Reservoir bank landslide displacement prediction method based on dynamic weight fusion and multi-modal decomposition

Abstract

The invention discloses a reservoir bank landslide displacement prediction method based on dynamic weight fusion and multi-modal decomposition. The method comprises the following steps: S1, data acquisition and preprocessing; s2, optimal input feature optimization: constructing a multi-source heterogeneous feature set based on a displacement evolution mechanism, and screening optimal input features by using MIC and RF algorithms; s3, multi-factor and multi-scale decomposition and reconstruction: reconstructing the accumulated displacement of the landslide into a trend term, a periodic term and a random term by adopting an MEMD algorithm, and decomposing the optimal input characteristics into high-frequency and low-frequency components; s4, trend term displacement prediction modeling: realizing trend term displacement prediction by using a double exponential smoothing algorithm DES; s5, periodic term and random term parallel prediction: constructing LSSVM, XGBoost and GRU multi-parallel prediction models, and realizing periodic term and random term displacement prediction; s6, multi-model dynamic empowerment fusion; and S7, cumulative displacement prediction. The displacement evolution law is revealed through multi-mode decomposition, the model precision and generalization ability are effectively improved in combination with a dynamic fusion mechanism, and the problem that traditional single-model prediction is insufficient in stability is solved.

Description

Technical Field

[0001] The present application relates to the field of reservoir bank landslide displacement prediction, and specifically to a reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition. Background Art

[0002] my country is one of the countries most threatened by landslides globally. The Three Gorges Reservoir area, particularly in the middle and upper reaches of the Yangtze River, has become a key area for landslide and collapse prevention and control due to its complex geological structure, heavy rainfall infiltration, and periodic reservoir water level fluctuations. Since the reservoir began filling in 2003, over 5,000 landslides or potential landslides have been identified within the reservoir area, posing a serious threat to settlements and navigation along the Yangtze River's golden waterway. Landslide displacement is a core quantitative indicator for assessing landslide stability and early warning, so high-precision landslide displacement prediction research is crucial for improving landslide disaster prevention and control capabilities.

[0003] In recent years, domestic and international research on reservoir bank landslide displacement prediction methods can be broadly categorized into two main approaches: physics-driven and data-driven. The former, because landslide displacement evolution is a complex geophysical and mechanical process with significant multiple spatiotemporal effects, makes it difficult to obtain key parameters such as geotechnical parameters and boundary conditions during mechanical modeling, thus limiting its application value. In contrast, data-driven methods, such as extreme learning machines (ELMs) and support vector regression (SVR), are gaining increasing attention due to their unique advantages in processing nonstationary displacement sequences and their nonlinear fitting capabilities. However, traditional single models suffer from drawbacks such as falling into local optima, overfitting, parameter sensitivity, and poor generalization, making them incapable of meeting the practical needs of landslide early warning. To overcome the limitations of single models, researchers have begun experimenting with combined models. However, existing research mostly relies on static fusion strategies, such as the inverse error method, entropy weighting, and equal-weighted averaging. These strategies suffer from two fundamental flaws: 1) Static weighting mechanisms ignore the complementarity of different models in the characteristic subspace. This prevents model weights from adaptively adjusting when the input data distribution shifts (e.g., a sudden drop in reservoir water level triggers a dramatic change in the seepage field); 2) Weight assignments lacking regularization constraints can easily lead to high-variance models dominating decision-making, exacerbating the uncertainty of prediction results. This has become a key bottleneck restricting the ability of combined models to improve the accuracy of landslide displacement prediction, necessitating the development of new dynamic fusion theories and methods. Summary of the Invention

[0004] To address the aforementioned technical deficiencies, this application proposes a reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition. This method is primarily implemented through a three-level collaborative mechanism: signal decoupling, feature optimization, and dynamic fusion. This method aims to improve the model's ability to extract dynamic features under multi-factor coupling. Compared with traditional fusion strategies, this application can dynamically optimize the weights of different prediction algorithms, thereby improving prediction accuracy and the model's generalization capabilities, providing more reliable technical support for reservoir bank landslide prediction and disaster prevention and mitigation.

