Steep slope stability prediction method and system based on manifold graph convolutional network

Abstract

The invention relates to a steep slope stability prediction method and system based on a manifold graph convolutional network, and belongs to the technical field of geological disaster monitoring and prediction. The method comprises the following steps: data acquisition and preprocessing; constructing a graph structure fused with multivariate features; constructing a manifold graph convolutional neural network model; model training; predicting the surface displacement of the steep slope; and according to the predicted earth surface displacement result, steep slope stability evaluation is carried out. The real-time state of the slope is reflected by integrating multi-source data such as geology and terrain; through multi-dimensional data fusion, key factors are captured, and prediction comprehensiveness and accuracy are improved. The method comprises the following steps: constructing a graph structure fusing multivariate features, and deeply mining spatial correlation and time dynamic change by using a manifold graph convolutional network and a Shenchang differential equation to realize deep fusion of spatio-temporal features. The model has good adaptability to slight deformation and complex geological conditions, has high robustness, and can be suitable for monitoring different types of slopes.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological disaster monitoring and prediction, and particularly relates to a method and system for predicting the stability of steep slopes based on a manifold graph convolutional network. Background Technique

[0002] With the global climate change, extreme weather events are becoming increasingly frequent, and natural disasters such as heavy rain and earthquakes have significantly increased the risk of slope collapses, especially in areas with complex terrain and steep slopes. Traditional slope stability prediction methods often ignore the dynamic changes of the terrain, are unable to accurately capture the potential risks during the slope deformation process, and have limited capabilities in processing real-time data. In recent years, monitoring slope deformation based on remote sensing technologies (such as synthetic aperture radar interferometry, InSAR) has become a popular research direction, but most existing methods are based on static terrain models and lack full utilization of the dynamic characteristics of the terrain. Therefore, there is an urgent need for an intelligent prediction system that can effectively combine multi-dimensional data to predict slope stability in real time, so as to improve the prevention and control capabilities of slope disasters.

[0003] Due to the scarcity and difficulty in obtaining historical accident data of landslides or collapses, the limitations of traditional machine learning methods in the training set are evident. For this reason, our method does not rely entirely on historical accident data, but is based on InSAR data and combines multi-dimensional data such as geology, terrain, and meteorology to detect the continuous changes of slopes in real time. By treating these changes as time series, the system can predict the deformation trend of slopes, thereby inferring potential accident risks. This method not only solves the problem of data scarcity but also improves the prediction accuracy, providing a new solution for effectively preventing and controlling slope disasters. Summary of the Invention

[0004] In order to solve the above problems, the present invention provides a method and system for predicting the stability of steep slopes based on a manifold graph convolutional network.

[0005] To achieve the above object, the present invention is realized through the following technical solutions: The present invention provides a method for predicting the stability of steep slopes based on a manifold graph convolutional network, including the following steps: S1. Data collection and preprocessing: Collect steep slope data, including InSAR data I, geological data G, terrain data T, environmental data E, mechanical data M, and manual monitoring data D, and preprocess the data to obtain preprocessed steep slope data, which is divided into a test set and a training set; S2. Construct a graph structure that fuses multiple features: Use the preprocessed InSAR data I as nodes in the graph, and establish edges between nodes according to spatial distance and slope difference to obtain a graph structure The graph structure includes the feature vectors of each node The adjacency matrix corresponding to the edges between nodes ; S3. Constructing a manifold graph convolutional neural network model: The manifold graph convolutional neural network model includes graph convolutional neural network and neural ordinary differential equation. The feature vector of the node at time and The adjacency matrix corresponding to the edges between nodes at the moment The spatial features of the steep slope are extracted by inputting into the graph convolutional neural network to obtain the potential information representation of the steep slope. , the steep slope of the latent information indicates The input is fed into the Godly ordinary differential equation for time dynamic modeling to obtain the predicted surface displacement of the steep slope; S4. Model training: The model is trained using mean square error as the loss function to obtain a trained model; S5. Prediction of surface displacement on steep slopes: The data in the test set are input into the trained model to obtain the predicted surface displacement; S6. Conduct steep slope stability assessment based on the predicted surface displacement results.

