A Novel Decomposition-Prediction Framework for Predicting InSAR-Derived Ground Displacement: A Case Study of the XMLC Landslide in China

Highlights

What are the main findings?

• Spatiotemporal displacement over the Xi’erguazi−Mawo landslide complex (XMLC) is mapped and the time series are predicted.
• A hybrid prediction framework significantly improves the prediction accuracy and robustness of InSAR-derived deformation time series.
• The combination of two-step decomposition and statistical hypothesis testing provides a reliable foundation for data-driven InSAR deformation prediction.

What are the implications of the main findings?

• Accurate and rapid deformation prediction based on InSAR time series provides support for landslide early warning systems and proactive slope hazard mitigation.
• The proposed framework could be extended to other InSAR-derived complicated displacement prediction.

Abstract

Interferometric Synthetic Aperture Radar (InSAR) is an advanced imaging geodesy technique for detecting and characterizing surface deformation with high spatial resolution and broad spatial coverage. However, as an inherently post-event observation method, InSAR suffers from limited capability for near-real-time and short-term updates of deformation time series. In this paper, we proposed a data-driven adaptive framework for deformation prediction based on a hybrid deep learning method to accurately predict the InSAR-derived deformation time series and take the Xi’erguazi−Mawo landslide complex (XMLC) as a case study. The InSAR-derived time series was initially decomposed into trend and periodic components with a two-step decomposition process, which were thereafter modeled separately to enhance the characterization of motion kinematics and prediction accuracy. After retrieving the observations from the multi-temporal InSAR method, two-step signal decomposition was then performed using the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Variational Mode Decomposition (VMD). The decomposed trend and periodic components were further evaluated using statistical hypothesis testing to verify their significance and reliability. Compared with the single-decomposition model, the further decomposition leads to an overall improvement in prediction accuracy, i.e., the Mean Absolute Errors (MAEs) and the Root Mean Square Errors (RMSEs) are reduced by 40–49% and 36–42%, respectively. Subsequently, the Radial Basis Function (RBF) neural network and the proposed CNN-BiLSTM-SelfAttention (CBS) models were constructed to predict the trend and periodic variations, respectively. The CNN and self-attention help to extract local features in time series and strengthen the ability to capture global dependencies and key fluctuation patterns. Compared with the single network model in prediction, the MAEs and RMSEs are reduced by 22–57% and 4–33%, respectively. Finally, the two predicted components were integrated to generate the fused deformation prediction results. Ablation experiments and comparative experiments show that the proposed method has superior ability. Through rapid and accurate prediction of InSAR-derived deformation time series, this research could contribute to the early-warning systems of slope instabilities.

1. Introduction

Landslides are one of the most common geological hazards, often causing severe casualties and economic losses [1]. Landslide prediction is highly uncertain and complex due to the coupled influence of multiple factors, including geological background, hydrological and meteorological conditions, and extreme events. Directly predicting whether and when a landslide will occur is extremely challenging. During the evolution process of landslide hazards, displacement is the most direct external manifestation reflecting their development status [2] and the core early-warning indicator in landslide early-warning systems. Therefore, accurate prediction of landslide displacement is crucial for risk assessment and the establishment of reliable early-warning systems, as landslide dynamics are influenced by external factors such as rainfall, reservoir, and groundwater fluctuations, earthquakes, and human activities. However, due to the nonlinearity and complexity of landslide deformation processes, accurately predicting the temporal evolution of displacement still remains a challenging task [3].

Traditional landslide deformation monitoring methods mainly rely on geomechanical and field-based approaches, including geological surveys, inclinometer measurements, and point-based displacement observations, to investigate slope stability, deformation mechanisms, and potential failure modes [4]. Consequently, Global Navigation Satellite System (GNSS) techniques enable accurate, all-weather, and continuous three-dimensional monitoring of landslide movement, whereas Light Detection and Ranging (LiDAR) provides millimeter-to-centimeter-scale detection of terrain changes using high-precision, high-density three-dimensional point cloud models [5,6]. However, their practical applications in regional-scale landslide monitoring and prediction remain constrained by limited spatial coverage and high deployment costs, highlighting the need for complementary large-area observation techniques. Interferometric Synthetic Aperture Radar (InSAR) technology, featuring high precision, all-weather operation, and full-time domain monitoring capabilities, enables large-scale surface deformation measurements with centimeter-to-millimeter-level accuracy [7]. Subsequently, the launch of Sentinel-1 satellite in 2014 ushered in a new era of global coverage monitoring. The revisit period of a single satellite is 12 days, and that of two satellites is 6 days, making regular monitoring of landslide displacement possible [8].

InSAR-derived observations provide spatiotemporal measurements of slope displacement and key information for identifying precursor deformation signals. Therefore, InSAR has been widely used to monitor and analyze landslide kinematics [9]. In addition, it can be integrated with empirical and statistical models to estimate landslide-related parameters (e.g., area and volume), identify acceleration trends, delineate potential release zones and predict possible flow paths [10,11]. It is thus evident that time-series InSAR, as an important technique for monitoring surface deformation, plays a crucial role in the early warning of landslides through rapid and accurate updates and predictions. With the progress of artificial intelligence, machine learning can process multivariate data and reveal hidden data relationships, and data-derived methods have gained prominence for their flexibility, scalability, and high predictive accuracy [12,13,14]. Therefore, combined InSAR with machine learning to improve the prediction accuracy of displacement time series has become a key research direction for capturing temporal slope movement patterns.

However, the landslide process is inherently complex, and the displacement time series of landslides also exhibit strong nonlinearity [15]. In long-term monitoring, surface deformation is generally related to geological conditions and exhibits a nearly monotonic trend, whereas periodic variations are primarily influenced by climatic and hydrological factors. The noise component, on the other hand, exists in each SAR acquisition and manifests as high-frequency fluctuations. Therefore, when directly fitting such complex temporal patterns, the model often exhibits poor performance, whereas the adoption of multi-modal signal decomposition techniques can effectively improve the accuracy and robustness of the landslide displacement prediction model. Nowadays, techniques such as Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Variational Mode Decomposition (VMD), Wavelet Transform, and Singular Spectrum Analysis (SSA) have been widely employed to decompose complex time-series signals into multiple intrinsic components. Existing studies typically decompose the time series into three components: periodic, non-periodic, and noise terms. This approach effectively enhances the feasibility of applying machine learning and deep learning models to different signal components [2,16].

