A hybrid metaheuristic approach using random forest and particle swarm optimization to study and evaluate backbreak in open-pit blasting
- Dai, Yong, Khandelwal, Manoj, Qiu, Yingui, Zhou, Jian, Monjezi, Monjezi, Yang, Peixi
- Authors: Dai, Yong , Khandelwal, Manoj , Qiu, Yingui , Zhou, Jian , Monjezi, Monjezi , Yang, Peixi
- Date: 2022
- Type: Text , Journal article
- Relation: Neural Computing and Applications Vol. 34, no. 8 (2022), p. 6273-6288
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- Description: Backbreak is a rock fracture problem that exceeds the limits of the last row of holes in an explosion operation. Excessive backbreak increases operational costs and also poses a threat to mine safety. In this regard, a new hybrid intelligence approach based on random forest (RF) and particle swarm optimization (PSO) is proposed for predicting backbreak with high accuracy to reduce the unsolicited phenomenon induced by backbreak in open-pit blasting. A data set of 234 samples with six input parameters including special drilling (SD), spacing (S), burden (B), hole length (L), stemming (T) and powder factor (PF) and one output parameter backbreak (BB) is set up in this study. Seven input combinations (one with six parameters, six with five parameters) are built to generate the optimal prediction model. The PSO algorithm is integrated with the RF algorithm to find the optimal hyper-parameters of each model and the fitness function, which is the mean absolute error (MAE) of ten cross-validations. The performance capacities of the optimal models are assessed using MAE, root-mean-square error (RMSE), Pearson correlation coefficient (R2) and mean absolute percentage error (MAPE). Findings demonstrated that the PSO–RF model combining L–S–B–T–PF with MAE of 0.0132 and 0.0568, RMSE of 0.0811 and 0.1686, R2 of 0.9990 and 0.9961 and MAPE of 0.0027 and 0.0116 in training and testing phases, respectively, has optimal prediction performance. The optimal PSO–RF models were compared with the classical artificial neural network, RF, genetic programming, support vector machine and convolutional neural network models and show that the PSO–RF model has superiority in predicting backbreak. The Gini index of each input variable has also been calculated in the RF model, which was 31.2 (L), 23.1 (S), 27.4 (B), 36.6 (T), 23.4 (PF) and 16.9 (SD), respectively. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
- Authors: Dai, Yong , Khandelwal, Manoj , Qiu, Yingui , Zhou, Jian , Monjezi, Monjezi , Yang, Peixi
- Date: 2022
- Type: Text , Journal article
- Relation: Neural Computing and Applications Vol. 34, no. 8 (2022), p. 6273-6288
- Full Text:
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- Description: Backbreak is a rock fracture problem that exceeds the limits of the last row of holes in an explosion operation. Excessive backbreak increases operational costs and also poses a threat to mine safety. In this regard, a new hybrid intelligence approach based on random forest (RF) and particle swarm optimization (PSO) is proposed for predicting backbreak with high accuracy to reduce the unsolicited phenomenon induced by backbreak in open-pit blasting. A data set of 234 samples with six input parameters including special drilling (SD), spacing (S), burden (B), hole length (L), stemming (T) and powder factor (PF) and one output parameter backbreak (BB) is set up in this study. Seven input combinations (one with six parameters, six with five parameters) are built to generate the optimal prediction model. The PSO algorithm is integrated with the RF algorithm to find the optimal hyper-parameters of each model and the fitness function, which is the mean absolute error (MAE) of ten cross-validations. The performance capacities of the optimal models are assessed using MAE, root-mean-square error (RMSE), Pearson correlation coefficient (R2) and mean absolute percentage error (MAPE). Findings demonstrated that the PSO–RF model combining L–S–B–T–PF with MAE of 0.0132 and 0.0568, RMSE of 0.0811 and 0.1686, R2 of 0.9990 and 0.9961 and MAPE of 0.0027 and 0.0116 in training and testing phases, respectively, has optimal prediction performance. The optimal PSO–RF models were compared with the classical artificial neural network, RF, genetic programming, support vector machine and convolutional neural network models and show that the PSO–RF model has superiority in predicting backbreak. The Gini index of each input variable has also been calculated in the RF model, which was 31.2 (L), 23.1 (S), 27.4 (B), 36.6 (T), 23.4 (PF) and 16.9 (SD), respectively. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
A true triaxial strength criterion for rocks by gene expression programming
- Zhou, Jian, Zhang, Rui, Qiu, Yingui, Khandelwal, Manoj
- Authors: Zhou, Jian , Zhang, Rui , Qiu, Yingui , Khandelwal, Manoj
- Date: 2023
- Type: Text , Journal article
- Relation: Journal of Rock Mechanics and Geotechnical Engineering Vol. 15, no. 10 (2023), p. 2508-2520
