# Random Forest and Whale Optimization Algorithm to Predict the Invalidation Risk of Backfilling Pipeline

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Engineering Background and Database Description

## 3. Modeling Methodology

#### 3.1. Random Forest

#### 3.2. Whale Optimization Algorithm

## 4. Modeling Results and Discussion

#### 4.1. Evaluation Indicators

#### 4.2. Development and Validation of the WOA–RF Model

#### 4.3. Comparison with Other Machine Learning Models

#### 4.4. Sensitivity Analysis of Predictor Variables

#### 4.5. Engineering Validation

## 5. Study Limitations

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

RF | random forest |

DT | decision tree |

ANN | artificial neural network |

AI | artificial intelligence |

HDD | Horizontal directional drilling |

GWO | grey wolf optimizer |

ACOA | ant colony optimization |

MCC | Matthews correlation coefficient |

ROC | the receiver operating characteristic |

TN | true negative rate |

FP | false positive |

FPR | false positive rate |

TOPSIS | technique for order preference by similarity to an ideal solution methods |

WOA | whale optimization algorithm |

SVM | support vector machine |

KNN | k-nearest neighbor |

ML | machine learning |

ANFIS | adaptive neural fuzzy reasoning system |

BAYES | bayes classifier |

PSO | particle swarm optimization |

IAHP | interval-based AHP |

AUC | area under curve |

TP | true positive rate |

TPR | true positive rate |

N | the number of the samples |

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**Figure 2.**Backfilling pipeline failure photos: (

**a**) pipeline blockages; (

**b**) pipeline wear; (

**c**) pipeline leakage; (

**d**) pipeline burst.

**Figure 9.**ROC curves and AUC values for different individual classifiers: (

**a**) extremely dangerous; (

**b**) significant risk; (

**c**) greater risk; (

**d**) general risk.

Volume Fraction of Backfilling Slurry I1/% | Density of Backfilling Slurry I2/t.m ^{−3} | The Internal Diameter of the Pipeline I3/mm | The Deviation Rate I4/% | Pipeline Absolute Roughness I5/um | Stowing Gradient I6 | The Ratio of Slurry Flow Rate with the Critical Velocity I7 | Weighted Average Particle Size I8/mm | Risk Level |
---|---|---|---|---|---|---|---|---|

≥50 | ≥1.9 | ≤100 | ≥5 | ≥500 | ≥7 | ≤1 | ≥2.5 | 1 |

≥40~<50 | ≥1.7~<1.9 | >100~≤150 | ≥3~<5 | ≥300~<500 | ≥5~<7 | >1~≤1.2 | ≥0.7~<2.5 | 2 |

≥30~<40 | ≥1.5~<1.7 | >150~≤200 | ≥1~<3 | ≥100~<300 | ≥3~<5 | >1.2~≤1.5 | ≥0.3~<0.7 | 3 |

<30 | <1.5 | >200 | <1 | <100 | ≥1~<3 | <1.5 | <0.3 | 4 |

**Table 2.**The statistical information of backfilling pipeline invalidation risk influence factors and level.

Sample of Filling Pipeline | Volume Fraction of Filling Slurry I1/% | Density of Filling Slurry I2/t.m ^{−3} | Internal Diameter of the Pipeline I3/mm | Deviation Rate I4/% | Pipeline Absolute Roughness I5/um | Stowing Gradient I6 | The Ratio of Slurry Flow Rate with the Critical Velocity I7 | Weighted Average Particle Size I8/mm | Risk Level |
---|---|---|---|---|---|---|---|---|---|

