1. Introduction
Landslides are one of the most severe types of geological hazards in nature [
1]. Landslide hazards often cause great losses, including property damage, injury and loss of life [
2,
3]. Due to the complex geological conditions and frequent tectonic activities in China, landslide disasters are frequent and may lead to catastrophic damage [
3,
4]. Displacement prediction is intuitive and important for real-time monitoring and early warning of landslides. Accurate prediction of landslide displacement can reduce the risk, and has become an increasingly important research issue in recent years [
5,
6]. Many researchers are committed to the prediction of landslide displacement [
7,
8,
9]. Early landslide prediction is mainly empirical, which uses certain macroscopic signs of landslides to speculate on the time of occurrence. With the continuous improvement of the landslide monitoring technology, more and more means are available to obtain landslide monitoring data [
10,
11,
12,
13]. Growing attention has been paid to landslide displacement prediction from the background of landslide conception and genesis mechanism, by combining landslide multi-source sensing information, displacement prediction-based mathematical statistical analysis, non-linear prediction and comprehensive coupling model, which can provide more complex analytical ideas [
3,
14,
15,
16]. The empirical model requires creep experiments to validate the prediction model and has limited application scenarios. Mathematical statistical models are better for the prediction of single influential factors, but cannot solve the displacement prediction of multiple influential factors. Nonlinear prediction suffers from slow convergence and is easily trapped in local minima. The integrated coupled model achieves the prediction of landslide displacement from multiple model perspectives and improves the accuracy of displacement prediction. It has been reported that the obvious step-like displacement can be affected by the periodic fluctuation of special geological environments, seasonal rainfall and reservoir water level adjustment [
5,
16,
17]. Landslide deformation is mainly caused by a variety of factors. The complex process of landslide deformation makes it difficult to accurately distinguish the stages of landslide deformation [
18,
19,
20,
21]. Therefore, the traditional empirical means are no longer applicable.
At present, nonlinear integrated models based on long time-series analysis is the most common displacement prediction method [
22,
23,
24]. Many studies have classified the original landslide displacement data into different characteristic components by analyzing the evolution mechanism of landslide deformation. These methods consider both external and internal factors that induce landslide deformation to achieve satisfactory prediction results [
17]. The conventional decomposition methods mainly include moving average method, fitting a polynomial trend and smoothing a priori method, which mainly extract trend displacement and periodic displacement [
8]. However, these methods do not fully consider the influence of random factors and failed to obtain the random displacement. More comparisons are needed to determine the decomposition parameters, and the computational efficiency is relatively low [
25]. In addition, researchers attempt to obtain different components of landslide displacement using the empirical mode decomposition (EMD) [
26,
27], the ensemble EMD (EEMD) [
18,
23,
28], the complete EEMD of adaptive noise (CEEMDAN) [
29,
30] and wavelet transform [
31]. The above methods can overcome the shortcomings of the conventional decomposition methods, and can completely decompose the displacement components with different characteristics. However, a fixed displacement component cannot be obtained by these methods. The EMD achieves a thorough decomposition of the original displacement of the landslide, but it also suffers from modal confounding and computational inefficiency [
29]. In recent years, several researchers have used variational mode decomposition (VMD) combined with artificial intelligence algorithms to achieve accurate prediction of landslide displacement [
32,
33]. The VMD can select the number of features of displacement decomposition according to the data size and type, which can determine the physical significance of each feature component. It has higher decomposition efficiency and accuracy than the conventional methods, including EMD and EEMD. Therefore, the original landslide displacement data are effectively extracted by VMD to obtain the most optimal landslide displacement component [
34].
