Optimized Data-Driven Models for Prediction of Flyrock due to Blasting in Surface Mines
Abstract
:1. Introduction
2. Research Significance
3. Materials and Methods
3.1. Materials
3.2. Methods
3.2.1. LSSVM Model
- (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 () 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 :
- -
- 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
4. Development of Predictive Models
5. Results and Discussion
5.1. Exploratory Analysis
5.2. Modelling Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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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 | and | [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/m3) | Density (gr/cm3) | 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 |
---|---|---|---|---|---|
M1 | CFNN-LMA | R2 | 0.9875 | 0.9347 | 0.977 |
AARE | 2.5163 | 7.512 | 3.5154 | ||
RMSE | 7.2292 | 16.5215 | 9.8184 | ||
LSSVM-ABC | R2 | 0.9867 | 0.9049 | 0.971 | |
AARE | 3.0419 | 8.0032 | 4.0341 | ||
RMSE | 7.4089 | 19.439 | 10.9311 | ||
LSSVM-GSA | R2 | 0.9828 | 0.904 | 0.967 | |
AARE | 3.4215 | 5.5193 | 3.8411 | ||
RMSE | 8.7308 | 16.1775 | 10.6453 | ||
LSSVM-WOA | R2 | 0.9926 | 0.9991 | 0.9943 | |
AARE | 1.6473 | 1.3017 | 1.5782 | ||
RMSE | 7.4847 | 3.4209 | 6.8671 | ||
M2 | CFNN-LMA | R2 | 0.9812 | 0.9366 | 0.972 |
AARE | 2.9261 | 8.5748 | 4.0558 | ||
RMSE | 8.4645 | 20.2612 | 11.8077 | ||
LSSVM-ABC | R2 | 0.9769 | 0.9235 | 0.9675 | |
AARE | 3.7643 | 7.083 | 4.428 | ||
RMSE | 9.8655 | 16.7483 | 11.5743 | ||
LSSVM-GSA | R2 | 0.9754 | 0.9054 | 0.9614 | |
AARE | 4.254 | 6.5356 | 4.7103 | ||
RMSE | 10.3962 | 18.0443 | 12.312 | ||
LSSVM-WOA | R2 | 0.9871 | 0.9896 | 0.9875 | |
AARE | 2.6662 | 2.8723 | 2.7074 | ||
RMSE | 10.105 | 10.4268 | 10.1702 | ||
M3 | CFNN-LMA | R2 | 0.883 | 0.9172 | 0.89 |
AARE | 7.2573 | 8.2441 | 7.4546 | ||
RMSE | 21.9097 | 18.6501 | 21.2977 | ||
LSSVM-ABC | R2 | 0.9191 | 0.7622 | 0.8811 | |
AARE | 6.7642 | 12.4379 | 7.8989 | ||
RMSE | 17.7366 | 34.5376 | 22.1413 | ||
LSSVM-GSA | R2 | 0.8874 | 0.7979 | 0.8714 | |
AARE | 7.8757 | 13.615 | 9.0236 | ||
RMSE | 21.7035 | 27.6908 | 23.0259 | ||
LSSVM-WOA | R2 | 0.9625 | 0.9398 | 0.9305 | |
AARE | 6.6657 | 21.8618 | 9.7049 | ||
RMSE | 17.5076 | 43.8141 | 25.0828 | ||
M4 | CFNN-LMA | R2 | 0.8878 | 0.8706 | 0.8856 |
AARE | 6.9643 | 10.5219 | 7.6758 | ||
RMSE | 21.6209 | 22.0891 | 21.7153 | ||
LSSVM-ABC | R2 | 0.892 | 0.8572 | 0.8849 | |
AARE | 7.0333 | 9.8644 | 7.5995 | ||
RMSE | 20.9307 | 24.9094 | 21.7846 | ||
LSSVM-GSA | R2 | 0.8689 | 0.8748 | 0.8707 | |
AARE | 8.1285 | 11.6169 | 8.8262 | ||
RMSE | 22.7463 | 24.3938 | 23.0852 | ||
LSSVM-WOA | R2 | 0.9921 | 0.9201 | 0.9777 | |
AARE | 2.7384 | 14.8704 | 5.1648 | ||
RMSE | 8.0666 | 31.6042 | 15.8689 | ||
M5 | CFNN-LMA | R2 | 0.8879 | 0.8456 | 0.8791 |
AARE | 7.6983 | 11.2721 | 8.413 | ||
RMSE | 21.3743 | 25.7841 | 22.326 | ||
LSSVM-ABC | R2 | 0.8891 | 0.8376 | 0.8823 | |
AARE | 8.3536 | 7.5541 | 8.1937 | ||
RMSE | 22.1859 | 21.3895 | 22.0289 | ||
LSSVM-GSA | R2 | 0.8983 | 0.831 | 0.8825 | |
AARE | 6.6676 | 11.6499 | 7.6641 | ||
RMSE | 19.9291 | 28.846 | 22.0035 | ||
LSSVM-WOA | R2 | 0.8979 | 0.7985 | 0.8859 | |
AARE | 12.374 | 13.7799 | 12.6551 | ||
RMSE | 29.5911 | 30.7061 | 29.8175 | ||
M6 | CFNN-LMA | R2 | 0.4324 | 0.3195 | 0.4186 |
AARE | 17.817 | 30.9799 | 20.4496 | ||
RMSE | 46.3091 | 58.3475 | 48.9542 | ||
LSSVM-ABC | R2 | 0.4856 | 0.1575 | 0.4327 | |
AARE | 17.9507 | 30.1723 | 20.395 | ||
RMSE | 44.6322 | 61.0195 | 48.356 | ||
LSSVM-GSA | R2 | 0.5574 | 0.4669 | 0.4329 | |
AARE | 18.587 | 24.6491 | 19.7994 | ||
RMSE | 44.7295 | 60.6898 | 48.3449 | ||
LSSVM-WOA | R2 | 0.806 | 0.3616 | 0.7228 | |
AARE | 15.5962 | 22.1002 | 16.897 | ||
RMSE | 40.172 | 58.5744 | 44.466 |
Overall R2 | 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 |
---|---|---|---|---|
Q25%-RD% | −0.5566 | −2.778 | −2.712 | −2.976 |
Q75%-RD% | 1.093 | 2.504 | 2.716 | 2.105 |
IQR-RD% | 1.650 | 5.282 | 5.428 | 5.081 |
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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
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 StyleDing, 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