1 | 56 | 1.98 | 199 | 2.72 | 300 | 3.8 | 1.30 | 0.58 | 2 |

2 | 33 | 1.69 | 160 | 0.98 | 500 | 9.6 | 3.00 | 0.05 | 3 |

3 | 24 | 1.68 | 82 | 0.56 | 100 | 5.2 | 1.60 | 0.21 | 4 |

4 | 52 | 1.94 | 107 | 1.27 | 200 | 5.8 | 3.50 | 0.11 | 3 |

5 | 60 | 1.92 | 104 | 1.01 | 300 | 3.5 | 3.20 | 0.05 | 3 |

6 | 30 | 1.76 | 69 | 2.65 | 200 | 3.2 | 1.50 | 0.05 | 4 |

7 | 60 | 1.68 | 69 | 1.03 | 100 | 5 | 1.57 | 0.25 | 3 |

8 | 56 | 1.77 | 120 | 0.69 | 300 | 3 | 1.60 | 0.13 | 3 |

9 | 28 | 1.86 | 65 | 1.65 | 200 | 6.8 | 1.62 | 0.65 | 4 |

10 | 68 | 1.78 | 148 | 1.58 | 100 | 4.7 | 1.66 | 0.05 | 3 |

11 | 51 | 1.93 | 152 | 1.23 | 300 | 4.1 | 1.13 | 0.26 | 2 |

12 | 27 | 1.49 | 79 | 2.41 | 100 | 4.7 | 1.39 | 0.17 | 4 |

13 | 55 | 1.77 | 120 | 0.69 | 300 | 3 | 1.60 | 0.13 | 3 |

14 | 43 | 1.73 | 170 | 1.37 | 200 | 6.6 | 1.72 | 0.19 | 3 |

15 | 51 | 1.97 | 158 | 1.74 | 300 | 7.8 | 1.30 | 0.21 | 2 |

16 | 26 | 1.89 | 72 | 1.37 | 100 | 5.4 | 1.43 | 0.24 | 4 |

17 | 57 | 1.99 | 197 | 2.71 | 300 | 3.7 | 1.30 | 0.55 | 2 |

18 | 34 | 1.71 | 154 | 0.99 | 500 | 9.5 | 3.00 | 0.07 | 3 |

19 | 22 | 1.64 | 78 | 0.54 | 100 | 5.3 | 1.60 | 0.19 | 4 |

20 | 51 | 1.91 | 104 | 1.25 | 200 | 5.9 | 3.50 | 0.13 | 3 |

21 | 61 | 1.94 | 108 | 1.03 | 300 | 3.6 | 3.20 | 0.03 | 3 |

22 | 56 | 1.71 | 71 | 2.61 | 200 | 3.3 | 1.50 | 0.04 | 4 |

23 | 59 | 1.73 | 71 | 1.01 | 100 | 5.1 | 1.57 | 0.26 | 3 |

24 | 55 | 1.81 | 118 | 0.72 | 300 | 3.2 | 1.60 | 0.15 | 3 |

25 | 27 | 1.81 | 67 | 1.63 | 200 | 6.9 | 1.62 | 6.47 | 4 |

26 | 64 | 1.75 | 151 | 1.61 | 100 | 4.5 | 1.66 | 0.04 | 3 |

27 | 53 | 1.77 | 121 | 0.69 | 300 | 3.1 | 1.56 | 0.14 | 3 |

28 | 61 | 1.71 | 149 | 1.58 | 100 | 4.3 | 1.63 | 0.05 | 3 |

29 | 52 | 1.91 | 201 | 2.66 | 300 | 3.5 | 1.35 | 0.56 | 2 |

30 | 30 | 1.69 | 161 | 1.02 | 500 | 9.3 | 3.05 | 0.08 | 3 |

31 | 56 | 1.98 | 199 | 2.72 | 300 | 3.2 | 1.30 | 0.24 | 2 |

32 | 33 | 1.69 | 160 | 0.98 | 500 | 9.6 | 3.00 | 0.43 | 3 |