[0006] Furthermore, step S1 specifically includes: S11. The InSAR data I includes the longitude, latitude and altitude coordinates of the surface displacement information of each steep slope; the geological data G includes the rock type GLT, the layer direction GSD and the groundwater level GWL; the terrain data T includes the steep slope gradient TSL, the slope aspect TAS, the height THG and the length TLG; the environmental data E includes the rainfall ERP, the temperature ETP, the humidity EHM and the wind speed EWS; the mechanical data M includes the gravity MDN, the shear strength MSS, the elastic modulus MEM, the stress distribution MSD and the deformation MDF of the slope; the artificial monitoring data D includes the surface displacement DSD, the underground displacement DUD and the crack development DCF; S12. Eliminate the abnormal values ​​in the data of step S11. When is an abnormal value, when When is an outlier; Indicates the variable value to be tested. represents the first quartile of the data, represents the third quartile of the data, represents the interquartile range, ; S13. Normalize the data after removing outliers. The formula is as follows: , Among them, represents the data after normalization, represents the minimum value of the variable, represents the maximum value of the variable; S14. Perform format conversion and cleaning on the normalized steep slope data, specifically: S141. The InSAR data I undergoes a conversion from phase to displacement, converting the phase information of the radar wave into surface displacement data, and at the same time unifying the surface displacement data into the longitude and latitude format of coordinate points. The formula is expressed as follows: , Among them, represents the surface displacement of the th InSAR point, represents the wavelength of the radar signal, represents the phase change amount of the th detection point; S142. Convert the rock type GLT in the geological data G into a numerical code. By establishing a mapping function, the rock type is converted into an integer label. The formula is expressed as follows: , Among them, represents the mapping function, represents the result after numericalization of the rock type GLT. The dip and dip angle of the bedding direction GSD in the geological data G are converted into the form of a unit vector to obtain the unit vector in three-dimensional space. The formula is expressed as follows: , Among them, , , respectively represent the x, y, and z components after converting the dip θ and dip angle α of the bedding direction into a three-dimensional space unit vector, which are used to represent the spatial orientation of the rock layer in the three-dimensional coordinate system in the subsequent model; Express the groundwater level as a function related to space and time, defined as: Among them, represents time, represents the geographical coordinates, represents the position at the moment of the groundwater level elevation, represents the groundwater level elevation at the initial moment . and represent rainfall intensity and evapotranspiration respectively, represents specific yield or hydraulic conductivity, represents the integration variable; if the water table depth needs to be evaluated, , the surface elevation and the water table elevation are used to represent the groundwater depth, so as to evaluate the influence of groundwater on slope stability or pore water pressure change in subsequent analysis; after discretizing these continuous forms in the data structure, the standardized geological data is finally obtained, and the formula is as follows: wherein, is the th geographical coordinate of the record, represents the numerical coding of rock types, are the three-dimensional unit vector components in the bedding direction respectively, represents the water table value obtained by monitoring or interpolation, is the total number of geological data records; S143. Process the slope TSL, height THG, and aspect TAS in the terrain data T, and the formula is as follows: , , , wherein, represents the slope angle, represents the altitude, and represent the lowest and highest altitudes in the study area respectively, represents the aspect azimuth, represents the processed slope, represents the processed height, represents the processed aspect; combine the processed slope, height, and aspect data with the spatial coordinates to form a unified terrain data format, and the standardized terrain data is finally obtained, and the formula is as follows: , wherein, is the abscissa and ordinate of the spatial coordinates of the th terrain sampling point, which is used to locate the specific position of this point in the study area. The spatial coordinates are provided by the digital elevation model DEM of the study area, remote sensing mapping, or the sampling point positions obtained by ground measurement; represents the total number of terrain sampling points; S144. Organize the environmental data E into a time series format, align the data in time, and unify it to the same time interval. Through the unified conversion of the time format, unit, and data type of the environmental data, standardized environmental data is formed. : , Among them, represents the timestamp corresponding to the environmental data; respectively represent the rainfall, temperature, humidity, and wind speed corresponding to the time ; represents the number of environmental data records; S145. Associate the mechanical data M with the spatial position, unify it into a standard format, and form structured mechanical data , and the formula is as follows: , Among them, represents the spatial position coordinates corresponding to the mechanical data, and the coordinates are determined by mapping the mechanical measurement points to the spatial positions corresponding to the InSAR data; respectively represent the specific gravity, shear strength, elastic modulus, stress distribution, and deformation conditions of the slope corresponding to the spatial position coordinates ; represents the number of mechanical data records; S146. After format conversion and structure unification of the manual monitoring data D, organize it into multi-dimensional manual monitoring data of time and space , and the formula is as follows: , Among them, represents the timestamp corresponding to the manual monitoring data, respectively represent the abscissa and ordinate of the geographical coordinates of the sensor, respectively represent the surface displacement, underground displacement, and crack development conditions corresponding to the time and position; represents the number of manual detection data; Finally, the feature vector representation of the model input is obtained through the above processing , and the formula is as follows: , Among them, respectively represent the surface displacement, numerical encoding of the rock type, x, y, z components of the three-dimensional unit vector in the layer direction, and groundwater level value corresponding to the th InSAR point; respectively represent the processed slope, height, and slope direction corresponding to the th InSAR point; respectively represent the Precipitation, temperature, humidity, and wind speed corresponding to each InSAR point; respectively represent the severity, shear strength, elastic modulus, stress distribution, and deformation of the slope corresponding to each InSAR point; respectively represent the surface displacement, underground displacement, and crack development corresponding to each InSAR point.

