1. Introduction
Being one of the primary geological disasters in China, landslides present a substantial scale and potential harm. A landslide refers to a geological disaster where soil, rock, or a mixture of soil and rock on the ground or slope is displaced due to factors such as the force of gravity and internal earth forces, moving downwards or laterally along a certain sliding surface or zone. The disasters caused by landslides are extremely severe, and once they occur, they can result in mass casualties, property damage, ecological environmental destruction, and other dire consequences. Accurate prediction of landslides has become crucial for timely response to dynamic situations and ensuring the safety of people’s lives and property. Accurate displacement prediction can issue early warnings hours or even days in advance, providing valuable time for evacuation and thus reducing casualties. For critical infrastructure such as dams, bridges, nuclear power plants, etc., precise displacement prediction can guide necessary reinforcement and maintenance to ensure their stability during disasters, avoiding catastrophic outcomes. Accurate prediction results can also provide a scientific basis for emergency management departments, optimizing resource allocation and rescue plans, and improving the efficiency and success rate of rescue operations. Information about displacement gathered during the evolutionary process of a landslide provides direct insights into the mechanisms and dynamic laws that govern such phenomena. As a result, the prediction of landslide displacement has become a pivotal research focus within the field of disaster prevention and reduction. Accurate displacement prediction can significantly enhance our ability to anticipate and mitigate the risks associated with landslides, thereby saving lives and reducing economic losses in susceptible areas [
1,
2,
3,
4,
5].
Models for predicting landslide displacement are typically categorized into two main groups: physical models and data-driven models. Physical models incorporate physical mechanisms to predict landslide occurrences through a comprehensive analysis of the physical attributes of the landslide body. However, the generalization ability of physical models is limited, and their effectiveness in long time series predictions does not match that of data-driven models. In recent years, there has been a surge of interest in hybrid prediction models that integrate time series analysis and deep learning techniques. These models have attracted significant attention due to their improved prediction accuracy and generalization capabilities in landslide displacement prediction, surpassing the performance of traditional models. Many intelligent, data-driven, nonlinear models have been utilized in predicting landslide displacement [
6,
7]. Concurrently, researchers have demonstrated the superiority of the “decomposition–reconstruction–prediction” model approach compared to single prediction models in examining landslide displacement prediction [
8]. For instance, Yang. (2022), Guo et al. (2020), and Y. Xing et al. (2019) [
9,
10,
11] utilized a time series analysis method and a variational mode decomposition algorithm (VMD) to decompose cumulative landslide displacement, thereby addressing the issues of incomplete or excessive decomposition when deciphering landslide displacement data. Finally, all projected values are combined to form the predicted cumulative displacement based on the time series model.
Although the composite model above has achieved notable results, there is still room for improvement and some limitations. Considering displacement sequence decomposition, it is worth noting that while the VMD method can perform adaptive decomposition based on data scale and yield highly reliable decomposed slope deformation data, the quality and effectiveness of decomposed data depend on parameter selection [
12]. To optimize the precision, robustness, and physical meaning of VMD [
13], the VMD method adapts its decomposition approach based on data scale. S. Guan et al. have demonstrated that the EMD-PSO-ELM model can effectively measure landslide displacement [
14]. In this study, both the genetic algorithm (GA) [
15] and the locust optimization algorithm (GOA) [
16] are utilized to automatically optimize VMD hyper-parameters. This serves to eliminate the influence of human factors and improve the efficiency of decomposition.
The development of a prediction model is a significant factor influencing the efficacy of landslide displacement prediction [
17,
18,
19]. Time series analysis can be applied to landslide displacement data due to the substantial correlation between past and future data [
20,
21]. Therefore, incorporating a time series research technique based on deep learning into the prediction of landslide displacement can utilize the temporal correlation between data at different time points, comprehensively understand the evolution mechanism of deformation in landslides, and enhance the accuracy and dependability of forecasts.