[0005] The technical solution of this application is to provide a reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition, which mainly includes the following steps:

[0006] S1. Data collection and preprocessing: Collect high-precision GNSS historical cumulative monitoring time series data of landslide deformation monitoring points on the reservoir bank in the study area and landslide displacement evolution-induced characteristic data such as rainfall and reservoir water level during the same period, complete data cleaning, and divide the data set into training set, validation set and test set;

[0007] S2. Optimal input feature selection: Based on the displacement evolution law of the reservoir bank landslide, a multi-source heterogeneous feature set is constructed. On this basis, the MIC algorithm is used to preliminarily screen the input features, and then the RF model is used to refine the optimal input features.

[0008] S3. Multi-factor and multi-scale decomposition and reconstruction: Multivariate empirical mode decomposition (MEMD) technology is used to reconstruct the accumulated displacement of the landslide into trend, periodic, and random displacement components, and on this basis, the optimal input features are simultaneously decomposed into high-frequency and low-frequency components;

[0009] S4. Trend item displacement prediction modeling: Use the double exponential smoothing algorithm DES to realize trend item displacement prediction;

[0010] S5. Multi-model parallel prediction of periodic terms and random term displacement: Construct LSSVM, XGBoost, and GRU multi-parallel prediction models to achieve periodic terms and random term displacement prediction;

[0011] S6, Multi-model Dynamic Weighted Fusion: A dynamic weighting strategy based on regularized error attenuation is proposed, and the weights are adaptively updated dynamically through the Grey Wolf Optimization Algorithm;

[0012] S7. Cumulative displacement prediction: Finally, the displacement prediction values ​​of the trend item, period item and random item are accumulated to obtain the cumulative displacement prediction result, and the accuracy of the cumulative displacement prediction result is evaluated by the determination coefficient R2 and root mean square error RMSE indicators.

[0013] This application includes but is not limited to machine learning models such as LSSVM, XGBoost, and GRU, and other learning models with similar functions and effects to the above models can be used.

[0014] Furthermore, the expression of the cumulative displacement decomposition and reconstruction result is as follows:

[0015] D t =φ t +η t +χ t Formula 1

[0016] Where: t is the time step; D t is the cumulative displacement; φ i is the trend term displacement; η t is the periodic displacement; t is the random term displacement.

[0017] Furthermore, in step S3, the landslide cumulative displacement is decomposed and reconstructed into trend term, period term and random term components by using the multivariate empirical mode decomposition (MEMD) algorithm, and on this basis, the optimal input feature is simultaneously decomposed into high-frequency component and low-frequency component, which is expressed as follows:

[0018] {f1(t),f2(t),f3(t)…f n (t)}=MEMD{φ t ,η t ,χ t ,feature high (f),feature low (f)}Formula 2

[0019] Where, {f1(t),f2(t),f3(t)…f n (t)} is multi-source input data; MEMD is the MEMD decomposition algorithm; feature high (f) and feature low (f) shows the high-frequency and low-frequency components of the optimal input features obtained by MEMD decomposition.

[0020] Furthermore, in step S4, the double exponential smoothing (DES) algorithm is used to predict the displacement of the trend item, and its expression is as follows:

[0021]

[0022] Where: Y t+1 for t+1 The trend item displacement prediction value at the moment S t and S t-1 Represent the exponential smoothing values ​​at time t and time t-1 respectively; b t and b t-1 represents the best estimate of the gradient at time t and time t-1; φ tis the trend term displacement; α and γ represent the smoothing factor and the trend factor, respectively. In this application, α is taken as 0.95 and γ is taken as 0.05 according to experience.

[0023] Furthermore, the MIC algorithm described in step S2 is used to preliminarily screen the input features, and its expression is:

[0024]

[0025] Where: x represents each influencing feature; η t represents the landslide displacement; P(x,η t ) is the joint probability density distribution function between the influencing feature and the displacement; P(x) and P(η t ) is the marginal probability density function of the two variables; I(x; η t ) is the mutual information value between variables; p and q are the values ​​of x and η t The number of grid divisions in the direction; B(n) is the grid division constraint, B(n)<n 0.6 ; n is the amount of data; is the normalization factor, and the mutual information I(x; η t ) is normalized to the range [0,1].

