysis methods. Vibration monitoring can use accelerometers, vibration sensors, ground deformation monitoring instruments, remote sensing technology, etc. In general engineering, vibration sensors are mainly used to monitor the speed and frequency of surface vibrations. The key parameter is the peak particle velocity (PPV), including the X-axis PPV (X-PPV), Y-axis PPV (Y-PPV), and Z-axis PPV (Z-PPV); therefore, PPV must be predicted and calculated to prevent potential harm to surface residential structures from underground mine blasting [2].

In the field’s early stages, scholars employed empirical methods and empirical formulae, such as the Sadowski formula, to make predictions of PPV [3]. Cardu et al. [4] proposed a new formula to calculate PPV that included a K-exponential. Wang et al. [5] investigated the predictor equations for determining the parameters of PPV. However, due to the complex geological environments of mines and differences between types of explosives, the accuracy of the prediction results was limited. With the development of computer technology, machine learning (ML) methods gained significant popularity [6,7,8]. Researchers have undertaken PPV regression predictions using artificial intelligence (AI) models; the corresponding research status is illustrated in Table 1.

As shown in Table 1, conventional ML algorithms, neural networks, and many AI-based soft computing models have been introduced to predict PPV. However, while the PPV of open-pit mines has been investigated in past decades [9,10,11,12,13,14,15,16,17], there is less ground vibration prediction research regarding underground mines, and the prediction accuracy is lower [18,19]. Unlike open-pit mines, the surface structures of underground mines are constructed around the ore body. As a result, residential areas are in closer proximity to the mining zone and are therefore exposed to more intense blasting vibrations. In addition, in open-pit mines, only the straight-line distance between the monitoring point and the blasting point is considered for the shallow surface ore bodies, while underground mines are deeper and the overlying rock layer at the blasting point is thicker, affecting the propagation of blasting vibrations. Therefore, the effect of blasting depth on surface blasting vibrations must be considered independently, and it is necessary to investigate the prediction of PPV for underground mines.

This study employed AI-based models to predict the PPV of underground mines based on three ML regression models (a random forest regressor (RFR), a bagging regressor (BR), and a gradient boosting regressor (GBR)) and three AI optimization algorithms (a genetic algorithm (GA), the gray wolf optimizer (GWO), and a particle swarm optimization (PSO)). In addition, nine AI-based models (GWO-RFR, GA-RFR, PSO-RFR, GWO-BR, GA-BR, PSO-BR, GWO-GBR, GA-GBR, and PSO-GBR) were used to predict the X-PPV, Y-PPV, and Z-PPV. A regression prediction of blast vibrations in underground mines was carried out.

Table 1. Summary of PPV prediction in metal mines.

Authors	Publish Date	Mine Type	Main Method	Input Parameters	Output
C Khandelwal, M. et al. [9]	2007	Open-pit mine	ANN	DMBS, Qmax	PPV
Bakhshandeh Amnieh, H et al. [10]	2010	Open-pit mine	ANN	Qmax, DMBS, HSC, NHR	PPV
Monjezi, M. et al. [11]	2010	Open-pit mine	MLPNN, GRNN, RBFNN	Qmax, DMBS, NHR	PPV
Longjun, D. et al. [12]	2011	Open-pit mine	RFR, SVM	Qmax, Qtotal, HD, ED, C, PPR, IC, a, VoD	PPV, first VF, duration time of first VF
Álvarez-Vigil, A.E. et al. [13]	2012	Open-pit mine	ANN	RMR, DMBS, DMBS, HoDi, HoDe, SBB, B, Qmax, Qtotal, NB, VoD	PPV, VF
Saadat, M. et al. [14]	2014	Open-pit mine	ANN, MLR	Qmax, DMBS, SD, HoDe	PPV
Parida, A. et al. [15]	2015	Open-pit mine	ANN	Qmax, DMBS	PPV
Saadat, M. et al. [16]	2015	Open-pit mine	DE algorithm theory	HoDe, B, S, CL, Qmax, DMBS, YM, PF, BI	PPV
Danial Jahed Armaghani et al. [20]	2021	Open-pit mine	AGPSO–ELM, PSO–ELM	B, Qmax, HS, DMBS, PF, HoDe	PPV
Abiodun Ismail Lawal et al. [21]	2021	Open-pit mine	GEP, ANFIS, SCA-ANN	DMBS, Qmax, RD, SRH	PPV
Xiliang Zhang et al. [22]	2021	Open-pit mine	MVO–ELM, ELM, MLP, USBM	C, Qtotal, HD, VD, B, PPR, DT, RMI, f, a, VoD	PPV
Yingui Qiu et al. [23]	2022	Open-pit mine	WOA-XGBoost, GWO-XGBoost, BO-XGBoost	B, S, CL, HoDi, HoDe, DE, VoD, DMBS	PPV
Nguyen, H. et al. [17]	2023	Open-pit mine	SpaSO-ELM, SalSO-ELM, MFO-ELM	B, S, f, PF, Qmax	PPV
Jiliang Kan et al. [18]	2022	Underground mine	GA-ANN	Qmax, Qtotal, HD, NB, ACC, SDC	PPV
Shida Xu et al. [19]	2021	Underground mine	GA-ANN	B, Qmax, ED, HS, DD, HV, VD	PPV