33 | 24 | 1.68 | 82 | 0.56 | 100 | 5.2 | 1.60 | 0.08 | 3 |

34 | 52 | 1.94 | 107 | 1.27 | 200 | 5.8 | 3.50 | 0.16 | 3 |

35 | 62 | 1.97 | 152 | 4.6 | 300 | 2.9 | 1.83 | 0.62 | 2 |

36 | 54 | 1.76 | 179 | 1.25 | 100 | 4.8 | 2.52 | 0.08 | 3 |

37 | 31 | 1.78 | 148 | 1.58 | 200 | 4.7 | 1.66 | 0.05 | 4 |

38 | 57 | 1.78 | 168 | 1.5 | 200 | 4.2 | 1.80 | 0.62 | 2 |

39 | 58 | 1.69 | 145 | 0.91 | 500 | 9.6 | 3.20 | 0.08 | 3 |

40 | 59 | 1.83 | 69 | 1.65 | 100 | 6.7 | 1.50 | 0.52 | 2 |

41 | 56 | 1.92 | 98 | 1.19 | 200 | 5.8 | 3.50 | 0.11 | 3 |

42 | 56 | 1.92 | 104 | 1.01 | 300 | 3.8 | 3.30 | 0.06 | 4 |

43 | 67 | 1.71 | 72 | 2.67 | 200 | 3.5 | 1.70 | 0.05 | 3 |

44 | 58 | 1.68 | 78 | 1.18 | 100 | 5.2 | 1.60 | 0.28 | 2 |

45 | 69 | 1.32 | 218 | 1.12 | 156 | 6.1 | 2.34 | 0.02 | 1 |

46 | 68 | 1.06 | 274 | 1.65 | 178 | 6.9 | 1.08 | 0.23 | 1 |

47 | 27 | 1.89 | 165 | 4.16 | 145 | 1.3 | 1.15 | 0.07 | 3 |

48 | 64 | 1.27 | 203 | 3.49 | 139 | 6.4 | 1.07 | 0.11 | 1 |

49 | 36 | 1.55 | 229 | 1.93 | 170 | 5.4 | 1.16 | 0.03 | 2 |

50 | 30 | 1.24 | 240 | 1.72 | 246 | 7.2 | 1.19 | 0.04 | 1 |

51 | 25 | 1.91 | 221 | 2.71 | 423 | 3.0 | 3.41 | 0.18 | 4 |

52 | 66 | 1.13 | 192 | 1.57 | 124 | 6.5 | 1.58 | 0.02 | 1 |

53 | 28 | 1.26 | 206 | 1.88 | 152 | 6.7 | 1.03 | 0.05 | 2 |

54 | 67 | 1.32 | 250 | 1.34 | 161 | 6.7 | 2.15 | 0.09 | 1 |

55 | 65 | 1.05 | 234 | 1.27 | 194 | 7.0 | 1.87 | 0.03 | 1 |

56 | 27 | 1.78 | 219 | 6.55 | 382 | 4.4 | 1.43 | 0.04 | 4 |

57 | 60 | 0.99 | 93 | 1.60 | 194 | 7.0 | 1.05 | 0.01 | 1 |

58 | 63 | 1.20 | 207 | 5.16 | 247 | 7.1 | 2.94 | 0.05 | 1 |

59 | 64 | 1.58 | 212 | 1.24 | 189 | 6.1 | 1.14 | 0.01 | 1 |

**Table 3.**Testing performance of different classifiers for the invalidation risk of the backfilling pipeline problem: extremely dangerous (Class 1), significant risk (Class 2), greater risk (Class 3), and general risk (Class 4).

