# An Improved Combination Model for the Multi-Scale Prediction of Slope Deformation

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Source

#### 2.3. Multiple Linear Regression Model

#### 2.4. Multiple Nonlinear Regression Model

#### 2.5. Modified Deformation Prediction Combination Model Based on GFW-Fisher Optimal Segmentation Method

#### 2.6. Model Accuracy Evaluation

## 3. Results and Discussion

#### 3.1. Slope Deformation Prediction Results

#### 3.2. The Results of Accuracy Evaluation

#### 3.3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The results of Fisher optimal segmentation method under the different number of grids. (

**a**) 100 grids; (

**b**) 200 grids.

**Figure 4.**The results of the different prediction combination model at different spatial scales with the different number of grids. (

**a**) Point scale and 100 grids; (

**b**) linear scale and 100 grids; (

**c**) surface scale and 100 grids; (

**d**) point scale and 200 grids; (

**e**) linear scale and 200 grids; and (

**f**) surface scale and 200 grids.

**Figure 5.**The comparing results of combination model, multiple linear regression model, and multiple nonlinear regression model.

Spatial and Scale | Intervals | Weights of Multiple Linear Regression Model | Weights of Multiple Nonlinear Regression Model |
---|---|---|---|

Deformation prediction at point scales with 100 grids | The first interval | 0.594 | 0.406 |

The second interval | 0.205 | 0.795 | |

The third interval | 0.813 | 0.187 | |

The forth interval | 0.322 | 0.678 | |

Deformation prediction at linear scales with 100 grids | The first interval | 0.256 | 0.744 |

The second interval | 0.090 | 0.910 | |

The third interval | 0.369 | 0.631 | |

The forth interval | 0.415 | 0.585 | |

Deformation prediction at surface scales with 100 grids | The first interval | 0.198 | 0.802 |

The second interval | 0.060 | 0.940 | |

The third interval | 0.440 | 0.560 | |

The forth interval | 0.076 | 0.924 | |

Deformation prediction at point scales with 200 grids | The first interval | 0.426 | 0.574 |

The second interval | 0.228 | 0.772 | |

The third interval | 0.330 | 0.670 | |

The forth interval | 0.654 | 0.346 | |

Deformation prediction at linear scales with 200 grids | The first interval | 0.184 | 0.816 |

The second interval | 0.358 | 0.642 | |

The third interval | 0.454 | 0.546 | |

The forth interval | 0.312 | 0.688 | |

Deformation prediction at surface scales with 200 grids | The first interval | 0.727 | 0.273 |

The second interval | 0.117 | 0.883 | |

The third interval | 0.366 | 0.634 | |

The forth interval | 0.366 | 0.634 |

**Table 2.**Determination coefficients (R

^{2}) of the modified slope deformation prediction model at different spatial scales with 100 grids.

Spatial Scale | Linear Combination Model | Weighted Geometric Average Model | Weighted Harmonic Average Model |
---|---|---|---|

Point scale | 0.89 | 0.88 | 0.83 |

Linear scale | 0.77 | 0.79 | 0.84 |

Surface scale | 0.93 | 0.93 | 0.95 |

**Table 3.**Determination coefficients (R

^{2}) of the modified slope deformation prediction model at different spatial scales with 200 grids.

Spatial Scale | Linear Combination Model | Weighted Geometric Average Model | Weighted Harmonic Average Model |
---|---|---|---|

Point scale | 0.88 | 0.87 | 0.88 |

Linear scale | 0.94 | 0.94 | 0.94 |

Surface scale | 0.95 | 0.95 | 0.96 |

Model | RMSE | MAE | Relative Error |
---|---|---|---|

Multiple linear regression model | 20.91% | 19.52% | 96.33% |

Multiple nonlinear regression model | 20.74% | 19.14% | 94.47% |

Linear combination model | 5.62% | 3.14% | 4.33% |

Weight geometric average model | 5.62% | 3.12% | 4.33% |

Weight harmonic average model | 5.57% | 3.11% | 3.98% |

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**MDPI and ACS Style**

Li, X.; Lei, T.; Qin, J.; Wang, J.; Wang, W.; Chen, D.; Qian, G.; Lu, J. An Improved Combination Model for the Multi-Scale Prediction of Slope Deformation. *Water* **2022**, *14*, 3667.
https://doi.org/10.3390/w14223667

**AMA Style**

Li X, Lei T, Qin J, Wang J, Wang W, Chen D, Qian G, Lu J. An Improved Combination Model for the Multi-Scale Prediction of Slope Deformation. *Water*. 2022; 14(22):3667.
https://doi.org/10.3390/w14223667

**Chicago/Turabian Style**

Li, Xiangyu, Tianjie Lei, Jing Qin, Jiabao Wang, Weiwei Wang, Dongpan Chen, Guansheng Qian, and Jingxuan Lu. 2022. "An Improved Combination Model for the Multi-Scale Prediction of Slope Deformation" *Water* 14, no. 22: 3667.
https://doi.org/10.3390/w14223667