Table 1. Summary of PPV prediction in metal mines.

Authors	Publish Date	Mine Type	Main Method	Input Parameters	Output
C Khandelwal, M. et al. [9]	2007	Open-pit mine	ANN	DMBS, Qmax	PPV
Bakhshandeh Amnieh, H et al. [10]	2010	Open-pit mine	ANN	Qmax, DMBS, HSC, NHR	PPV
Monjezi, M. et al. [11]	2010	Open-pit mine	MLPNN, GRNN, RBFNN	Qmax, DMBS, NHR	PPV
Longjun, D. et al. [12]	2011	Open-pit mine	RFR, SVM	Qmax, Qtotal, HD, ED, C, PPR, IC, a, VoD	PPV, first VF, duration time of first VF
Álvarez-Vigil, A.E. et al. [13]	2012	Open-pit mine	ANN	RMR, DMBS, DMBS, HoDi, HoDe, SBB, B, Qmax, Qtotal, NB, VoD	PPV, VF
Saadat, M. et al. [14]	2014	Open-pit mine	ANN, MLR	Qmax, DMBS, SD, HoDe	PPV
Parida, A. et al. [15]	2015	Open-pit mine	ANN	Qmax, DMBS	PPV
Saadat, M. et al. [16]	2015	Open-pit mine	DE algorithm theory	HoDe, B, S, CL, Qmax, DMBS, YM, PF, BI	PPV
Danial Jahed Armaghani et al. [20]	2021	Open-pit mine	AGPSO–ELM, PSO–ELM	B, Qmax, HS, DMBS, PF, HoDe	PPV
Abiodun Ismail Lawal et al. [21]	2021	Open-pit mine	GEP, ANFIS, SCA-ANN	DMBS, Qmax, RD, SRH	PPV
Xiliang Zhang et al. [22]	2021	Open-pit mine	MVO–ELM, ELM, MLP, USBM	C, Qtotal, HD, VD, B, PPR, DT, RMI, f, a, VoD	PPV
Yingui Qiu et al. [23]	2022	Open-pit mine	WOA-XGBoost, GWO-XGBoost, BO-XGBoost	B, S, CL, HoDi, HoDe, DE, VoD, DMBS	PPV
Nguyen, H. et al. [17]	2023	Open-pit mine	SpaSO-ELM, SalSO-ELM, MFO-ELM	B, S, f, PF, Qmax	PPV
Jiliang Kan et al. [18]	2022	Underground mine	GA-ANN	Qmax, Qtotal, HD, NB, ACC, SDC	PPV
Shida Xu et al. [19]	2021	Underground mine	GA-ANN	B, Qmax, ED, HS, DD, HV, VD	PPV

