# Combined Forecasting Method of Landslide Deformation Based on MEEMD, Approximate Entropy, and WLS-SVM

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Landslide Prediction Model Based on MEEMD, Approximation Entropy, and WLS-SVM

#### 2.1. Modified Ensemble Empirical Mode Decomposition

#### 2.2. Approximate Entropy Principle

#### 2.3. Phase Space Reconstruction Theory

#### 2.4. Weighted Least Squares Support Vector Machine

#### 2.4.1. Least Squares Support Vector Machine

#### 2.4.2. Weighted Least Squares Support Vector Machine

#### 2.4.3. Parameters Optimization of WLS-SVM

- (1)
- Setting the value range, the step size, and grid spacing of parameters $\left(\sigma ,\gamma \right)$, the optimization process in this paper is divided into two steps of coarse selection and accurate selection. The parameters are set as follows; the optimization interval of $\sigma $ and $\gamma $ is $\left[0,{10}^{10}\right]$, the number of grid points is ${10}^{10}\times {10}^{10}$, the search step size of coarse selection is 1, and the search step size of accurate selection is 0.1.
- (2)
- Since the optimization process is a traversal process, the selection of parameter initial value has no effect on the result. The initial values of this search process are $\sigma =0$ and $\gamma =1$. Selecting the position of the first cross-validation grid point, obtaining the training RMSE using the cross-validation method as the objective function of the grid point calculation, and calculating all of the grid point values.
- (3)
- Selecting the $\left(\sigma ,\gamma \right)$ with the smallest RMSE as the optimal parameters. If the selected parameters cannot satisfy the accuracy requirement, then take the selecting parameters as the center grid point, build a new 2-dimensional grid plane in a smaller range to recalculate the objective function, and select the parameter $\left(\sigma ,\gamma \right)$ with the smallest RMSE again as the optimal parameter. If the accuracy requirement is satisfied, stop or repeat the above steps, acquire the accurate parameters $\left(\sigma ,\gamma \right)$, and take them as the optimal values.

#### 2.4.4. Computational Procedure of WLS-SVM

- (1)
- According to the given sample of landside deformation data $\left\{\left({x}_{i},{y}_{i}\right)|i=1,2,\cdots ,N\right\}$, determining the optimal parameter $\left(\sigma ,\gamma \right)$, obtaining ${a}_{i}$ from formula (12), and then calculating ${e}_{i}={a}_{i}/\gamma $;
- (2)
- Calculating the robust estimation $\widehat{S}$ according to the distribution of error ${e}_{i}$;
- (3)
- Determining the corresponding weight values ${v}_{i}$ according to ${e}_{i}$ and $\widehat{S}$ through formulation (17);
- (4)
- Finally ${a}^{*}$ and ${b}^{*}$ can be got by formulation (16). Accordingly the final nonlinear prediction model can be obtained as follows:$$y\left(x\right)={\displaystyle \sum}_{i=k1}^{N}{a}_{i}^{*}K\left(x,{x}_{i}\right)+{b}^{*}$$

## 3. Analysis of Examples

#### 3.1. Basic Characteristics of Landside

^{2}, the thickness is 18–45.23 m, the average thickness is about 30 m, and the volume is about 2.2 million m

^{3}. According to the investigation and dynamic monitoring of the ground, the deformation of the landslide surface is very obvious, including the tensile crack in the back, the bulging deformation on the front edge, the shear crack on both sides of the landslide, and so on. The displacement of the landslide surface is more than 30 mm/day; the displacement velocity in the middle and front of the landslide is more than 35 mm/day. Cracks in the landslide perimeter are connected. All as shown in Figure 2.

#### 3.2. Experimental Data

#### 3.3. Modeling Process

- (1)
- To make the complex sequence smooth, the landslide sequence was decomposed to obtain a finite number of IMF components and a margin using MEEMD.
- (2)
- Analyzing the complexity of each component using approximate entropy, combining the adjacent components with a small difference in entropy, and obtaining a new subsequence to reduce the size of the calculation.
- (3)
- Reconstructing the phase space of each new subsequence using the C-C method, which could avoid the random selection of the input dimensions of the prediction model.
- (4)
- Establishing the WLS-SVM prediction model based on the reconstructed phase space of the new subsequences by Step 3 to make a forecast.
- (5)
- Superposing the prediction result of each new subsequence to obtain the final forecast value of landslide deformation, and then evaluating the accuracy of each model.