[0007] Furthermore, step S2 specifically includes: S21. Take each InSAR point as a node in the graph, and the feature vector of the corresponding node is ; S22. Establish edges between nodes based on spatial distance and slope difference. The formula is as follows: , , , where represents the edge weight between node and node , represents the Euclidean distance, represents the distance scale parameter, represents the slope difference scale parameter, represents the spatial distance weight, represents the slope difference weight; when exceeds the set threshold , establish an edge between node and ; S23. Construct a complete graph structure , and the formula is as follows: , , , where represents the set of nodes, represents the set of edges, represents the total number of InSAR points, represents the edge between node and , represents the edge weight threshold; further obtain the adjacency matrix , and the formula is as follows: , where Indicates a node and The adjacency matrix between them.

[0008] Furthermore, the threshold in step S22 is determined comprehensively according to the spatial scale of the research area, the density of monitoring points, and the experimental verification results. Specifically, it is set as follows: an empirical value is given based on prior knowledge, or all are sorted and the top several percentiles are selected as the threshold.

[0009] Furthermore, step S3 specifically includes: S31. Spatial feature extraction based on graph convolutional neural network: Perform multi-layer graph convolutional operations in the graph convolutional neural network. The feature extraction formula for the layer is expressed as follows: , , , , where represents the node representation of the layer. The initial layer , represents the symmetrically normalized adjacency matrix, represents the degree matrix, represents the adjacency relationship weight between node and node at time , that is, the element in the row and column of the adjacency matrix , represents the node representation of the layer, represents the trainable weight matrix of the layer, represents the ReLU activation function. When , , when , ; After multi-layer graph convolutional operations, the potential information representation of the steep slope is finally obtained; S32. Temporal dynamics modeling based on neural ordinary differential equations: The ordinary differential equation formula for the temporal evolution of the slope state is expressed as follows: , where represents the hidden state of the slope at time , Represents a parameterized dynamic function, represents the trainable parameters; using the Runge-Kutta method, calculate the evolution of the ramp state from time to as follows: , where, represents the hidden state of the ramp at the future time , represents the dynamic function of the ramp state changing with time, represents the hidden state of the ramp at time , is the integration variable, representing time, , integrating from the current time to the future time ; the hidden state of the ramp at the future time is linearly mapped to obtain the predicted ground surface displacement as follows: , where, represents the hidden state vector of node at time , represents the trainable weight matrix in the linear mapping process, represents the bias vector in the linear mapping process, represents the ReLU activation function.

