# A Novel Model for Landslide Displacement Prediction Based on EDR Selection and Multi-Swarm Intelligence Optimization Algorithm

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Data Preprocessing with CEEMD

#### 2.2. Selection of Optimal Related Factors via EDR

#### 2.3. Support Vector Regression (SVR)

#### 2.4. Multiple Swarm Intelligence

#### 2.4.1. Bat Algorithm (BA)

#### 2.4.2. Grey Wolf Optimization (GWO)

#### 2.4.3. Dragonfly Algorithm (DA)

#### 2.4.4. Whale Optimization Algorithm (WOA)

#### 2.4.5. Grasshopper Optimization Algorithm (GOA)

#### 2.4.6. Sparrow Search Algorithm (SSA)

#### 2.5. Procedure of the Proposed Hybrid Algorithm

#### 2.6. Performance Evaluation Formula

^{2}), root mean square error (RMSE), mean absolute error (MAE), and mean average percentage error (MAPE). These indicators were used in this study and are defined as:

## 3. Cases Study

#### 3.1. Geological Conditions

^{6}m

^{3}and covers an area of 0.34 km

^{2}. The top of the landslide is at an elevation of 340 to 358 m with a width of 140 m, and the toe of the landslide is at an elevation of 68 to 80 m with a width of 570 m.

#### 3.2. Rainfall and Reservoir Levels

#### 3.3. Deformation Characteristics

^{3}. The toe area is very unstable, and slope movements at the toe affect the rest of the slope. At present, the slope’s deformation processes are causing small collapses under the influence of rainfall or reservoir level fluctuations.

#### 3.4. Landslide Monitoring

#### 3.5. Analysis of Monitoring Data

## 4. Data Processing and Statistical Analysis

#### 4.1. CEEMD Decomposition of Landslide Displacement Versus Time Data

- ensemble member = 200
- standard deviation of added white noise in each ensemble member = 0.2
- threshold variance = 0.2
- threshold for first iteration = 4

#### 4.2. CEEMD Decomposition of Related Factors

_{1}was compared to the other IMFs by a paired t-test with a significance set at 0.05 (two-tailed) for each decomposed and restructured factor. If the significance values of IMF

_{i}are greater than 0.05, the difference between IMF

_{1}and IMF

_{i}is not significant. Therefore, the superposition of IMFs from IMF

_{1}to IMF

_{i}is the high-frequency component, and the superposition of the remaining IMFs is the low-frequency component. The IMFs of each restructured factors are shown in Figure 11, and the results of the paired t-test are shown in Table 1.

_{1}usually has the highest frequency and fluctuation amplitude. Since there is only one IMF after the CEEMD decomposition of D2, it is considered that there are only high-frequency components in D2. The paired t-test results indicate that only IMF

_{3}in X1 and IMF

_{4}in X3 has a significance value that is less than 0.05, which denotes that the low-frequency components only exist in X1 and X3. Taking these two as the low-frequency components of X1 and X3, the high-frequency components of the other factors will be the sum of the remaining IMFs. Therefore, in addition to the variables mentioned above, new variables can also be chosen as input to an SVR model of the periodic displacements after reconstruction: high-frequency current monthly rainfall sequence (L1

^{H}), high-frequency accrued precipitation of the previous two months (L2

^{H}), high-frequency accrued precipitation of the previous month and the current month (L3

^{H}), high-frequency accrued precipitation of the previous two and the current months (L4

^{H}), high-frequency current monthly reservoir level data (X1

^{H}), low-frequency current monthly reservoir level data (X1

^{L}), high-frequency reservoir level monthly change (X2

^{H}), high-frequency change of reservoir level between two months (X3

^{H}), low-frequency change of reservoir level between two months (X3

^{L}), high-frequency previous month displacement (D1

^{H}), and high-frequency accrued displacement of the previous month and the current month (D2

^{H}).