Liu et al. (2023) [
22] proposed a reliable prediction of reservoir landslides based on an SVR model that responds to triggering factors. Li et al. (2021) [
23] proposed a landslide displacement dynamic prediction model based on singular Spectrum Analysis (SSA) and a stacked Long Short Term memory (SLSTM) network. It makes up for the dynamic characteristics of landslide evolution and the shortcomings of traditional static prediction models, and the prediction accuracy is improved. Meng et al. (2023) [
24] used a dynamic hybrid model of gated recurrent unit (GRU) and error correction for landslide displacement prediction. It can not only better capture the local change of the accelerated deformation state, but also effectively reduce the extended error in the displacement prediction of long time series.
The aforementioned deep learning network notably improved the accuracy of prediction, but practical application and promotion have limitations. These methods primarily concentrate on “deformation information + an inducing factor” [
25] and exclude the appraisal of the physical connotation of each displacement component, the feature data of the triggering factor subsequence, and the interdependence between displacement components and the influencing factor. To address this issue and enhance the comprehensibility of the nonlinear model [
26], the proposed solution in this study is to link the major scientific challenge of landslide prediction with a time series network. This involves examining the multivariate time series data to analyze the values of several variables at a given time step and the values of a single variable over multiple time steps. By doing so, the physical interpretability of the model can be improved. Thus, the correlation between factors and the correlation across time intervals can be extracted. The intricate dependence relationship between the landslide displacement input prediction model and the group of feature vectors composed of influencing factors can be analyzed, subsequently improving prediction accuracy.
Utilizing the Bazimen landslide dataset from Yichang, Hubei Province, as a case study, this research introduces a composite forecasting framework for analyzing time series data of landslide displacement. The framework begins by decomposing the landslide displacement time series into components with distinct physical meanings and scale characteristics. This decomposition is achieved through the application of time series analysis methods and Variational Mode Decomposition (VMD), which is fine-tuned using a swarm intelligence coupling algorithm. Following the decomposition, a response analysis is conducted to identify the most relevant factors influencing each displacement component. Feature vector groups of various scales are then constructed, reflecting the relationships between the displacement components and their corresponding inducing factors. These groups serve as inputs for the subsequent prediction model. The study proposes a Transformer-based prediction model, enhanced with a time series variability analysis module (TempoVar-Transformer), designed to extract multi-scale information from landslide sequences and integrate it to predict the displacement components with accuracy. The model reconstructs the cumulative displacements of trend, periodic, and random components, and the prediction results are thoroughly evaluated and analyzed to validate the framework’s efficacy.
6. Slippery Slope Analysis and Example Application of the Bazimen Landslide
6.1. Geological Profile of the Bazimen Landslide
The Bazimen landslide (110°45′ E, 30°58′ N) is located in Xiangxi Village, Guizhou Town, Zigui County, Hubei Province, within the Three Gorges Reservoir area, approximately 38 km from the Three Gorges Dam. Located on the right bank of the Xiangxi River, 0.8 km from its confluence with the Yangtze River, the slope morphology resembles an irregular fan. Homologous alluvial gullies develop on both sides of the boundaries, forming a circular trailing edge and a water facing leading edge. The longitudinal length of the landslide is 550 m, with a narrow top and a wide bottom, covering a total area of 13.5 × 10
4 m
2. The average thickness of the landslide body is around 30 m, with a total volume of approximately 400 × 10
4 m
3. The slope ranges from 40° to 60°, and the landslide body mainly consists of a yellowish-brown, purplish-red, and dark grey fragmented stone soil layer, composed of blocks, gravels, and pulverized clay. The structure of the landslide body is loosely accumulated, and unfavorable factors such as rainfall and upper catchment water scouring can impact the stability of the entire landslide area, making it prone to overall instability-induced landslides. The Bazimen landslides are located in a subtropical monsoon climate, experiencing year-round rainy weather, with rainfall being a significant factor influencing landslide displacement. The Bazimen landslide entered its initial resurrection stage during the Gezhouba dam water storage in 1981. Since 2003, with the Three Gorges Dam water storage, Bazimen landslides have exhibited noticeable deformation. During the rainy season from May to July 2004, coupled with a drop in the Three Gorges reservoir level, shear cracks formed in the middle and upper parts of the landslide. The landslides are frequently active during the annual rainy season, primarily located in the middle and at the back edge, significantly affecting the normal life and access of neighboring areas. The satellite map of the Bazimen landslide is shown in
Figure 7, and its planar contour map is shown in
Figure 8.