[0010] Furthermore, step S4 specifically includes: Using the mean square error as the loss function, which is expressed as follows: , where, represents the total number of nodes, represents the ground surface displacement of node predicted by the model at the future time , represents the actual observed ground surface displacement of node .

[0011] Furthermore, step S6 specifically includes: According to the predicted value of the ground surface displacement of node at time , compare it with the observed value at the previous time or the reference time, and calculate the displacement rate, which is expressed as follows: , Among them, represents the displacement rate of the node at time . The displacement rate, represents the predicted surface displacement value of the node at this moment by the model. is the measured displacement at the previous moment or the reference moment . If and the difference is larger, it indicates that the displacement increment of the node in this time period is larger, indicating that the slope has a higher risk of instability; by comparing the displacement rates of different nodes, local high-displacement-rate areas can also be identified, providing a scientific basis for slope monitoring and disaster warning.

[0012] The present invention also provides a steep slope stability prediction system based on a manifold graph convolutional network, which executes the above-mentioned steep slope stability prediction method based on a manifold graph convolutional network, including: Data acquisition and preprocessing module: used to collect steep slope data, including InSAR data, geological data, terrain data, environmental data, mechanical data, and manual monitoring data, and preprocess the data to obtain preprocessed steep slope data; Graph structure construction module for fusing multi-source features: used to take the preprocessed InSAR data as nodes in the graph, and establish edges between nodes according to spatial distance and slope difference to obtain a graph structure; Manifold graph convolutional neural network model construction module: used to construct a manifold graph convolutional neural network model, and the model includes a graph convolutional neural network and a neural ordinary differential equation; Model training module: used to train and optimize the model with the mean square error as the loss function to obtain a trained model; Steep slope surface displacement prediction module: used to input the data in the test set into the trained model to obtain the predicted surface displacement; Steep slope stability evaluation module: used to evaluate the steep slope stability according to the predicted surface displacement result.

[0013] The advantages of the present invention are: The present invention comprehensively utilizes multi-source data such as geology, terrain, environment, InSAR, and manual monitoring to comprehensively reflect the real-time state of the slope. Through the organic integration of multi-dimensional data, the model can capture the key factors affecting slope stability, improving the comprehensiveness and accuracy of prediction; by constructing a graph structure integrating multiple features, the model uses manifold graph convolutional network and neural ordinary differential equations to deeply explore the spatial correlation and temporal dynamic changes of the slope. The graph convolutional neural network effectively extracts the complex correlations between each monitoring point inside the slope, and the neural ordinary differential equation accurately simulates the continuous time evolution of the slope state, realizing the deep integration of spatial and temporal features; the model has good adaptability to slight deformation and complex geological conditions. In the experiment, even if the slope only undergoes a small displacement, the model can still keenly capture it and provide accurate prediction results, indicating that the model has high robustness, is applicable to different types of slope monitoring, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention.