Consequently, a variety of machine/deep learning algorithms have been applied to time-series landslide prediction, including Gated Recurrent Unit (GRU), Convolutional Neural Networks (CNN), Auto-Regressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM), eXtreme Gradient Boosting (XGBoost), Support Vector Machine (SVM), and Random Forest (RF) [14,16,17,18,19]. Nevertheless, the dynamic, nonlinear, and unstable nature of landslide deformation poses challenges to the prediction accuracy of single-network models. Thus, combining multiple models and leveraging their respective strengths has become an effective strategy for processing landslide displacement time-series data. For example, integrating CNN with Recurrent Neural Networks (RNN) can improve the accuracy of landslide displacement prediction; combining CNN with recurrent architectures such as LSTM and GRU further optimizes landslide displacement prediction performance. These hybrid deep learning models can simultaneously capture spatial features and temporal dependencies, achieving higher accuracy and stability compared with single-network models [20,21,22,23].

However, multi-structure deep learning models struggle to effectively distinguish the dynamic relationships among various components when confronted with the coexistence of strong trend components, periodic variations, and high-frequency disturbances, which may lead to prediction deviations and even overfitting. Therefore, combining multi-modal signal decomposition techniques with multi-structure deep learning models can enhance model accuracy. In this paper, we focus on the time series prediction of InSAR-derived surface deformation and propose a two-step signal decomposition strategy along with a novel CNN-BiLSTM-SelfAttention (CBS) model for predicting nonlinear components from a data-driven perspective. These components are subsequently integrated into a unified framework for predicting InSAR-derived landslide displacements. Subsequently, taking the Xi’erguazi−Mawo landslide complex (XMLC) as a representative case, which is mainly affected by a large amount of farmland irrigation and fluctuation in reservoir water level (RWL). By isolating distinct frequency bands via decomposition and applying component-specific models before fusing their outputs, this approach enables multi-scale characterization of nonlinear deformation behaviors in InSAR time-series data and time series prediction performance. Although the proposed prediction model does not explicitly incorporate physical mechanism modeling, it establishes an effective data-driven framework for characterizing and predicting landslide displacement associated with instability. This framework could be further coupled with physics-based models in future studies, potentially enhancing the accuracy and reliability of landslide early warning.

2. Datasets and Methods

2.1. Study Area and Datasets

2.1.1. Study Area

As revealed in Figure 1, the Xi’erguazi and Mawo landslide is located near the reach from Hongyan Township to Eshiba along the middle reaches of the Heishui River in Maoxian County, Aba Tibetan and Qiang Autonomous Prefecture, Sichuan Province, China (32°50′N–32°58′N, 103°35′E–103°45′E). The Xi’erguazi Landslide, situated on the right bank of the Heishui River near the Mao’ergai Hydropower Station, is located about 3.2 km from the dam site and 23 km from Heishui County. It is identified as a reservoir-induced landslide. Additionally, the landslide is located in the Zhaku Village on the top of the mountain, with large areas of terraced fields distributed between the village and landslide. The eastern area of the landslide is a ridge with a slope of 25–35°, and at the lower part of the ridge is the Xinmawo Town. The section of Provincial Highway S302, with a total length of 1768 m, passes through the rock mass at the lower part of the landslide.

Due to the Wenchuan earthquake, the consolidated sediments were loosened. With the infiltration of reservoir water, new sliding occurred in the ancient Xi’erguazi landslide, forming the current Xi’erguazi Landslide [24]. With the commissioning of the Mao’ergai Hydropower Station and the rise of the RWL, the submerged area within the Xi’erguazi Landslide has expanded. Satellite imagery shows that part of the front end of the landslide has been submerged in water, and obvious cracks have appeared at the upper edge at an altitude of 2650 m. The terrain of the landslide generally decreases gradually from northwest to southeast, with a relatively gentle transition. The maximum topographic relief is approximately 800 m, and it is located in an erosive valley landform. Moreover, researchers have found that the deformation zone of the Mawo landslide is gradually merging with the reactive part of the Xi’erguazi landslide to form the landslide complex.

The entire landslide area has experienced different formation periods and is distinct from rainfall-induced landslides. This landslide is primarily affected by large-scale farmland irrigation and changes in RWLs, and directly threatening the hydropower station, the tunnel, and surrounding villages.

2.1.2. Datasets

This study utilized 208 ascending-orbit SAR images acquired by the Sentinel-1A satellite from October 2014 to October 2022. A total of 281 interferograms were generated to capture the spatiotemporal slope displacement characteristics of the XMLC landslide.

2.2. Methodology

Figure 2 presents the schematic framework of the proposed method, which predicts InSAR-derived landslide deformation time series through a three-step procedure: (i) InSAR deformation generation; (ii) time series decomposition; (iii) prediction results fusion and accuracy evaluation. To comprehensively evaluate the performance of the proposed prediction model, ablation and comparative analyses were conducted.