2. Materials and Methods

To obtain the BIGV dataset, we conducted BIGV monitoring in a mine in Anhui, China, using integrated vibrometers (Isv-420, Sichuan TDEC MEASUREMENT & CONTROL Co., Ltd., Chengdu, China). Following a comprehensive site survey and analysis of the mine’s surrounding environment, the monitoring instruments were placed strategically along the north–south axis of the ore body. The monitoring period was from 27 October to 17 November 2022, during which 72 BIGV records were obtained. As in previous studies [24,25,26], maximum charge per delay (MCPD), horizontal distance (HD), and vertical distance (VD) were used as input features. The X-PPV, Y-PPV, and Z-PPV were used as output features. Figure 1 employs violin plots (VIP) to illustrate data quartiles, probability densities (indicated by shaded color areas), and outliers (represented through box-and-whisker plots), and the maximum, median, and minimum values are represented at the top, center, and bottom of the plot, respectively. Additionally, the thick line at the VIP’s core marks the third and first quartiles at its bottom and top, respectively. The number of outliers of the MCPD, HD, VD, X-PPV, Y-PPV, and Z-PPV were 3, 0, 0, 2, 6, and 2, respectively. The presence of some outliers is normal in seismic velocity monitoring [27]. Furthermore, the data were randomly divided into training data (80%) and testing data (20%). A summary of the datasets is provided in

Table 2. The datasets of blasting vibration for the prediction of X-PPV, Y-PPV, and Z-PPV.

Category	Max Charge of Per Delay (kg)	Vertical Distance (m)	Horizontal Distance (m)	X-PPV (cm/s)	Y-PPV (cm/s)	Z-PPV (cm/s)
	Training dataset (80%)
Min	180.000	250.000	143.000	0.035	0.031	0.071
First quartile	240.000	300.000	260.000	0.073	0.061	0.132
Median	265.000	375.000	455.000	0.105	0.093	0.169
Mean	269.211	348.684	408.649	0.107	0.099	0.191
Third quartile	285.000	400.000	530.000	0.134	0.125	0.240
Max	412.500	400.000	673.000	0.291	0.274	0.471
	Testing dataset (20%)
Min	180.000	250.000	159.000	0.039	0.032	0.066
First quartile	230.000	337.500	192.000	0.063	0.056	0.133
Median	265.000	375.000	456.000	0.074	0.075	0.163
Mean	264.333	355.000	392.133	0.100	0.113	0.173
Third quartile	290.000	400.000	518.000	0.124	0.110	0.179
Max	397.500	400.000	667.000	0.234	0.320	0.349

.

2.1. The Study Area

The mine, a large metamorphic iron ore deposit in Anhui, China, stretches over 4 km with a maximum depth of −862 m, the geography of which is shown in Figure 2. The majority of the ore deposit area is covered by Quaternary deposits. The main rock types include granite, gneiss, iron ore, and diabase. Among them, the gneiss rock mass has a good quality, while the ore body, granite, and diabase rock masses range from moderate to good quality. The rocks in the mining area are mainly characterized by stratified and disseminated structures, with blocky structures being secondary. The overall stability of the ore rocks is good. The mine uses a mining method of subsequent backfilling of the stage empty field and fan-shaped medium-deep hole drilling and blasting. A large number of residential areas and offices are distributed around the mining area, and blasting vibrations can affect the safety of buildings.

2.2. BIGV Monitoring

To monitor the BIGV around the mining area, vibrometers (iSV-420, Sichuan TDEC MEASUREMENT & CONTROL Co., Ltd., China) were deployed. The iSV-420 vibrometer integrates three-axis vibration sensors and digital measurement, storage, and wireless transmission. Low frequency response can be lowered to 0.01 Hz, with a built-in GPS function and automatic positioning function supporting distributed synchronous measurement. It can be used for shock and vibration monitoring and safety evaluation in blasting engineering. According to the “Code for Seismic Design of Buildings” (GB50011-2010) [28], the location of blasting vibration monitoring should be easy for operators to approach, and the ground should be flat without accumulated water. The plan should be developed through multiple on-site investigations of villages, roads, factories, etc. that may be affected by blasting operations. Based on an on-site investigation and the distribution of a large number of residential areas and office buildings around the ore body, in order to monitor the impact of surface vibrations caused by underground blasting operations on residential areas and office buildings on the surface, four monitoring points were arranged around the ore body. As shown in Figure 3, the settlement M1 was located to the north of the ore body, settlement M2 was west of the ore body, settlement M3 was located directly above the ore body, and settlement M4 was south of the ore body. The refraction and transmission of the blasting vibration wave is shown in Figure S1.