#### 4.3. Factors Affecting Landslide Displacement Selected by EDR

^{H}), the high-frequency current monthly reservoir level data (X1

^{H}), and the high-frequency previous month displacement (D1

^{H}) are the most relevant factors in each group. Thus, when predicting periodic displacement, L4

^{H}, X1

^{H}, and D1

^{H}are the input variables for the periodic displacement SVR model. Similarly, related factors for predicting trend displacement are the residual terms of L2, X1, and D2 according to the EDR results in each group, and these were chosen as the input parameters for the trend displacement SVR model.

^{H}), the high-frequency current monthly reservoir level data (X1

^{H}), and the high-frequency previous month displacement (D1

^{H}) are the most relevant related factors in each group, which is consistent with the results selected by EDR.

## 5. Prediction Results and Comparison

#### 5.1. Parameter Optimization

_{1}and x

_{2}. The calculation results and process show that the slopes of the convergence curves of SSA and GWO are close, indicating that the convergence performance of the two is close and is the best among the six algorithms. The solutions obtained by each SI in ${F}_{1}\left(x\right)$ and ${F}_{3}\left(x\right)$ are relatively scattered, and some algorithms (such as BA) will fall into a local optimum.

#### 5.2. Prediction of Periodic and Trend Displacements

^{2}and smallest MAPE, RMSE, and MAE was obtained using the DA algorithm among all of the given models. The corresponding result of MAPE, RMSE, MAE, and R

^{2}is 3.654173, 63.0435, 119.2786, 0.824217, respectively. Meanwhile, the GWO-based SVR model gave the best prediction for the trend displacements compared to the other optimization algorithms, with the result of MAPE, RMSE, MAE, and R

^{2}being 0.010273, 95.9178, 184.4194, and 0.99473, respectively. Overall, the prediction results provided by the SVR model optimized by MSI matched well with the observation results.

#### 5.3. Prediction of Cumulative Displacements

^{2}, which is 0.762 and 0.9998, respectively. The cumulative displacement prediction results are in good agreement with the measured displacement, with an absolute error of monthly displacement that is generally less than 67mm and the maximum relative error of monthly displacement that less than 3%. The average relative error of the proposed prediction model is 0.898%, which is slightly smaller than the result obtained by the prediction model of Deng et al. [54]. The comparative study shows the effective improvement of the proposed model in terms of prediction performance and the universality of it to predict the displacement of slow-moving landslides all around the world.

