# Soil Liquefaction Prediction Based on Bayesian Optimization and Support Vector Machines

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## Abstract

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## 1. Introduction

## 2. Process of Soil Liquefaction

## 3. Method

#### 3.1. Evolutionary Random Forest (ERF)

#### 3.2. Support Vector Machines

#### 3.3. Bayesian Optimization Algorithm

#### 3.4. Performance Criteria

#### 3.5. Data for Modeling

## 4. Results and Discussion

#### 4.1. Input Selection

#### 4.2. BOSVM Model Development

- Examination of fitness: The fitness function is computed and assessed before optimizing the target parameter value. The fitness function in this study is classification error.
- Adjusting the settings: hyperparameter optimization criteria may be adjusted according to the outcomes of each iteration, if desired.
- Stop checking for conditions: Optimization stops once the best parameters have been found.

## 5. Limitations and Future Works

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Acronym | Term |

AUC | Area Under the ROC Curve |

ANN | Artificial Neural Network |

BO | Bayesian Optimization |

CPT | Cone Penetration Test |

CSR | Cyclic Stress Ratio |

DT | Decision Tree |

DE | Differential Evolution |

EGMDH | Ensemble Group Method of Data Handling |

ERF | Evolutionary Random Forest |

DMT | Flat Dilatometer Test |

FSVM | Fuzzy Support Vector Machine |

GA | Genetic Algorithm |

GWO | Grey Wolf Optimization |

KELM | Kernel Extreme Learning Machine |

KFDA | Kernel Fisher Discriminant Analysis |

LSSVM | Least Squares Support Vector Machine |

ML | Machine Learning |

MGGP | Multi-Gene Genetic Programming |

ANFIS | Neuro Fuzzy Inference System |

PSO | Particle Swarm Optimization |

RBFNN | Radial Basis Function Neural Network |

RF | Random Forest |

ROC | Receiver Operating Characteristic Curve |

Vs | Shear Wave Velocity |

SPT | Standard Penetration Test |

SVM | Support Vector Machine |

## Appendix A

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Variable | Symbol | Unit | Min | Max |
---|---|---|---|---|

Earthquake magnitude | M | - | 7.8 | 7.8 |

Effective vertical stress | ${\sigma}_{v0}^{\prime}$ | kPa | 20.6 | 120.4 |

Total vertical stress | ${\sigma}_{v}$ | kPa | 16.7 | 244.2 |

Mean grain size | ${D}_{50}$ | mm | 0.06 | 0.48 |

Water table | ${d}_{w}$ | m | 0.21 | 3.6 |

Peak acceleration at the ground surface | ${a}_{max}$ | g | 0.1 | 1.1 |

Depth | ${d}_{s}$ | m | 0.9 | 13.1 |

Measured CPT tip resistance | ${q}_{c}$ | MPa | 0.98 | 18.57 |

CSR | $\frac{{\tau}_{av}}{{\sigma}_{v0}^{\prime}}$ | - | 0.08 | 0.42 |

Liquefaction observed * | - | - | 0 | 1 |

Model | Train | Test | |||||
---|---|---|---|---|---|---|---|

Actual | Prediction | Prediction | |||||

0 | 1 | Accuracy (%) | 0 | 1 | Accuracy (%) | ||

SVM | 0 | 9 | 5 | 90.9 | 9 | 1 | 91.7 |

1 | 0 | 41 | 1 | 13 | |||

BOSVM | 0 | 12 | 2 | 96.4 | 10 | 0 | 95.8 |

1 | 0 | 41 | 1 | 13 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; He, B.; Sabri, M.M.S.; Al-Bahrani, M.; Ulrikh, D.V.
Soil Liquefaction Prediction Based on Bayesian Optimization and Support Vector Machines. *Sustainability* **2022**, *14*, 11944.
https://doi.org/10.3390/su141911944

**AMA Style**

Zhang X, He B, Sabri MMS, Al-Bahrani M, Ulrikh DV.
Soil Liquefaction Prediction Based on Bayesian Optimization and Support Vector Machines. *Sustainability*. 2022; 14(19):11944.
https://doi.org/10.3390/su141911944

**Chicago/Turabian Style**

Zhang, Xuesong, Biao He, Mohanad Muayad Sabri Sabri, Mohammed Al-Bahrani, and Dmitrii Vladimirovich Ulrikh.
2022. "Soil Liquefaction Prediction Based on Bayesian Optimization and Support Vector Machines" *Sustainability* 14, no. 19: 11944.
https://doi.org/10.3390/su141911944