2.3. Machine Learning Algorithms

2.3.1. Random Forest Regressor (RFR)

RFR is a machine learning method based on regression trees and the bagging ensemble learning method [29]. On the basis of regression trees, random forest introduces the random attribute selection method and integrates the parallel operation of multiple regression trees [30,31]. An RFR model consists of multiple regression trees, each with no association to the others. The RFR models use the bootstrap method to randomly sample the dataset, which results in approximately 33% of the dataset not being selected. Unselected samples are defined as out-of-bag (OOB), with the prediction error of the OBB (i.e., the OBB score) enabling the calculation of the error estimate of the RFR model [32]. The final output predicted value of the model is determined by each regression tree in the forest.

2.3.2. Gradient Boosting Regressor (GBR)

GBR is a powerful machine learning technique used for predictive modeling and regression analysis [33]. It works by iteratively improving a set of weak models by combining them in a weighted manner to obtain a more accurate model. The algorithm starts with a single, simple model, then builds additional models by focusing on the residuals or errors of the previous models. These models are trained using a gradient descent approach to minimize the overall loss function [34].

2.3.3. Bagging Regressor (BR)

A BR is an ensemble learning technique that improves the performance of regression models by reducing variance. It accomplishes this by training multiple copies of the same algorithm on different random subsets of the training data, then combining their predictions to form a more accurate final prediction. This technique can be applied to various regression models, such as decision trees, linear regression, and support vector machines. It is easy to implement and can be used to improve the performance of existing regression models without significant modifications. The predictions of these individual models are then combined to form a final prediction that is more accurate than the predictions of any individual model [35].

2.4. Artificial Intelligence Optimization Models

2.4.1. Genetic Algorithm (GA)

GA is a class of algorithms inspired by natural selection, crossover, and mutation processes that enables the generation of new solution candidates. These algorithms are therefore ideal for solving complex optimization problems with large search spaces [36]. (1) A GA algorithm starts with a random population, then uses the object function to evaluate the fitness scores of individuals in the initial population. (2) The GA algorithm uses a roulette wheel selection method to choose individuals based on their fitness. The selected individuals form the next generation. (3) The GA algorithm exchanges the chromosomes of selected pairs of individuals with a certain probability. (4) The GA algorithm utilizes a mutation operator to alter one or multiple genes in the children solution after the crossover phase. (5) The fitness of the next generation is calculated based on selection, crossover, and mutation. Steps 1–4 are repeated, and, finally, the optimal solution is outputted based on the termination condition [36,37]. The mechanism of GA is shown in Figure S2.

2.4.2. Gray Wolf Optimizer (GWO)

GWO is a meta-algorithm that mimics the leadership, heuristic, and hunting mechanisms of the gray wolf [38]. The GWO algorithm includes four hierarchical levels. The first level, alpha, corresponds to the optimal solution in the algorithm. Beta, the second level, corresponds to the suboptimal solution in the algorithm. Omega is the third level, following the decisions of alpha and beta. The fourth level of wolf is at the bottom of the hierarchy [38]. The social hierarchy of gray wolves is shown in Figure S3 [39].

The mathematical model of the gray wolf algorithm is shown below [38]:

(1)

Encircling prey

The gray wolf encircles prey during hunting.

$$\overrightarrow{D}=|\overrightarrow{\mathrm{C}}\cdot {\overrightarrow{X}}_p(\mathrm{t})-\overrightarrow{\mathrm{X}}(\mathrm{t})|$$

(1)

$$\overrightarrow{X}(\mathrm{t}+1)={\overrightarrow{X}}_p(\mathrm{t})-\overrightarrow{A}\cdot \overrightarrow{D}$$

(2)

where t indicates the current iteration, $\overrightarrow{A}$ and $\overrightarrow{C}$ are coefficient vectors, ${\overrightarrow{X}}_p$ is the position vector of the prey, and $\overrightarrow{X}$ indicates the position vector of the gray wolf.

$$\overrightarrow{A}=2\overrightarrow{a}\cdot {\overrightarrow{r}}_1-\overrightarrow{a}$$

(3)

$$\overrightarrow{C}=2\cdot {\overrightarrow{r}}_2$$

(4)

where components of $\overrightarrow{a}$ are linearly decreased from 2 to 0 over the course of the iterations and r₁ and r₂ are random vectors in [0, 1].