[0015] Figure 1 It is a flowchart of the steps of the method of the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0016] Embodiment 1 In this embodiment, as Figure 1 shown, the present invention provides a method for predicting the stability of a steep slope based on a manifold graph convolutional network. The specific steps include: S1. Data collection and preprocessing: Collect data of the steep slope, including InSAR data I, geological data G, terrain data T, environmental data E, mechanical data M, and manual monitoring data D, and preprocess the data to obtain preprocessed data of the steep slope, which is divided into a test set and a training set; Specifically, in S11, the InSAR data I includes the longitude, latitude, and altitude coordinates of the displacement information of each steep slope surface; the geological data G includes the rock type GLT, the bedding direction GSD, and the groundwater level GWL; the terrain data T includes the steep slope gradient TSL, the slope aspect TAS, the height THG, and the length TLG; the environmental data E includes the rainfall ERP, the temperature ETP, the humidity EHM, and the wind speed EWS; the mechanical data M includes the unit weight MDN, the shear strength MSS, the elastic modulus MEM, the stress distribution MSD of the slope, and the deformation condition MDF; the artificial monitoring data D includes the surface displacement DSD, the underground displacement DUD, and the crack development condition DCF; S12. Remove the outliers from the data in step S11. When holds, then it is determined that is an outlier. When holds, similarly determine that is an outlier; where represents the variable value to be detected, represents the first quartile of the data, represents the third quartile of the data, represents the interquartile range, ; S13. Normalize the data after removing the outliers. The formula is as follows: , where represents the data after normalization, represents the minimum value of the variable, represents the maximum value of the variable; S14. Perform format conversion and cleaning on the normalized steep slope data. Specifically: S141. The InSAR data I undergoes a conversion from phase to displacement, converting the phase information of the radar wave into surface displacement data, and at the same time unifying the surface displacement data into the longitude and latitude format of coordinate points. The formula is as follows: , where represents the surface displacement of the th InSAR point, represents the wavelength of the radar signal, represents the th detection point's phase change amount; S142. Convert the rock type GLT in the geological data G into a numerical code. By establishing a mapping function, convert the rock type into an integer label. The formula is as follows: , where represents the mapping function, represents the result after numericalizing the rock type GLT, converting the dip and dip angle of the bedding plane direction GSD in the geological data G into the form of unit vectors, obtaining the unit vectors in three-dimensional space , and the formula is as follows: , where, , , respectively represent the x, y, and z components after converting the dip θ and dip angle α of the bedding plane direction into unit vectors in three-dimensional space, and are used to represent the spatial orientation of the rock formation in the three-dimensional coordinate system in the subsequent model; represent the groundwater level as a function related to space and time, defined as: where, represents time, represents the geographical coordinates, represents the position at the moment the elevation of the groundwater level, represents the elevation of the groundwater level at the initial moment , and respectively represent the rainfall intensity and evapotranspiration, represents the specific yield or permeability coefficient, represents the integration variable; if it is necessary to evaluate the water level depth, , use the difference between the surface elevation and the water level elevation to represent the groundwater depth, so as to evaluate the influence of groundwater on slope stability or pore water pressure change in the subsequent analysis; after discretizing these continuous forms in the data structure, the finally standardized geological data is obtained, and the formula is as follows: where, is the geographical coordinates of the th record, represents the numerical encoding of the rock type, are respectively the three-dimensional unit vector components of the bedding plane direction, represents the groundwater level value obtained by monitoring or interpolation, is the total number of records of the geological data; S143. Process the slope TSL, height THG, and aspect TAS in the terrain data T, and the formula is as follows: , , , wherein, represents the slope angle, represents the altitude, and respectively represent the lowest and highest altitudes of the study area, represents the aspect azimuth angle, represents the processed slope, represents the processed height, represents the processed aspect; combining the processed slope, height, and aspect data with spatial coordinates to form a unified topographic data format, obtaining the standardized topographic data , and the formula is as follows: , wherein, represents the abscissa and ordinate of the spatial coordinates of the th topographic sampling point, used to locate the specific position of this point in the study area, and the spatial coordinates are provided by the position of the sampling points obtained from the digital elevation model DEM, remote sensing mapping, or ground measurement of the study area; represents the total number of topographic sampling points; S144. Organize the environmental data E into a time series format, align the data in time, and unify it to the same time interval. By uniformly converting the time format, unit, and data type of the environmental data, form the standardized environmental data : , wherein, represents the timestamp corresponding to the environmental data; respectively represent the rainfall, temperature, humidity, and wind speed corresponding to the time ; represents the number of environmental data records; S145. Associate the mechanical data M with the spatial position, unify it into a standard format, and form the structured mechanical data , and the formula is as follows: , wherein, represents the spatial position coordinates corresponding to the mechanical data, and the coordinates are determined by mapping the mechanical measurement points to the spatial positions corresponding to the InSAR data; respectively represent the specific gravity, shear strength, elastic modulus, stress distribution, and deformation condition of the slope corresponding to the spatial position coordinates ; Indicates the number of mechanical data records; S146. Organize the manually monitored data D after format conversion and structure unification into multi-dimensional manually monitored data in terms of time and space , which is expressed by the formula as follows: , where, Indicates the time stamp corresponding to the manually monitored data, respectively represent the abscissa and ordinate of the geographical coordinates of the sensor, respectively represent the surface displacement, underground displacement, and crack development corresponding to the corresponding time and location; Indicates the number of manually detected data; Finally, the feature vector representation of the model input is obtained through the above processing , which is expressed by the formula as follows: , where, respectively represent the surface displacement, numerical encoding of rock type, x, y, z components of the three-dimensional unit vector in the bedding direction, and groundwater level value corresponding to the respectively represent the processed slope, height, and aspect corresponding to the respectively represent the precipitation, temperature, humidity, and wind speed corresponding to the respectively represent the specific gravity, shear strength, elastic modulus, stress distribution, and deformation of the slope corresponding to the respectively represent the surface displacement, underground displacement, and crack development corresponding to the