Precision | Recall | F1-Score | Precision | Recall | F1-Score | ||
---|---|---|---|---|---|---|---|

WOA–RF | RF | ||||||

class1 | 1.00 | 1.00 | 1.00 | class1 | 1.00 | 1.00 | 1.00 |

class2 | 1.00 | 1.00 | 1.00 | class2 | 1.00 | 1.00 | 1.00 |

class3 | 1.00 | 0.80 | 0.89 | class3 | 1.00 | 0.80 | 0.89 |

class4 | 0.75 | 1.00 | 0.86 | class4 | 0.75 | 1.00 | 0.86 |

DT | ANN | ||||||

class1 | 1.00 | 1.00 | 1.00 | class1 | 1.00 | 1.00 | 1.00 |

class2 | 0.67 | 1.00 | 0.80 | class2 | 0.67 | 1.00 | 0.80 |

class3 | 1.00 | 0.80 | 0.89 | class3 | 1.00 | 0.80 | 0.89 |

class4 | 0.67 | 0.67 | 0.67 | class4 | 0.67 | 0.67 | 0.67 |

KNN | SVM | ||||||

class1 | 0.50 | 1.00 | 0.67 | class1 | 0.67 | 1.00 | 0.80 |

class2 | 0.40 | 1.00 | 0.57 | class2 | 0.67 | 1.00 | 0.80 |

class3 | 1.00 | 0.40 | 0.57 | class3 | 1.00 | 0.80 | 0.89 |

class4 | 0.00 | 0.00 | 0.00 | class4 | 0.50 | 0.33 | 0.40 |

Engineering | Volume Fraction of Filling Slurry I1/% | Density of Filling Slurry I2/t.m ^{−3} | Internal Diameter of the Pipeline I3/mm | Deviation Rate I4/% | Pipeline Absolute Roughness I5/um | Stowing Gradient I6 | The Ratio of Slurry Flow Rate with the Critical Velocity I7 | Weighted Average Particle Size I8/mm | Risk Level | Predicted Level |
---|---|---|---|---|---|---|---|---|---|---|

Gacun Xinyuan mine | 62 | 1.94 | 205 | 5.78 | 300 | 3.5 | 1.45 | 2.65 | 1 | 1 |

Dulang gou gold mine | 30 | 1.32 | 74 | 1.37 | 100 | 5.6 | 1.47 | 0.25 | 4 | 4 |

Guanyinshan mine | 57 | 1.85 | 150 | 3.71 | 400 | 6.7 | 1.10 | 0.75 | 2 | 2 |

Liwu copper mine | 45 | 1.65 | 154 | 2.10 | 250 | 4.5 | 1.42 | 0.47 | 3 | 3 |

Suoluo Gou gold mine | 28 | 1.45 | 215 | 0.54 | 85 | 5.3 | 1.60 | 0.19 | 4 | 4 |

Huili Lala copper mine | 51 | 1.51 | 180 | 1.25 | 200 | 5.9 | 3.50 | 0.43 | 3 | 3 |

Damaopo Lead Zinc Mine | 66 | 2.05 | 92 | 5.57 | 524 | 7.5 | 0.78 | 2.00 | 1 | 1 |

Tianbaoshan polymetallic Mine | 58 | 1.76 | 136 | 1.88 | 152 | 6.7 | 1.03 | 0.95 | 2 | 2 |

Yinchanggou Copper mine | 68 | 1.98 | 90 | 1.34 | 512 | 6.7 | 2.15 | 3.09 | 1 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Liu, Z.; Liu, Z.; Xiong, S.; Zhang, S. Random Forest and Whale Optimization Algorithm to Predict the Invalidation Risk of Backfilling Pipeline. *Mathematics* **2023**, *11*, 1636.
https://doi.org/10.3390/math11071636

**AMA Style**

Liu W, Liu Z, Liu Z, Xiong S, Zhang S. Random Forest and Whale Optimization Algorithm to Predict the Invalidation Risk of Backfilling Pipeline. *Mathematics*. 2023; 11(7):1636.
https://doi.org/10.3390/math11071636

**Chicago/Turabian Style**

Liu, Weijun, Zhixiang Liu, Zida Liu, Shuai Xiong, and Shuangxia Zhang. 2023. "Random Forest and Whale Optimization Algorithm to Predict the Invalidation Risk of Backfilling Pipeline" *Mathematics* 11, no. 7: 1636.
https://doi.org/10.3390/math11071636