2.2.1. Deformation Time Series Generation Using InSAR

The PS-InSAR approach was applied to derive both displacement rates and time series [25,26,27]. After the Single Look Complex (SLC) data were pre-processed for interferometric analysis, subsequent steps including persistent scatterer identification, phase unwrapping, and time-series inversion were performed using the Stanford Method for Persistent Scatterers (StaMPS) toolbox. Interferograms were constructed with a maximum temporal separation of 36 days to reduce decorrelation effects. It should be noted that the StaMPS software (v2018) was selected in this study because it utilizes the spatial correlation of deformations rather than any prior assumptions, which can effectively mitigate the impacts of atmospheric interference and temporal decorrelation and achieve accurate measurement of surface motion [28]. To remove topographic contributions, a 30 m resolution Digital Elevation Model (DEM) was employed. A single-look configuration was adopted to preserve the native resolution of the SLC images. The PS-InSAR algorithm identifies phase-stable pixels with low amplitude dispersion (0.4–0.6) as persistent scatterer candidates [29]. These candidates are then refined through phase noise estimation, followed by corrections for spatially uncorrelated look angle errors. The interferometric phases of the final persistent scatterers are processed via 3D unwrapping, and spatially correlated artifacts including residual DEM inaccuracies, atmospheric contributions, and orbital errors are subsequently filtered and removed [30]. The filtered and corrected unwrapped phases are ultimately inverted through a least-squares procedure to estimate the line-of-sight (LOS) displacement rates and time series. The specific processing steps are shown in Figure 2.

2.2.2. Two-Step Decomposition of Displacement Time Series

Before the decomposition of InSAR-derived displacement, the time series needs to be pre-processed. The Sentinel-1 SAR images used in this study have been acquired since October 2014. Due to the absence of a stable revisit cycle and relatively low quality of some early acquisitions, the InSAR-derived accumulative displacement exhibited irregular temporal intervals during the initial observation period. Therefore, linear interpolation was performed on the irregular time series to unify it into a landslide accumulative displacement time series with a 12-day time interval.

(1)

Initial decomposition and hypothesis testing

Given that the time-series data of landslide displacement exhibit complex nonlinear accumulative deformation behavior, traditional time-series prediction methods often fail to achieve satisfactory accuracy. On the one hand, surface deformation is usually related to geological conditions and shows an almost monotonic trend; on the other hand, periodic variations are mainly affected by climatic and hydrological factors and present periodic changes; in addition, noise components exist in each SAR data acquisition process, manifesting as high-frequency fluctuations. Therefore, it is necessary to decompose the time-series data to obtain periodic components, non-periodic components, and noise components.

CEEMDAN is an improvement version of the Empirical Mode Decomposition (EMD) algorithm [31]. By introducing adaptive noise and a multi-iteration strategy, this algorithm significantly mitigates the mode mixing and edge distortion problems that commonly occur in traditional EMD during signal decomposition, thereby improving the accuracy and stability of the decomposition results. After the original landslide accumulative displacement time series is implemented decomposition by CEEMDAN, multiple intrinsic mode functions (IMFs) with different frequency patterns can be obtained, effectively avoiding the complexity of parameter selection and adjustment in traditional methods.

Sample Entropy (SampEn) is an index used to quantify the regularity and complexity in time series data, measuring the irregularity, chaos, or unpredictability in signals [32]. Therefore, this paper introduces SampEn as a complexity metric, sets a reasonable threshold to distinguish high-frequency periodicity components from low-frequency trend components and classifies the decomposed signal components into two categories accordingly. Signal components with SampEn values lower than the set threshold are labeled as trend terms, while those higher than the threshold are classified as periodicity components.

To enhance the rigor of the experiment and the accuracy of classification, this paper further performs trend analysis on all time-series components classified as trend terms to verify the validity of their long-term trend characteristics. Specifically, the trend detection method used in this paper is the Mann−Kendall trend test to statistically test each trend component. This method is a non-parametric testing technique that can assess whether there is a significant monotonic trend (i.e., continuous upward or downward) in the time series without making prior assumptions such as normality or linearity about the original data. Due to its insensitivity to outliers and distribution assumptions, it is particularly suitable for trend identification in non-stationary surface motion including landslides. The procedure involves calculating the sign of all pairwise differences between observations to obtain the Mann−Kendall statistic S, which is then standardized into a Z-value. A positive Z indicates an upward trend, while a negative Z indicates a downward trend. The corresponding p-value, derived from the standard normal distribution, is used to assess significance, and a trend is typically considered significant when p < 0.05.

(2)

Refined the decomposition result

Notably, when decomposing signals using CEEMDAN, the number of IMFs cannot be predetermined. This is because CEEMDAN is a data-driven and adaptive method, and the number of IMFs depends on the intrinsic characteristics of the input signal. The original landslide accumulative displacement time series may be decomposed into more than 10 sub-signals. The trend component can be easily identified, whereas multiple signals exhibit periodic characteristics. These periodic signals, therefore, will be further clustered.

K-means is a classic machine learning method widely used in data clustering and belongs to the typical unsupervised learning paradigm. Its core objective is to automatically classify input data into K different groups, making the samples within the same group as compact as possible while maintaining high dissimilarity between samples in different groups. K-means divides different categories by minimizing the squared distance between sample points within a cluster and the cluster center. Specifically, the algorithm is based on distance metrics (usually Euclidean distance) and gradually updates the cluster centers through an iterative optimization process, eventually converging to a local optimal solution.

The decomposed periodic signals were clustered into three groups using the K-means algorithm, corresponding to high-, medium-, and low-frequency components of the periodic term. Among them, the high-frequency signals have larger fluctuation amplitudes, and their sample entropy is significantly higher than that of medium-frequency and low-frequency signals. If a deep learning model is directly used to predict the high-, medium-, and low-frequency components, it is likely to cause large prediction errors and affect the overall landslide time series prediction accuracy.

It can be reasonably inferred that the high-frequency signal component still needs further decomposition to improve the performance, which will be in the following Section 4.2 using the ablation. Therefore, this paper applies the VMD to perform further decomposition on the high-frequency non-stationary signal. In VMD, the number of decomposition modes must be determined [33]. To prevent over- or under-decomposition, the Newton−Raphson optimization algorithm (Broyden’s Rank One Update, NRBO) was applied to optimize the decomposition layer number (K) and the balance parameter (α) for data fidelity. The approach is enhanced by integrating the Newton−Raphson search rule for faster convergence and a trap-avoidance operator that prevents local optima through genetic and cooperative mechanisms [34].

