Displacement prediction method for step-type landslide based on VMD-Mamba algorithm

Abstract

This paper discloses a method for predicting step-type landslide displacement based on the VMD-Mamba algorithm. This method includes constructing a dataset within a region, performing variational mode decomposition (VMD), predicting periodic displacement components, and superimposing and evaluating these components for accuracy. Based on the Mamba model, the method constructs unit prediction models and multivariate prediction models for different displacement components, improving the accuracy of cumulative landslide displacement prediction.

Description

Technical Field

[0001] The invention relates to a landslide displacement prediction method, in particular to a step-type landslide displacement prediction method based on a VMD-Mamba algorithm, and belongs to the technical field of geological disaster prevention and control. Background Art

[0002] Landslides, a complex and common natural geological hazard, are widespread and devastating worldwide, causing significant harm and damage to humans and their environment. In China, particularly due to its numerous mountainous areas and complex terrain, landslides are frequent and have far-reaching consequences, making them one of the country's most serious geological hazards. In recent years, with the acceleration of urbanization and the impact of climate change, the frequency and destructive power of landslides have increased, posing a significant threat to the safety of life and property and economic development.

[0003] However, due to the complexity of landslide formation mechanisms and inducing factors, predicting landslide displacement remains a daunting task. For example, the Bazimen landslide in the Three Gorges Reservoir area exhibits a step-like deformation pattern over time, influenced by both its own internal control conditions and multiple external inducing factors. This deformation curve increases dramatically during the rainy season, making landslide deformation prediction more difficult. Directly predicting this sudden, step-like displacement curve presents significant model fitting challenges, resulting in poor prediction results for step-like landslides. Therefore, when dealing with step-like landslides like those in the Three Gorges area, where multiple inducing factors exist, utilizing existing monitoring data to accurately predict landslide displacement remains a thorny issue.

[0004] In the prior art, patent publication number CN113111573B discloses a GRU-based landslide displacement prediction method. This method monitors landslide surface displacement deformation and calculates replacement values ​​for outliers in the resulting landslide displacement data using a constructed polynomial model. All landslide displacement data replaced with the replacement values ​​is mean-normalized, and a GRU model and training, validation, and test sets are constructed. The GRU model is iterated using the training set, and the trained GRU model parameters are adjusted using the validation set. The adjusted GRU model is tested using the test set, and the resulting model prediction results are inversely mean-normalized to complete landslide displacement prediction and improve prediction accuracy. However, in the prior art, prediction models based on recurrent neural networks, with gated recurrent units (GRUs) and long short-term memory networks (LSTMs) being the most widely used, can suffer from vanishing or exploding gradients, making it difficult for the model to capture long-range dependencies. At the same time, while LSTM and GRU can handle nonlinear relationships, their modeling capabilities are limited in complex and highly nonlinear sequence data, resulting in poor prediction results. Furthermore, in the field of step-type landslide prediction, improving the accuracy of landslide prediction models requires a suitable landslide displacement decomposition algorithm. However, traditional landslide displacement decomposition algorithms, such as sliding average, HP filtering, and empirical mode decomposition, have various drawbacks. Summary of the Invention

[0005] The purpose of the present invention is to provide a step-type landslide displacement prediction method based on the VMD-Mamba algorithm in order to solve at least one of the above technical problems. This method is based on the combination of the variational mode decomposition algorithm and the Mamba model framework. The prediction results are more accurate and reliable than the current mainstream landslide prediction models. The model structure is simple and the computational complexity is low. It has great practical value and can improve the accuracy and timeliness of landslide displacement prediction.

