Blasting in surface mines aims to fragment rock masses to a proper size. However, flyrock is an undesirable effect of blasting that can result in human injuries. In this study, support vector regression (SVR) is combined with four algorithms: gravitational search algorithm (GSA), biogeography-based optimization (BBO), ant colony optimization (ACO), and whale optimization algorithm (WOA) for predicting flyrock in two surface mines in Iran. Additionally, three other methods, including artificial neural network (ANN), kernel extreme learning machine (KELM), and general regression neural network (GRNN), are employed, and their performances are compared to those of four hybrid SVR models. After modeling, the measured and predicted flyrock values are validated with some performance indices, such as root mean squared error (RMSE). The results revealed that the SVR-WOA model has the most optimal accuracy, with an RMSE of 7.218, while the RMSEs of the KELM, GRNN, SVR-GSA, ANN, SVR-BBO, and SVR-ACO models are 10.668, 10.867, 15.305, 15.661, 16.239, and 18.228, respectively. Therefore, combining WOA and SVR can be a valuable tool for accurately predicting flyrock distance in surface mines.

Drilling and blasting is a frequent and typical method for fragmenting rock masses in surface mines due to its high adaptability and low cost. However, it can produce serious effects, i.e., ground vibration, flyrock, and airblast [

For the aim of flyrock prediction, Trivedi et al. [

This research develops four SVR models for predicting the flyrock. The main contribution of this research is to develop a new and accurate method to predict flyrock. In this regard, the SVR is combined with the whale optimization algorithm (WOA). To the best of our knowledge, it is the first work that predicts flyrock through the proposed SVR-WOA model. To verify the accuracy of the proposed model, three other algorithms, i.e., gravitational search algorithm (GSA), ant colony optimization (ACO) and biogeography-based optimization (BBO), are combined with SVR. The GSA, BBO, ACO, and WOA are utilized to fine-tune the hyperparameters of the SVR model. Additionally, the GRNN, ANN, and KELM are employed.

The required database was gathered from two surface mines in Kerman Province, Iran, to construct the predictive models. In these mines, the drilling and blasting methods were employed to fragment and displace rock masses using ANFO as the explosive material. The gathered database included 83 sets of data, encompassing four input parameters and one output parameter (flyrock). In this context, the input parameters were designated as the B, S, ST, and maximum charge per delay (MCPD) parameters. These blast design parameters were measured before all 83 blasting events. In addition, the values of flyrock were measured using a handheld Global Positioning System (GPS).

Descriptive statistics | Parameters | ||||
---|---|---|---|---|---|

Inputs | Output | ||||

B (m) | S (m) | ST (m) | MCPD (kg) | Flyrock (m) | |

Mean | 3.183 | 3.615 | 2.468 | 1334.759 | 168.867 |

Standard error | 0.064 | 0.085 | 0.057 | 33.352 | 5.244 |

Standard deviation | 0.591 | 0.775 | 0.521 | 303.851 | 47.775 |

Minimum | 1.6 | 1.9 | 1.4 | 780 | 94 |

Maximum | 4.2 | 5.5 | 3.4 | 2050 | 269 |

The General Regression Neural Network (GRNN), a type of radial basis function (RBF) network, was first introduced by Specht [

Support Vector Regression (SVR), a part of the Support Vector Machines (SVM) family, was presented by Vapnik [

The use of the SVR model for prediction purposes in several mining and civil engineering fields has been underlined. For instance, Xu et al. [

This study uses the GSA, BBO, WOA, and ACO algorithms to select the optimal hyperparameters of the SVR model.

Compared to some evolutionary algorithms, the GSA, as a stochastic local search heuristic, is an effective and successful algorithm. Rashedi et al. [

Colorni et al. [

ACO has been employed in several studies within the field of engineering for optimization purposes. Saghatforoush et al. [

Simon [

BBO’s ability to balance exploration and exploitation, inspired by the principles of biogeography, makes it a promising algorithm for solving complex optimization problems [

Mirjalili et al. [

WOA has been successfully utilized for various optimization issues, including feature selection, data clustering, scheduling, and engineering design. Its ability to balance exploration and exploitation makes it a promising tool for solving complex problems in civil and mining engineering, where finding optimal solutions is crucial. A hybrid of ANN and WOA was used by Tien Bui et al. [

Before proceeding with the modeling of the data using the aforementioned data-driven methods, a preliminary step involving data processing was conducted. In this step, the collected data points were normalized between −1 and 1 to enhance the effectiveness of the applied methods and mitigate potential issues related to the learning process. Hence, the following equation was employed for data normalization:

where x_{i} represents the original measurement value, X_{n,i} denotes the normalized value, and x_{max} and x_{min} correspond to the maximum and minimum values of the variable, respectively. The normalization of the database was followed by data-splitting. After normalizing the database, the data was split into two main parts for constructing and verifying the models. Specifically, 80% of the entire dataset was allocated for the construction (training) part, while the remaining datasets were used for verification (testing). This resulted in 67 datasets for the construction part and 17 datasets for the verification part.