2.2.3. Displacement Prediction Model

In the following study, deep learning networks will be utilized to independently predict each signal component of the landslide accumulative displacement time series. Therefore, prior to model construction, a unified time-series prediction dataset needs to be established for all signal components. This paper adopts the sliding window method to construct input and output samples for the time-series prediction dataset. For the original time-series data, it was first partitioned using windows with a fixed step size, where each window contained 8 consecutive time steps and was employed to predict the value of the subsequent time step. Upon the completion of dataset construction, the dataset was split into training and testing subsets at a ratio of 7:3, with 70% of the data allocated for model training and the remaining 30% for model performance evaluation.

After performing equidistant interpolation on the accumulative displacement time series of each monitoring point in the Xi’erguazi−Mawo landslide area, a total of 240 time-series data points were obtained. Following dataset construction, each time-series signal component of the landslide at every monitoring point was divided into a training set with a time length of 162 and a testing set with a time length of 70.

(1)

Prediction model of trend term

In this study, the Radial Basis Function (RBF) neural network is used to predict trend-term signals [35]. In time series prediction, the RBF model exhibits strong nonlinear modeling capabilities, local adaptability, fast training speed, and high fault tolerance. They are suitable for processing time series data with nonlinearity and local fluctuations, enabling rapid prediction.

The RBF model is a type of feedforward neural network that activates neurons through the distance between input data and central points, thus effectively capturing the local characteristics of the data. As shown in Figure 3e, the RBF neural network consists of three functional layers. The input layer receives feature data from external sources and transmits them to subsequent parts of the network. The middle hidden layer is composed of multiple neurons, each distributed around a specific central point and using a radial basis function as the activation mechanism to calculate the response intensity based on the distance between the input sample and the central point. Finally, the output layer performs weighted integration of the response results generated by the hidden layer to form the final prediction output.

(2)

Prediction model of periodic term

In this study, a CNN-BiLSTM-SelfAttention model is used to predict periodic displacement. The model is mainly divided into two parts. The first is the CNN-BiLSTM module. It primarily extracts local features through an independent CNN to capture spatial and local patterns in data, such as short-term trends and periodicity changes. Activation functions are then applied to enable the network to learn nonlinear features. A pooling layer is further used to compress dimensional features, reducing computational complexity while preserving information about important features. The features extracted by the entire CNN layer are then transmitted to the BiLSTM layer, which is used to capture long-term dependencies in time series data. By leveraging forward and backward LSTMs, the BiLSTM layer obtains contextual information from both past and future time steps. Finally, the features obtained by the CNN-BiLSTM model are outputted. Second, a self-attention layer is added based on the CNN-BiLSTM model. Its role is to enable the model to assign different weights to each time step, allowing the network to weight according to the importance in time series data, capture long-range dependency relationships and enhance the model’s learning ability. It is worth noting that a dedicated quantile regression layer is incorporated after the self-attention layer, which means setting the loss function of the prediction model as a quantile loss function.

CNN consists of multiple convolutional layers, pooling layers, and fully connected layers, with strong feature extraction capabilities. It can automatically learn and extract local patterns in data through convolution operations, while gradually constructing complex abstract features through multi-layer convolutional layers. The sliding window mechanism of convolution kernels and the weight-sharing mechanism enable 1D CNN to efficiently capture meaningful features when processing sequence data. Combined with other layers such as pooling layers and fully connected layers, 1D CNN can further extract more abstract and rich features, making it suitable for time series analysis. The structural diagram of the CNN is shown in Figure 3b.

LSTM is a model architecture that structurally optimizes traditional recurrent neural networks, specifically designed to handle long-sequence problems [36]. By introducing multiple gating mechanisms, LSTM not only alleviates the gradient vanishing and exploding problems faced by recurrent neural networks during long-sequence training but also precisely controls information flow, enabling selective memory and forgetting of input content. This allows it to effectively model long-term dependencies, with notable advantages such as selective information storage and update, as well as higher training stability. The network structure of LSTM mainly consists of four key components: forget gate, input gate, update cell state, and output gate [19]. These components work collaboratively to enable the LSTM network to effectively retain or discard historical information while processing sequential data and control the transmission of state information at the current moment.

BiLSTM is an improvement based on LSTM [37]. The structure of BiLSTM consists of two LSTMs, i.e., one is a forward LSTM, and the other one is a backward LSTM, as shown in Figure 3c [38]. By training the model in both directions simultaneously, BiLSTM can capture the contextual dependency and variation patterns in sequential data, improving the ability to model sequence information and demonstrating more superior performance.

The attention mechanism is a signal processing mechanism discovered by scientists in the study of human vision. Attention can be understood as “focus” in machine learning; it refers to assigning specific weights (usually between 0 and 1) to each element during information processing to highlight important information, emphasize the role of key information and thus improve model performance [39]. Self-attention is a special type of attention mechanism. When processing signals, it enables the model to autonomously capture long-range dependency features by establishing dynamic interaction weights between sequence elements [40]. This mechanism also allows the model to more effectively understand the interactions between various parts of the signal, thereby enhancing the ability to process signals (Figure 3d).

2.2.4. Model Parameters and Accuracy Evaluation

The parameter settings of the proposed model, which is designed to predict the periodic components in InSAR-derived time series, are elaborated in Table 1.

(1)

CNN convolutional layer: Two-dimensional convolution operations were used, with a kernel size set to 3 × 1 (width = 3, height = 1) and 16 convolution kernels employed;

(2)

Normalization layer: Normalizes the output of the convolutional layer to stabilize the mean and variance of the data, preventing gradient vanishing or explosion;

(3)

ReLU activation layer: Applies non-linear transformations to the output of the convolutional layer to enhance the network’s expressive power. The pooling layer uses a 2 × 1 pooling window with a stride of 1 and “same” padding; the sequence unfolding layer restores the sequence processed by convolution;

(4)

BiLSTM layer: This layer has a single hidden layer containing 80 neurons. A dropout layer is added subsequently to randomly discard outputs of some neurons with a probability of 0.1 to prevent overfitting;

(5)

Self-Attention layer: Uses single-head attention, with each head having a dimension of 4;

(6)

Fully connected layer and QR Regression layer: The QR regression layer employs median regression.