[0006] The present invention achieves the above-mentioned object through the following technical solution: a step-type landslide displacement prediction method based on the VMD-Mamba algorithm, the step-type landslide displacement prediction method comprising the following steps:

[0007] Step 1: constructing a data set within the same area: the data set includes a landslide displacement monitoring data set and a landslide influencing factor data set, and preprocessing the landslide displacement monitoring data set and the landslide influencing factor data set to obtain a landslide prediction data set within the area;

[0008] Step 2, variational mode decomposition: selecting the landslide displacement monitoring data set in the landslide prediction data set, and decomposing the accumulated landslide displacement into a trend term displacement component and a period term displacement component by using a variational mode decomposition algorithm;

[0009] Step 3: Predicting the displacement component of the trend item: Based on the trend characteristics of the displacement component of the trend item obtained by variational mode decomposition, a Mamba-trend item prediction model is constructed. The Mamba-trend item prediction model is a unit prediction model. The trend item displacement component of the trend item of the next three days is predicted based on the displacement component of the trend item of the previous five days to obtain the predicted value of the displacement component of the trend item;

[0010] Step 4: Prediction of periodic displacement components: Select a data set of landslide influencing factors from the landslide prediction data set, screen out the most relevant factor set affecting landslide displacement through grey correlation analysis, and construct a Mamba-periodic displacement prediction model based on the trend characteristics of the periodic displacement components obtained by variational modal decomposition. The Mamba-periodic displacement prediction model is a multivariate model that predicts the periodic displacement components for the next three days based on the most relevant factor set and the periodic displacement components of the previous five days to obtain the predicted value of the periodic displacement components.

[0011] Step 5. Superposition of prediction components and evaluation of prediction accuracy: The predicted value of the trend term displacement component is superimposed with the predicted value of the period term displacement component to obtain the cumulative landslide displacement prediction value. The comprehensive prediction ability of the landslide displacement prediction model is evaluated by calculating the root mean square error, mean absolute error, mean absolute percentage error and determination coefficient, and the accuracy of the prediction results is analyzed and evaluated.

[0012] As a further technical solution of the present invention: in the step 1, the landslide displacement monitoring data set is constructed in units of days for training and validating the landslide displacement prediction model;

[0013] The landslide influencing factor dataset includes all relevant inducing factors in the region, including but not limited to topography, hydrogeological conditions, rainfall, reservoir water level changes, surface porosity changes and human engineering activities.

[0014] As a further technical solution of the present invention: in the step 1, the preprocessing of the landslide displacement monitoring data set includes monitoring outliers and processing missing values ​​on the data set and normalizing the data set, including the following steps:

[0015] A. Preprocess the dataset by removing outliers and filling in missing values, and then normalize it to between 0 and 1 to eliminate the impact of different dimensions on model training;

[0016] B. The landslide displacement monitoring dataset is divided into the ratio of 7:2:1, that is, the first 70% of the dataset is used as the training set of the model, the subsequent 20% is used as the validation set of the model, and finally 10% of the dataset is retained as the test set of the model.

[0017] As a further technical solution of the present invention: in step 2, the variational mode decomposition algorithm specifically includes:

[0018] 1) Decompose the landslide displacement time series into multiple IMFs, each of which represents an oscillation mode with different frequency components, where IMF is the intrinsic mode function;

[0019] 2) Through recursive iterative algorithms, each IMF is gradually optimized to achieve input signal decomposition;

[0020] 3) Combine the decomposed IMFs to extract the components representing trend displacement T and periodic displacement P, thereby achieving data noise reduction and feature extraction.

[0021] As a further technical solution of the present invention: decomposing the input signal into a plurality of IMFs, each IMF corresponding to a center frequency;

[0022] The center frequency calculation is to update the center frequency and bandwidth of each IMF in each iteration so that each IMF is concentrated in the frequency domain.

[0023] As a further technical solution of the present invention: the Mamba-trend item prediction model in step 3 and the Mamba-period item prediction model in step 4 together constitute a Mamba model, and the Mamba model includes a state space model, a dynamic selection mechanism, and a hardware perception architecture;

[0024] The state space model is used to capture and model long-term dependencies in time series data. The state space model represents the evolution of the time series as a sequence of hidden states through a state transition and observation mechanism.

