# Optimized Data-Driven Models for Prediction of Flyrock due to Blasting in Surface Mines

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^{2}

^{3}

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^{5}

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## Abstract

**:**

## 1. Introduction

## 2. Research Significance

## 3. Materials and Methods

#### 3.1. Materials

#### 3.2. Methods

#### 3.2.1. LSSVM Model

^{T}points out the transpose operator, $w$ and $b$ are the weight and bias parameters, respectively, and $\phi $ is a nonlinear mapping function.

- (A)
- Gravitational search algorithm (GSA)

- (B)
- Whale optimization algorithm (WOA)

- (C)
- Artificial Bee Colony (ABC)

- -
- An initial population of bees is generated randomly. Each bee has its own position x. The numbers of employed and onlookers are the same in the population. A fitness function is considered for assessing the quality of the bees.
- -
- Employed bees: this step consists of updating the positions of bees at the generation ($g+1$) using the following equation:

- -
- Onlooker bees: by carrying out the previous step which emulates the exploitation phase, the gained information by the employed bees is exposed to the onlookers, which select the proper ones by applying the following equation bases on the probability $P$:

- -
- Scout bees: this step consists of randomly changing the position of a given employed bee after a defined number of generations if it does not show any improvements in its fitness quality.

#### 3.2.2. CFNN Model

#### 3.2.3. Model Performance Evaluation

^{2}):

## 4. Development of Predictive Models

## 5. Results and Discussion

#### 5.1. Exploratory Analysis

#### 5.2. Modelling Results

^{2}, and RMSE are reported for the training set, the test set, and the whole dataset. According to this table, and based on the schemes, it can be seen that M

_{1}is the best one, followed by M

_{2}. In the combination of M

_{1}including all inputs for the testing phase, the LSSVM-WOA in terms of (R

^{2}= 0.999, RMSE = 3.4209 m, and AARE = 1.3017) was identified as the superior predictive model, followed by CFNN-LMA (R

^{2}= 0.9347, RMSE = 16.5215 m, and AARE = 7.512), LSSVM-GSA (R

^{2}= 0.904, RMSE = 16.1775 m, and AARE = 5.5193), and LSSVM-ABC (R

^{2}= 0.9049, RMSE = 19.439 m, and AARE = 8.0032), respectively. In the M

_{2}(in testing phase), as the second-best combination, the LSSVM-WOA with respect to the highest R

^{2}(0.9896) and smallest RMSE (10.4268) outperformed the other models. The result assessment demonstrated that M

_{6}on account of poorest performance (R

^{2}= 0.3616 and RMSE = 58.5744 for the LSSVM-WOA) was recognized as the worst scheme regardless of the ML type. Typically, it can be understood from this remark that S is the most impacting input parameter on FR as its exclusion from the input variables (M

_{6}) caused the worst prediction performance regardless of the type of ML techniques, while density has a small effect on FR since its elimination from the input parameters (M

_{2}) did not significantly affect the degree of prediction accuracy. In addition, it can also be deduced that for each of the six schemes, the LSSVM-WOA yielded more accurate predictions compared with the other LSSVM-metaheuristic algorithms and the CFNN-LMA. According to Table 3, it was found that M

_{1}outperformed other combinations followed by M

_{2}, M

_{4}, M

_{3}, M

_{5}, and M

_{6}, respectively. Additionally, it can be said that the LSSVM-WOA in all input combinations was the best predictive model developed in this study for prediction of FR. For better comparison between the predictive performances of the provided models in all combinations, the probability density function violin plots are exhibited in Figure 4. According to this figure, considering the best agreement between measured and predicted values of FR, it can be clearly implied that the LSSVM-WOA was the superior model for accurately estimating FR, the CFNN-LMA was identified as the second-best model, and LSSVM-ABC yielded the worst results in all combinations. Regarding the mentioned analysis, the combination of M

_{1}was kept for further performance investigation and validations. It is necessary to add that in order to confirm that the ANN scheme did not suffer from the overfitting issue, a 4-fold cross-validation was performed on our best ANN paradigm (the case of M

_{1}) to assess the generalization of the model when dealing with new sets of data. To do so, the database was randomly divided into 4 folds, then, the modelling was done by considering a sole fold as the test sub-data and devoting the rest for the training phase. In order to swap between the folds involved in the training and testing phases, the aforesaid step was repeated 4 times. The results gained from the 4-fold cross-validation are reported in Table 4. As can be seen, the consistency of the model is confirmed for all the folds, thus, the overfitting issue is avoided.