6.2. Characterization of Landslide Deformation Based on Monitoring Data
Two GPS deformation monitoring points (ZG111, ZG110) were strategically placed in the landslide area, and data were obtained from the National Field Scientific Observation and Research Station of the Three Gorges Landslide of the Yangtze River in Hubei Province. The dataset initiation coincided with the impoundment of the water level in front of the Three Gorges Dam to 135 m in mid-June 2003. Subsequent monitoring took place monthly. The timeline of the Bazimen Landslide Displacement Monitoring Points is illustrated in
Figure 9, depicting the cumulative displacement-reservoir level-rainfall curve at the Bazimen landslide displacement monitoring point. The utilized data cover the period from January 2007 to December 2012. Analysis of the monitoring data reveals that during periods of low rainfall each year (January 2007 to March 2007, October 2007 to March 2008, November 2008 to March 2009, October 2009 to April 2010, November 2010 to April 2011, December 2011 to April 2012, October 2012 to December 2012), the time accumulated displacement-reservoir level-displacement curves at the Bazimen landslide monitoring site are delineated. In contrast, during periods of elevated and concentrated rainfall (April to July 2007, July to August 2008, May to June 2009, May to August 2010, June to August 2011), the cumulative displacement exhibited rapid, step like increments. Notably, the “step period” and concentrated rainfall periods each year did not precisely align. A time lag between the “step period” and concentrated rainfall period is evident, signifying that the landslide displacement “step” occurs subsequent to continuous or heavy rainfall—a pattern observed consistently. During “step” periods, significant changes in the reservoir water level were also noted. For instance, from April 2008 to September 2008, the reservoir water level experienced a decline, followed by an increase from September 2008 to November 2008. In this period, from April 2008 to November 2008, the cumulative displacement of the landslide exhibited a sudden increasing trend. Similar patterns were observed in other time periods. It is evident that the primary factors influencing Bazimen landslide displacement are rainfall and reservoir water level.
6.3. Analysis of Influencing Factors
Choosing appropriate triggering factors for landslides is crucial for the accuracy of predictions, especially for predicting periodic components. Studies have shown that rainfall and reservoir water level are the main triggering factors for landslides in the Three Gorges Reservoir area [
37,
38], and Bazimen landslide is located in this area. Rainfall increases soil pore water pressure, thereby reducing the effective stress of the soil. When the effective stress of the soil decreases to a certain extent, the shear strength of the soil mass also decreases, making it prone to landslide occurrence. Additionally, rainfall saturates the soil, increasing its weight, which in turn increases the downslope force, further promoting landslide occurrence. Changes in reservoir water level can cause changes in groundwater levels, further affecting soil pore water pressure and effective stress. By comparing the changes in landslide displacement deformation with rainfall and reservoir water level changes, it can be seen that months with concentrated rainfall and stages with significant changes in reservoir water level can lead to larger deformations of landslides.
Landslides are complex natural phenomena that are undoubtedly caused by a combination of multiple factors, such as soil, geological structure, groundwater, and human activities, among others. However, this study did not consider other factors for several reasons. Firstly, the changes in other factors are more random and difficult to capture regular patterns, and their general impact is smaller. Secondly, our composite model, when using rainfall and reservoir water level as the dominant triggering factors, decomposes the displacement into three components: trend term, periodic term, and random term. The periodic term displacement is key and depends on the dominant factor, while the random term displacement includes not only some noise errors but also other small influencing factors from the perspective of landslide mechanisms. Finally, by reconstructing all terms, we obtain the total predicted displacement, which also shows that our model has a high degree of tolerance and robustness, with practical significance.