[0025] The dynamic selection mechanism inputs parameterized state-space model parameters, enabling the state-space model to filter out irrelevant information and remember relevant information indefinitely, thus achieving selective replication and sensor head synthesis tasks;

[0026] The hardware-aware architecture uses scans to loop through the computation model but does not implement extended state to avoid IO accesses between different levels of the GPU memory hierarchy, thereby achieving faster inference and linear scaling to longer sequence lengths.

[0027] As a further technical solution of the present invention: in step 4, the grey relational analysis specifically includes:

[0028] The influence of the influencing factors on the landslide is judged by grey correlation analysis. The larger the correlation influence factor, the more important the influencing factor is for predicting the landslide displacement; the smaller the correlation influence factor, the less important the influencing factor is for predicting the landslide displacement.

[0029] The beneficial effects of the present invention are:

[0030] 1) The variational mode decomposition algorithm adopted in this paper is a new signal decomposition method proposed based on empirical mode decomposition (EMD). It can handle nonlinear and non-stationary signals. Compared with traditional EMD, it avoids the problem of modal aliasing and the decomposition result is more accurate. The variational mode decomposition algorithm decomposes the sub-signals with limited frequency bands to ensure the frequency distribution of each mode is concentrated, thereby enhancing the ability to capture the local characteristics of the signal. At the same time, the variational mode decomposition algorithm can effectively handle noise interference and introduce constraints by Lagrange multipliers to ensure the stability and robustness of signal decomposition. Compared with linear filtering methods such as sliding average and HP filtering, VMD can decompose multiple intrinsic mode functions (IMFs) in the signal, revealing richer signal characteristics.

[0031] 2) The Mamba model used in this paper is a structured state-space sequence model with a selection mechanism and a scanning module. It has stronger data feature extraction and memory capabilities, and can fully learn and describe landslide displacement components with different characteristics. Compared with models such as LSTM and Transformer, the Mamba model shows higher fit and prediction performance in learning short-term landslide data, especially when dealing with the complex local changes in landslide characteristics. It also outperforms traditional LSTM and GRU models in terms of computational efficiency and prediction accuracy.

[0032] 3) Since the influencing factors of different periodic displacement components and trend displacement components are different, the present invention constructs a unit prediction model and a multivariate prediction model for different displacement components based on the Mamba model, which further improves the prediction accuracy of the landslide cumulative displacement. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the process structure of the present invention. DETAILED DESCRIPTION

[0034] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0035] Example 1, as Figure 1 As shown, this embodiment provides a step-type landslide displacement prediction method based on the VMD-Mamba algorithm, and the step-type landslide displacement prediction method specifically includes the following steps:

[0036] S1: Construct a dataset within the same region.

[0037] The dataset includes a landslide displacement monitoring dataset and a landslide influencing factor dataset within the same area. The landslide displacement monitoring dataset is the most representative and typical displacement monitoring point data selected from the area (i.e., the target area). The landslide influencing factor dataset collects data on factors affecting landslides, such as reservoir water level and rainfall, within the target area.

[0038] The landslide displacement monitoring dataset is constructed on a daily basis and is mainly used for training and validating landslide displacement prediction models. The landslide influencing factor dataset needs to collect all relevant inducing factors in the target area, including but not limited to topography, hydrogeology, rainfall, reservoir water level changes, surface porosity changes, and human engineering activities.

[0039] The landslide displacement monitoring dataset and landslide influencing factor dataset are preprocessed to obtain the landslide prediction dataset in the target area.

[0040] The landslide displacement monitoring dataset is divided into a target dataset and a label dataset. The preprocessing of the landslide displacement monitoring dataset includes outlier monitoring, missing value processing, and normalization of the target dataset and the label dataset. The specific steps include:

[0041] 1) Preprocess the target dataset and the label dataset by handling outliers and filling missing values, and then normalize the target dataset and the label dataset to between 0 and 1 to eliminate the impact of different dimensions on model training;

[0042] 2) The landslide displacement monitoring dataset is divided into 7:2:1 ratios, where the first 70% of the dataset is used as the training set for the model, the middle 20% is used as the validation set for the model, and the last 10% of the dataset is retained as the test set for the model.