## 6. Discussion

^{H}, X1

^{H}, and D1

^{H}, and the most relevant factors for the trend displacements are the residual terms of L2, X1, and D2. MSI (BA, DA, GOA, GWO, SSA, and WOA) was used to optimize the proposed prediction model. For the Shiliushubao landslide, the DA-based SVR model performs best to predict periodic displacements, and the GWO-based SVR model works best for predicting trend displacements. The prediction of cumulative displacements is in good agreement with the measured displacements with a maximum relative error of monthly displacement of less than 3%. The trail of the proposed model on the Baishuihe landslide, another landslide in the reservoir area, is also satisfied with the average relative error of 0.898%, which performs slightly better than that from the previous study.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Tang, H.; Wasowski, J.; Juang, C.H. Geohazards in the three Gorges Reservoir Area, China–Lessons learned from decades of research. Eng. Geol.
**2019**, 261, 105267. [Google Scholar] [CrossRef] - Niu, M.; Wang, Y.; Sun, S.; Li, Y. A novel hybrid decomposition-and-ensemble model based on CEEMD and GWO for short-term PM2.5 concentration forecasting. Atmos. Environ.
**2016**, 134, 168–180. [Google Scholar] [CrossRef] - Wang, J.; Schweizer, D.; Liu, Q.; Su, A.; Hu, X.; Blum, P. Three-dimensional landslide evolution model at the Yangtze River. Eng. Geol.
**2021**, 292, 106275. [Google Scholar] [CrossRef] - Wang, Y.; Tang, H.; Wen, T.; Ma, J. A hybrid intelligent approach for constructing landslide displacement prediction intervals. Appl. Soft Comput.
**2019**, 81, 105506. [Google Scholar] [CrossRef] - Zhang, Y.G.; Tang, J.; He, Z.Y.; Tan, J.; Li, C. A novel displacement prediction method using gated recurrent unit model with time series analysis in the Erdaohe landslide. Nat. Hazards
**2020**, 105, 783–813. [Google Scholar] [CrossRef] - Zhang, J.; Tang, H.; Tannant, D.D.; Lin, C.; Xia, D.; Liu, X.; Zhang, Y.; Ma, J. Combined forecasting model with CEEMD-LCSS reconstruction and the ABC-SVR method for landslide displacement prediction. J. Clean. Prod.
**2021**, 293, 126205. [Google Scholar] [CrossRef] - Yin, Y.P.; Huang, B.L.; Wang, W.P.; Wei, Y.J.; Ma, X.H.; Ma, F.; Zhao, C.J. Reservoir-induced landslides and risk control in Three Gorges Project on Yangtze River, China. J. Rock Mech. Geotech. Eng.
**2016**, 8, 577–595. [Google Scholar] [CrossRef] [Green Version] - Zhou, C.; Yin, K.; Cao, Y.; Intrieri, E.; Ahmed, B.; Catani, F. Displacement prediction of step-like landslide by applying a novel kernel extreme learning machine method. Landslides
**2018**, 15, 2211–2225. [Google Scholar] [CrossRef] [Green Version] - Ma, J.; Niu, X.; Tang, H.; Wang, Y.; Wen, T.; Zhang, J. Displacement Prediction of a Complex Landslide in the Three Gorges Reservoir Area (China) Using a Hybrid Computational Intelligence Approach. Complexity
**2020**, 2020, 2624547. [Google Scholar] [CrossRef] - Saito, M. Forecasting the time of occurrence of a slope failure. In Proceedings of the 6th International Congress on Soil Mechanics and Foundation Engineering, Montreal, QC, Canada, 8–15 September 1965; pp. 537–541. [Google Scholar]
- Crosta, G.B.; Agliardi, F. Failure forecast for large rock slides by surface displacement measurements. Can. Geotech. J.