As mentioned, two machine learning approaches, namely GRNN and SVR, were employed to model the datasets. It was crucial to select appropriate control parameters to achieve optimal prediction performance with these approaches. The spreading coefficient of GRNN was optimized through a trial-and-error technique, while the three hyperparameters of SVR models were investigated using four nature-inspired algorithms: WOA, BBO, ACO, and GSA. In this study, linear, polynomial, RBF and sigmoid kernels were considered, and the RBF was chosen as the most optimal kernel function.

For GRNN modeling, a spread coefficient of 0.075 was chosen. The SVR parameters (C, ε, and γ) utilized in the four hybrid models are presented in

Model | C | ε | γ |
---|---|---|---|

SVR-GSA | 48152.3420 | 3.9704 | 9.6599 |

SVR-BBO | 82350.1721 | 3.9701 | 9.1805 |

SVR-ACO | 550208.5260 | 0.2246 | 0.8734 |

SVR-WOA | 1192118.4731 | 0.2173 | 0.8774 |

Algorithm | Parameter | Value |
---|---|---|

BBO | Keep rate | 0.2 |

Alpha | 0.9 | |

Mutation probability | 1 | |

Mutation step size | 0.05 | |

Mutation step size damp | 0.99 | |

Maximum iterations | 40 | |

Population size | 40 | |

GSA | [0,1] | |

Number of generations | 40 | |

Number of individuals | 40 | |

ACO | Population size | 40 |

Archive size | 40 | |

Selection pressure | 0.5 | |

Max number of generations | 40 | |

WOA | a | 2 to 0 |

r | [0,1] | |

Number of iterations | 40 | |

Number of whales | 40 |

In addition to the models discussed earlier, two traditional models, namely the ANN and KELM, were also utilized in this study. Further information regarding the ANN and KELM can be found in the literature [

In the ANN modeling, a three-layer structure was implemented, consisting of the input, hidden, and output layers with four, seven, and one neurons, respectively. For the hidden layer, multiple options ranging from 1 to 9 neurons (as suggested by Hecht-Nielsen [

This study utilized four hybrid models, namely SVR-WOA, SVR-BBO, SVR-ACO, and SVR-GSA, for flyrock prediction. Three other models, GRNN, ANN, and KELM, were employed. The accuracy of these models was assessed using six performance indices: MAPE, RMSD, Nash-Sutcliffe efficiency (NSE), RMSE [^{2} [^{2} values is considered the most optimal model.

Model | Performance indices | ||||||
---|---|---|---|---|---|---|---|

R^{2} (rank) |
RMSE (rank) | MAPE (rank) | RMSD (rank) | NSE (rank) | d (rank) | Total rank | |

SVR-BBO | 0.927 (2) | 16.239 (2) | 8.058 (1) | 16.24 (2) | 0.898 (2) | 0.975 (3) | 12 |

SVR-GSA | 0.932 (4) | 15.305 (4) | 7.947 (2) | 15.305 (4) | 0.91 (4) | 0.977 (4) | 22 |

SVR-ACO | 0.929 (3) | 18.228 (1) | 7.871 (3) | 18.228 (1) | 0.872 (1) | 0.958 (1) | 10 |

SVR-WOA | 0.984 (7) | 7.218 (7) | 3.463 (7) | 7.219 (7) | 0.98 (7) | 0.995 (7) | 42 |

GRNN | 0.969 (6) | 10.867 (5) | 5.573 (6) | 10.867 (5) | 0.961 (6) | 0.992 (6) | 34 |

ANN | 0.927 (2) | 15.661 (3) | 7.537 (4) | 15.662 (3) | 0.905 (3) | 0.971 (2) | 17 |

KELM | 0.958 (5) | 10.668 (6) | 6.395 (5) | 10.669 (6) | 0.956 (5) | 0.989 (5) | 32 |

^{2} values of all models for the testing phase, confirming that the SVR-WOA model achieves the best prediction performance and highest accuracy (0.984) among all the models. Furthermore, _{0.25}, Q_{0.75}, Median, and interquartile range (IQR). The table indicates that the SVR-WOA exhibits quartile values (Q_{0.25} and IQR) (128.83 and 73.80) that are closer to the actual values (131.48 and 74.15) compared to other models. In terms of Q_{0.75} values, KELM, SVR-GSA, SVR-BBO, SVR-WOA, GRNN, ANN, and SVR-ACO demonstrate closer values to the actual amounts. When considering the median values, the SVR-WOA model is found to have a value closer to the actual amount. Based on these findings, it is evident that the developed SVR-WOA model is more robust and provides more accurate flyrock predictions than the other models.