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- Description: Rock strength is a crucial factor to consider when designing and constructing underground projects. This study utilizes a gene expression programming (GEP) algorithm-based model to predict the true triaxial strength of rocks, taking into account the influence of rock genesis on their mechanical behavior during the model building process. A true triaxial strength criterion based on the GEP model for igneous, metamorphic and magmatic rocks was obtained by training the model using collected data. Compared to the modified Weibols-Cook criterion, the modified Mohr-Coulomb criterion, and the modified Lade criterion, the strength criterion based on the GEP model exhibits superior prediction accuracy performance. The strength criterion based on the GEP model has better performance in R2, RMSE and MAPE for the data set used in this study. Furthermore, the strength criterion based on the GEP model shows greater stability in predicting the true triaxial strength of rocks across different types. Compared to the existing strength criterion based on the genetic programming (GP) model, the proposed criterion based on GEP model achieves more accurate predictions of the variation of true triaxial strength (
- Authors: Zhou, Jian , Zhang, Rui , Qiu, Yingui , Khandelwal, Manoj
- Date: 2023
- Type: Text , Journal article
- Relation: Journal of Rock Mechanics and Geotechnical Engineering Vol. 15, no. 10 (2023), p. 2508-2520
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- Description: Rock strength is a crucial factor to consider when designing and constructing underground projects. This study utilizes a gene expression programming (GEP) algorithm-based model to predict the true triaxial strength of rocks, taking into account the influence of rock genesis on their mechanical behavior during the model building process. A true triaxial strength criterion based on the GEP model for igneous, metamorphic and magmatic rocks was obtained by training the model using collected data. Compared to the modified Weibols-Cook criterion, the modified Mohr-Coulomb criterion, and the modified Lade criterion, the strength criterion based on the GEP model exhibits superior prediction accuracy performance. The strength criterion based on the GEP model has better performance in R2, RMSE and MAPE for the data set used in this study. Furthermore, the strength criterion based on the GEP model shows greater stability in predicting the true triaxial strength of rocks across different types. Compared to the existing strength criterion based on the genetic programming (GP) model, the proposed criterion based on GEP model achieves more accurate predictions of the variation of true triaxial strength (
Developing a hybrid model of Jaya algorithm-based extreme gradient boosting machine to estimate blast-induced ground vibrations
- Zhou, Jian, Qiu, Yingui, Khandelwal, Manoj, Zhu, Shuangli, Zhang, Xiliang
- Authors: Zhou, Jian , Qiu, Yingui , Khandelwal, Manoj , Zhu, Shuangli , Zhang, Xiliang
- Date: 2021
- Type: Text , Journal article
- Relation: International Journal of Rock Mechanics and Mining Sciences Vol. 145, no. (2021), p.
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- Description: Blasting is still being considered to be one the most important applicable alternatives for conventional excavations. Ground vibration generated due to blasting is an undesirable phenomenon which is harmful for the nearby structures and should be prevented. In this regard, a novel intelligent approach for predicting blast-induced PPV was developed. The distinctive Jaya algorithm and high efficient extreme gradient boosting machine (XGBoost) were applied to obtain the goal, called the Jaya-XGBoost model. Accordingly, 150 sets of data composed of 13 controllable and uncontrollable parameters are chosen as input independent variables and the measured peak particle velocity (PPV) is chosen as an output dependent variable. Also, the Jaya algorithm was used for optimization of hyper-parameters of XGBoost. Additionally, six empirical models and several machine learning models such as XGBoost, random forest, AdaBoost, artificial neural network and Bagging were also considered and applied for comparison of the proposed Jaya-XGBoost model. Accuracy criteria including determination coefficient (R2), root-mean-square error (RMSE), mean absolute error (MAE), and the variance accounted for (VAF) were used for the assessment of models. For this study, 150 blasting operations were analyzed. Also, the Shapley Additive Explanations (SHAP) method is used to interpret the importance of features and their contribution to PPV prediction. Findings reveal that the proposed Jaya-XGBoost emerged as the most reliable model in contrast to other machine learning models and traditional empirical models. This study may be helpful to mining researchers and engineers who use intelligent machine learning algorithms to predict blast-induced ground vibration. © 2021 Elsevier Ltd
- Authors: Zhou, Jian , Qiu, Yingui , Khandelwal, Manoj , Zhu, Shuangli , Zhang, Xiliang
- Date: 2021
- Type: Text , Journal article
- Relation: International Journal of Rock Mechanics and Mining Sciences Vol. 145, no. (2021), p.