[0026] Furthermore, in step S2, the RF model is used to extract the best input features, and its expression is:

[0027]

[0028] Where: ρ(x i ) represents the importance of the i-th feature; ntree represents the number of decision trees in the model; errooB1 t is the out-of-bag error corresponding to the t-th decision tree; errooB2 t is the feature x in the t-th decision tree i The error of the out-of-bag data after adding random noise. When random noise is added, if the error of the out-of-bag data increases, it means that the importance of the feature is greater, thereby quantifying the importance of each feature to the predicted value.

[0029] Furthermore, the weight function expression in step S6 is as follows:

[0030]

[0031] Where: RMSE i is the RMSE corresponding to the predicted value of base model i compared with the measured value; GWO(c) is the regularization parameter variable, GWO(c)∈[0,1], where GWO(c) uses the gray wolf optimization algorithm to minimize RMSE as the objective function and dynamically adjusts the weight. The objective function is as follows:

[0032]

[0033] Where: y k is the measured value of landslide displacement at the kth time step; is the predicted value of landslide displacement of the i-th base model for the k-th time step; N is the total number of data; M is the total number of base models.

[0034] The present application provides a method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition. Its beneficial effects are mainly reflected in the synergistic mechanism of multimodal signal decomposition and dynamic weight fusion strategy, which significantly improves the accuracy, robustness and engineering adaptability of reservoir bank landslide displacement prediction. Compared with the traditional static weighting method, the present application can effectively capture the dynamic evolution characteristics of reservoir bank landslides under the coupling of multiple features such as reservoir water level and rainfall infiltration, and adaptively adjust the model weights to adapt to different working conditions. At the same time, the strategy effectively balances model accuracy and diversity, and dynamically adjusts the model weights with the help of regularized error attenuation function and intelligent optimization algorithm, which not only maintains the dominance of high-precision models, but also retains the differentiated feature contributions of low-precision models through regularization constraints. Compared with fixed weight allocation, the dynamic fusion strategy significantly improves the model's ability to characterize complex mechanical behaviors such as reservoir water level and rainfall infiltration, so that the integrated system can still maintain prediction stability through elastic weight adjustment when encountering extreme climate, while suppressing the risk of overfitting, providing a fusion decision-making framework with both high accuracy and strong generalization for reservoir bank landslide displacement prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of the reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition in this application;

[0036] Figure 2 This is a data graph of cumulative displacement, rainfall, and reservoir water level fluctuation in the embodiment of this application;

[0037] Figure 3 for Figure 2 The predicted result diagram of the cumulative displacement of the monitoring point X-04 using the method of this application; DETAILED DESCRIPTION

[0038] The present application is described in detail below with reference to the accompanying drawings.

[0039] like Figure 1 As shown in the figure, a flow chart of a reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition is proposed, which includes the following steps:

[0040] S1. Data collection and preprocessing: Collect high-precision GNSS historical cumulative monitoring time series data of landslide deformation monitoring points on the reservoir bank in the study area and landslide displacement evolution-induced characteristic data such as rainfall and reservoir water level during the same period, complete data cleaning, and divide the data into training set, validation set, and test set;

[0041] S2. Optimal input feature selection: Based on the displacement evolution law of the reservoir bank landslide, a multi-source heterogeneous feature set is constructed. On this basis, the MIC algorithm is used to preliminarily screen the input features, and then the RF model is used to refine the optimal input features.

[0042] S3. Multi-factor and multi-scale decomposition and reconstruction: Multivariate empirical mode decomposition (MEMD) technology is used to reconstruct the accumulated displacement of the landslide into trend, periodic, and random displacement components, and on this basis, the optimal input features are simultaneously decomposed into high-frequency and low-frequency components;

[0043] S4. Trend item displacement prediction modeling: Use the double exponential smoothing algorithm DES to realize trend item displacement prediction;

[0044] S5. Multi-model parallel prediction of periodic terms and random term displacement: Construct LSSVM, XGBoost, and GRU multi-parallel prediction models to realize periodic terms and random term displacement prediction;

[0045] S6, Multi-model dynamic fusion: A dynamic weighting strategy based on regularized error attenuation is proposed, and the weights are adaptively updated dynamically through the gray wolf optimization algorithm;

[0046] S7, cumulative displacement prediction: Finally, the displacement prediction values ​​of trend item, period item and random item are accumulated to obtain the cumulative displacement prediction result, and the result is obtained by the determination coefficient R 2 The accuracy of the cumulative displacement prediction results is evaluated using the root mean square error (RMSE) indicator.