[0017] S2. Construct a graph structure that fuses multiple features: Use the preprocessed InSAR data I as the nodes in the graph, and establish edges between the nodes according to the spatial distance and slope difference to obtain the graph structure , the graph structure includes the feature vector of each node and the adjacency matrix corresponding to the edges between the nodes ; Specifically, S21. Take each InSAR point as a node in the graph, and the feature vector of the corresponding node is ; S22. Establish edges between the nodes based on the spatial distance and slope difference, and the formula is expressed as follows: , , , Among them, represents the edge weight between node and node . represents the Euclidean distance, represents the distance scale parameter, represents the slope difference scale parameter, represents the spatial distance weight, represents the slope difference weight; when exceeds the set threshold , an edge is established between node and . Specifically, the threshold is determined comprehensively according to the spatial scale of the research area, the density of monitoring points, and the experimental verification results, and is specifically set as: giving an empirical value based on prior knowledge, or sorting all and selecting the top several percentiles as the threshold.

[0018] S23. Construct a complete graph structure , and the formula is as follows: , , , Among them, represents the node set, represents the edge set, represents the total number of InSAR points, represents node and The edge between them, represents the edge weight threshold; further obtain the adjacency matrix , and the formula is as follows: , Among them, represents the adjacency matrix between node and .

[0019] S3. Construct a manifold graph convolutional neural network model: The manifold graph convolutional neural network model includes a graph convolutional neural network and a neural ordinary differential equation. The feature vector of the node at the th moment in the test set and the adjacency matrix corresponding to the edge between the nodes at the th moment Input into the graph convolutional neural network to extract the spatial features of the steep slope, and obtain the latent information representation of the steep slope , the latent information representation of the steep slope is input into the neural ordinary differential equation for time dynamics modeling to obtain the predicted ground displacement of the steep slope; Specifically, S31. Spatial feature extraction based on the graph convolutional neural network: Perform multi-layer graph convolutional operations in the graph convolutional neural network. The feature extraction formula for the th layer is expressed as follows: , , , , where, represents the node representation of the th layer. The initial layer , represents the adjacency matrix after symmetric normalization processing, represents the degree matrix, represents the adjacency relationship weight between node and node at time , that is, the th row and th column element of the adjacency matrix , represents the node representation of the th layer, represents the trainable weight matrix of the th layer, represents the ReLU activation function. When , , when , ; After multi-layer graph convolutional operations, the latent information representation of the steep slope is finally obtained; S32. Time dynamics modeling based on the neural ordinary differential equation: The ordinary differential equation formula for the time evolution of the slope state is expressed as follows: , where, represents the hidden state of the slope at time , represents the parameterized dynamic function, represents the trainable parameter; By the Runge-Kutta method, calculate the evolution of the slope state from time to , and the formula is expressed as follows: , in, Indicates the slope at the future time The hidden state of A dynamic function that represents the change of the ramp state over time, represents the slope at time The hidden state of is the integrating variable, representing time, , from the current moment Integrate into the future ; will slope at the future moment The hidden state of The predicted surface displacement is obtained by linear mapping , the formula is as follows: , in, Representation Node At the moment The hidden state vector of represents the trainable weight matrix in the linear mapping process, represents the bias vector in the linear mapping process, Represents the ReLU activation function.

