Landslide Displacement Prediction of Shu** Landslide Combining PSO and LSSVM Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Time Series Theory
2.2. PSO Algorithm
2.3. LSSVM Algorithm
2.4. PSO-LSSVM Algorithm
- (a)
- Initialize parameters containing population size m, number of iterations , learning factor c, initial position , and initial velocity 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 and 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
3. Case Study
3.1. Geological Condition
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 is [0.01, 1000], the number of the particle swarm is 20, the maximum number of iterations is 200, the learning factor = = 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 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
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Correlation ( ) | 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 ( ) | 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 | |
---|---|---|---|---|
R2 | 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 | |
---|---|---|---|---|
R2 | 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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Jia, W.; Wen, T.; Li, D.; Guo, W.; Quan, Z.; Wang, Y.; Huang, D.; Hu, M. Landslide Displacement Prediction of Shu** Landslide Combining PSO and LSSVM Model. Water 2023, 15, 612. https://doi.org/10.3390/w15040612
Jia W, Wen T, Li D, Guo W, Quan Z, Wang Y, Huang D, Hu M. Landslide Displacement Prediction of Shu** Landslide Combining PSO and LSSVM Model. Water. 2023; 15(4):612. https://doi.org/10.3390/w15040612
Chicago/Turabian StyleJia, Wenjun, Tao Wen, Decheng Li, Wei Guo, Zhi Quan, Yihui Wang, Dexin Huang, and Mingyi Hu. 2023. "Landslide Displacement Prediction of Shu** Landslide Combining PSO and LSSVM Model" Water 15, no. 4: 612. https://doi.org/10.3390/w15040612