6.4. Evaluation Index
In order to accurately evaluate the prediction effect of our designed model, the evaluation metrics are Root Mean Square Error (
) and Mean Absolute Percentage Error (
,which are defined as follows:
where,
is the size of the predicted sample,
is the actual value at time
,
is the predicted value at time
, and
is the arithmetic mean of all the actual values.
The range of is , the smaller the value, the stronger the model fitting ability; The range of is , where an of 0% indicates a perfect model, and an greater than 100% suggests a poor-quality model. When both and are sufficiently small, it indicates that the predictive model has a good forecasting performance.
6.5. Assumptions and Limitations
This section discusses the assumptions and limitations of the research presented in this paper. We aim to provide readers with a transparent and comprehensive understanding of our research methodology, and to assist them in evaluating the applicability and credibility of our research results in real-world applications.
6.5.1. Assumptions
We assume that the displacement of landslides is primarily influenced by the selected input variables (rainfall, reservoir water level, past displacement). Although these variables have been widely recognized as key factors affecting landslide displacement, other relevant factors may not be included in the model.
Our model assumes that the quality and integrity of the data are sufficiently high to enable effective training and prediction. However, in reality, the data may contain noise, outliers, or missing values, which could potentially affect the model’s performance.
We assume that the physical processes of landslides remain consistent throughout the study period. This means that we have not considered possible geological changes or long-term impacts of external factors on slope stability.
6.5.2. Limitations
Deep learning models typically require a large amount of data for training, but high-quality long-term time series data may be difficult to obtain in the field of landslide prediction. Consequently, our model may not fully utilize all the information in the data.
Our model does not account for the spatial and temporal variability of landslide displacement. Landslide events may exhibit different characteristics in different regions, which could limit the generalizability of the model.
6.6. Experimental Analysis and Model Comparison
6.6.1. Data Selection
In order to enhance the training of the prediction model in this paper, the selected monitoring point is ZG111, situated in the middle and rear part of the landslide body. This location provides ample data on displacement and deformation, precipitation, reservoir level, and frequent deformation. The research and analysis focus on the data collected during the monitoring period from January 2007 to December 2012. The experimental data are measured in monthly units, with a total of 70 months considered. The first 50 months’ data are designated as the training set for model training and parameter adjustment, while the remaining 20 months’ data serve as the test set for assessing the model’s accuracy. Due to the scarcity of data, we employed a cross-validation approach to evaluate the model’s generalization capability and to avoid overfitting. This method allows us to make the most of the limited data available and provides a more robust assessment of the model’s performance without the need for a separate validation set.
6.6.2. Parameter Optimization
Before performing the optimization, the optimization range of the penalty factor for the hyper-parameter combination of VMD decomposition is set to
; the optimization range of the rise time step is set to
; the population size in the GOA algorithm is set to 100; and the maximum number of iterations is set to 100. The hyper-parameter combination obtained from the final optimization is shown in
Table 2:
6.6.3. Results of Displacement Sequence Decomposition
The VMD algorithm, with hyper-parameters obtained through the crowd-wise coupled optimization algorithm in the preceding subsection, is utilized to successively decompose the original cumulative displacement into trend, periodic, and random terms. The total observed displacement is depicted in
Figure 10, and the decomposition results are illustrated in
Figure 11,
Figure 12 and
Figure 13, respectively.
6.6.4. Comparative Experimental Analysis of Coupled Optimal Decomposition Algorithms
To verify that the coupled optimization algorithm proposed in this paper produces better decomposition effect and fidelity for VMD decomposition than traditional optimization algorithms, the following particle swarm optimization algorithm (PSO), genetic algorithm (GA), and locust optimization algorithm (GOA) are selected for comparison with the method of this paper, as shown in
Table 3 and
Figure 14:
The comparative results indicate that the combined GOA-GA optimization algorithm minimizes the VMD decomposition loss, ensuring both effective decomposition and fidelity. It can be inferred that the decomposition achieved using either the GOA or GA algorithm alone is less effective than the fusion optimization of the two. This supports the effectiveness of the combined optimization algorithms presented in this paper.
