# Compressive Strength Prediction of Cemented Backfill Containing Phosphate Tailings Using Extreme Gradient Boosting Optimized by Whale Optimization Algorithm

^{*}

## Abstract

**:**

^{2}), and mean absolute error (MAE) obtained from the WOA-XGBoost model, XGBoost model, PSO-XGBoost model, and DT model were equal to (0.241, 0.967, 0.184), (0.426, 0.917, 0.336), (0.316, 0.943, 0.258), and (0.464, 0.852, 0.357), respectively. The results show that the proposed WOA-XGBoost has better prediction accuracy than the other machine learning models, confirming the ability of the WOA to enhance XGBoost in cemented PT backfill strength prediction. The WOA-XGBoost model could be a fast and accurate method for the UCS prediction of cemented PT backfill.

## 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

^{2}), mean absolute error (MAE), and root mean square error (RMSE). RMSE, MAE, and R

^{2}are calculated using Equations (13)–(15), respectively, as follows:

^{2}is expressed as a percentage. A hybrid model with lower RMSE and MAE and higher R

^{2}could exhibit a better prediction performance.

## 4. Results and Discussion

#### 4.1. UCS Development

#### 4.2. Performance of WOA-XGBoost Model

^{2}value. Therefore, the population size of 100 (Num_boosting_rounds = 167, Learning_rate = 0.5235, Reg_lambda = 0.2167) was selected as the optimal parameter for the WOA-XGBoost model. Figure 6 shows a comparison of the predicted and actual values when the WOA-XGBoost model was subjected to a population size of 100. It was found that the predicted values are close to the actual values, indicating that the WOA-XGBoost model performed well in the UCS prediction of the cemented PT backfill.

#### 4.3. Comparison with Machine Learning Models

^{2}value and lowest RMSE and MAE values in both the training and test sets. Specifically, compared with PSO-XGBoost, XGBoost, and DT, the performance indexes of WOA-XGBoost on the test set showed a reduction of 37.08%, 47.86%, and 55.39% in RMSE, respectively, and 40.55%, 45.29% and 57.70% in MAE, respectively, and the R

^{2}increased by 3.39%, 6.20%, and 14.55%, respectively. The actual and predicted results for the training set and test set of the four models are shown in Figure 8. It was observed that the point of the WOA-XGBoost model is located near the perfect-fitting line, indicating that the predicted values and actual values are close. On the other hand, the remaining three models exhibited larger errors (Table 5) and larger discreteness (Figure 7).

#### 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 R
^{2}, 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

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**Figure 3.**Variation of the UCS of backfill specimens with FA:OPC:PT ratio and solid concentration (using sole OPC as the binder): (

**a**) 7 days; (

**b**) 14 days; (

**c**) 28 days.

**Figure 4.**Variation of the UCS of backfill specimens with FA:OPC:PT ratio and solid concentration (using FA and OPC as the binder): (

**a**) 7 days; (

**b**) 14 days; (

**c**) 28 days.

**Figure 5.**Variation of fitness value and the number of iterations of the WOA-XGBoost model with different population sizes.

**Figure 6.**Comparison of the predicted and actual values of the WOA-XGBoost model (population size of 100).

Chemical Components | FA (%) | OPC (%) | PT (%) |
---|---|---|---|

SiO_{2} | 51.41 | 29.00 | 61.10 |

CaO | 4.38 | 45.12 | 18.74 |

P_{2}O_{5} | 0.15 | 0.28 | 8.80 |

MgO | 0.54 | 2.85 | 5.61 |

Fe_{2}O_{3} | 3.82 | 5.70 | 0.86 |

Al_{2}O_{3} | 35.17 | 0.01 | 0.83 |

SO3 | 1.30 | 3.31 | 0.67 |

K_{2}O | 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 | ||||
---|---|---|---|---|---|---|

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

R^{2} | RMSE | MAE | R^{2} | 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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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Xiong, 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