#### 3.4. Analysis of the Forecast Results

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Intrinsic Mode Function | Component Serial Number | ||
---|---|---|---|

New IMF | IMF1 | IMF2 | IMF3 |

Original IMF | IMF1 | IMF2,IMF3 | IMF4,IMF5,IMF6 |

Sample | Prediction Model | Step Size: 1 to 5 | Step Size: 6 to 10 | Step Size: 11 to 15 | Step Size: 16 to 20 | Running Time/s | ||||
---|---|---|---|---|---|---|---|---|---|---|

IAA | EAA | IAA | EAA | IAA | EAA | IAA | EAA | |||

Original data | Scheme 1 | ±0.44 | ±0.53 | ±0.95 | ±1.22 | ±1.34 | ±1.66 | ±1.52 | ±1.93 | 13.92 |

Scheme 2 | ±0.20 | ±0.28 | ±0.61 | ±0.81 | ±1.11 | ±1.22 | ±1.32 | ±1.62 | 10.27 | |

Scheme 3 | ±0.13 | ±0.20 | ±0.50 | ±0.61 | ±0.84 | ±0.96 | ±1.24 | ±1.42 | 8.13 | |

Scheme 4 | ±0.39 | ±0.47 | ±0.84 | ±0.96 | ±0.99 | ±1.16 | ±1.37 | ±1.50 | 17.35 | |

Scheme 5 | ±0.13 | ±0.19 | ±0.48 | ±0.57 | ±0.75 | ±0.86 | ±1.09 | ±1.20 | 11.97 | |

IMF1 | Scheme 6 | ±0.09 | ±0.13 | ±0.11 | ±0.15 | ±0.15 | ±0.19 | ±0.20 | ±0.23 | 11.42 |

Scheme 7 | ±0.06 | ±0.10 | ±0.10 | ±0.14 | ±0.13 | ±0.17 | ±0.16 | ±0.20 | 14.84 | |

Scheme 8 | ±0.03 | ±0.08 | ±0.06 | ±0.10 | ±0.10 | ±0.16 | ±0.13 | ±0.18 | 7.51 | |

Scheme 9 | ±0.03 | ±0.07 | ±0.03 | ±0.08 | ±0.09 | ±0.13 | ±0.10 | ±0.15 | 9.14 | |

Scheme 10 | ±0.03 | ±0.07 | ±0.04 | ±0.09 | ±0.08 | ±0.13 | ±0.10 | ±0.15 | 5.84 | |

Scheme 11 | ±0.00 | ±0.05 | ±0.03 | ±0.08 | ±0.05 | ±0.11 | ±0.08 | ±0.14 | 7.92 | |

IMF2 | Scheme 6 | ±0.19 | ±0.24 | ±0.47 | ±0.54 | ±0.89 | ±1.06 | ±1.10 | ±1.21 | 12.67 |

Scheme 7 | ±0.16 | ±0.20 | ±0.36 | ±0.41 | ±0.60 | ±0.68 | ±0.67 | ±0.76 | 16.79 | |

Scheme 8 | ±0.10 | ±0.15 | ±0.21 | ±0.27 | ±0.35 | ±0.41 | ±0.39 | ±0.48 | 7.94 | |

Scheme 9 | ±0.09 | ±0.13 | ±0.13 | ±0.18 | ±0.27 | ±0.33 | ±0.36 | ±0.41 | 10.97 | |

Scheme 10 | ±0.10 | ±0.14 | ±0.18 | ±0.24 | ±0.29 | ±0.37 | ±0.38 | ±0.45 | 6.96 | |

Scheme 11 | ±0.07 | ±0.11 | ±0.06 | ±0.10 | ±0.19 | ±0.28 | ±0.29 | ±0.37 | 8.27 | |

IMF3 | Scheme 6 | ±0.31 | ±0.38 | ±0.56 | ±0.64 | ±1.01 | ±1.19 | ±1.15 | ±1.30 | 13.57 |

Scheme 7 | ±0.21 | ±0.26 | ±0.37 | ±0.43 | ±0.79 | ±0.85 | ±0.90 | ±0.97 | 16.91 | |