Table 4 shows the results of the sensitivity analysis performed on each optimization algorithm.
Through sensitivity analysis of the hyperparameters optimized by various optimization algorithms for VMD, it can be observed that the hyperparameters optimized by GOA and PSO have a wide range of variations, which makes VMD prone to mode aliasing and feature loss. This also indicates the superiority of the GA-GOA joint optimization algorithm.
6.6.5. Quantitative Analysis of the Association Degree between Landslide Displacements and Influencing Factors
Utilizing the rainfall and reservoir level data recorded during the same period, the influencing factors underwent Grey correlation analysis with the displacement data. The results are depicted in
Figure 15.
From the confusion matrix in
Figure 16, it is evident that the correlation between displacement and rainfall, as well as the reservoir level at monitoring point ZG111 of the Bazimen landslide, are 0.75 and 0.79, respectively. The correlation values exceed 0.7, indicating a strong correlation between landslide changes and rainfall as well as the reservoir level. Consequently, to achieve accurate displacement prediction, these impactful factors cannot be disregarded. Additionally, a correlation of 0.7 is observed between rainfall and reservoir water level, suggesting a relationship between the two. Upon analyzing the evolution process of the landslide, it is evident that rainfall generates surface runoff on the landslide body’s surface. Through infiltration, it elevates the groundwater level, resulting in increased pressure between rock layers. Simultaneously, the rise in reservoir water level amplifies buoyancy forces in the base–cover interface, inducing significant landslide deformation and decreasing stability. As the reservoir water level decreases, the landslide loses the groundwater buoyancy effect, and deformation automatically halts to some extent, leading to increased stability. After substantial rainfall, landslide displacement continues to rise because the groundwater is not entirely evaporated, and the landslide remains in an unbalanced environmental state, as depicted in
Figure 9. When the reservoir water level drops to its lowest point, the rate of landslide displacement rise increases. These observations reveal a certain lag in the impact of rainfall and reservoir water level on landslides. Rainfall increases both surface and underground runoff, contributing to reservoir area infiltration, leading to a subsequent rise in reservoir water, exhibiting a hysteresis effect [
39].
In most cases, the abrupt change of landslide displacement is directly caused by the abrupt change of inducing factors [
40]. Considering the action process of the inducing factors can effectively improve the reliability of the displacement prediction model.
In most cases, sudden changes in landslide displacements are directly caused by abrupt changes in the predisposing factors. Considering the changes in triggering factors, along with their direct influence on landslide displacements, will effectively enhance the reliability of the displacement prediction model. Addressing the above issues, this paper constructs a trigger factor database using precipitation, reservoir level, landslide deformation, and other relevant data:
- (1)
Rainfall Factors: Cumulative rainfall for the entire 70 months (), and rainfall for the initial 40 months ().
- (2)
Reservoir Level Factors: Cumulative reservoir level for the entire 70 months (), and the average reservoir level ().
- (3)
Landslide Displacement Factors: Monitoring cycle displacement (), and average landslide displacement ().
In order to dig into the correlation information between the influencing factors and landslide displacement, the trigger factor data are decomposed to obtain the high-frequency and low-frequency components, and
= 2,
= 1858,
= 0.2 are set. The decomposition results are presented in
Figure 16,
Figure 17 and
Figure 18. Subsequently, the Grey correlation between the high-frequency and low-frequency sequences with the components after the decomposition of the landslide displacements is calculated, as shown in
Figure 19,
Figure 20 and
Figure 21, respectively.