**2003**, 40, 176–191. [Google Scholar] [CrossRef] - Ma, J.W.; Tang, H.M.; Liu, X.; Hu, X.L.; Sun, M.J.; Song, Y.J. Establishment of a deformation forecasting model for a step-like landslide based on decision tree C5.0 and two-step cluster algorithms: A case study in the Three Gorges Reservoir area, China. Landslides
**2017**, 14, 1275–1281. [Google Scholar] [CrossRef] - Zou, Z.; Yang, Y.; Fan, Z.; Tang, H.; Zou, M.; Hu, X.; Xiong, C.; Ma, J. Suitability of data preprocessing methods for landslide displacement forecasting. Stoch. Environ. Res. Risk Assess.
**2020**, 34, 1105–1119. [Google Scholar] [CrossRef] - Ma, J.; Liu, X.; Niu, X.; Wang, Y.; Wen, T.; Zhang, J.; Zou, Z. Forecasting of landslide displacement using a probability-scheme combination ensemble prediction technique. Int. J. Environ. Res. Public Health
**2020**, 17, 4788. [Google Scholar] [CrossRef] - Tharwat, A.; Gabel, T. Parameters optimization of support vector machines for imbalanced data using social ski driver algorithm. Neural. Comput. Appl.
**2019**, 32, 6925–6938. [Google Scholar] [CrossRef] - Cai, Z.; Xu, W.; Meng, Y.; Shi, C.; Wang, R. Prediction of landslide displacement based on GA-LSSVM with multiple factors. Bull. Eng. Geol. Environ.
**2015**, 75, 637–646. [Google Scholar] [CrossRef] - Zhou, C.; Yin, K.; Cao, Y.; Ahmed, B. Application of time series analysis and PSO–SVM model in predicting the Bazimen landslide in the Three Gorges Reservoir, China. Eng. Geol.
**2016**, 204, 108–120. [Google Scholar] [CrossRef] - Zhang, J.; Yin, K.; Wang, J.; Huang, F. Displacement prediction of Baishuihe landslide based on time series and PSO-SVR model. Chin. J. Rock Mech. Eng.
**2015**, 34, 382–391. [Google Scholar] - Peng, L.; Niu, R.; Wu, T. Time series analysis and support vector machine for landslide displacement prediction. J. Zhejiang Univ. (Eng. Sci.)
**2013**, 47, 1672–1679. [Google Scholar] - Zhou, C.; Yin, K.; Cao, Y.; Ahmed, B.; Fu, X. A novel method for landslide displacement prediction by integrating advanced computational intelligence algorithms. Sci. Rep.
**2018**, 8, 7287. [Google Scholar] [CrossRef] [Green Version] - Ding, L.; Lv, J.; Li, X.; Li, L. Support vector regression and ant colony optimization for HVAC cooling load prediction. In Proceedings of the 2010 International Symposium on Computer, Communication, Control and Automation (3CA), IEEE, Tainan, Taiwan, 5–7 May 2010; Volume 1, pp. 537–541. [Google Scholar]
- Balogun, A.L.; Rezaie, F.; Pham, Q.B.; Gigović, L.; Drobnjak, S.; Aina, Y.A.; Panahi, M.; Yekeen, S.T.; Lee, S. Spatial prediction of landslide susceptibility in western Serbia using hybrid support vector regression (SVR) with GWO, BAT and COA algorithms. Geosci. Front.
**2021**, 12, 101104. [Google Scholar] [CrossRef] - Li, L.W.; Wu, Y.P.; Miao, F.S.; Liao, K.; Zhang, F.L. Displacement prediction of landslides based on variational mode decomposition and GWO-MIC-SVR model. Chin. J. Rock Mech. Eng.
**2018**, 37, 1395–1406. (In Chinese) [Google Scholar] - Miao, F.; Wu, Y.; Xie, Y.; Li, Y. Prediction of landslide displacement with step-like behavior based on multialgorithm optimization and a support vector regression model. Landslides
**2018**, 15, 475–488. [Google Scholar] [CrossRef] - Zhang, J.; Tang, H.; Wen, T.; Ma, J.; Tan, Q.; Xia, D.; Liu, X.; Zhang, Y. A Hybrid Landslide Displacement Prediction Method Based on CEEMD and DTW-ACO-SVR—Cases Studied in the Three Gorges Reservoir Area. Sensors
**2020**, 20, 4287. [Google Scholar] [CrossRef] - Zhang, Y.; Agarwal, P.; Bhatnagar, V.; Balochian, S.; Yan, J. Swarm Intelligence and Its Applications. Sci. World J.