Variable | Actual | SVR-ACO | SVR-GSA | SVR-BBO | SVR-WOA | GRNN | ANN | KELM |
---|---|---|---|---|---|---|---|---|

Q_{0.25} |
131.48 | 136.50 | 124.61 | 122.76 | 128.83 | 128.12 | 138.15 | 127.19 |

Median | 178.42 | 175.77 | 155.28 | 157.11 | 178.18 | 175.04 | 174.22 | 179.35 |

Q_{0.75} |
205.63 | 194.95 | 203.97 | 202.01 | 201.63 | 201.13 | 195.18 | 204.16 |

IQR | 74.15 | 58.45 | 79.36 | 79.25 | 73.80 | 73.01 | 57.03 | 76.97 |

Blasting is considered the most frequent and typical method for fragmenting rocks in surface mines. Among the undesirable effects of blasting, flyrock is unquestionably one of the most dangerous. Therefore, controlling and minimizing flyrock is of paramount importance. In this study, the flyrock distance in two surface mines located in Iran is predicted using four hybrid SVR models: SVR-WOA, SVR-BBO, SVR-ACO, and SVR-GSA, as well as three other models including GRNN, ANN, and KELM. MAPE, RMSE, R^{2}, RMSD, NSE, and d are calculated to test the developed models’ accuracy. The results demonstrated the superiority of SVR-WOA over other models, as it exhibited the lowest MAPE, RMSE, and RMSD values and the highest R^{2}, NSE, and d values. For instance, GRNN, KELM, SVR-GSA, SVR-ACO, ANN, and SVR-BBO predicted flyrock values with an R^{2} higher than 0.92, which is considered good performance. However, SVR-WOA had the highest accuracy with an R^{2} of 0.984. Therefore, it can be concluded that WOA optimized SVR performance better than the other employed algorithms and can be generalized. It should be noted that the results yielded in this study are specific to the investigated mines, and for other mines, the modeling processes need to be repeated to select the most accurate model. This study utilized four input parameters (B, S, ST, and MCPD) to model flyrock. These parameters are blast design parameters, while other blast design parameters, particularly rock property parameters, have an influence on the intensity of flyrock. However, due to difficulties in collecting rock properties at our sites, we were unable to incorporate these parameters into our study. Therefore, for future research, it is recommended to consider the inclusion of rock property parameters, such as rock density. In future works, it would be interesting to explore the combination of other metaheuristic algorithms, such as African Buffalo Optimization, Artificial Root Foraging, Bottlenose Dolphin Optimization, and Coral Reefs Optimization algorithms with SVR and ANN models for prediction purposes in various mining and geotechnical fields. Although SVR-WOA demonstrated excellent performance and was selected as this study’s most accurate model, data-driven models have limitations. These models often rely on input-output mapping methods that solely estimate static field parameters, neglecting the capturing of the dynamic response process. Graph and transformer neural networks can be considered valuable approaches to address this limitation.

None.

Adaptive neuro-fuzzy inference system

Ammonium Nitrate Fuel Oil

Ant colony optimization

Artificial intelligence

Artificial neural network

Back-propagation neural network

Biogeography-based optimization

Boosted regression tree

Burden

Coefficient of determination

Deep neural network

Extreme learning machine

Firefly algorithm

General regression neural network

Index of agreement

Genetic algorithm

Gravitational search algorithm

Grey wolf optimization algorithm

Kernel extreme learning machine

Maximum charge per delay

Mean absolute percentage error

Nash-Sutcliffe efficiency

Particle swarm optimization

Quartile

Radial basic function

Random forest

Root mean square deviation

Root mean square error

Spacing

Stemming

Structural risk minimization

Support vector regression

Tunnel boring machine

Unconfined compressive strength

Whale optimization algorithm

The authors received no specific funding for this study.

The authors confirm contribution to the paper as follows: study conception and design: Mahdi Hasanipanah, Jiandong Huang; data collection: Mahdi Hasanipanah; analysis and interpretation of results: Ji Zhou, Yijun Lu, Qiong Tian, Haichuan Liu; draft manuscript preparation: Ji Zhou, Yijun Lu, Qiong Tian, Haichuan Liu, Mahdi Hasanipanah, Jiandong Huang. All authors reviewed the results and approved the final version of the manuscript.

The data of this research can be available from the corresponding author upon request.

The authors declare that they have no conflicts of interest to report regarding the present study.