(2)

Hunting

$${\overrightarrow{D}}_{\alpha }=|{\overrightarrow{\mathrm{C}}}_1\cdot {\overrightarrow{\mathrm{X}}}_{\alpha }-\overrightarrow{\mathrm{X}}|,{\overrightarrow{\mathrm{D}}}_{\beta }=|{\overrightarrow{\mathrm{C}}}_2\cdot {\overrightarrow{\mathrm{X}}}_{\beta }-\overrightarrow{\mathrm{X}}|,{\overrightarrow{\mathrm{D}}}_{\delta }=|{\overrightarrow{\mathrm{C}}}_3\cdot {\overrightarrow{\mathrm{X}}}_{\delta }-\overrightarrow{\mathrm{X}}|$$

(5)

$${\overrightarrow{X}}_1={\overrightarrow{\mathrm{X}}}_{\alpha }-{\overrightarrow{A}}_1\cdot ({\overrightarrow{\mathrm{D}}}_{\alpha }),{\overrightarrow{\mathrm{X}}}_2={\overrightarrow{\mathrm{X}}}_{\beta }-{\overrightarrow{\mathrm{A}}}_2\cdot ({\overrightarrow{\mathrm{D}}}_{\beta }),{\overrightarrow{\mathrm{X}}}_3={\overrightarrow{\mathrm{X}}}_{\delta }-{\overrightarrow{\mathrm{A}}}_3\cdot ({\overrightarrow{\mathrm{D}}}_{\delta })$$

(6)

$$\overrightarrow{X}(t+1)=\frac{{\overrightarrow{X}}_1+{\overrightarrow{X}}_2+{\overrightarrow{X}}_3}{3}$$

(7)

where ${\overrightarrow{X}}_{\alpha }$, ${\overrightarrow{X}}_{\beta }$ represent the current position vectors of the $\alpha$, $\beta$, and $\delta$ wolves, respectively, and ${\overrightarrow{D}}_{\alpha }$, ${\overrightarrow{D}}_{\beta }$, and ${\overrightarrow{D}}_{\delta }$ denote the distances between the current candidate gray and the $\alpha$, $\beta$, and $\delta$ wolves, respectively. When $|\overrightarrow{\mathrm{A}}|$ > 1, the gray wolves disperse to different areas to search for prey. When $|\overrightarrow{\mathrm{A}}|$ < 1, the gray wolves all search for prey in certain areas.

2.4.3. Particle Swarm Optimization (PSO)

PSO is a meta-algorithm that was inspired by social behaviors, including bird flocking, fish schooling, and, particularly, swarming theory [40]. The new velocity and the new position of each particle are determined by (8) and (9) [41]. The operation mechanism of the PSO algorithm is shown in Figure S4 [37].

$${\nu }_q(t+1)=\omega (t){\nu }_q(t)+c_1{r}_1(t)(P_{best,q}(t)-x_q(t))+c_2{r}_2[G_{best}(t)-x_q(t)]$$

(8)

$$xq(t+1)=xq(t)+\nu q(t+1), \forall q=1,2,\cdots ,M$$

(9)

where t is the current number of iterations, M is the number of partials in each iteration (swarm population), x_i(t) is the position of the q_th particle in the t_th iteration, ${\nu }_q(t)$ is the velocity of the q_th particle in the t_th iteration, positive numbers c₁ and c₂ are the acceleration constants, r₁(t) and r₂(t) are the random numbers uniformly distributed between 0 and 1 in the t_th iteration, and w(t) represents the inertial weight factor in the t_th iteration. In addition, the best position of any individual in the swarm in their own memories is recorded in the variable P_best,q(t) in the t_th iteration. The position of the individuals closest to the optimum within the swarm is stored in the variable G_best(t) in the t_th iteration.