[0047] In this example, the Xinpu landslide, a typical Three Gorges reservoir bank landslide, was used as the research object. The Xinpu landslide is located in Xinpu Village, Fengjie County, Chongqing, about 158 ​​km away from the Three Gorges Dam. It is a large-scale landslide group in the bedding-micro-cut layer, with a total landslide volume of approximately 3410.8994×10 4 m 3 The landslide complex is narrow at the top and wide at the bottom, with a main sliding direction of approximately 345° and a relative elevation difference of 643.4 meters, resulting in a prominent multi-level terraced landform. The strata primarily consist of the Xujiahe Formation of the Upper Triassic, artificial deposits of the Quaternary, and landslides. The landslide area features a blend of steep and gentle terrain, with steep slopes and sloping edges forming at the front and a slope exceeding 35° at the rear, gradually decreasing to 24°. To capture the deformation patterns of the Xinpu landslide, a real-time monitoring system, including GNSS surface displacement monitoring points and rain gauges, was deployed in key areas of the Xinpu landslide.

[0048] This embodiment selects the monitoring data of the key monitoring point of the Xinpu landslide - X-04 station from January 10, 2020 to January 10, 2024 as the research object, and conducts experimental verification on this application.

[0049] like Figure 2 The figure shows the cumulative displacement, rainfall and reservoir water level data of Xinpu landslide. Figure 2 It can be seen that the displacement curve of Xinpu landslide shows obvious step characteristics, and the step period of each year is from May to September, and the deformation is small in the rest of the year. Figure 2 It can also be seen that rainfall and reservoir water level have a great influence on landslide deformation. From May to September each year, with the continuous rainfall in the rainy season and the sharp drop in reservoir water level, the cumulative displacement of the landslide shows a step-like increase with a certain hysteresis. In other time periods, with the rise of reservoir water level and the decrease of rainfall, the cumulative displacement curve of the landslide tends to be flat. Through the above qualitative analysis, it can be seen that the deformation of the Xinpu landslide is mainly controlled by reservoir water level and rainfall.

[0050] Based on the above analysis, the displacement and deformation data of the monitoring points and the data of rainfall and reservoir water level during the same period are used to carry out the landslide displacement coupling analysis. Taking into account the non-stationarity of the original data, this embodiment preprocesses and standardizes the data and divides the data into training set, validation set and test set.

[0051] Construct a multi-source heterogeneous feature set, including: rainfall factors: such as the average rainfall of the previous n days, the rainfall lagged n days, and the rainfall on the current day; reservoir water level factors: such as the average reservoir water level of the previous n days, the reservoir water level lagged n days, and the reservoir water level on the current day.

[0052] On this basis, the MIC algorithm is used to preliminarily screen the input features, and then the RF model is used to refine the best input features. The final results of the best input features are shown in Table 1:

[0053]

[0054] (Table 1)

[0055] On this basis, the multivariate empirical mode decomposition (MEMD) algorithm is used to reconstruct the accumulated displacement of the landslide into trend term, period term and random term displacement components, and on this basis, the optimal input features are simultaneously decomposed into high-frequency components and low-frequency components.

[0056] Since the displacement of the trend item in this embodiment is mainly controlled by its own geological conditions and thus presents a long-term stable trend, this embodiment adopts the double exponential smoothing (DES) algorithm to realize the prediction of the displacement of the trend item. The specific method is shown in Formula 3.

[0057] In this example, the high-frequency and low-frequency components of the optimal input features are used as input factors for the periodic and random terms, respectively. Based on this, a multi-parallel prediction model consisting of LSSVM, XGBoost, and GRU is constructed to achieve displacement prediction for the periodic and random terms. A dynamic weighting strategy with regularized error attenuation is employed, and model fusion is achieved through the adaptive dynamic weight update method of the Grey Wolf Optimization Algorithm. The weight functions are expressed in Equations 6 and 7.