_{1}which illustrate a comparison of the measured and predicted FR values during both the training and testing phases. Based on the scatter plots, a tight cloud of points is located nearby the line Y = X for all datasets. This means that the LSSVM-WOA can predict FR values with a great degree of accuracy as its predictions are very close to the perfect case shown by the unit-slop line. The left side of Figure 6 shows the ability of the predictive models to capture the non-linearity behaviour of the datasets. The LSSVM-WOA yields the best agreement with the measured FR compared with other LSSVM models and the CFNN-LMA model.

## 6. Conclusions

^{2}, and RMSE, were used to check the performance of the models and to compare their results.

^{2}= 0.9991 and RMSE = 3.4209), LSSVM-GSA (AARE = 5.5193, R

^{2}= 0.904 and RMSE = 16.1775), and CFNN-LMA (AARE = 7.512, R

^{2}= 0.9347 and RMSE = 16.5215) were obtained from the first scheme, while that for the LSSVM-ABC model (AARE = 7.083, R

^{2}= 0.9235 and RMSE = 16.7483) was obtained from the second scheme. It is important to note that the above results were related to the testing phase. On the other hand, the sixth scheme had the worst performance. In this scheme, the S parameter was removed from the modelling. Therefore, it can be suggested that the S was an effective parameter in the modelling. Additionally, according to RD%, the LSSVM-WOA model had very low prediction errors regardless of the considered conditions. The presented results in this study cannot be compared with results of the previous studies because different fields investigation as well as different range of input parameters were used in the previous studies. Nevertheless, for a comparison with the literature, the LSSVM-WOA presented in this study predicted the FR with a very good R

^{2}, while Koopialipoor et al. [55], Faradonbeh et al. [56], Zhou et al. [57], Nguyen et al. [58], and Marto et al. [59] predicted the FR with an R

^{2}of 0.959, 0.924, 0.944, 0.986, and 0.981, respectively. The aforementioned results indicate the effectiveness of the LSSVM-WOA model in predicting the FR.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Correlogram for assessing the Pearson correlation coefficient between input and target parameters. Green: Histogram, Red: Regression line, and Blue: Distribution points.

**Figure 4.**Probability density function of the predictive models of M

_{1}for prediction of FR for all datasets used in the simulation process.

**Figure 5.**Comparing the predicted and measured FR values in the form of the cross plot and trend variation plot for all datasets.

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

ABC | Number of employer bees | 20 |

Number of onlooker bees | 20 | |

Number of generations | 30 | |

Number of generations to scout bees | 4 | |

GSA | ${r}_{1j}$ and ${r}_{2j}$ | [0, 1] |

Number of generations | 30 | |

Number of individuals | 40 | |

WOA | a | 2 to 0 |

r | [0, 1] | |

Number of generations | 30 | |

Number of whales | 40 |

Metric/Feature | S (m) | B (m) | ST (m) | PF (kg/m^{3}) | Density (gr/cm^{3}) | FR (m) |
---|---|---|---|---|---|---|