The optimized Variational Mode Decomposition (VMD) algorithm is utilized to decompose the sequence of triggering factors into high-frequency and low-frequency components. The low-frequency component exhibits discernible periodicity, with trend changes that evolve gradually over time. Conversely, the high-frequency component presents a more complex pattern, characterized by substantial and irregular fluctuations, which signify abrupt changes in the signal. Furthermore, the Grey correlation analysis (GRA) confusion matrix reveals a strong correlation close to 1 between the low-frequency trigger factors and the periodic term of displacement, as well as between the high-frequency trigger factors and the random term of displacement. This indicates that these trigger factors exhibit a significant influence on the corresponding displacement components. Consequently, it is essential to incorporate these highly correlated trigger factors into the prediction model for their respective displacement components, thereby enhancing the model’s accuracy and reliability.
6.6.6. The Displacement Prediction Result of the Trend Term
The predicted displacements of the trend term exhibit a smooth curve over time, without considering the induced factors. The trend term displacement values of each monitoring point in the test set are used as inputs to the model to predict the trend term displacement values at the next time point. The results of the model prediction are depicted in
Figure 22, illustrating that the model effectively captures the trend term displacement, and the predicted values closely align with the actual values.
6.6.7. The Displacement Prediction Result of the Periodic Term
Based on the calculated correlation results between the cycle term displacement components and the inducing factors, it is determined that the low-frequency component of the first 40 months in the rainfall influencing factor of the eight gates exhibits the highest correlation with the cycle term displacement. Similarly, the low-frequency component of the average reservoir level in the reservoir level influencing factor has the highest correlation with the cycle term displacement. Consequently,
and
are identified as key inducing factors, forming a set of eigenvectors with the values of the cycle term displacements. These serve as inputs for predicting the cycle term displacements, and the prediction results are illustrated in
Figure 23.
6.6.8. The Displacement Prediction Result of the Random Term
Based on the correlation results between the random term displacement components and the inducing factors, it is determined that the high-frequency component of the average rainfall among the rainfall influencing factors of the Bazimen landslide exhibits the highest correlation with the random term displacement. Similarly, the high-frequency component of the average borehole reservoir level among the reservoir level influencing factors has the highest correlation with the random term displacement. Consequently,
and
are identified as key inducing factors, forming a set of eigenvectors with the values of the random term displacement as inputs to the prediction model for forecasting the periodic term displacement. The prediction results are depicted in
Figure 24.
Observational analysis indicates that the prediction error for random displacement components is notably higher than that for periodic term displacement components. This discrepancy can be attributed to the random displacement being subject to significant nonlinear fluctuations, which exhibit minimal regularity and present a more substantial challenge for precise fitting. Despite this, the model exhibits improved predictability around periods of sudden change in landslides, leading to an overall enhancement in prediction accuracy.
6.6.9. Comparative Analysis of Total Displacement Prediction Results
Utilizing the time series addition model of Equation (1), the overall displacement prediction is derived by superimposing the predictions of trend term, periodic term, and random term displacements. The prediction results are illustrated in
Figure 25, demonstrating high prediction accuracy when comparing the predicted values with the actual observed values.
To validate that the proposed prediction model outperforms traditional methods and to ensure the consistency of the optimized VMD decomposition method, this paper compares the proposed model with the time-displacement sequence prediction models Transformer, MHA-LSTM, GRU, and SVR proposed by previous researchers. The results of the comparative experiments are presented in
Table 5, and the prediction outcomes of various models are depicted in
Figure 26, The REC curve of the TempoVar-Transformer prediction model is shown in
Figure 27.
Observing the displacement time curves in
Figure 24, it is evident that the predicted values obtained by the proposed model closely align with the trend and magnitude of the actual displacement values. Additionally, as indicated in
Table 3, the root-mean-square error of the prediction model in this paper has been reduced by 69.4% compared to the best-performing previous model, and the Mean Absolute Percentage Error has reduced by 23.3%. These enhancements underscore a substantial improvement in prediction accuracy. In the REC curve diagram, “area” refers to the area under the curve (AUC), which is used to measure the classifier’s ability to distinguish between positive and negative samples. The value of “area” in the diagram (0.92) indicates that the prediction accuracy of landslide displacement is relatively high, possessing significant practical meaning.
Simultaneously, it is found that the obvious accelerated deformation of the Bazimen landslide usually occurs after rainfall, and the focus of the prediction model on rainfall events is consistent with the deformation law of the landslide.