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- Description: Blasting is still being considered to be one the most important applicable alternatives for conventional excavations. Ground vibration generated due to blasting is an undesirable phenomenon which is harmful for the nearby structures and should be prevented. In this regard, a novel intelligent approach for predicting blast-induced PPV was developed. The distinctive Jaya algorithm and high efficient extreme gradient boosting machine (XGBoost) were applied to obtain the goal, called the Jaya-XGBoost model. Accordingly, 150 sets of data composed of 13 controllable and uncontrollable parameters are chosen as input independent variables and the measured peak particle velocity (PPV) is chosen as an output dependent variable. Also, the Jaya algorithm was used for optimization of hyper-parameters of XGBoost. Additionally, six empirical models and several machine learning models such as XGBoost, random forest, AdaBoost, artificial neural network and Bagging were also considered and applied for comparison of the proposed Jaya-XGBoost model. Accuracy criteria including determination coefficient (R2), root-mean-square error (RMSE), mean absolute error (MAE), and the variance accounted for (VAF) were used for the assessment of models. For this study, 150 blasting operations were analyzed. Also, the Shapley Additive Explanations (SHAP) method is used to interpret the importance of features and their contribution to PPV prediction. Findings reveal that the proposed Jaya-XGBoost emerged as the most reliable model in contrast to other machine learning models and traditional empirical models. This study may be helpful to mining researchers and engineers who use intelligent machine learning algorithms to predict blast-induced ground vibration. © 2021 Elsevier Ltd
Estimation of the TBM advance rate under hard rock conditions using XGBoost and Bayesian optimization
- Zhou, Jian, Qiu, Yingui, Zhu, Shuangli, Armaghani, Danial, Khandelwal, Manoj, Mohamad, Edy
- Authors: Zhou, Jian , Qiu, Yingui , Zhu, Shuangli , Armaghani, Danial , Khandelwal, Manoj , Mohamad, Edy
- Date: 2021
- Type: Text , Journal article
- Relation: Underground Space Vol. 6, no. 5 (Oct 2021), p. 506-515
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- Description: The advance rate (AR) of a tunnel boring machine (TBM) under hard rock conditions is a key parameter in the successful implementation of tunneling engineering. In this study, we improved the accuracy of prediction models by employing a hybrid model of extreme gradient boosting (XGBoost) with Bayesian optimization (BO) to model the TBM AR. To develop the proposed models, 1286 sets of data were collected from the Peng Selangor Raw Water Transfer tunnel project in Malaysia. The database consists of rock mass and intact rock features, including rock mass rating, rock quality designation, weathered zone, uniaxial compressive strength, and Brazilian tensile strength. Machine specifications, including revolution per minute and thrust force, were considered to predict the TBM AR. The accuracies of the predictive models were examined using the root mean squares error (RMSE) and the coefficient of determination (R-2) between the observed and predicted yield by employing a five-fold cross-validation procedure. Results showed that the BO algorithm can capture better hyper-parameters for the XGBoost prediction model than can the default XGBoost model. The robustness and generalization of the BO-XGBoost model yielded prominent results with RMSE and R-2 values of 0.0967 and 0.9806 (for the testing phase), respectively. The results demonstrated the merits of the proposed BO-XGBoost model. In addition, variable importance through mutual information tests was applied to interpret the XGBoost model and demonstrated that machine parameters have the greatest impact as compared to rock mass and material properties.