[0020] S4. Model training: The model is trained using mean square error as the loss function to obtain a trained model; Specifically, the mean square error is used as the loss function, and the formula is as follows: , in, Indicates the total number of nodes, Nodes representing model predictions In the future The surface displacement of Representation Node The actual observed surface displacement.

[0021] S5. Prediction of surface displacement on steep slopes: The data in the test set are input into the trained model to obtain the predicted surface displacement; S6. Conduct steep slope stability assessment based on the predicted surface displacement results.

[0022] Specifically, according to the node At the moment Predicted ground displacement , compared with the observed value at the previous moment or the reference moment Compare and calculate the displacement rate, the formula is as follows: , Among them, represents the displacement rate of node at time , represents the surface displacement value of this node predicted by the model at this time, is the measured displacement at the previous time or reference time . If and the difference is larger, it indicates that the displacement increment of node in this time period is larger, indicating that the slope has a higher risk of instability; by comparing the displacement rates of different nodes, local high-displacement-rate areas can also be identified, providing a scientific basis for slope monitoring and disaster warning.

[0023] Example 2 In this example, in order to verify the beneficial effects of the present invention, a comparative experiment was conducted on the application effects of the steep slope stability prediction model based on the manifold graph convolutional network (MGCN) and five existing methods in slope stability prediction. The experimental scenario selected an actual steep slope area where only slight deformation occurred and no accidents such as collapses occurred.

[0024] The data sources include: Geological data: Obtain information such as rock type, bedding direction, and fracture distribution through geological exploration and on-site surveys; Topographic data: Use LiDAR and ground measurement techniques to obtain the digital elevation model (DEM) of the slope and calculate parameters such as slope, aspect, and height; Environmental data: Obtain meteorological data such as rainfall, temperature, humidity, and wind speed from the local meteorological department; InSAR data: Obtain InSAR point cloud data of the slope area from the Sentinel-1 satellite to provide high-precision surface displacement information; Artificial monitoring data: Install sensors at key positions on the slope to monitor surface displacement, underground displacement, and crack development in real time. During the data preprocessing process, data cleaning was first performed to handle missing values and outliers to ensure data quality. Then, the numerical data was standardized and normalized to the [0,1] interval. For categorical data such as rock type, numerical encoding was performed to facilitate model processing. Finally, various types of data were integrated to form a unified feature vector for preparing model input.

[0025] The following five existing methods were compared in this experiment: Linear Regression (LR): Linear regression analysis based on historical data.

[0026] ARIMA model (Autoregressive Integrated Moving Average, ARIMA): A time series analysis method for predicting slope displacement changes.

[0027] Long Short-Term Memory (LSTM) network: A deep learning method that captures time dependencies.

[0028] Support Vector Regression (SVR): A machine learning method for dealing with non-linear relationships.

[0029] Random Forest Regression (RF): An ensemble learning method that uses multiple decision trees for prediction.

[0030] The experimental steps are as follows: First, multi-source data in the slope area was collected over a time span of 6 months. Then the dataset was divided into a training set and a test set in a ratio of 8:2. The training set data was used to train five existing method models and the MGCN model of the present invention respectively.

[0031] Among the existing methods, the linear regression, ARIMA, and LSTM models mainly model based on time series data; the SVR and RF methods use multivariate features for modeling. The MGCN model of the present invention extracts spatial features through a manifold graph convolutional network and combines neural ordinary differential equations to capture time dynamic changes.

[0032] In the model testing stage, six methods were respectively applied on the test set for slope stability prediction, and the predicted surface displacement, underground displacement, and crack development were recorded. In the result evaluation, the mean square error (MSE) and the mean absolute error (MAE) were used as evaluation indicators to evaluate the prediction accuracy. By comparing the prediction results of each model with the actual observed values, their performances in different time periods and under slight deformation conditions were evaluated. The experimental results are shown in Table 1. Table 1 Comparison results between the MGCN model of the present invention and existing methods It can be clearly seen from the experimental results that the MGCN model of the present invention has achieved the lowest mean square error (MSE) and mean absolute error (MAE) in the prediction of surface displacement, crack width, and underground displacement, which fully demonstrates its high precision and reliability in slope stability prediction. The specific analysis is as follows: In the prediction of surface displacement, the MSE of the MGCN model is 0.40 mm² and the MAE is 0.35 mm, which are significantly lower than those of other comparison models; in the prediction of crack width, the MSE of the MGCN model is 0.36 mm² and the MAE is 0.31 mm, showing the best performance; in the prediction of underground displacement, the MSE of the MGCN model is 0.38 mm² and the MAE is 0.33 mm, which is significantly better than other models. These data are significantly lower than those of models such as linear regression (LR), ARIMA, LSTM, support vector regression (SVR), and random forest regression (RF), proving the excellent performance of the MGCN model.