Scheme 8 | ±0.17 | ±0.22 | ±0.28 | ±0.34 | ±0.59 | ±0.67 | ±0.61 | ±0.69 | 8.10 | |

Scheme 9 | ±0.13 | ±0.18 | ±0.15 | ±0.21 | ±0.45 | ±0.51 | ±0.47 | ±0.56 | 11.37 | |

Scheme 10 | ±0.16 | ±0.20 | ±0.23 | ±0.29 | ±0.55 | ±0.61 | ±0.57 | ±0.64 | 7.24 | |

Scheme 11 | ±0.11 | ±0.18 | ±0.11 | ±0.19 | ±0.44 | ±0.51 | ±0.46 | ±0.53 | 9.14 |

Model | Prediction Step: 5 | Prediction Step: 10 | Prediction Step: 20 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Max | Min | RMSE | MAE | Max | Min | RMSE | MAE | Max | Min | RMSE | MAE | |

Scheme 1 | −2.17 | 0.13 | 1.283 | 1.141 | −2.31 | 0.34 | 1.312 | 1.273 | −3.11 | 0.27 | 1.482 | 1.395 |

Scheme 2 | 2.04 | −0.16 | 0.986 | 0.793 | 1.98 | 0.15 | 1.141 | 0.904 | 2.14 | 0.57 | 1.207 | 1.016 |

Scheme 3 | 1.70 | −0.10 | 0.820 | 0.647 | 1.67 | −0.24 | 0.956 | 0.741 | 1.99 | 0.34 | 1.189 | 0.861 |

Scheme 4 | −1.71 | −0.17 | 0.974 | 0.878 | −1.83 | −0.34 | 1.085 | 0.957 | −2.01 | 0.47 | 1.261 | 1.204 |

Scheme 5 | −1.32 | 0.10 | 0.711 | 0.595 | −1.18 | 0.21 | 0.854 | 0.611 | −1.57 | 0.29 | 1.097 | 0.773 |

Scheme 6 | −1.34 | 0.21 | 0.973 | 0.857 | −1.57 | 0.18 | 1.037 | 0.911 | −1.61 | −0.17 | 1.197 | 0.999 |

Scheme 7 | −1.21 | −0.16 | 0.673 | 0.599 | −1.39 | 0.09 | 0.794 | 0.715 | −1.45 | −0.27 | 0.897 | 0.809 |

Scheme 8 | 1.04 | −0.11 | 0.617 | 0.515 | 1.21 | −0.10 | 0.698 | 0.601 | 1.28 | −0.09 | 0.788 | 0.689 |

Scheme 9 | −0.91 | −0.10 | 0.480 | 0.390 | −0.95 | −0.10 | 0.492 | 0.397 | −1.00 | 0.07 | 0.504 | 0.407 |

Scheme 10 | 0.98 | 0.10 | 0.496 | 0.417 | 0.89 | −0.13 | 0.579 | 0.497 | 0.95 | −0.09 | 0.657 | 0.479 |

Scheme 11 | −0.86 | 0.05 | 0.472 | 0.373 | −0.88 | 0.01 | 0.484 | 0.380 | 0.91 | −0.04 | 0.495 | 0.397 |

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**MDPI and ACS Style**

Xie, S.; Liang, Y.; Zheng, Z.; Liu, H.
Combined Forecasting Method of Landslide Deformation Based on MEEMD, Approximate Entropy, and WLS-SVM. *ISPRS Int. J. Geo-Inf.* **2017**, *6*, 5.
https://doi.org/10.3390/ijgi6010005

**AMA Style**

Xie S, Liang Y, Zheng Z, Liu H.
Combined Forecasting Method of Landslide Deformation Based on MEEMD, Approximate Entropy, and WLS-SVM. *ISPRS International Journal of Geo-Information*. 2017; 6(1):5.
https://doi.org/10.3390/ijgi6010005

**Chicago/Turabian Style**

Xie, Shaofeng, Yueji Liang, Zhongtian Zheng, and Haifeng Liu.
2017. "Combined Forecasting Method of Landslide Deformation Based on MEEMD, Approximate Entropy, and WLS-SVM" *ISPRS International Journal of Geo-Information* 6, no. 1: 5.
https://doi.org/10.3390/ijgi6010005