**2013**, 2013, 528069. [Google Scholar] [CrossRef] - Chen, W.; Tsangaratos, P.; Ilia, I.; Duan, Z.; Chen, X. Groundwater spring potential mapping using population-based evolutionary algorithms and data mining methods. Sci. Total Environ.
**2019**, 684, 31–49. [Google Scholar] [CrossRef] - Kişi, Ö. Streamflow Forecasting Using Different Artificial Neural Network Algorithms. J. Hydrol. Eng.
**2007**, 12, 532–539. [Google Scholar] [CrossRef] - Beni, G. From Swarm Intelligence to Swarm Robotics. In Swarm Robotics; Springer: Berlin/Heidelberg, Germany, 2005; pp. 1–9. [Google Scholar]
- Liu, Y.; Wang, R. Study on network traffic forecast model of SVR optimized by GAFSA. Chaos Solitons Fractals
**2016**, 89, 153–159. [Google Scholar] [CrossRef] - Ali, E.S.; Abd Elazim, S.M.; Abdelaziz, A.Y. Ant Lion Optimization Algorithm for Renewable Distributed Generations. Energy
**2016**, 116, 445–458. [Google Scholar] [CrossRef] - Jiang, H.; Yang, Y.; Ping, W.; Dong, Y. A Novel Hybrid Classification Method Based on the Opposition-Based Seagull Optimization Algorithm. IEEE Access
**2020**, 8, 100778–100790. [Google Scholar] [CrossRef] - Yang, X.S.; He, X. Bat algorithm: Literature review and applications. Int. J. Bio-Inspir. Comput.
**2013**, 5, 141. [Google Scholar] [CrossRef] [Green Version] - Emary, E.; Zawbaa, H.M.; Hassanien, A.E. Binary grey wolf optimization approaches for feature selection. Neurocomputing
**2016**, 172, 371–381. [Google Scholar] [CrossRef] - Mirjalili, S. Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl.
**2015**, 27, 1053–1073. [Google Scholar] [CrossRef] - Mirjalili, S.; Lewis, A. The Whale Optimization Algorithm. Adv. Eng. Softw.
**2016**, 95, 51–67. [Google Scholar] [CrossRef] - Mirjalili, S.Z.; Mirjalili, S.; Saremi, S.; Faris, H.; Aljarah, I. Grasshopper optimization algorithm for multi-objective optimization problems. Appl. Intell.
**2017**, 48, 805–820. [Google Scholar] [CrossRef] - Xue, J.; Shen, B. A novel swarm intelligence optimization approach: Sparrow search algorithm. Syst. Sci. Control
**2020**, 8, 22–34. [Google Scholar] [CrossRef] - Du, H.; Song, D.; Chen, Z.; Shu, H.; Guo, Z. Prediction model oriented for landslide displacement with step-like curve by applying ensemble empirical mode decomposition and the PSO-ELM method. J. Clean. Prod.
**2020**, 270, 122248. [Google Scholar] [CrossRef] - Li, Y.; Sun, R.; Yin, K.; Xu, Y.; Chai, B.; Xiao, L. Forecasting of landslide displacements using a chaos theory based wavelet analysis-Volterra filter model. Sci. Rep.
**2019**, 9, 19853. [Google Scholar] [CrossRef] - Xu, S.; Niu, R. Displacement prediction of Baijiabao landslide based on empirical mode decomposition and long short-term memory neural network in Three Gorges area, China. Comput. Geosci.
**2018**, 111, 87–96. [Google Scholar] [CrossRef] - Ren, F.; Wu, X.; Zhang, K.; Niu, R. Application of wavelet analysis and a particle swarm-optimized support vector machine to predict the displacement of the Shuping landslide in the Three Gorges, China. Environ. Earth Sci.
**2014**, 73, 4791–4804. [Google Scholar] [CrossRef] - Yang, B.; Yin, K.; Lacasse, S.; Liu, Z. Time series analysis and long short-term memory neural network to predict landslide displacement. Landslides
**2019**, 16, 677–694. [Google Scholar] [CrossRef] - Huang, H.F.; Wu, Y.I.; Yi-Liang, L. Study on variables selection using SVR-MIV method in displacement prediction of landslides. Chin. J. Undergr. Space Eng.