- Authors: Zhou, Jian , Qiu, Yingui , Zhu, Shuangli , Armaghani, Danial , Khandelwal, Manoj , Mohamad, Edy
- Date: 2021
- Type: Text , Journal article
- Relation: Underground Space Vol. 6, no. 5 (Oct 2021), p. 506-515
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- Description: The advance rate (AR) of a tunnel boring machine (TBM) under hard rock conditions is a key parameter in the successful implementation of tunneling engineering. In this study, we improved the accuracy of prediction models by employing a hybrid model of extreme gradient boosting (XGBoost) with Bayesian optimization (BO) to model the TBM AR. To develop the proposed models, 1286 sets of data were collected from the Peng Selangor Raw Water Transfer tunnel project in Malaysia. The database consists of rock mass and intact rock features, including rock mass rating, rock quality designation, weathered zone, uniaxial compressive strength, and Brazilian tensile strength. Machine specifications, including revolution per minute and thrust force, were considered to predict the TBM AR. The accuracies of the predictive models were examined using the root mean squares error (RMSE) and the coefficient of determination (R-2) between the observed and predicted yield by employing a five-fold cross-validation procedure. Results showed that the BO algorithm can capture better hyper-parameters for the XGBoost prediction model than can the default XGBoost model. The robustness and generalization of the BO-XGBoost model yielded prominent results with RMSE and R-2 values of 0.0967 and 0.9806 (for the testing phase), respectively. The results demonstrated the merits of the proposed BO-XGBoost model. In addition, variable importance through mutual information tests was applied to interpret the XGBoost model and demonstrated that machine parameters have the greatest impact as compared to rock mass and material properties.
Performance evaluation of rockburst prediction based on PSO-SVM, HHO-SVM, and MFO-SVM hybrid models
- Zhou, Jian, Yang, Peixi, Peng, Pingan, Khandelwal, Manoj, Qiu, Yingui
- Authors: Zhou, Jian , Yang, Peixi , Peng, Pingan , Khandelwal, Manoj , Qiu, Yingui
- Date: 2023
- Type: Text , Journal article
- Relation: Mining, Metallurgy and Exploration Vol. 40, no. 2 (2023), p. 617-635
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- Description: Rockburst prediction is crucial in deep hard rock mines and tunnels to make safer working conditions. Due to the complex interaction of many factors involved in rockburst prediction, such as multi-variable and multi-interference factors, three hybrid support vector machine (SVM) models optimized by particle swarm optimization (PSO), Harris hawk optimization (HHO), and moth flame optimization (MFO) are proposed to predict rockburst hazard level (RHL). The RHL is determined according to four kinds of microseismic characteristic parameters including angular frequency ratio, total energy, apparent stress, and convexity radius. Then, six types of microseismic characteristic parameters are taken as input variables in 343 sets of data, including angular frequency ratio and total energy, etc. And the RHL is taken as the output target of rockburst prediction. The classification performance of PSO-SVM, HHO-SVM, and MFO-SVM hybrid models is evaluated by accuracy (ACC), precision (PRE), and kappa coefficient. Findings reveal that the MFO-SVM model performs best in terms of accuracy, with ACC, PRE, and kappa coefficients reaching 0.9559, 0.9063, and 0.9094 respectively, while PSO-SVM and HHO-SVM have similar performances. However, the PSO-SVM, HHO-SVM, and MFO-SVM all perform better than the unoptimized SVM model. This confirms that the three optimization algorithms significantly enhance the rockburst prediction capacity of the SVM model to help mine practitioners apply machine learning methods to rockburst prediction problems appropriately. © 2023, Society for Mining, Metallurgy & Exploration Inc.
- Authors: Zhou, Jian , Yang, Peixi , Peng, Pingan , Khandelwal, Manoj , Qiu, Yingui
- Date: 2023
- Type: Text , Journal article
- Relation: Mining, Metallurgy and Exploration Vol. 40, no. 2 (2023), p. 617-635
- Full Text:
- Reviewed:
- Description: Rockburst prediction is crucial in deep hard rock mines and tunnels to make safer working conditions. Due to the complex interaction of many factors involved in rockburst prediction, such as multi-variable and multi-interference factors, three hybrid support vector machine (SVM) models optimized by particle swarm optimization (PSO), Harris hawk optimization (HHO), and moth flame optimization (MFO) are proposed to predict rockburst hazard level (RHL). The RHL is determined according to four kinds of microseismic characteristic parameters including angular frequency ratio, total energy, apparent stress, and convexity radius. Then, six types of microseismic characteristic parameters are taken as input variables in 343 sets of data, including angular frequency ratio and total energy, etc. And the RHL is taken as the output target of rockburst prediction. The classification performance of PSO-SVM, HHO-SVM, and MFO-SVM hybrid models is evaluated by accuracy (ACC), precision (PRE), and kappa coefficient. Findings reveal that the MFO-SVM model performs best in terms of accuracy, with ACC, PRE, and kappa coefficients reaching 0.9559, 0.9063, and 0.9094 respectively, while PSO-SVM and HHO-SVM have similar performances. However, the PSO-SVM, HHO-SVM, and MFO-SVM all perform better than the unoptimized SVM model. This confirms that the three optimization algorithms significantly enhance the rockburst prediction capacity of the SVM model to help mine practitioners apply machine learning methods to rockburst prediction problems appropriately. © 2023, Society for Mining, Metallurgy & Exploration Inc.