Minimum | 2.65 | 1.5 | 1.7 | 0.67 | 2.3 | 61 |

Maximum | 4 | 3.2 | 3.6 | 1.05 | 2.8 | 334 |

Mean | 3.324 | 2.415 | 2.171 | 0.8908 | 2.579 | 223.5 |

Std. Deviation | 0.4228 | 0.4776 | 0.4022 | 0.113 | 0.1684 | 64.61 |

CV | 12.72% | 19.78% | 18.53% | 12.69% | 6.529% | 28.91% |

Skewness | −0.2032 | 0.2017 | 1.608 | −0.2148 | −0.2942 | −0.5848 |

Kurtosis | −1.556 | −1.518 | 2.82 | −1.058 | −1.247 | −0.1065 |

Scheme | Model | Statistical Criteria | Train Data | Test Data | All Data |
---|---|---|---|---|---|

M_{1} | CFNN-LMA | R^{2} | 0.9875 | 0.9347 | 0.977 |

AARE | 2.5163 | 7.512 | 3.5154 | ||

RMSE | 7.2292 | 16.5215 | 9.8184 | ||

LSSVM-ABC | R^{2} | 0.9867 | 0.9049 | 0.971 | |

AARE | 3.0419 | 8.0032 | 4.0341 | ||

RMSE | 7.4089 | 19.439 | 10.9311 | ||

LSSVM-GSA | R^{2} | 0.9828 | 0.904 | 0.967 | |

AARE | 3.4215 | 5.5193 | 3.8411 | ||

RMSE | 8.7308 | 16.1775 | 10.6453 | ||

LSSVM-WOA | R^{2} | 0.9926 | 0.9991 | 0.9943 | |

AARE | 1.6473 | 1.3017 | 1.5782 | ||

RMSE | 7.4847 | 3.4209 | 6.8671 | ||

M_{2} | CFNN-LMA | R^{2} | 0.9812 | 0.9366 | 0.972 |

AARE | 2.9261 | 8.5748 | 4.0558 | ||

RMSE | 8.4645 | 20.2612 | 11.8077 | ||

LSSVM-ABC | R^{2} | 0.9769 | 0.9235 | 0.9675 | |

AARE | 3.7643 | 7.083 | 4.428 | ||

RMSE | 9.8655 | 16.7483 | 11.5743 | ||

LSSVM-GSA | R^{2} | 0.9754 | 0.9054 | 0.9614 | |

AARE | 4.254 | 6.5356 | 4.7103 | ||

RMSE | 10.3962 | 18.0443 | 12.312 | ||

LSSVM-WOA | R^{2} | 0.9871 | 0.9896 | 0.9875 | |

AARE | 2.6662 | 2.8723 | 2.7074 | ||

RMSE | 10.105 | 10.4268 | 10.1702 | ||

M_{3} | CFNN-LMA | R^{2} | 0.883 | 0.9172 | 0.89 |

AARE | 7.2573 | 8.2441 | 7.4546 | ||

RMSE | 21.9097 | 18.6501 | 21.2977 | ||

LSSVM-ABC | R^{2} | 0.9191 | 0.7622 | 0.8811 | |

AARE | 6.7642 | 12.4379 | 7.8989 | ||

RMSE | 17.7366 | 34.5376 | 22.1413 | ||

LSSVM-GSA | R^{2} | 0.8874 | 0.7979 | 0.8714 | |

AARE | 7.8757 | 13.615 | 9.0236 | ||

RMSE | 21.7035 | 27.6908 | 23.0259 | ||

LSSVM-WOA | R^{2} | 0.9625 | 0.9398 | 0.9305 | |

AARE | 6.6657 | 21.8618 | 9.7049 | ||

RMSE | 17.5076 | 43.8141 | 25.0828 | ||

M_{4} | CFNN-LMA | R^{2} | 0.8878 | 0.8706 | 0.8856 |

AARE | 6.9643 | 10.5219 | 7.6758 | ||

RMSE | 21.6209 | 22.0891 | 21.7153 | ||

LSSVM-ABC | R^{2} | 0.892 | 0.8572 | 0.8849 | |

AARE | 7.0333 | 9.8644 | 7.5995 | ||

RMSE | 20.9307 | 24.9094 | 21.7846 | ||

LSSVM-GSA | R^{2} | 0.8689 | 0.8748 | 0.8707 | |

AARE | 8.1285 | 11.6169 | 8.8262 | ||