[0043] It should be noted that the dataset used is from the Bazimen landslide in the Three Gorges Reservoir area, where the target dataset is the landslide displacement monitoring dataset of the monitoring point GSCX3, and the label dataset is the reservoir water level and rainfall daily record dataset.

[0044] S2: Variational Mode Decomposition (VMD).

[0045] The landslide displacement monitoring dataset in the landslide prediction dataset is selected, and the cumulative landslide displacement is decomposed into trend term displacement component and period term displacement component by using the variational mode decomposition (VMD) algorithm.

[0046] The variational mode decomposition algorithm specifically includes the following steps:

[0047] 1) Due to the complexity of the landslide displacement time series, the landslide displacement time series is decomposed into multiple intrinsic mode functions (IMFs), each of which represents an oscillation mode with different frequency components;

[0048] 2) Through a recursive iterative algorithm, each intrinsic mode function is gradually optimized to make it physically meaningful, thereby achieving input signal decomposition and ultimately achieving optimal decomposition of the input signal;

[0049] 3) Combine the decomposed IMFs to extract the components representing trend displacement T and periodic displacement P, thereby achieving data noise reduction and feature extraction.

[0050] It should be noted here that the decomposition of the input signal is optimized through a recursive iterative algorithm, that is, the input signal is decomposed into several intrinsic mode functions (IMFs), each IMF corresponds to a center frequency; since each part of the input signal has a clear separation in the frequency domain, the different frequency components in the input signal can be effectively decomposed; the calculation of the center frequency is to update the center frequency and bandwidth of each IMF in each iteration step, so that each IMF is as concentrated as possible in the frequency domain.

[0051] Variational modal decomposition is modal reconstruction. Through optimization, each IMF has good interpretability in both the time and frequency domains, so that the reconstructed mode can truly reflect the characteristics of the original signal (input signal). In addition, the parameters of variational modal decomposition are appropriately selected according to the specific changes in the cumulative displacement curve and the optuna parameter optimization framework.

[0052] S3: Prediction of the displacement component of the trend term.

[0053] Based on the trend characteristics of the displacement component of the trend term obtained by variational mode decomposition, a Mamba-trend term prediction model is constructed; among them, the Mamba-trend term prediction model is a unit prediction model, which predicts the trend term prediction value of the next three days based on the displacement component of the trend term of the previous five days to obtain the predicted value of the trend term displacement component.

[0054] S4: Prediction of the displacement component of the periodic term.

[0055] A landslide influencing factor dataset was selected from the landslide prediction dataset. The most relevant factor set influencing landslide displacement was screened out through grey correlation analysis (the purpose is to eliminate unnecessary factors and reduce the difficulty of model training). The trend characteristics of the periodic displacement component were obtained based on variational mode decomposition, and a Mamba-periodic term prediction model was constructed. Among them, the Mamba-periodic term prediction model is a multivariate model. Based on the most relevant factor set and the periodic displacement component of the previous five days, the periodic displacement component of the next three days is predicted to obtain the predicted value of the periodic displacement component.

[0056] Grey correlation analysis is used to determine the influence of factors in the landslide influencing factor dataset on landslides. A larger correlation factor indicates a more important factor for predicting landslide displacement, while a smaller correlation factor indicates a less important factor for predicting landslide displacement. In this example, factors with a correlation less than 0.6 are excluded, and the remaining factors are constructed as the most relevant factor set.

[0057] The Mamba-trend item prediction model in step S3 and the Mamba-period item prediction model in step S4 together constitute a Mamba model, which includes a state space model, a dynamic selection mechanism, and a hardware-aware architecture.

[0058] Among them, the state-space model (SSM) is used to capture and model long-term dependencies in time series data. The SSM represents the evolution of the time series as a sequence of hidden states through a state transition and observation mechanism. The state-space model can not only effectively process long-sequence data, but also has significant advantages in capturing dynamic changes in the data. Specifically, the state-space model maps the input sequence to a series of state vectors and makes predictions based on the state transition matrix and output matrix. This enables the state-space model to accurately predict future sequences while maintaining long-term memory.