[0058] Finally, the displacement prediction results of trend term, period term and random term are superimposed to obtain the cumulative displacement prediction result, and the determination coefficient R is calculated based on the actual value of the cumulative displacement and the cumulative displacement prediction value. 2 The accuracy of the cumulative displacement prediction results is evaluated by using indicators such as the root mean square error (RMSE). Figure 3 As shown, this embodiment selects the monitoring data of the Xinpu landslide X-04 monitoring point from January 10, 2020 to January 10, 2024, and uses the reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition proposed in this application to perform displacement prediction. Figure 3 It can be seen that the overall prediction accuracy of the reservoir bank landslide prediction method based on dynamic weight fusion and multimodal decomposition strategy proposed in this application is high. 2 is 0.99 and the RMSE is 1.18 mm.

[0059] In order to verify the superiority of the reservoir bank landslide prediction method based on dynamic weight fusion strategy and multimodal decomposition strategy proposed in this application, the error inverse method and equal weighted average method model fusion methods were selected for comparative experiments.

[0060] Table 2 is a comparison table of the prediction performance of the present application and the comparative method.

[0061]

[0062] (Table 2)

[0063] As shown in Table 2, this application achieves a 36.9% lower RMSE than the equal-weighted average method and a 13.2% lower RMSE than the inverse error method. This is primarily due to the fact that the proposed dynamic weight fusion and multimodal decomposition strategy effectively combines the dynamic feature extraction capabilities of different models under multi-modal coupling, thus overcoming the low prediction accuracy and weak generalization capabilities of traditional single models.

[0064] This application proposes a reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition. Its beneficial effects are mainly reflected in the following points:

[0065] 1. Through the synergistic mechanism of multimodal signal decomposition and dynamic weight fusion strategy, the accuracy, robustness and generalization ability of reservoir bank landslide displacement prediction are significantly improved.

[0066] 2. Compared with the traditional static weighting method, this application can effectively capture the dynamic evolution characteristics of reservoir bank landslides under the coupling of multiple characteristics such as reservoir water level and rainfall infiltration, and adaptively adjust the model weights to adapt to different working conditions. At the same time, this strategy effectively balances model accuracy and diversity, and dynamically adjusts the model weights with the help of regularized error attenuation function and intelligent optimization algorithm, which not only maintains the dominance of high-precision models, but also retains the differentiated feature contributions of low-precision models through regularization constraints.

[0067] 3. Compared with fixed weight allocation, the dynamic fusion strategy significantly improves the model's ability to represent complex mechanical behaviors such as reservoir water level and rainfall infiltration, enabling the integrated system to maintain prediction stability through elastic weight adjustment even when encountering extreme working conditions. At the same time, it suppresses the risk of overfitting and provides a fusion decision-making framework with both high precision and strong generalization for reservoir bank landslide displacement prediction.

[0068] The above description is only a feasible implementation example of the present application, and does not limit the scope of rights of the present application. All equivalent structural changes made using the present application are included in the protection scope of the present application.

Claims

1. A reservoir bank landslide displacement prediction method based on dynamic weight fusion and multimodal decomposition, characterized in that: The following steps are involved: S1. Data collection and preprocessing: Collect high-precision GNSS historical cumulative monitoring time series data of landslide deformation monitoring points on the reservoir bank in the study area and characteristic data of landslide displacement evolution induced by rainfall and reservoir water level during the same period, complete the feature data cleaning, and then divide the feature data into training set, validation set and test set; S2. Optimal input feature selection: Based on the displacement evolution law of the reservoir bank landslide, a multi-source heterogeneous feature set is constructed. On this basis, the MIC algorithm is used to preliminarily screen the input features, and finally the RF model is used to refine the optimal input features. S3. Multi-factor and multi-scale decomposition and reconstruction: The multivariate empirical mode decomposition (MEMD) algorithm is used to reconstruct the accumulated displacement of the landslide into trend, periodic, and random displacement components, and on this basis, the optimal input features are simultaneously decomposed into high-frequency and low-frequency components; S4. Trend item displacement prediction modeling: Use the double exponential smoothing algorithm DES to realize trend item displacement prediction; S5. Multi-model parallel prediction of periodic terms and random term displacement: Construct LSSVM, XGBoost, and GRU multi-parallel prediction models to achieve periodic terms and random term displacement prediction; S6, Multi-model Dynamic Weighted Fusion: A dynamic weighting strategy based on regularized error attenuation is proposed, and the weights are adaptively updated dynamically through the Grey Wolf Optimization Algorithm; S7, cumulative displacement prediction: Finally, the displacement prediction values ​​of trend item, period item and random item are accumulated to obtain the cumulative displacement prediction result, and the result is obtained by the determination coefficient R 2 The accuracy of the cumulative displacement prediction results is evaluated using the root mean square error (RMSE) indicator.

