# Landslide Displacement Prediction of Shuping Landslide Combining PSO and LSSVM Model

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}of three monitoring stations is larger than 0.98, and the MAE values and the RMSE values are the smallest among the three models. The outcomes demonstrate that the PSO-LSSVM model has a high accuracy in predicting landslide displacement.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Time Series Theory

#### 2.2. PSO Algorithm

_{i}= {X

_{i1}, X

_{i2}… X

_{iD}} ($i$ = 1, 2... m), and the flight velocity of each particle constitutes the set V

_{i}= {V

_{i1}, V

_{i2}... V

_{iD}}. Based on the matching degree of each particle, the position of each particle is evaluated, and the optimal position is found as Pbest

_{i}= {p

_{i1}, p

_{i2}... p

_{iD}}, which is the individual extreme value. The optimal position of all particles is currently found as Gbest

_{i}= {g

_{1}, g

_{2}...g

_{D}}, which is the global extreme value. Then the velocity and position of the next iteration of particles are updated by Equations (5) and (6).

#### 2.3. LSSVM Algorithm

#### 2.4. PSO-LSSVM Algorithm

- (a)
- Initialize parameters containing population size m, number of iterations $k$, learning factor c, initial position $x$, and initial velocity $v$ of the particles, etc.;
- (b)
- Predict learning samples by the particle vectors in the LSSVM. A prediction error of the current position of each particle is regarded as a fitness value of each particle. By comparing the current fitness value of each particle with its optimal fitness value, the current position is taken as the optimal position if the former is better than the latter;
- (c)
- Compare the adaptation value of each particle’s optimal position with the adaptation value of the population’s optimal position. If the former is better than the latter, this particle’s optimal position is replaced with the population’s optimal position;
- (d)
- Calculate an inertial weight and update the $x$ and $v$ of each particle by Equations (5) and (6);
- (e)
- Judge whether the maximum iteration is achieved or the accuracy requirement is satisfied. If any condition is reached, the procedure is ended and the optimal solution is found. Contrarily, step (b) will continue to be executed, and a new round of searches will be conducted.

#### 2.5. Prediction Performance Measure

^{2}, Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). R

^{2}is the percentage of explainable variation to the total variation. A model with R

^{2}of closely 1 means better performance results. The RMSE is used to reflect the deviation between the predicted value and the measured value. The MAE reflects the actual situation of the prediction error. The smaller the RMSE and the MAE, the higher the accuracy of the model. They are calculated as follows.

## 3. Case Study

#### 3.1. Geological Condition

^{4}m

^{2}, a thickness of 20–70 m, and a total volume of 2750 × 10

^{4}m

^{3}. The primary deformation region is in the center and east of the landslide, with the volume of approximately 1575 × 10

^{4}m

^{3}[27].

_{2}b

^{1–3}). The first section of the Badong Formation (T

_{2}b

^{1}) has light grey and grey-green marl interbedded with mudstone and shale, the second section (T

_{2}b

^{2}) has purple-red mudstone and argillaceous siltstone interbedded, and the third section (T

_{2}b

^{3}) has greyish brown and light grey argillaceous limestone [28,29].

#### 3.2. Deformation Characteristics

#### 3.2.1. Ground Deformation Characteristics

#### 3.2.2. Analysis of Test Data

#### 3.3. Triggering Factors Analysis

#### 3.3.1. Foundation of Geological Factors

#### 3.3.2. Effects of Reservoir Water Level and Rainfall

## 4. Results

#### 4.1. Training Process

- (a)
- Divide the data set. The PTD from June 2004 to October 2011 is considered as the training data, and the two years of data from November 2011 to September 2013 are considered as the prediction data;
- (b)
- Set the parameters in the PSO. Supposing that the penalty factor C is [0.1, 1000], the kernel parameter $\gamma $ is [0.01, 1000], the number of the particle swarm is 20, the maximum number of iterations is 200, the learning factor ${c}_{1}$ = ${c}_{2}$ = 1.5, and the inertial weight ω = 0.5;
- (c)
- Determine the value of optimization parameters;
- (d)
- Train the LSSVM model. The optimal penalty factor C is installed as 229.12, and the kernel parameter $\gamma $ is installed as 0.01 in the LSSVM, obtained by the optimization of the PSO. Afterward, the fitness value of the model is calculated by the optimal parameters.

#### 4.2. Results and Analysis

^{2}of the BP model is the smallest of the three models. Except for individual points, both the BP model and the PSO-SVM model predicted results inferior to the PSO-LSSVM model at each point. For this reason, the MAE values and RMSE values of the PSO-LSSVM model are much smaller than the others. In ZG86 (Figure 7b), the PSO-SVM model had poor prediction from June 2012 to February 2013. Thus, the MAE and RMSE values of the model are exceptionally large. In ZG87 (Figure 7c), the predicted results of the PSO-SVM model are generally poor, and the predicted results of the BP model are better than those of the PSO-LSSVM model except for August 2012 and October 2012. Therefore, the R

^{2}of the BP model is closer to 1, while that of the PSO-SVM model is the smallest. It means that the single prediction of the BP model is quite good. Overall, the PSO-LSSVM model shows good predicted results at the three monitoring stations, which means that the model is stable and accurate.