[0059] The dynamic selection mechanism enables the state-space model to filter out irrelevant information and remember relevant information indefinitely through SSM parameters parameterized according to the input, achieving important synthesis tasks such as selective copying and sensing head.

[0060] The hardware-aware architecture uses scans instead of convolutions to circulate the computation model, but does not implement extended state to avoid IO accesses between different levels of the GPU memory hierarchy, thereby achieving faster inference and linear scalability with longer sequence lengths.

[0061] S5: Superposition of prediction components and evaluation of prediction accuracy.

[0062] The predicted value of the displacement component of the trend term is superimposed with the predicted value of the displacement component of the period term to obtain the predicted value of the cumulative landslide displacement, and the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R 2 ), evaluate the comprehensive prediction ability of the prediction model, and analyze and evaluate the accuracy of the prediction results.

[0063] In Example 2, two comparative examples (an LSTM method based on a recurrent neural network and a state-of-the-art Transformer method based on a self-attention mechanism) are compared with the present invention's step-type landslide displacement prediction method based on the VMD-Mamba algorithm. To verify the generalization performance of this method, the GSCX5 monitoring dataset from the Bazimen landslide monitoring site in the Three Gorges Reservoir area is added as a generalization performance validation dataset.

[0064]

[0065]

[0066] It can be seen from Table 1 and Table 2 that the experimental results of the present invention and other landslide prediction methods on the monitoring points GSCX3 and GSCX5 of the Bajimen landslide in the Three Gorges Reservoir area are compared, and the performance of the method in predicting step-type landslides and stage-by-stage sudden displacement differences is evaluated. In general, the R2 of the displacement prediction results of the two monitoring points of the present invention reached above 0.97, and its average RMSE and R2 were improved by 112% and 2.43% compared with the other two prediction models. At the same time, the generalization performance of the model is also better than the other two models, and the average RMSE and R2 are 35.44% and 2.79% higher than the best advanced method "Transformer". It is worth noting that the present invention achieved the best accuracy in all three days of prediction, which is significantly better than other advanced methods. The results show that the method proposed by the present invention is an effective improvement of the existing step-type landslide prediction method, and verify that the method proposed by the present invention has stronger feature learning ability and prediction ability.

[0067] Working Principle: Given the extremely complex influencing factors and displacement processes of step-type landslides, the variational mode decomposition (VMD) algorithm is used to decompose the cumulative landslide displacement into trend-term and period-term landslide displacement. Mamaba-trend-term prediction models and Mamba-periodic-term prediction models are constructed to fit and predict the displacement components. Grey correlation analysis is used to screen influencing factors and select appropriate influencing factors as the influencing factor set for the periodic-term model, thereby reducing the complexity and computational difficulty of model fitting. A step-type landslide displacement prediction model combining the VMD algorithm and the Mamba model is constructed, and the prediction results are analyzed and evaluated for accuracy.