**2016**, 12, 213–219. (In Chinese) [Google Scholar] - Chen, L.; Özsu, M.T.; Oria, V. Robust and fast similarity search for moving object trajectories. In SIGMOD ’05, Proceedings of the 24th ACM International Conference on Management of Data, New York, NY, USA, 13–15 June 2005; ACM Press: New York, NY, USA, 2005; pp. 491–502. [Google Scholar] [CrossRef]
- Mai, S.T.; Goebl, S.; Plant, C. A Similarity Model and Segmentation Algorithm for White Matter Fiber Tracts. In Proceedings of the 2012 IEEE 12th International Conference on Data Mining, IEEE, Washington, DC, USA, 10–13 December 2012. [Google Scholar]
- Xu, Y.; Zhang, M.; Zhu, Q.; He, Y. An improved multi-kernel RVM integrated with CEEMD for high-quality intervals prediction construction and its intelligent modeling application. Chemometr. Intell. Lab. Syst.
**2017**, 171, 151–160. [Google Scholar] [CrossRef] - Ranacher, P.; Tzavella, K. How to compare movement? A review of physical movement similarity measures in geographic information science and beyond. Cartogr. Geogr. Inf. Sci.
**2014**, 41, 286–307. [Google Scholar] [CrossRef] - Moayedi, A.; Abbaspour, R.A.; Chehreghan, A. An evaluation of the efficiency of similarity functions in density-based clustering of spatial trajectories. Ann. GIS
**2019**, 25, 313–327. [Google Scholar] [CrossRef] [Green Version] - Liu, H.; Mi, X.; Li, Y.; Duan, Z.; Xu, Y. Smart wind speed deep learning based multi-step forecasting model using singular spectrum analysis, convolutional Gated Recurrent Unit network and Support Vector Regression. Renew. Energy
**2019**, 143, 842–854. [Google Scholar] [CrossRef] - Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey Wolf Optimizer. Adv. Eng. Softw.
**2014**, 69, 46–61. [Google Scholar] [CrossRef] [Green Version] - Li, Z.; Xie, Y.; Li, X.; Zhao, W. Prediction and application of porosity based on support vector regression model optimized by adaptive dragonfly algorithm. Energy Sources Part A Recovery Util. Environ. Eff.
**2019**, 43, 1073–1086. [Google Scholar] [CrossRef] - Barman, M.; Dev Choudhury, N.B. Hybrid GOA-SVR technique for short term load forecasting during periods with substantial weather changes in North-East India. Procedia Comput. Sci.
**2018**, 143, 124–132. [Google Scholar] [CrossRef] - Deng, D.; Liang, Y.; Wang, L.; Wang, C.-S.; Sun, Z.-H.; Wang, C.; Dong, M.-M. Displacement prediction method based on ensemble empirical mode decomposition and support vector machine regression—A case of landslides in Three Gorges Reservoir area. Rock Soil Mech.
**2017**, 38, 3660–3669. [Google Scholar] - Hongtao, N. Smart safety early warning model of landslide geological hazard based on BP neural network. Saf. Sci.
**2020**, 123, 104572. [Google Scholar] [CrossRef] - Adnan, M.S.G.; Rahman, M.S.; Ahmed, N.; Ahmed, B.; Rabbi, M.F.; Rahman, R.M. Improving Spatial Agreement in Machine Learning-Based Landslide Susceptibility Mapping. Remote. Sens.
**2020**, 12, 3347. [Google Scholar] [CrossRef] - Ahmad, H.; Ningsheng, C.; Rahman, M.; Islam, M.M.; Pourghasemi, H.R.; Hussain, S.F.; Habumugisha, J.M.; Liu, E.; Zheng, H.; Ni, H.; et al. Geohazards Susceptibility Assessment along the Upper Indus Basin Using Four Machine Learning and Statistical Models. ISPRS Int. J. Geo-Inf.
**2021**, 10, 315. [Google Scholar] [CrossRef]