Table 1. Parameters for the proposed model.

Index	Parameter
Number of CNN convolution channels	16
CNN convolution kernel size	[3, 1]
Pooling window size	[2, 1]
Pooling step size	1
Number of neurons in the hidden layer of BiLSTM	80
Self-attention layer method	Single head attention
Dimension of each head in single head attention	4
QR regression layer method	Median regression

Table 1. Parameters for the proposed model.

Index	Parameter
Number of CNN convolution channels	16
CNN convolution kernel size	[3, 1]
Pooling window size	[2, 1]
Pooling step size	1
Number of neurons in the hidden layer of BiLSTM	80
Self-attention layer method	Single head attention
Dimension of each head in single head attention	4
QR regression layer method	Median regression

Additionally, to evaluate the performance of the proposed method, the root mean square error (RMSE), mean absolute error (MAE), and R² were used to test the accuracy of the experimental models. R² was used to measure the goodness of fit of a regression model, indicating the degree to which the model explains the observed data. It reflects the explanatory power of independent variables for dependent variables. The closer the value is to 1, the stronger the model’s predictive ability and the higher the goodness of fit. MAE measured the average magnitude of prediction errors without considering their direction, reflecting the overall deviation between predicted and observed values. RMSE emphasized larger errors by squaring the residuals before averaging, thereby providing a more sensitive indicator of prediction accuracy and model stability.

3. Results

3.1. Accumulative Displacement of the XMLC Landslide

Figure 4 shows the spatiotemporal evolution of surface displacement along LOS over XMLC calculated by the PS-InSAR technique. Although there is a lack of field observation data such as GNSS or LiDAR in this study area through comprehensive investigation, the density and accuracy of monitoring points obtained by the PS-InSAR technology meet the requirements from the validated by multi-path SAR observations [28]. The maximum deformation of the Mawo landslide is mainly concentrated in the middle part of the slope, whereas that of the Xi’erguazi landslide occurs at the toe, where it is close to the river. Consequently, the Mawo and Xi’erguazi landslides display different deformation behaviors over time. In this study, three representative points, P1, P2, and P3, located in the Mawo landslide, the Xi’erguazi landslide, and stable area, respectively, were selected for time series analysis and displacement prediction. Accumulative displacement time series are shown in Figure 5.

The accumulative displacement time series of monitoring points over the Mawo landslide body are highly similar to the variation trend of point P1, which notably shows a significant acceleration trend after November 2019 (Figure 5). After excluding the influences of external disturbance factors such as earthquakes, volcanic eruptions, and extreme rainfall, a large area of farmland distributed over the upper part of the landslide body may play an important role [28]. From previous investigation, we can assume that the observed acceleration in accumulative displacement is likely linked to intensive agricultural irrigation activities [28,41].

Monitoring kinematics from point P2 exhibits distinct periodic fluctuation characteristics, appearing all over the landslide body. We can assume that the periodic deformation may be related to periodic behaviors from rainfall or RWL fluctuations. Previous studies have excluded periodic rainfall as one dominant triggering factor for this landslide [3]. Moreover, an inverse relationship was observed between the nonlinear displacement time series and the 24-day accumulative rainfall record (Figure 1d). According to relevant literature and the observed deformation characteristics, the periodic fluctuations at point P2 are more likely related to the annual impoundment and drawdown from the reservoir operations [28,42].

The accumulative landslide displacement time series of point P3 differs significantly from those of P1 and P2. The overall accumulative displacement amplitude at this point is relatively small. In the end of the monitoring period, the accumulative displacement only reaches approximately −40 mm, which is far below the variation amplitude exceeding −700 mm at P1 and P2. This indicates that the location of P3 is relatively stable. Additionally, although the accumulative displacement time series of the landslide at P2 also exhibits periodic fluctuations, the amplitude is relatively small. In contrast, the accumulative displacement series of the landslide at point P3 shows more drastic fluctuations.

Although points P1, P2, and P3 are all located in the XMLC area, their time series characteristics of accumulative displacement significantly differ from each other and might be controlled by various influencing factors. This heterogeneity increases the complexity of landslide time series prediction and makes it difficult to directly incorporate specific influencing factors into the model as auxiliary variables to predict.

3.2. Initial Decomposed Displacement Components

3.2.1. Signal Decomposition with the CEEMDAN Method

The CEEMDAN algorithm was used to decompose the original accumulative landslide displacement time series. This algorithm does not require pre-defining basis functions and can adaptively decompose non-stationary signals into multiple IMFs, effectively avoiding the complexity of parameter selection and adjustment in traditional methods. As shown in Figure 6, the pre-processed original signal at point P1 is presented, along with the IMF components obtained through CEEMDAN decomposition. From top to bottom, these are sequentially IMF1, IMF2, …, up to IMF7.

As revealed in Figure 6, the original signal exhibits a gradually increasing trend in accumulative displacement and contains certain periodicity low-frequency fluctuations. In the decomposition results, IMF1, IMF2, and IMF3 show high-frequency fluctuation characteristics. Among the decomposed components, IMF3 exhibits the strongest fluctuations, representing the rapidly varying or abrupt elements in the original time series. Distinct spikes observed at specific epochs further indicate its high sensitivity to sudden deformation events. IMF2 displays slightly lower frequency variations than IMF3, corresponding to relatively moderate high-frequency components. In contrast, IMF1 maintains comparatively stable oscillations, which may be associated with periodic variations or medium-term fluctuations, which are inherent in the original signal. IMF4 has more regular fluctuations and a more obvious periodicity, indicating that it contains signal components on a longer time scale. In contrast, although the fluctuation pattern of IMF5 is slightly irregular, its periodicity characteristics are significant, potentially capturing short-term periodicity components in the original signal. The fluctuation frequency of IMF6 is significantly reduced, presenting low-frequency oscillations that reflect variations over longer time scales. The IMF7 component almost shows a stable and slow downward trend, representing the main long-term trend part of the original signal and serving as the core structure of overall accumulative displacement changes.