2.5. Model Evaluation

Generalization errors were introduced to evaluate regression performance and manage the overfitting and underfitting of the models. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²), and correlation coefficient (R) were used as evaluation metrics [42,43]. The equations are as follows:

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_i-f(x_i)\right|}$$

(10)

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{(y_i-f(x_i))}^2}}$$

(11)

$$R^2=1-\frac{{\displaystyle {\sum }_{i=1}^n{(y_i-f({\mathrm{x}}_i))}^2}}{{\displaystyle {\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$$

(12)

$$R=1-\frac{{\displaystyle {\sum }_{i=1}^n[(y_i-\overline{y_i})(f(x_i)-\overline{f(x_i)})]}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(y_i-\overline{y})}^2}}\cdot \sqrt{{\displaystyle {\sum }_{i=1}^n{(f(x_i)-\overline{f(x_i)})}^2}}}$$

(13)

In equations, $y$ is the true value, $f(x_i)$ is the predicted value, $\overline{y}$ is the mean of the true value, $\overline{f(x_i)}$ is the mean value of the predicted value, and n is the number of the sample.

2.6. Prediction Models

In ML models, parameters are adjustable variables that directly affect a model’s performance and prediction ability. By adjusting parameters, a model can better fit data and predict unknown data. However, there are many combinations of parameters in ML models due to the large number of parameters and the wide range of values for each parameter. Therefore, for ML model parameter tuning, GA, GWO, and PSO AI optimization algorithms were used to find the optimal parameters to predict PPV. This method has the advantages of efficiency and optimality compared to traditional parameter tuning methods. The proposed method is shown in Figure 4. In this study, the construction and estimation of the ML models were achieved using the scikit-learn library in the Python 3.10 environment.

3. Comparison and Selection of ML Models

As in previous studies [44,45,46], 13 ML regression models have been used to predict the X-PPV, Y-PPV, and Z-PPV in underground metal mines. To eliminate dimensional effects and balance the weights of input features, all data were preprocessed through a normalization method before model training [47]. According to the previous studies [23,48], the larger the values of R and R² in the evaluation indicators, the better the performance of the model; additionally, the smaller the MAE and RMSE values, the higher the performance of the model. Therefore, to obtain the best models of prediction for the X-PPV, Y-PPV, and Z-PPV, the R², R, RMSE, and MAE of each model were sorted, with the best one achieving nine points. Finally, the total rank scores of each model were sorted. The results are shown in Figure 5. The top three models, RFR, BR, and GBR, scored 136, 123, and 129, respectively. This indicates that the regression performance of these three models is better; therefore, they were selected to be the prediction ML models. As shown in Figure 6, these prediction models have poor predictive performance for the X-PPV, Y-PPV, and Z-PPV, and they require parameter tuning.

4. Optimization of ML Models and Results

4.1. Parametric Configuration

The main parameters of the RFR model are n_estimators, max_depth, min_samples_leaf, min_samples_split, and max_features. The main parameters of a BR are n_estimators, max_samples, and max_features. The main parameters of a GBR are n_estimators, learning_rate, min_samples_leaf, min_samples_split, and max_features. In order to effectively improve the predictive performance of the ML models, AI optimization algorithms were introduced for parameter tuning.

4.2. Model Performance

GWO, GA, and PSO algorithms were used to optimize the parameters of the RFR, BR, and GBR. The R², R, RMSE, and MAE were used as the evaluation indicators for each regression model. To comprehensively evaluate the prediction performance of each model, a ranking method was adopted, i.e., the R², R, RMSE, and MAE of each model were sorted, with the best one achieving nine points. Finally, the total scores of each model were sorted.