**Figure 1.**Residual terms of Baishuihe landslide displacements obtained through EMD, EEMD, and CEEMD.

**Figure 2.**Framework of the proposed ensemble prediction model, (

**a**) data preparation step, (

**b**) displacement prediction step, and (

**c**) MSI optimization step.

**Figure 3.**Location (

**a**,

**b**) and an oblique view (

**c**) of Shiliushubao landslide captured by UAV, October 2020.

**Figure 6.**The ground collapses (

**a**,

**b**) and cracking (

**c**,

**d**) in the toe area captured by UAV, October 2020.

**Figure 8.**Correlation of displacement velocity at G1 versus the reservoir level, rainfall, and fluctuation of reservoir level.

**Figure 13.**Landslide periodic displacement compared with selected factors affecting landslide movement.

Groups | Restructured Factor | Component | t | Sig. | Mean (mm) | Std. Deviation (mm) |
---|---|---|---|---|---|---|

Rainfall | L1 | IMF_{2} | 0.22 | 0.83 | 1.50 | 56.92 |

IMF_{3} | −0.20 | 0.84 | −1.23 | 50.75 | ||

IMF_{4} | 0.60 | 0.55 | 3.02 | 42.24 | ||

IMF_{5} | 0.10 | 0.92 | 0.41 | 36.49 | ||

L2 | IMF_{2} | 0.47 | 0.64 | 6.16 | 110.1 | |

IMF_{3} | −1.34 | 0.18 | −10.09 | 63.28 | ||

L3 | IMF_{2} | 0.23 | 0.82 | 3.05 | 111.1 | |

IMF_{3} | −1.70 | 0.09 | −12.42 | 61.56 | ||

IMF_{4} | −1.08 | 0.28 | −6.75 | 52.48 | ||

L4 | IMF_{2} | 0.38 | 0.70 | 5.43 | 120.1 | |

IMF_{3} | −0.61 | 0.54 | −5.02 | 69.11 | ||

Reservoir water level | X1 | IMF_{2} | 0.47 | 0.64 | 0.26 | 4.73 |

IMF_{3} | 2.07 | 0.04 | 0.66 | 2.70 | ||

X2 | IMF_{2} | 0.22 | 0.83 | 2.91 | 111.6 | |

IMF_{3} | −1.58 | 0.12 | −11.65 | 62.23 | ||

IMF_{4} | −0.98 | 0.33 | −6.13 | 52.64 | ||

X3 | IMF_{2} | −0.17 | 0.86 | −0.37 | 18.16 | |

IMF_{3} | −0.52 | 0.61 | −1.49 | 24.30 | ||

IMF_{4} | −2.19 | 0.03 | −10.94 | 42.05 | ||

Displacement | D1 | IMF_{2} | −0.04 | 0.97 | −1.16 | 229.4 |

IMF_{3} | −1.07 | 0.29 | −40.82 | 320.5 |

Groups | Component | Periodic Displacement | Trend Displacement | ||
---|---|---|---|---|---|

Origin | High | Low | |||

Rainfall | L1 | 61 | 60 | / | 68 |

L2 | 56 | 53 | / | 24 | |

L3 | 56 | 53 | / | 42 | |

L4 | 54 | 49 | / | 42 | |

Reservoir level | X1 | 53 | 33 | 44 | 22 |

X2 | 56 | 53 | / | 41 | |

X3 | 69 | 41 | 58 | 60 | |

Displacement | D1 | 67 | 21 | / | 3 |

D2 | 66 | 32 | / | 2 |

Function | Range | Theoretical Minimum Value |
---|---|---|

${F}_{1}\left(x\right)={{\displaystyle \sum}}_{i=1}^{n}{x}_{i}^{2}$ | ${x}_{i}\in \left[-100,100\right],i=1,2$ | 0 |

${F}_{2}\left(x\right)={{\displaystyle \sum}}_{i-1}^{n}i{x}_{i}^{4}+random\left(0,1\right)$ | ${x}_{i}\in \left[-1.28,1.28\right],i=1,2$ | 0 |

${F}_{3}\left(x\right)={{\displaystyle \sum}}_{i=1}^{n}\left[{x}_{i}^{2}-10\mathrm{cos}\left(2\pi {x}_{i}\right)+10\right]$ | ${x}_{i}\in \left[-5.12,5.12\right],i=1,2$ | 0 |

Algorithm | Parameters | Periodic | Trend | ||||
---|---|---|---|---|---|---|---|