3.2.2. Sample Entropy Calculation

After completing the preliminary CEEMDAN decomposition of the signal, we further calculated the sample entropy of each component signal. The SampEn results calculated for each signal component are shown in

Table 2. SampEn calculation results and trend test results of each component.

Signal Component	SampEn	p-Value
IMF1	1.8692	0.99294
IMF2	1.9402	0.57723
IMF3	2.0008	0.78139
IMF4	1.3493	0.40149
IMF5	0.6104	0.089195
IMF6	0.3537	0.16478
IMF7	0.0124	0

, which are basically consistent with the previous time series characteristic analysis of each component. Specifically, as high-frequency components, IMF1, IMF2, and IMF3 typically reflect the violently fluctuating or abrupt parts of the signal, so their SampEn values are high, indicating that these components have strong irregularity and complexity. In contrast, IMF4, IMF5, and IMF6 have lower frequencies and relatively stable fluctuations, with relatively low SampEn values, reflecting strong periodicity and regularity. Further, IMF7 has the lowest SampEn value, indicating that its structure is the most stable, mainly representing the general trend component and constituting the dominant change trend of the landslide accumulative displacement sequence.

In this study, the sample entropy threshold was set at 0.2. As verified by the Mann−Kendall trend test method, this threshold can effectively divide the decomposed time-series components into trend terms and periodicity terms, as shown in Table 2.

3.3. Further Decomposition of the High-Frequency Signal

The initial decomposition results are clustered into three categories automatically with the K-means method, representing the high-frequency, medium-frequency, and low-frequency components, respectively, in the periodicity term signals. Taking point P1 as a representative, after clustering of the periodicity sub-signals, it is found that IMFs with higher sample entropy (IMF1, IMF2, and IMF3) are classified as high-frequency components. These three component signals are merged and denoted as high-frequency component. IMF4 is classified as a medium-frequency component. Finally, IMFs 5 and 6 are merged as a low-frequency component. The merged results are shown in Figure 7.

Subsequently, the NRBO-VMD algorithm was applied to perform further decomposition of the high-frequency signals at the P1 points of the XMLC, yielding the following components, as shown in Figure 8.

3.4. Integrated Landslide Displacement Prediction

In this study, the final landslide time series prediction output was obtained by fusing and superimposing the predicted outputs of the trend-term component and periodicity-term component of landslide data. Figure 9 shows the prediction effects of the accumulative displacement time series of landslides at points P1, P2, and P3, and

Table 3. Time series prediction accuracy of the landslide accumulative displacement at Points P1, P2, and P3 by the prediction model.

Evaluation Index	Point P1	Point P2	Point P3
R2	0.997	0.995	0.935
MAE (mm)	2.371	3.488	2.503
RMSE (mm)	4.517	4.590	3.751

quantifies their prediction accuracy and errors.

From Table 3, it can be analyzed that for the time series data of point P1 in the landslide monitoring area, the time series prediction model proposed in this paper exhibits high prediction accuracy, with an R² value reaching 99.7%, and several error evaluation indicators are very low. In Figure 9a, the true values coincidence with the fused predicted values, not only capturing the overall linear trend but also accurately predicting the fluctuations. However, for the last 10 data points (from 4 July 2022 to 20 October 2022), the prediction accuracies of the model decrease. Although the fused predicted values have similar fluctuation patterns and change trends compared with the true values, the overall values are smaller than the true values. In other words, the model underestimates the sudden acceleration of the accumulative landslide displacement during this period. It can be concluded that the proposed prediction framework has strong capability and stability in predicting the accumulative landslide displacement sequences.

For point P2, the overall time series of accumulative landslide displacement shows a significant linear downward trend, accompanied by obvious periodic fluctuations, resulting in a complex signal. As revealed in Figure 9b, the model should have learned the characteristics of periodic signals during the training process, which is reflected in the follow-up of periodic fluctuations during prediction. Particularly, from 27 June 2021 to 4 July 2022, the predicted values are basically consistent with the true values in terms of fluctuation trends. However, at the initial and terminal stages of periodic fluctuations, some fused predicted values have slight deviations, while the remaining predicted parts are basically consistent with the actual InSAR monitoring results. In terms of the indicators of accuracy evaluation, the MAE (3.488 mm) of the time series prediction for point P2 is larger than that of point P1, which may be related to the lagging response at the initial stage of periodic changes. Consequently, it shows that the model proposed in this study has a good fitting effect for the time series prediction of accumulative displacement of such landslides.

As shown in Figure 9c, the variation in the accumulative landslide displacement time series at point P3 exhibits obvious nonlinear characteristics and generally lacks obvious regularity, making time series prediction for this point the most difficult. However, the analysis of the evaluation indicators (Table 3) shows that the R² of the prediction results is 0.953. Although the prediction accuracy is lower compared to the landslide data at the other two points, the model can basically capture the basic trends of accumulative displacement changes and fluctuations. The prediction performs well when the amplitude of accumulative displacement fluctuations is not very large; on the contrary, in areas with large amplitude changes, the predicted data show smaller variation amplitudes than the InSAR observed values. For the special accumulative landslide displacement time series with high nonlinearity and uncertainty represented by point P3, the model can still perform relatively good time series prediction, despite deviations occurring during sudden large fluctuations in partial accumulative displacements.

In conclusion, the proposed fused time series prediction model demonstrates good performance in predicting the accumulative landslide displacement time series at the monitoring points in the XMLC area. It can not only capture the overall changes in displacement trend terms but also accurately identify the periodic fluctuations during the variation process.

4. Discussion

4.1. Ablation Experiment for the Proposed Prediction Model

To verify the capability of the proposed CBS model in predicting the periodic deformation signals of landslides, ablation experiments were conducted. Three comparative models were established: model A1, which employs a BiLSTM network; model A2, which integrates BiLSTM with a self-attention mechanism; and model A3, which combines CNN and BiLSTM architectures. Here, the input data of the model underwent further decomposition, where the trend components were predicted using the RBF model.