Performance of hybrid SCA-RF and HHO-RF models for predicting backbreak in open-pit mine blasting operations
- Zhou, Jian, Dai, Yong, Khandelwal, Manoj, Monjezi, Masoud, Yu, Zhi, Qiu, Yingui
- Authors: Zhou, Jian , Dai, Yong , Khandelwal, Manoj , Monjezi, Masoud , Yu, Zhi , Qiu, Yingui
- Date: 2021
- Type: Text , Journal article
- Relation: Natural Resources Research Vol. 30, no. 6 (2021), p. 4753-4771
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- Description: Backbreak is an adverse phenomenon in blasting operation, which can cause, among others, mine walls instability, falling down of machinery, drilling efficiency reduction and stripping ratio enhancement. Therefore, this research aimed to develop two-hybrid RF (Random Forest) prediction models of random forest, which are optimized by Harris hawks optimizer (HHO) and sine cosine algorithm (SCA), for estimation of the backbreak distance. The HHO and SCA algorithms were adopted to determine two hyper-parameters (mtry and ntree) in the RF models, in which root mean square error (RMSE) was utilized as a fitness function. A database with 234 samples was established, in which six variables [i.e., hole length (L), burden (B), spacing (S), stemming (T), special drilling (SD) and powder factor (PF)] were used as input variables, and backbreak was defined as output variable. Additionally, three classical regression models (i.e., extreme learning machine, radial basis function network and general regression neural network) were adopted to verify the superiority of the hybrid RF prediction models. The predictive reliability of the proposed models was assessed by the combination of mean absolute error (MAE), RMSE, variance accounted for (VAF) and Pearson correlation coefficient (R2). The results revealed that the SCA-RF model outperformed all the other prediction models with MAE of (0.0444 and 0.0470), RMSE of (0.0816 and 0.0996), VAF of (96.82 and 95.88) and R2 of (0.9876 and 0.9829) in training and testing stages, respectively. A Gini index generated internally in the RF model showed that backbreak was significantly more sensitive to L and T than to SD. © 2021, International Association for Mathematical Geosciences.
- Authors: Zhou, Jian , Dai, Yong , Khandelwal, Manoj , Monjezi, Masoud , Yu, Zhi , Qiu, Yingui
- Date: 2021
- Type: Text , Journal article
- Relation: Natural Resources Research Vol. 30, no. 6 (2021), p. 4753-4771
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- Description: Backbreak is an adverse phenomenon in blasting operation, which can cause, among others, mine walls instability, falling down of machinery, drilling efficiency reduction and stripping ratio enhancement. Therefore, this research aimed to develop two-hybrid RF (Random Forest) prediction models of random forest, which are optimized by Harris hawks optimizer (HHO) and sine cosine algorithm (SCA), for estimation of the backbreak distance. The HHO and SCA algorithms were adopted to determine two hyper-parameters (mtry and ntree) in the RF models, in which root mean square error (RMSE) was utilized as a fitness function. A database with 234 samples was established, in which six variables [i.e., hole length (L), burden (B), spacing (S), stemming (T), special drilling (SD) and powder factor (PF)] were used as input variables, and backbreak was defined as output variable. Additionally, three classical regression models (i.e., extreme learning machine, radial basis function network and general regression neural network) were adopted to verify the superiority of the hybrid RF prediction models. The predictive reliability of the proposed models was assessed by the combination of mean absolute error (MAE), RMSE, variance accounted for (VAF) and Pearson correlation coefficient (R2). The results revealed that the SCA-RF model outperformed all the other prediction models with MAE of (0.0444 and 0.0470), RMSE of (0.0816 and 0.0996), VAF of (96.82 and 95.88) and R2 of (0.9876 and 0.9829) in training and testing stages, respectively. A Gini index generated internally in the RF model showed that backbreak was significantly more sensitive to L and T than to SD. © 2021, International Association for Mathematical Geosciences.
