*3.4. Prediction Process with the Proposed Model*

The basic flow of the proposed CEEMDAN-AMLSTM model is shown in Figure 5. Firstly, the landslide cumulative displacement is decomposed into three components: the trend term, the periodic term, and the residual term. The three terms are then predicted separately. The trend displacement is expressed as a monotone increasing function under the influence of internal geological factors. The prediction of the trend term can be carried out by fitting the growth curve with the univariate AMLSTM model. During the construction of the model, the displacement time series is put into the model only. The periodic displacement fluctuates under the influence of two external triggers: rainfall and reservoir water level. Therefore, a multivariable AMLSTM model is established and used to predict the periodic term. Three time series, the historical periodic displacement, rainfall, and reservoir water level are put into the model. Furthermore, the residual displacement affected by random factors shows smooth fluctuation function. The univariate AMLSTM model is adopted for the prediction work.

**Figure 5.** The architecture of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)-AMLSTM model for landslide displacement prediction.

In the prediction experiments, the majority dataset is used to train the model. The original time series should be normalized and reshaped to meet the requirements of the model. After the AMLSTM model is constructed, the prediction ability is tested and demonstrated with the rest of the dataset.

Ultimately, the cumulative prediction displacement is obtained by adding the trend, the periodic, and the residual prediction displacements. The prediction results should be compared with the actual value to verity the performance.

#### *3.5. Evaluation of Model Accuracy*

Quantitative analysis were carried out to access the performance of the model. Three criterions—Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and R2—were employed to evaluate the prediction work. These metrics are described as follows:

$$\text{RMSE} = \sqrt{\frac{I}{N} \* \sum\_{i=1}^{N} (y\_i - \mathcal{y}\_i)^2} \tag{16}$$

$$\text{MAE} = \frac{1}{N} \ast \sum\_{i=1}^{N} |y\_i - \hat{y}\_i| \tag{17}$$

$$R^2 = 1 - \frac{\sum\_{i=1}^{N} (y\_i - \hat{y}\_i)^2}{\sum\_{i=1}^{N} (y\_i - \overline{y})^2} \tag{18}$$

where *yi* is the measured value, *y*ˆ*<sup>i</sup>* is the prediction value, and *y* is the average value.

### **4. Experiment and Results**

#### *4.1. Study Area*

The experimental area is located in Baishuihe, Zigui County, the Three Gorges Reservoir area of the Yangtze River in China. The Baishuihe landslide is located on the south bank of the Yangtze River, with a longitude of 110◦32 09 and a latitude of 31◦01 34 (Figure 6a). The slope is located on the south bank of the Yangtze River, spreading towards the Yangtze River in a ladder shape. The elevation of the back edge of the landslide is 410 m, bounded by the rock-soil boundary, and the front edge is about 70 m. It has been submerged below the reservoir water level. The east and west sides are bounded by bedrock ridges, and the overall slope is about 30◦. The length of the north-south direction is 600 m, the width of the east-west direction is 700 m, the average thickness of the sliding body is about 30 m, and the volume is 1.26×10<sup>7</sup> m3. Six Global Navigation Satellite System (GNSS) deformation monitoring points were installed on the surface of the landslide to form three longitudinal monitoring profiles (Figure 6b). The displacement was monitored once a month. Figure 7 shows the calculated displacement results from December 2006 to December 2012.

**Figure 6.** (**a**) Location map from Google Earth and (**b**) Locations of the monitoring Global Navigation Satellite System (GNSS) stations on the landslide.

**Figure 7.** Cumulative displacement monitoring data based on six GNSS points.

It can be seen from Figure 7 that the landslide deformation is characterized by stepwise progressive creep deformation, and the landslide is still in the energy accumulation stage, showing a slow creep deformation state. In this experiment, ZG118 and XD01, the two points with the most abundant dataset, are selected for the prediction work. The measurements from December 2006 to November 2011 are used for training and the measurements obtained from November 2011 to November 2012 are used for testing. Each time interval of the train and test dataset is one month. The cumulative displacements, the reservoir water level, and the rainfall are plotted in Figure 8.

**Figure 8.** Relationship between rainfall, reservoir water level, and landslide displacement on ZG118 and XD01.

Figure 8 shows that the external periodic rainfall and reservoir water level both have an important influence. The displacement of XD01 and ZG118 increased significantly during a period of drastic decrease of the reservoir water level. For example, from May 2009 to July 2009, the reservoir water level dropped from 160 m to 145 m, and their periodic displacement increased by 200~300 mm, presenting a large step. In addition, heavy rain also had an important effect on landslide displacement fluctuations. For example, from August 2008 to September 2008, the reservoir water level basically did not change but, due to the occurrence of 300 mm of heavy rain during this period, the landslide also showed a large deformation of 200 mm. Therefore, the reservoir water level and rainfall are considered to be the trigger factors of the Baishuihe landslide, leading to the occurrence of the periodic term displacement.

### *4.2. GNSS Time Series Analysis*

According to landslide analysis theory, the cumulative displacement can be decomposed into trend displacement, periodic displacement, and residual displacement using the CEEMDAN algorithm. The results are as follows (Figure 9):

**Figure 9.** Three decomposed terms of the GNSS time series: (**a**) ZG118, (**b**) XD01.