As shown in Figure 7, the rank score of GWO-GBR for the X-PPV, Y-PPV, and Z-PPV were 36, 34, and 36, respectively. The rank score of GA-GBR for the X-PPV, Y-PPV, and Z-PPV were 31, 31, and 32, respectively. The rank score of PSO-GBR for the X-PPV, Y-PPV, and Z-PPV were 29, 31, and 28, respectively. Thus, GWO-GBR, GA-GBR, and PSO-GBR were the first three models used to predict the performance of the X-PPV, Y-PPV, and Z-PPV.

4.2.1. Results of Models for X-PPV Prediction

To better demonstrate the performance of the first three models to predict the X-PPV, the results of the prediction of the validation set using GWO-GBR, GA-GBR, and PSO-GBR are shown in Figure 8. In addition, the parameters of these models are shown in Table S1.

As shown in Figure 8a–f, the R² of GWO-GBR, GA-GBR, and PSO-GBR were 0.8072, 0.7642, and 0.7488, respectively. The R of GWO-GBR, GA-GBR, and PSO-GBR were 0.9044, 0.8751, and 0.8898, respectively. The RMSE of GWO-GBR, GA-GBR, and PSO-GBR were 0.0959, 0.1061 and 0.1095, respectively. The MAE of GWO-GBR, GA-GBR, and PSO-GBR were 0.0796, 0.0859, and 0.0911, respectively. According to Figure 6a–c and Figure 8b,d,f, the hybrid models had higher R² and R and lower RMSE and MAE compared to the standalone models. This indicates that the hybrid model had a higher performance in terms of X-PPV regression prediction than the standalone model. The evaluation indicators R² and R of GWO-GBR were higher than the other models, and the RMSE and MAE of GWO-GBR were lower than the other models. This shows that GWO-GBR had the best performance for X-PPV regression.

As shown in Figure 8b,d,f, the confidence band and prediction band of GWO-GBR, GA-GBR, and PSO-GBR for the X-PPV prediction were similar. This illustrates that the uncertainty performance of X-PPV prediction models was similar [27]. Therefore, the GWO-GBR model had the best performance for X-PPV regression.

4.2.2. Results of Models for Y-PPV Prediction

To better demonstrate the performance of the first three models for the prediction of Y-PPV, the results of the prediction of the validation set using GWO-GBR, GA-GBR, and PSO-GBR are shown in Figure 9. In addition, the parameters of these models are shown in Table S2.

As shown in Figure 9a–f, the R² of GWO-GBR, GA-GBR, and PSO-GBR were 0.9147, 0.8894, and 0.8771, respectively. The R of GWO-GBR, GA-GBR, and PSO-GBR were 0.9589, 0.9589, and 0.9683, respectively. The RMSE of GWO-GBR, GA-GBR, and PSO-GBR were 0.0954, 0.1086, and 0.1145, respectively. The MAE of GWO-GBR, GA-GBR, and PSO-GBR were 0.0734, 0.0938, and 0.0886, respectively. According to Figure 6d–f and Figure 9b,d,f, the hybrid models had higher R² and R and lower RMSE and MAE compared to the standalone models. This indicates that the hybrid model had a higher performance of Y-PPV regression prediction than the standalone model. The evaluation indicator R² of GWO-GBR was higher than the other models, and the R of GWO-GBR was similar to the other models. The RMSE and MAE were all lower than the other models. This shows that GWO-GBR had the best performance for Y-PPV regression.

According to Figure 9b,d,f, the confidence band and prediction band of GWO-GBR, GA-GBR, and PSO-GBR for Y-PPV prediction were similar, which illustrates that the uncertainty performance of the X-PPV prediction models was similar [27]. Therefore, the GWO-GBR model had the best performance of Y-PPV regression.

4.2.3. Results of Models for Z-PPV Prediction

To better demonstrate the performance of the first three models for predicting Z-PPV, the results of the prediction of the validation set using GWO-GBR, GA-GBR, and PSO-GBR are shown in Figure 10. Additionally, the parameters of these models are shown in Table S3.