[0068] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0069] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A step-type landslide displacement prediction method based on VMD-Mamba algorithm, characterized in that: The step-type landslide displacement prediction method comprises the following steps: Step 1: constructing a data set within the same area: the data set includes a landslide displacement monitoring data set and a landslide influencing factor data set, and preprocessing the landslide displacement monitoring data set and the landslide influencing factor data set to obtain a landslide prediction data set within the area; Step 2, variational mode decomposition: selecting the landslide displacement monitoring data set in the landslide prediction data set, and decomposing the accumulated landslide displacement into a trend term displacement component and a period term displacement component by using a variational mode decomposition algorithm; Step 3: Predicting the displacement component of the trend item: Based on the trend characteristics of the displacement component of the trend item obtained by variational mode decomposition, a Mamba-trend item prediction model is constructed. The Mamba-trend item prediction model is a multivariate prediction model. The trend item displacement component of the trend item of the next three days is predicted based on the displacement component of the trend item of the previous five days to obtain the predicted value of the displacement component of the trend item; Step 4: Prediction of periodic displacement components: Select a data set of landslide influencing factors from the landslide prediction data set, screen out the most relevant factor set affecting landslide displacement through grey correlation analysis, and construct a Mamba-periodic displacement prediction model based on the trend characteristics of the periodic displacement components obtained by variational modal decomposition. The Mamba-periodic displacement prediction model is a unit model that predicts the periodic displacement components for the next three days based on the most relevant factor set and the periodic displacement components of the previous five days to obtain the predicted value of the periodic displacement components. Step 5. Superposition of prediction components and evaluation of prediction accuracy: The predicted value of the trend term displacement component is superimposed with the predicted value of the period term displacement component to obtain the cumulative landslide displacement prediction value. The comprehensive prediction ability of the landslide displacement prediction model is evaluated by calculating the root mean square error, mean absolute error, mean absolute percentage error and determination coefficient, and the accuracy of the prediction results is analyzed and evaluated.

2. The step-type landslide displacement prediction method according to claim 1, characterized in that: In the step 1, the landslide displacement monitoring data set is constructed in days for training and validating the landslide displacement prediction model; The landslide influencing factor dataset includes all relevant inducing factors in the region, including but not limited to topography, hydrogeological conditions, rainfall, reservoir water level changes, surface porosity changes and human engineering activities.

3. The step-type landslide displacement prediction method according to claim 1, characterized in that: In the step 1, the landslide displacement monitoring data set is preprocessed, including monitoring outliers and processing missing values ​​on the data set, and normalizing the data set, including the following steps: A. Preprocess the dataset by removing outliers and filling in missing values, and then normalize it to between 0 and 1 to eliminate the impact of different dimensions on model training; B. The landslide displacement monitoring dataset is divided into the ratio of 7:2:1, that is, the first 70% of the dataset is used as the training set of the model, the subsequent 20% is used as the validation set of the model, and finally 10% of the dataset is retained as the test set of the model.

4. The method for predicting step-type landslide displacement according to claim 1, wherein: In the second step, the variational mode decomposition algorithm specifically includes: 1) Decompose the landslide displacement time series into multiple IMFs, each of which represents an oscillation mode with different frequency components, where IMF is the intrinsic mode function; 2) Through recursive iterative algorithms, each IMF is gradually optimized to achieve input signal decomposition; 3) Combine the decomposed IMFs to extract the components representing trend displacement T and periodic displacement P, thereby achieving data noise reduction and feature extraction.

5. The method for predicting step-type landslide displacement according to claim 4, characterized in that: Decompose the input signal into several IMFs, each of which corresponds to a center frequency; The center frequency calculation is to update the center frequency and bandwidth of each IMF in each iteration so that each IMF is concentrated in the frequency domain.

6. The method for predicting step-type landslide displacement according to claim 1, characterized in that: The Mamba-trend item prediction model in step 3 and the Mamba-period item prediction model in step 4 together constitute a Mamba model, which includes a state space model, a dynamic selection mechanism, and a hardware-aware architecture; The state space model is used to capture and model long-term dependencies in time series data. The state space model represents the evolution of the time series as a sequence of hidden states through a state transition and observation mechanism. The dynamic selection mechanism inputs parameterized state-space model parameters, enabling the state-space model to filter out irrelevant information and remember relevant information indefinitely, thus achieving selective replication and sensor head synthesis tasks; The hardware-aware architecture uses scans to loop through the computation model but does not implement extended state to avoid IO accesses between different levels of the GPU memory hierarchy, thereby achieving faster inference and linear scaling to longer sequence lengths.

7. The method for predicting step-type landslide displacement according to claim 1, characterized in that: In the fourth step, the grey relational analysis specifically includes: The influence of the influencing factors on the landslide is judged by grey correlation analysis. The larger the correlation influence factor, the more important the influencing factor is for predicting the landslide displacement; the smaller the correlation influence factor, the less important the influencing factor is for predicting the landslide displacement.

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