RMSE | 22.7463 | 24.3938 | 23.0852 | ||

LSSVM-WOA | R^{2} | 0.9921 | 0.9201 | 0.9777 | |

AARE | 2.7384 | 14.8704 | 5.1648 | ||

RMSE | 8.0666 | 31.6042 | 15.8689 | ||

M_{5} | CFNN-LMA | R^{2} | 0.8879 | 0.8456 | 0.8791 |

AARE | 7.6983 | 11.2721 | 8.413 | ||

RMSE | 21.3743 | 25.7841 | 22.326 | ||

LSSVM-ABC | R^{2} | 0.8891 | 0.8376 | 0.8823 | |

AARE | 8.3536 | 7.5541 | 8.1937 | ||

RMSE | 22.1859 | 21.3895 | 22.0289 | ||

LSSVM-GSA | R^{2} | 0.8983 | 0.831 | 0.8825 | |

AARE | 6.6676 | 11.6499 | 7.6641 | ||

RMSE | 19.9291 | 28.846 | 22.0035 | ||

LSSVM-WOA | R^{2} | 0.8979 | 0.7985 | 0.8859 | |

AARE | 12.374 | 13.7799 | 12.6551 | ||

RMSE | 29.5911 | 30.7061 | 29.8175 | ||

M_{6} | CFNN-LMA | R^{2} | 0.4324 | 0.3195 | 0.4186 |

AARE | 17.817 | 30.9799 | 20.4496 | ||

RMSE | 46.3091 | 58.3475 | 48.9542 | ||

LSSVM-ABC | R^{2} | 0.4856 | 0.1575 | 0.4327 | |

AARE | 17.9507 | 30.1723 | 20.395 | ||

RMSE | 44.6322 | 61.0195 | 48.356 | ||

LSSVM-GSA | R^{2} | 0.5574 | 0.4669 | 0.4329 | |

AARE | 18.587 | 24.6491 | 19.7994 | ||

RMSE | 44.7295 | 60.6898 | 48.3449 | ||

LSSVM-WOA | R^{2} | 0.806 | 0.3616 | 0.7228 | |

AARE | 15.5962 | 22.1002 | 16.897 | ||

RMSE | 40.172 | 58.5744 | 44.466 |

Overall R^{2} | Overall RMSE | |
---|---|---|

Fold 1 | 0.9759 | 9.8664 |

Fold 2 | 0.9761 | 9.8601 |

Fold 3 | 0.9754 | 9.9361 |

Fold 4 | 0.9762 | 9.8597 |

Model | CFNN-LMA | LSSVM-ABC | LSSVM-GSA | LSSVM-WOA |
---|---|---|---|---|

Q_{25%}-RD% | −0.5566 | −2.778 | −2.712 | −2.976 |

Q_{75%}-RD% | 1.093 | 2.504 | 2.716 | 2.105 |

IQR-RD% | 1.650 | 5.282 | 5.428 | 5.081 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ding, X.; Jamei, M.; Hasanipanah, M.; Abdullah, R.A.; Le, B.N.
Optimized Data-Driven Models for Prediction of Flyrock due to Blasting in Surface Mines. *Sustainability* **2023**, *15*, 8424.
https://doi.org/10.3390/su15108424

**AMA Style**

Ding X, Jamei M, Hasanipanah M, Abdullah RA, Le BN.
Optimized Data-Driven Models for Prediction of Flyrock due to Blasting in Surface Mines. *Sustainability*. 2023; 15(10):8424.
https://doi.org/10.3390/su15108424

**Chicago/Turabian Style**

Ding, Xiaohua, Mehdi Jamei, Mahdi Hasanipanah, Rini Asnida Abdullah, and Binh Nguyen Le.
2023. "Optimized Data-Driven Models for Prediction of Flyrock due to Blasting in Surface Mines" *Sustainability* 15, no. 10: 8424.
https://doi.org/10.3390/su15108424