As illustrated in Figure 10a–f, the R² of GWO-GBR, GA-GBR, and PSO-GBR were 0.9265, 0.9103, and 0.8956, respectively. The R of GWO-GBR, GA-GBR, and PSO-GBR were 0.9657, 0.9587, and 0.9470, respectively. The RMSE of GWO-GBR, GA-GBR, and PSO-GBR were 0.0476, 0.0525, and 0.0567, respectively. The MAE of GWO-GBR, GA-GBR, and PSO-GBR were 0.0406, 0.0424, and 0.0475, respectively. According to Figure 6g–i and Figure 10b,d,f, the hybrid models had higher R² and R and lower RMSE and MAE compared to the standalone models. This indicates that the hybrid model had a higher performance of Z-PPV regression prediction than the standalone model. The evaluation indicators R² and R of GWO-GBR were all higher than the other models, and the RMSE and MAE of GWO-GBR were all lower than the other models. This shows that GWO-GBR had the best performance for Z-PPV regression.

As shown in Figure 10b,d,f, the confidence band and prediction band of GWO-GBR, GA-GBR, and PSO-GBR for Z-PPV prediction were similar. This shows that the uncertainty performance of Z-PPV prediction models was similar [27]. Therefore, the GWO-GBR model had the best performance for Z-PPV regression.

4.3. Analysis of Results

To evaluate prediction performance, an error distribution between the true values and prediction values of nine models is shown in Figure 11, and the Taylor diagrams were used to comprehensively consider the performance of each model through multiple evaluation criteria, as shown in Figure 12.

As illustrated in Figure 11, the errors of the X-PPV and Y-PPV were mainly distributed between (−0.04, 0.06), while the errors of Z-PPV were mainly distributed between (−0.04, 0.04), indicating that Z-PPV had higher prediction accuracy. In addition, based on the mean and standard deviation of prediction errors for the X-PPV, Y-PPV, and Z-PPV, it was found that GWO-GBR had the smallest prediction error. This illustrates that GWO-GBR had the best prediction performance in regard to the X-PPV, Y-PPV, and Z-PPV. As illustrated in Figure 12, among the selected models, the GWO-GBR model was the best in predicting the X-PPV, Y-PPV and Z-PPV. Based on the above evaluation results, it can be obtained that the GWO-GBR had a better learning and prediction capability in predicting the X-PPV, Y-PPV and Z-PPV.

5. Control BIGV Methods

In this paper, the GWO-GBR model was used to predict PPV and then control BIGV by adjusting the blasting design to reduce potential hazards to surface buildings around underground mines. In addition, the application of electronic detonators in blasting operations and the use of a precise delay time can be used to control BIGV. This study shows that closer region delay time is shorter (6~8 ms), medium and long region delay time is longer (10~20 ms), and the comprehensive proposed delay time is 7~12 ms [49]. BIGV can also be controlled by setting the blast hole spacing, hole depth, and blasting sequence. Blasting vibration can be reduced by pre-treatment, using pre-cracking blasting to reduce the propagation of blasting energy in the rock. Shock-absorbing materials, such as damping mats, can be installed at the site to absorb some of the blasting energy and achieve vibration reduction.

These methods can be applied based on the specific conditions and requirements of the mining operation to effectively control and minimize the impact of BIGV.

6. Conclusions

Underground mining blasting has a significant impact on the stability and safety of surrounding structures. Thus, 72 records measured at the iron mine and nine AI-based models (GWO-RFR, GA-RFR, PSO-RFR, GWO-BR, GA-BR, PSO-BR, GWO-GBR, GA-GBR, and PSO-GBR) were used to predict the X-PPV, Y-PPV, and Z-PPV. Among these AI-based models, GWO-GBR, GA-GBR, and PSO-GBR were the first three models used to predict the X-PPV, Y-PPV, and Z-PPV, with the GWO-GBR model providing the best performance for the prediction of the X-PPV, Y-PPV, and Z-PPV. In addition, the error distribution performance of GWO-GBR, GA-GBR, and PSO-GBR were similar, and the standard deviations and mean of errors of GWO-GBR were the lowest. This reveals that the GWO-GBR model had strong robustness and generalization for the prediction of the X-PPV, Y-PPV, and Z-PPV. This investigation can provide an accurate prediction of ground vibration and advise underground BIGV controlling. In addition, the optimization of underground blasting parameters can be further investigated using the GWO-GBR prediction model.