In recent years, artificial intelligence algorithms, such as the back propagation neural network (BPNN), Support Vector Regression model (SVR) and Elman neural network model, have been increasingly used for the prediction of landslide displacement [
35,
36]. For complex nonlinear curves, BPNN converges slowly and may not achieve satisfactory fitting performance. The weights and threshold inputs of the Elman neural network have a random nature and result in reduced model prediction accuracy [
36]. Classical machine learning algorithms often have difficulty in determining the parameters of the optimization model. SVR has great flexibility in dealing with nonlinear data and helps to solve the nonlinear regression problem [
37]. However, it suffers from a shortage of parameter selection, which requires appropriate parameter optimization methods to solve the problem and improve the prediction accuracy [
38]. Numerous parameter search methods have been proposed by researchers in recent years, including the grid search method, genetic algorithm (GA) [
39,
40] and particle swarm optimization (PSO) [
5,
27,
35,
41]. The gray wolf optimizer (GWO) has been widely used in combinatorial model optimization problems compared to some existing algorithms (GA, PSO), and in particular, it can greatly improve the efficiency of parameter optimization. Therefore, the GWO algorithm has also been introduced to realize the optimization of the SVR model parameters [
25,
42].
The aim of this study is to establish a novel landslide displacement prediction method based on the VMD and GWO-SVR model. Taking the Shuizhuyuan landslide in the Three Gorges Reservoir area as an example, the original landslide displacement data are decomposed by the VMD method into trend, periodic and random components. The external and internal influence factors of landslide displacement are selected by combining the gray relational degree analysis (GRDA). Then, the data are divided into training and validation sets with different time scales. The optimal combination model is established using the GWO-SVR model, which can achieve displacement prediction for the test set. Finally, the effectiveness of the model is analyzed.
5. Discussion
In general, the causes of landslide deformation in the Three Gorges Reservoir area are influenced by a variety of integrated factors, such as the landslide’s geological structure, precipitation and other factors. In this study, seasonal rainfall and adjustment of reservoir water level are found to control the occurrence of step-like displacement through landslide mechanism and monitoring data analysis. The landslide underwent accelerated deformation mainly during the period of heavy precipitation and water level drop, followed by a step-like displacement deformation. Therefore, an effective displacement decomposition method is beneficial for better displacement prediction.
The characteristic components obtained from the decomposition of cumulative displacements by conventional EMD methods are often not fixed [
26,
27]. Therefore, it is necessary to combine and reconstruct these components to obtain the displacement characteristic components of the landslides. The conventional decomposition method normally produces no less than five characteristic components. The procedures for reconstructing and combining these feature components to obtain the landslide trend, periodic and random components are more complicated and the workload increases significantly, which leads to lower computational efficiency. In this work, landslide displacements are decomposed according to VMD theory, determining the explicit physical meaning of each component. In addition, the VMD theory, which has good adaptive ability, can be used to decompose the displacement based on the actual situation of the landslide [
32,
33]. Therefore, the trend, period and random displacements of landslides are well extracted in this study. This avoids the phenomenon of over-decomposition or incomplete decomposition of the components caused by the uncertain number of components, especially in the conventional methods such as EMD.
SVR is one of the most typical prediction methods, and landslide displacement can be predicted by optimizing relevant parameters. The reasonable selection of input parameters is helpful to improve the training efficiency of SVR. GWO has the characteristics of fast convergence and high optimization accuracy [
25], and it is introduced into SVR for parameter optimization [
14,
49]. In addition, to improve the prediction accuracy, different factors affecting landslide deformation are analyzed using GRDA, and precipitation and reservoir level fluctuation data are added to the landslide displacement prediction model as additional influential factors. To further compare the pros and cons of algorithms, prediction analysis is performed with the GWO-SVR and VMD-PSO-SVR models for the test set data, respectively. A comparison of the prediction models is shown in
Figure 12. The evaluation indicators of each model are shown in
Table 7. The VMD-PSO-SVR and the VMD-GWO-SVR optimization algorithms with VMD decomposition are effective in improving the prediction accuracy compared to that without VMD decomposition. As demonstrated in
Figure 12 and
Table 7, the RMSE and R
2 of VMD-GWO-SVR are greater than those of other models. The VMD-GWO-SVR model has the best prediction performance, which can provide a good decision basis for real-time landslide warning.