Compressive Strength Prediction of Cemented Backfill Containing Phosphate Tailings Using Extreme Gradient Boosting Optimized by Whale Optimization Algorithm
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Methods
2.2.1. Preparation of Backfill Specimens
2.2.2. UCS Test
3. Results
3.1. Extreme Gradient Boosting Model
3.2. Whale Optimization Algorithm
3.2.1. Encircling Prey
3.2.2. Bubble-Net Attacking Method
3.2.3. Search for Prey
3.3. WOA-XGBoost Model
3.4. The Process of WOA-XGBoost Modeling
3.5. Evaluation Methodology
4. Results and Discussion
4.1. UCS Development
4.2. Performance of WOA-XGBoost Model
4.3. Comparison with Machine Learning Models
4.4. Feature Importance Analysis of Input Variables
5. Conclusions
- The WOA-XGBoost prediction model had high accuracy for the UCS prediction of cemented PT backfill. Compared with PSO-XGBoost, XGBoost, and DT, the prediction results of WOA-XGBoost showed a 37.08%, 47.86%, and 55.39% reduction in RMSE, 40.55%, 45.29%, and 57.70% reduction in MAE, 3.39%, 6.20%, and 14.55% improvement in R2, respectively. The results indicated that the prediction performance of the XGBoost model can be greatly improved by the WOA algorithm.
- The results of the feature importance analysis showed that PT proportion was the most important input variable, followed by curing age, OPC proportion, FA proportion, and solid concentration. The importance score of the PT proportion was 0.48, and the total importance score of the proportions of raw materials was 0.72, indicating that the binder/aggregate ratio was the key to obtaining sufficient UCS for cemented PT backfill.
- WOA-XGBoost model could provide a promising method for the UCS prediction of cemented PT backfill. Therefore, the model can facilitate mine production. The model achieved better performance than other machine learning models and demonstrated potential for use in other geotechnical applications. In the future, with the addition of more training data, the performance of the WOA-XGBoost model may be more accurate.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Chemical Components | FA (%) | OPC (%) | PT (%) |
---|---|---|---|
SiO2 | 51.41 | 29.00 | 61.10 |
CaO | 4.38 | 45.12 | 18.74 |
P2O5 | 0.15 | 0.28 | 8.80 |
MgO | 0.54 | 2.85 | 5.61 |
Fe2O3 | 3.82 | 5.70 | 0.86 |
Al2O3 | 35.17 | 0.01 | 0.83 |
SO3 | 1.30 | 3.31 | 0.67 |
K2O | 1.18 | 1.35 | 0.62 |
F | 0.00 | 0.00 | 0.50 |
Name | FA:OPC:PT Ratio | Solid Concentration |
---|---|---|
T1 | 0:1:2 | 70% |
T2 | 0:1:4 | 70% |
T3 | 0:1:6 | 70% |
T4 | 0:1:2 | 72% |
T5 | 0:1:4 | 72% |
T6 | 0:1:6 | 72% |
T7 | 0:1:2 | 75% |
T8 | 0:1:4 | 75% |
T9 | 0:1:6 | 75% |
T10 | 1:1:4 | 70% |
T11 | 1:1:6 | 70% |
T12 | 1:1:8 | 70% |
T13 | 1:1:10 | 70% |
T14 | 1:1:4 | 72% |
T15 | 1:1:6 | 72% |
T16 | 1:1:8 | 72% |
T17 | 1:1:10 | 72% |
T18 | 1:1:4 | 75% |
T19 | 1:1:6 | 75% |
T20 | 1:1:8 | 75% |
T21 | 1:1:10 | 75% |
Swarm Size | Training Set | Test Set | ||||
---|---|---|---|---|---|---|
R2 | RMSE | MAE | R2 | RMSE | MAE | |
25 | 0.983 | 0.174 | 0.151 | 0.95 | 0.344 | 0.217 |
50 | 0.989 | 0.169 | 0.136 | 0.964 | 0.272 | 0.244 |
75 | 0.987 | 0.171 | 0.139 | 0.955 | 0.344 | 0.274 |
100 | 0.995 | 0.156 | 0.114 | 0.976 | 0.207 | 0.151 |
125 | 0.992 | 0.165 | 0.120 | 0.973 | 0.246 | 0.191 |
150 | 0.991 | 0.179 | 0.135 | 0.966 | 0.279 | 0.222 |
175 | 0.987 | 0.171 | 0.139 | 0.959 | 0.33 | 0.239 |
200 | 0.984 | 0.173 | 0.145 | 0.955 | 0.349 | 0.258 |
Population Size | Maximum Number of Iterations | Local Learning Factor | Global Learning Factor | The Proportionality Constant of the Rate |
---|---|---|---|---|
50 | 100 | 1.8 | 1.8 | 0.6 |
Model | Training Set | Test Set | ||||
---|---|---|---|---|---|---|
R2 | RMSE | MAE | R2 | RMSE | MAE | |
WOA-XGBoost | 0.995 | 0.156 | 0.114 | 0.976 | 0.207 | 0.151 |
PSO-XGBoost | 0.981 | 0.201 | 0.153 | 0.944 | 0.329 | 0.254 |
XGBoost | 0.973 | 0.246 | 0.191 | 0.919 | 0.397 | 0.276 |
DT | 0.969 | 0.276 | 0.215 | 0.852 | 0.464 | 0.357 |
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Xiong, S.; Liu, Z.; Min, C.; Shi, Y.; Zhang, S.; Liu, W. Compressive Strength Prediction of Cemented Backfill Containing Phosphate Tailings Using Extreme Gradient Boosting Optimized by Whale Optimization Algorithm. Materials 2023, 16, 308. https://doi.org/10.3390/ma16010308
Xiong S, Liu Z, Min C, Shi Y, Zhang S, Liu W. Compressive Strength Prediction of Cemented Backfill Containing Phosphate Tailings Using Extreme Gradient Boosting Optimized by Whale Optimization Algorithm. Materials. 2023; 16(1):308. https://doi.org/10.3390/ma16010308
Chicago/Turabian StyleXiong, Shuai, Zhixiang Liu, Chendi Min, Ying Shi, Shuangxia Zhang, and Weijun Liu. 2023. "Compressive Strength Prediction of Cemented Backfill Containing Phosphate Tailings Using Extreme Gradient Boosting Optimized by Whale Optimization Algorithm" Materials 16, no. 1: 308. https://doi.org/10.3390/ma16010308