As shown in the results of ablation experiment 1 on the accumulative landslide displacement time series at point P1 (Figure 10a and

Table 4. Comparison of prediction accuracy for the accumulative landslide displacement time series at points P1, P2, and P3 in ablation experiment 1.

	Evaluation Index	Proposed Model	Model A1	Model A2	Model A3
P1	R2	0.997	0.993	0.995	0.996
	MAE (mm)	2.371	5.409	3.950	3.441
	RMSE (mm)	4.517	6.529	5.033	4.691
P2	R2	0.995	0.988	0.991	0.995
	MAE (mm)	3.488	5.307	4.606	3.249
	RMSE (mm)	4.590	6.841	5.852	4.347
P3	R2	0.935	0.857	0.858	0.907
	MAE (mm)	2.503	4.037	3.995	3.273
	RMSE (mm)	3.751	5.538	5.525	4.462

), the CBS model combination for periodicity component prediction in the proposed combined prediction model is the optimal choice. Since the accumulative landslide displacement time series at point P1 has an obvious overall linear trend and small fluctuations, models A1, A2, and A3 all performed well in prediction. However, the prediction model proposed in this study achieved higher prediction accuracy (RMSE = 4.517 mm). As seen in Figure 10a, the prediction curve (blue) representing the model proposed in this study more closely matches the real InSAR time series deformation monitoring values, while the prediction values of the other models deviate upward or downward in some periods.

As observed from Table 4 and Figure 10, ablation experiment 1 on the accumulative landslide displacement time series at points P2 and P3 demonstrates the superiority of the periodicity term prediction model CBS over models A1, A2, and A3. The time series prediction results using model A1 have the lowest accuracy, followed by model A2. The accumulative landslide displacement time series at points P2 and P3 have large fluctuations, and the model’s ability to capture local nonlinear changes during prediction is particularly critical. Incorporating CNN and self-attention into the model can help extract local features in the time series, enhancing the modeling capability for global dependency relationships and key fluctuation patterns, thereby improving the accuracy of time series prediction.

4.2. Ablation Experiment for the Decomposition and Prediction Model

In this ablation experiment, five comparative models were established. Model B1 employs only the CEEMDAN algorithm for preliminary signal decomposition, in which the periodic component is predicted using the CBS model and the trend component is predicted using the RBF model. Models B2 and B3 both adopt a two-step decomposition approach: in model B2, the decomposed trend and periodic components are each predicted using the CBS model, whereas in model B3, both components are predicted using the RBF model. Models B4 and B5 are constructed without any signal decomposition, where the original time series is directly modeled using only the CBS model and the RBF model, respectively.

Table 5. Comparison of prediction accuracy for the accumulative landslide displacement time series at points P1, P2, and P3 in ablation experiment 2.

	Evaluation Index	Proposed Model	Model B1	Model B2	Model B3	Model B4	Model B5
P1	R2	0.997	0.993	−2.107	0.932	0.869	0.945
	MAE (mm)	2.371	4.682	123.869	16.441	22.011	14.975
	RMSE (mm)	4.517	6.112	139.032	20.701	28.577	18.374
P2	R2	0.995	0.984	0.300	0.988	0.911	0.971
	MAE (mm)	3.488	5.949	67.037	4.407	16.455	7.688
	RMSE (mm)	4.590	7.930	72.945	6.822	19.069	10.752
P3	R2	0.935	0.839	0.837	0.852	0.376	0.433
	MAE (mm)	2.503	4.186	4.328	2.859	8.369	8.113
	RMSE (mm)	3.751	5.875	5.922	5.368	11.585	11.042

and Figure 11 show the results of ablation experiment 2 conducted on the accumulative displacement time series of landslides at all points. The proposed model achieves the best overall prediction performance and accuracy. Using model B1, satisfactory predictions are obtained for the accumulative displacement time series at points P1 and P2, whereas prediction accuracy at point P3 is considerably lower. This is mainly due to the lack of VMD decomposition for clustered high-frequency components, which leads to overly complex inputs to the CBS module and limits its ability to capture large-amplitude fluctuations. Specially, the displacement time series at P3 exhibits stronger non-periodic, complex variations and less predictable amplitudes than those at P1 and P2. In contrast, model B2 shows higher prediction accuracy at point P3 than at P1 and P2, where negative R² values indicate poor predictive performance. This behavior arises because model B2 does not distinguish trend and periodic components after the initial CEEMDAN decomposition, instead applying a complex deep learning model to all components. Such models tend to overfit relatively simple and linear signals, which dominate the displacement series at P1 and P2, resulting in degraded performance. The opposite signal characteristics at P3 lead to smaller variations in prediction accuracy.

Model B3 follows a similar strategy to model B2 but employs an RBF model to predict all CEEMDAN-decomposed components. With the radial basis parameter set to 1000, the RBF model demonstrates strong fitting capability for both linear and nonlinear data, yielding higher accuracy for P1 and P2 where trend components are dominant. However, for the more complex time series at P3, its limited ability to capture intricate variations results in reduced accuracy compared with deep neural networks. Models B4 and B5 directly predict the original displacement time series without signal decomposition. Their prediction accuracies at three points are lower than that of the proposed two-stage decomposition-based hybrid model. By progressively separating features through secondary decomposition, the proposed approach reduces the learning burden of individual networks and enables more precise extraction of component-specific characteristics, thereby substantially improving time-series prediction accuracy, especially for complex signals.

Overall, compared with other models, the proposed model has the best prediction accuracy, proving that the two-step decomposition of signals will improve the overall time series prediction accuracy, especially for complex landslide accumulative displacement time series.

The above analysis illustrates that the improvement in model accuracy has been achieved through the two-step decomposition. From the perspective of landslide mechanisms, the periodic component of the landslide deformation is inherently linked to periodic variations in RWL and rainfall fluctuations. After the initial decomposition of the overall time series signal, the trend term was separated, and the periodic term was further divided into high-, medium-, and low-frequency components.