Due to the model being tested only on a specific dataset, lacking credibility and generalization ability, this study will also compare predictions on two different monitoring points simultaneously on the training and test sets, providing compelling data to support the findings.
Table 6 shows that the composite prediction model proposed in this paper outperforms other models at both GPS monitoring points, with both groups exhibiting optimal performance. However, due to the relatively stable landslide data at the monitoring point ZG110 during some time periods, the change characteristics of the influencing factors are not obvious, resulting in a larger gap between the test and training data. This experiment demonstrates the model’s versatility across different locations, enhancing its generalizability and robustness beyond the specific case studies.
In summary, the proposed model excels in extracting topographic change information, with a particular emphasis on significant events such as displacement peaks and rainfall episodes. It adeptly captures the underlying patterns governing landslide displacement, aligning closely with geological principles. This adherence to geological laws instills high confidence in the model’s results, making it a robust tool for predicting and understanding landslide dynamics.
7. Discussion and Conclusions
In this paper, we have proposed a novel composite time series displacement prediction model, termed (GOA-GA-VMD)-GRA-(TempoVar-Transformer). This model delves into the evolutionary mechanisms underlying the dynamic interplay between landslide triggers and displacement. Building on the foundation of previous studies, we have improved the accuracy of our predictions [
41]. Its versatility and applicability make it a promising tool for researchers.
Our model harnesses a swarm intelligence coupling optimization algorithm to optimize the hyper-parameters of Variational Mode Decomposition (VMD) automatically. This algorithm leverages the synergistic benefits of diverse optimization methods, ensuring a decomposition effect of higher fidelity and enhancing the efficiency of the VMD process. This strategy not only improves the decomposition quality but also validates the prediction through a layered reconstruction of landslide displacement data.
By analyzing the dynamic responses of landslides to various inducing factors, we have dismantled the sequence of these factors and conducted a quantitative Grey correlation degree evaluation. This evaluation, based on displacement components, accurately identifies the pivotal inducing factors. Consequently, we have established feature vector groups with varying scales as inputs for the subsequent prediction model. This approach effectively captures a range of time evolution characteristics and the effects of displacement deformation.
The TempoVar-Transformer model introduced in this paper adeptly captures the dynamic temporal relationships between different trigger sequences within the same time step and across different time steps for the same trigger feature. This granular time-series modeling provides a comprehensive analysis of the evolutionary dynamics of landslide displacement, leading to more precise and reliable displacement predictions.
Although the composite prediction model proposed in this paper has achieved satisfactory results on the existing landslide data, there are some shortcomings. The factors affecting landslides may lead to repetitions, omissions, and prediction delays. The model only considers the influence of rainfall and reservoir water level on landslide displacement separately, leading to repetitions in the intermediate effects. This is because a portion of the rainfall enters the reservoir through runoff, increasing the reservoir water level. This, in turn, results in increased errors and a lack of cohesion with the geographical significance of the landslide. Future research can enhance the precision of data analysis, combine geographical and physical knowledge to simulate the direct relationship model between rainfall and reservoir water level, and then apply it comprehensively to landslide prediction.
Although the model proposed in this paper has high prediction accuracy, it is large in size, requires extensive training data, and has low computational efficiency. With the availability of more effective long-term time series data and stronger data processing algorithms in the future, this shortcoming can be avoided.
In conclusion, the prediction model still achieved good results. Building on the research presented in this paper, the predictive model can be integrated into existing landslide prediction systems to enable real-time monitoring of landslide activities. By issuing alerts in advance of potential displacements, the model can help reduce casualties and property damage. In urban planning and land use, the results of landslide displacement predictions can be used to avoid constructing important infrastructure and residential areas in high-risk zones, or to implement reinforcement measures to ensure safety. Continuous monitoring and data collection will assist researchers in further refining and optimizing the predictive model, enhancing its accuracy, and thereby providing more reliable support for long-term landslide prevention and management efforts.