Six novel hybrid extreme learning machine–swarm intelligence optimization (ELM–SIO) models for predicting backbreak in open-pit blasting
- Li, Chuanqi, Zhou, Jian, Khandelwal, Manoj, Zhang, Xiliang, Monjezi, Masoud, Qiu, Yingui
- Authors: Li, Chuanqi , Zhou, Jian , Khandelwal, Manoj , Zhang, Xiliang , Monjezi, Masoud , Qiu, Yingui
- Date: 2022
- Type: Text , Journal article
- Relation: Natural Resources Research Vol. 31, no. 5 (2022), p. 3017-3039
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- Description: Backbreak (BB) is one of the serious adverse blasting consequences in open-pit mines, because it frequently reduces economic benefits and seriously affects the safety of mines. Therefore, rapid and accurate prediction of BB is of great significance to mine blasting design and other production activities. For this purpose, six different swarm intelligence optimization (SIO) algorithms were proposed to optimize the extreme learning machine (ELM) model for BB prediction, i.e., ELM-based particle swarm optimization (ELM–PSO), ELM-based fruit fly optimization (ELM–FOA), ELM-based whale optimization algorithm (ELM–WOA), ELM-based lion swarm optimization (ELM–LOA), ELM-based seagull optimization algorithm (ELM–SOA) and ELM-based sparrow search algorithm (ELM–SSA). In total, 234 data records from blasting operations in the Sungun mine in Iran were used in this study, including six input parameters (special drilling, spacing, burden, hole length, stemming, powder factor) and one output parameter (i.e., BB). To evaluate the predictive performance of the different optimization models and initial models, six performance indicators including the root mean square error (RMSE), Pearson correlation coefficient (R), determination coefficient (R2), variance accounted for (VAF), mean absolute error (MAE) and sum of square error (SSE) were used to evaluate the models in the training and testing phases. The results show that the ELM–LSO was the best model to predict BB with RMSE of 0.1129 (R: 0.9991, R2: 0.9981, VAF: 99.8135%, MAE: 0.0706 and SSE: 2.0917) in the training phase and 0.2441 in the testing phase (R: 0.9949, R2: 0.9891, VAF: 98.9806%, MAE: 0.1669 and SSE: 4.1710). Hence, ELM techniques combined with SIO algorithms are an effective method to predict BB. © 2022, The Author(s).
- Authors: Li, Chuanqi , Zhou, Jian , Khandelwal, Manoj , Zhang, Xiliang , Monjezi, Masoud , Qiu, Yingui
- Date: 2022
- Type: Text , Journal article
- Relation: Natural Resources Research Vol. 31, no. 5 (2022), p. 3017-3039
- Full Text:
- Reviewed:
- Description: Backbreak (BB) is one of the serious adverse blasting consequences in open-pit mines, because it frequently reduces economic benefits and seriously affects the safety of mines. Therefore, rapid and accurate prediction of BB is of great significance to mine blasting design and other production activities. For this purpose, six different swarm intelligence optimization (SIO) algorithms were proposed to optimize the extreme learning machine (ELM) model for BB prediction, i.e., ELM-based particle swarm optimization (ELM–PSO), ELM-based fruit fly optimization (ELM–FOA), ELM-based whale optimization algorithm (ELM–WOA), ELM-based lion swarm optimization (ELM–LOA), ELM-based seagull optimization algorithm (ELM–SOA) and ELM-based sparrow search algorithm (ELM–SSA). In total, 234 data records from blasting operations in the Sungun mine in Iran were used in this study, including six input parameters (special drilling, spacing, burden, hole length, stemming, powder factor) and one output parameter (i.e., BB). To evaluate the predictive performance of the different optimization models and initial models, six performance indicators including the root mean square error (RMSE), Pearson correlation coefficient (R), determination coefficient (R2), variance accounted for (VAF), mean absolute error (MAE) and sum of square error (SSE) were used to evaluate the models in the training and testing phases. The results show that the ELM–LSO was the best model to predict BB with RMSE of 0.1129 (R: 0.9991, R2: 0.9981, VAF: 99.8135%, MAE: 0.0706 and SSE: 2.0917) in the training phase and 0.2441 in the testing phase (R: 0.9949, R2: 0.9891, VAF: 98.9806%, MAE: 0.1669 and SSE: 4.1710). Hence, ELM techniques combined with SIO algorithms are an effective method to predict BB. © 2022, The Author(s).
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