Typically, the medium- and low-frequency signals are considered to capture the periodic characteristics. To further validate this assumption, wavelet analyses were performed between the medium- and high-frequency signals and both rainfall and reservoir time series, as shown in Figure 12. The cross wavelet transform (XWT) can be employed to analyze the relationship between deformation and potential triggering factors in the time–frequency domain. The XWT can also reveal time lag between two sequential signals; however, in this study, the discussion focuses on the relationship between the decomposed signals and the two primary periodic driving factors, rather than on their time lag relationships.

It should be emphasized that the decomposition strategy employed in this study does not fully distinguish the periodic deformation components driven by RWL fluctuations and rainfall. Moreover, it cannot be asserted that the medium-frequency signals are exclusively attributable to rainfall or reservoir variations, nor that the low-frequency components correspond solely to either factor. Figure 12 demonstrates that the lower the decomposed frequency, the stronger the ability to capture long periodic components (e.g., the distinct annual period compared with rainfall/RWL). The high-frequency signals are often regarded as random noise or other error signals that were not fully removed during InSAR data processing.

Nevertheless, wavelet analysis of the high-frequency signals against rainfall- and reservoir-induced periodic deformation reveals that part of the high-frequency signal exhibits periodicity consistent with RWL variations (Figure 13). This further highlights the necessity of further decomposition of the high-frequency component. If the high-frequency signals were arbitrarily treated entirely as noise and removed, or directly employed for prediction using the proposed composite model, the predictive accuracy of the landslide would inevitably be compromised.

4.3. Advancement of the Proposed Model

To test the prediction performance of the proposed model, we conducted comparative experiments with other models. This experiment selected some published landslide time series prediction models to carry out the following comparative experiments. Three models were selected for comparison: the HP-DES-LSTM, HP-Polyval-LSSVM, and WD-GRU models, which are denoted as model C1, model C2, and model C3, respectively, in this experiment [14,43,44].

Quantitative evidence presented in

Table 6. Comparison of prediction accuracy for the accumulative landslide displacement time series at points P1, P2, and P3 in the comparative experiment.

	Evaluation Index	Proposed Model	Model C1	Model C2	Model C3
P1	R2	0.997	0.996	0.473	0.746
	MAE (mm)	2.371	11.600	176.531	34.032
	RMSE (mm)	4.517	14.396	188.864	39.689
P2	R2	0.995	0.920	0.761	0.973
	MAE (mm)	3.488	15.142	27.746	8.677
	RMSE (mm)	4.590	18.075	31.294	10.385
P3	R2	0.935	0.459	0.496	0.756
	MAE (mm)	2.503	9.088	15.555	5.626
	RMSE (mm)	3.751	10.782	17.944	7.237

and Figure 14 indicates that, the proposed prediction model achieves the best overall performance and the highest predictive accuracy among all compared models, highest R² value and significantly lower MAE and RMSE values at the three observation points compared with other models. For accumulative displacement time series at points P1 and P2, where trend components are dominant, model C1 achieves relatively good prediction performance, whereas its performance deteriorates significantly for the more complex time series at point P3. Model C1 employs the HP filter to decompose the signal into trend and periodic components, predicting the trend component using DES and the periodic component using an LSTM model. As a conventional time-series prediction approach, the LSTM model has limited capability in capturing irregular and non-stationary fluctuations, which hinders its effectiveness in predicting the complex displacement dynamics observed at point P3. Model C2 exhibits the poorest prediction accuracy across all three types time series. This is primarily because, after HP-based decomposition, a polynomial fitting function is used to predict the trend component. However, the trend component extracted by the HP filter does not represent a strictly linear process and still contains substantial fluctuations, making polynomial fitting an unsuitable prediction strategy. Model C3 adopts wavelet decomposition but only applies a GRU model to predict the periodic component. As a result, the temporal characteristics of accumulative displacement may not be fully captured, leading to suboptimal prediction performance.

By jointly emphasizing the accuracy and effectiveness of signal decomposition and matching different signal components with appropriate prediction models, the proposed framework enables targeted feature extraction and fitting of diverse temporal characteristics, thereby substantially enhancing overall prediction accuracy and robustness.

5. Conclusions

In this study, we proposed a new framework to predict InSAR-derived time series, which is based on a two-step decomposition strategy, targeted modeling, and fusion prediction to enhance prediction performance. Our proposed method was applied to the XMLC landslide close to the Mao’ergai Reservoir, where the multi-temporal InSAR method and Sentinel-1 SAR datasets are used to obtain and map the spatiotemporal landslide kinematics.

Based on the InSAR-derived time series, the proposed method first adopts a two-step decomposition strategy to capture the trend and periodic components from landslide kinematics using CEEMDAN and VMD algorithms. The decomposed time series are then evaluated using hypothesis testing and the SampEn index. The proposed framework considers the modeling requirements of different frequency components. The RBF and the proposed CBS models were constructed for the trend and periodic components for modeling, respectively, and finally were fused to obtain high-accuracy prediction results. Furthermore, ablation experiments were set up to verify the effectiveness of the signal decomposition mechanism and the multi-model combination structure. Comparative experiments were conducted to further confirm the adaptability and accuracy advantages of the proposed method in landslide prediction. A comparison between the original model and the model with only one decomposition shows that the MAEs are reduced by 40%−49% and RMSEs are reduced by 36%−42%. In contrast to the single-network model, the proposed hybrid prediction model decreases the MAEs by 22%−57% and RMSEs by 4%−33%. Additionally, compared with others prediction methods, our proposed model has superior denoising ability, higher accuracy, and greater robustness when predicting different motion characteristics. The proposed decomposition strategy and multi-model architecture can effectively enhance the adaptability and reliability of the prediction system, providing a unique solution for landslide time series prediction.

In future, we aim to advance toward a more accurate prediction framework that seamlessly integrates physical process modeling with deep learning methodologies, thereby enhancing both interpretability and generalization capability. For data-driven prediction strategies, the incorporation of additional environmental and geotechnical variables will be pursued to establish more comprehensive and robust models capable of capturing complex deformation mechanisms.