C | g | C | g | ||||

BA-SVR | Sizepop = 20 | Max_iter. = 200 | A = 0.2 | 220.67 | 0.00109 | 657.16 | 0.00106 |

Lb = 1 × 10^{−2} | Ub =1 × 10^{2} | r = 0.5 | |||||

Freq_min = 0.1 | Freq_min = 0.2 | Alpha = 0.2 | |||||

DA-SVR | Sizepop = 30 | Max_iter. = 200 | e = f = 0.1 | 66506 | 0.00001 | 83702 | 0.00001 |

lb = 1 × 10^{−5} | ub = 1 × 10^{5} | c = 0.7 | |||||

w = 0.5 | s = 0.1 | a = 0.1 | |||||

GOA-SVR | Sizepop = 30 | Max_iter. = 200 | l = 1.5 | 16.13 | 0.00100 | 29.68 | 0.01000 |

lb = 1 × 10^{−3} | ub = 1 × 10^{3} | f = 0.5 | |||||

GWO-SVR | Sizepop = 30 | Max_iter. = 200 | dim = 2 | 474.94 | 0.00100 | 706.29 | 0.00100 |

lb = 1 × 10^{−3} | ub = 1 × 10^{3} | / | |||||

SSA-SVR | Sizepop = 30 | Max_iter. = 200 | pNum = 20% | 16.17 | 0.00100 | 9677.9 | 0.00014 |

lb = 1 × 10^{−4} | ub = 1 × 10^{4} | sNum = 20% | |||||

OA-SVR | Sizepop = 20 | Max_iter. = 200 | dim = 2 | 1.74 | 0.01000 | 48277.4 | 0.00001 |

lb = 1 × 10^{−5} | ub = 1 × 10^{5} | b = 1 |

Optimization Algorithm | Periodic Displacement | Trend Displacement | ||||||
---|---|---|---|---|---|---|---|---|

MAPE | RMSE | MAE | R^{2} | MAPE | RMSE | MAE | R^{2} | |

BA | 0.688 | 13.691 | 30.118 | 0.757 | 0.395 | 1065.132 | 926.683 | 0.8621 |

DA | 0.788 | 13.652 | 30.367 | 0.761 | 0.008 | 20.448 | 66.336 | 0.9997 |

GOA | 0.692 | 13.663 | 30.110 | 0.758 | 0.008 | 19.649 | 66.214 | 0.9997 |

GWO | 0.680 | 13.592 | 29.558 | 0.751 | 0.008 | 20.448 | 66.336 | 0.9997 |

SSA | 0.786 | 13.589 | 30.307 | 0.762 | 0.009 | 22.766 | 64.733 | 0.9998 |

WOA | 0.788 | 13.629 | 30.329 | 0.761 | 0.008 | 20.448 | 66.336 | 0.9997 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Tang, H.; Tannant, D.D.; Lin, C.; Xia, D.; Wang, Y.; Wang, Q.
A Novel Model for Landslide Displacement Prediction Based on EDR Selection and Multi-Swarm Intelligence Optimization Algorithm. *Sensors* **2021**, *21*, 8352.
https://doi.org/10.3390/s21248352

**AMA Style**

Zhang J, Tang H, Tannant DD, Lin C, Xia D, Wang Y, Wang Q.
A Novel Model for Landslide Displacement Prediction Based on EDR Selection and Multi-Swarm Intelligence Optimization Algorithm. *Sensors*. 2021; 21(24):8352.
https://doi.org/10.3390/s21248352

**Chicago/Turabian Style**

Zhang, Junrong, Huiming Tang, Dwayne D. Tannant, Chengyuan Lin, Ding Xia, Yankun Wang, and Qianyun Wang.
2021. "A Novel Model for Landslide Displacement Prediction Based on EDR Selection and Multi-Swarm Intelligence Optimization Algorithm" *Sensors* 21, no. 24: 8352.
https://doi.org/10.3390/s21248352