^{2}of three monitoring stations is larger than 0.98, and the RMSE values are the smallest among the three models. Thus, the PSO-LSSVM model has good accuracy in the landslide displacement prediction.

## 5. Discussion

## 6. Conclusions

^{2}, MAE, and RMSE. In the CD predicted results, the R

^{2}of the PSO-LSSVM model in three monitoring stations is larger than 0.98, and the MAE values and the RMSE values are the smallest among the three models. The results reveal that the PSO-LSSVM model has good accuracy and has a certain application value in landslide prediction.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Basic information of Shuping landslide. (

**a**) Location of the Shuping landslide, modified from [31]. (

**b**) Photo of the Shuping landslide. (

**c**) Topographic map of the Shuping landslide displayed at the monitoring stations. (

**d**) Geologic profile of section A–B. Note: 1, Siltstone mixed with mudstone and shale in T2b1; 2, Limestone and marble in T2b2; 3, Mudstone and siltstone in T2b3; 4, Quaternary residual slope deposits; 5, Quaternary landslide deposits; 6, Ground surface GPS monitoring stations and numbers; 7, Deep inclinometer hole and its number; 8, Road; 9, Buildings; 10, Landslide boundary; 11, Landslide boundary of main sliding area; 12, Sliding belt; 13, Rock occurrence; 14, Long ground fissures; 15, Sectional line; 16, Contour elevation; 17, The lowest RWL line; 18, the highest RWL line; 19, Stratum boundary; 20, Road in section; 21, Formation occurrence; 22, Quaternary landslide deposits; 23, Silty mudstone; 24, Argillaceous limestone.

**Figure 5.**Correlation of monthly displacement change rate at each monitoring station with the RWL, rainfall, and the change in the RWL.

**Table 1.**Correlation of displacement change at different times with the PTD of each monitoring station.

Correlation ( ${\mathit{g}}_{\mathit{i}}$) | ZG85 | ZG86 | ZG87 |
---|---|---|---|

Period displacement over previous month | 0.855 | 0.842 | 0.822 |

Period displacement over two previous months | 0.871 | 0.863 | 0.836 |

Period displacement over three previous months | 0.844 | 0.882 | 0.849 |

Period displacement over previous half year | 0.921 | 0.931 | 0.890 |

Period displacement over previous year | 0.788 | 0.804 | 0.899 |

Correlation ( ${\mathit{g}}_{\mathit{i}}$) | ZG85 | ZG86 | ZG87 |
---|---|---|---|

Rainfall over previous month | 0.849 | 0.843 | 0.862 |

Rainfall over previous two months | 0.845 | 0.861 | 0.866 |

RWL | 0.851 | 0.818 | 0.808 |

Change in RWL over previous month | 0.837 | 0.852 | 0.844 |

Model | BP | PSO-SVM | PSO-LSSVM | |
---|---|---|---|---|

R^{2} | ZG85 | 0.7157 | 0.7955 | 0.9095 |

ZG86 | 0.8631 | 0.8079 | 0.9091 | |

ZG87 | 0.8047 | 0.4813 | 0.7727 | |

MAE | ZG85 | 45.3365 | 45.8643 | 26.9320 |

ZG86 | 33.1825 | 58.2599 | 30.7913 | |

ZG87 | 6.4461 | 9.6564 | 5.5371 | |

RMSE | ZG85 | 55.3498 | 54.5718 | 31.9132 |

ZG86 | 49.8766 | 83.9435 | 41.6055 | |

ZG87 | 8.4063 | 13.1436 | 7.2638 |

Model | BP | PSO-SVM | PSO-LSSVM | |
---|---|---|---|---|

R^{2} | ZG85 | 0.9607 | 0.9718 | 0.9810 |

ZG86 | 0.9753 | 0.9680 | 0.9823 | |

ZG87 | 0.9875 | 0.9834 | 0.9932 | |

MAE | ZG85 | 47.5004 | 45.4348 | 34.6488 |

ZG86 | 49.5306 | 69.0451 | 44.5890 | |

ZG87 | 7.2304 | 9.7076 | 5.7296 | |

RMSE | ZG85 | 57.8430 | 54.1392 | 42.4378 |

ZG86 | 64.1690 | 86.0639 | 55.4179 | |

ZG87 | 9.2874 | 13.6112 | 7.3380 |

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## Share and Cite

**MDPI and ACS Style**

Jia, W.; Wen, T.; Li, D.; Guo, W.; Quan, Z.; Wang, Y.; Huang, D.; Hu, M.
Landslide Displacement Prediction of Shuping Landslide Combining PSO and LSSVM Model. *Water* **2023**, *15*, 612.
https://doi.org/10.3390/w15040612

**AMA Style**

Jia W, Wen T, Li D, Guo W, Quan Z, Wang Y, Huang D, Hu M.
Landslide Displacement Prediction of Shuping Landslide Combining PSO and LSSVM Model. *Water*. 2023; 15(4):612.
https://doi.org/10.3390/w15040612

**Chicago/Turabian Style**

Jia, Wenjun, Tao Wen, Decheng Li, Wei Guo, Zhi Quan, Yihui Wang, Dexin Huang, and Mingyi Hu.
2023. "Landslide Displacement Prediction of Shuping Landslide Combining PSO and LSSVM Model" *Water* 15, no. 4: 612.
https://doi.org/10.3390/w15040612