2. The method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition according to claim 1, characterized in that: The expression of the landslide cumulative displacement reconstruction result in step S3 is as follows: D t = φ t + η t + χ t Equation 1 Where: t is the time step; D t is the cumulative displacement; φ t is the trend term displacement; η t is the periodic displacement; t is the random term displacement.

3. The method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition according to claim 1, characterized in that: In step S3, the landslide cumulative displacement is decomposed and reconstructed into trend term, period term and random term displacement components by using the multivariate empirical mode decomposition (MEMD) algorithm. On this basis, the optimal input feature is simultaneously decomposed into high-frequency component and low-frequency component. The expression is: {f1(t), f2(t), f3(t)…f n (t)} = MEMD{φ t , η t , χ t , feature high (f), feature low (f)} Equation 2 Where: {f1(t),f2(t),f3(t)…f n (t)} is multi-source input data; MEMD is the MEMD decomposition algorithm; feature high (f) and feature low (f) shows the high-frequency and low-frequency components of the optimal input features obtained by MEMD decomposition.

4. The method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition according to claim 1, characterized in that: The double exponential smoothing method DES described in step S4 is used to predict the displacement of the trend term, and its expression is as follows: Where Y t+1 is the predicted displacement value of the trend item at time t+1; S t and S t-1 Represent the exponential smoothing values ​​at time t and time t-1 respectively; b t and b t-1 Represents the best estimate of the gradient at time t and time t-1 respectively; φ t is the trend term displacement; α and γ represent the smoothing factor and the trend factor, respectively. In this application, α is taken as 0.95 and γ is taken as 0.05 according to experience.

5. The method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition according to claim 1, characterized in that: The MIC algorithm described in step S2 is used to preliminarily screen the input features, and its expression is: Where: I(x; η t ) is the mutual information value between variables, and x represents each influencing feature; η t represents the landslide displacement; P(x,η t ) is the joint probability density distribution function between the influencing feature and the displacement; P(x) and P(η t ) is the marginal probability density function of the two variables; p and q are the marginal probability density functions of x and η t The number of grid divisions in the direction, B(n) is the grid division constraint, B(n)<n 0.6 , n is the amount of data, log2min(p,q)q is the normalization factor, and the mutual information I(x;η t ) is normalized to the range [0,1].

6. The method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition according to claim 1, characterized in that: The expression for extracting the best input features using the RF model in step S2 is: Where: ρ(x i ) represents the importance of the i-th feature; ntree represents the number of decision trees in the model; errooB1 t is the out-of-bag error corresponding to the t-th decision tree; errooB2 t is the feature x in the t-th decision tree i The error of the out-of-bag data after adding random noise. When random noise is added, if the error of the out-of-bag data increases, it means that the importance of the feature is greater, thereby quantifying the importance of each feature to the predicted value.

7. The method for predicting reservoir bank landslide displacement based on dynamic weight fusion and multimodal decomposition according to claim 1, characterized in that: The weight function expression in step S6 is as follows: Where: RMSE i is the RMSE corresponding to the predicted value of base model i compared with the measured value; GWO(c) is the regularization parameter variable, GWO(c)∈[0,1], where GWO(c) uses the gray wolf optimization algorithm to minimize RMSE as the objective function and dynamically adjusts the weight. The objective function is as follows: Where: y k is the measured value of landslide displacement at the kth time step; is the predicted value of landslide displacement of the i-th base model for the k-th time step; N is the total number of data; M is the total number of base models.

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