# A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil

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## Abstract

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## 1. Introduction

## 2. Case Study and Data Collection

#### 2.1. Description of the Study Area

#### 2.2. Data Used

#### 2.2.1. Output (Undrained Shear Strength of Soil)

#### 2.2.2. Input Variables

## 3. Methods Used

#### 3.1. Random Forest

#### 3.2. Particle Swarm Optimization (PSO)

_{best}) in search space and the whole swarm best position (G

_{best}). The particle position and velocities are computed as follows:

_{1,}and m

_{2}correspond to the cognitive, social effect, and inertia parameters, respectively; n

_{1}and n

_{2}indicate arbitrary numbers with the range of [0, 1]; ${p}_{best,i}^{t}$ and ${g}_{best,i}^{t}$ symbolize the best position of particle i and swarm, respectively.

#### 3.3. Dataset Splitting

#### 3.4. Modeling and Hyperparameters Tuning

#### 3.5. RF Model Assessment

## 4. Results and Discussion

#### 4.1. Influence of Training Set Size (TSS)

#### 4.2. Hyperparameters Tuning

#### 4.3. Predictive Capability of the Models

#### 4.4. Sensitivity Analysis of Input Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Experimental and predicted values of shear strength using the model: (

**a**) training set, (

**b**) testing set.

No | Parameters | Min Values | Max Values | Mean Values | Standard Deviation |
---|---|---|---|---|---|

1 | Clay content (%) | 1.00 | 47.5 | 25.72 | 10.172 |

2 | Water content (%) | 23.04 | 70.74 | 48.3 | 11.73 |

3 | Specific gravity | 2.67 | 2.72 | 2.69 | 0.01 |

4 | Void ratio | 0.63 | 1.92 | 1.36 | 0.31 |

5 | Liquid limit (%) | 26.08 | 79.76 | 53.34 | 13.39 |

6 | Plastic limit (%) | 15.36 | 40.48 | 28.38 | 5.01 |

7 | Undrained total normal shear strength (kG/cm^{2}) | 0.29 | 0.57 | 0.41 | 0.06 |

No | Hyperparameters | Explanation | Range |
---|---|---|---|

1 | Max_depth | The maximum depth of DTs. | 1–20 |

2 | Min_samples_split | The minimum number of samples for the split. | 2–10 |

3 | Min_samples_leaf | The minimum number of samples at the leaf node. | 1–10 |

4 | Max_DT | The maximum number of RT models in the ensemble | 1–1000 |

5 | Max_features | The number of features considered during the selection of the best splitting | 0.4–1 |

No | Models | RMSE | |
---|---|---|---|

Training | Testing | ||

1 | RF | 0.517 | 0.480 |

2 | RF-PSO | 0.487 | 0.453 |

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## Share and Cite

**MDPI and ACS Style**

Pham, B.T.; Qi, C.; Ho, L.S.; Nguyen-Thoi, T.; Al-Ansari, N.; Nguyen, M.D.; Nguyen, H.D.; Ly, H.-B.; Le, H.V.; Prakash, I.
A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil. *Sustainability* **2020**, *12*, 2218.
https://doi.org/10.3390/su12062218

**AMA Style**

Pham BT, Qi C, Ho LS, Nguyen-Thoi T, Al-Ansari N, Nguyen MD, Nguyen HD, Ly H-B, Le HV, Prakash I.
A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil. *Sustainability*. 2020; 12(6):2218.
https://doi.org/10.3390/su12062218

**Chicago/Turabian Style**

Pham, Binh Thai, Chongchong Qi, Lanh Si Ho, Trung Nguyen-Thoi, Nadhir Al-Ansari, Manh Duc Nguyen, Huu Duy Nguyen, Hai-Bang Ly, Hiep Van Le, and Indra Prakash.
2020. "A Novel Hybrid Soft Computing Model Using Random Forest and Particle Swarm Optimization for Estimation of Undrained Shear Strength of Soil" *Sustainability* 12, no. 6: 2218.
https://doi.org/10.3390/su12062218