[0033] By analyzing the performance differences of each model in depth, it can be seen that the linear regression (LR) and ARIMA models mainly rely on the historical time series data of slope displacement and fail to fully utilize the spatial characteristics and multi-source data of the slope, resulting in low prediction accuracy. Although the LSTM model can capture the long-term and short-term dependencies in time series data, it lacks the modeling of spatial characteristics and cannot fully consider the mutual influence and spatial correlation between monitoring points inside the slope, so the performance improvement is limited. The support vector regression (SVR) and random forest regression (RF) models utilize multiple features and the prediction accuracy has been improved, but there are still limitations in dealing with high-dimensional non-linear data and complex spatial correlations and cannot achieve the best results.

[0034] The MGCN model of the present invention comprehensively captures the spatial and time characteristics of the slope by fusing multi-source data, constructing a graph structure, and using graph convolutional networks and neural ordinary differential equations. By regarding the monitoring points as nodes and establishing a graph structure that reflects the complex spatial relationships inside the slope, the model can effectively capture the mutual influence between each monitoring point. In the case where the slope only undergoes slight deformation, the MGCN model can still accurately predict the stability change of the slope, reflecting its sensitivity and adaptability to small displacements and deformations. This provides an advanced technical means for slope stability monitoring and early warning and has important theoretical significance and practical application value.

[0035] The experimental results fully demonstrate the effectiveness and superiority of the steep slope stability prediction model based on the manifold graph convolutional network (MGCN) proposed in the present invention in practical applications. Compared with the five existing methods of linear regression (LR), ARIMA, LSTM, support vector regression (SVR), and random forest regression (RF), the MGCN model has significantly improved in terms of prediction accuracy and real-time performance. Especially when the slope only undergoes slight deformation and no obvious disasters are formed, the MGCN model can still accurately capture the dynamic changes of the slope, reflecting its sensitivity to subtle deformation and adaptability to complex geological conditions.

[0036] Example 3 This embodiment provides a steep slope stability prediction system based on a manifold graph convolutional network, including: Data acquisition and preprocessing module: used to collect steep slope data, including InSAR data, geological data, topographic data, environmental data, mechanical data, and manual monitoring data, and preprocess the data to obtain preprocessed steep slope data; Graph structure construction module for fusing multiple features: used to take the preprocessed InSAR data as nodes in the graph, and establish edges between nodes according to spatial distance and slope difference to obtain a graph structure; Manifold graph convolutional neural network model construction module: used to construct a manifold graph convolutional neural network model, and the model includes a graph convolutional neural network and a neural ordinary differential equation; Model training module: used to train and optimize the model with the mean square error as the loss function to obtain a trained model; Steep slope surface displacement prediction module: used to input the data in the test set into the trained model to obtain the predicted surface displacement; Steep slope stability evaluation module: used to evaluate the steep slope stability according to the predicted surface displacement results.

[0037] In this system, through the results of future surface displacement, underground displacement, and crack expansion output by the manifold graph convolutional network (MGCN) model, the instability risk of the slope can be further quantitatively evaluated, and stability determination and early warning can be carried out according to the risk grading standard. The evaluation and determination process is as follows: 1. Risk level classification According to slope monitoring experience, geological conditions, and relevant industry standards, the slope instability risk can be divided into several levels (such as levels I-IV), and corresponding thresholds are set for each level. The following numerical values are only for examples and should be adjusted in combination with on-site conditions and expert opinions in actual applications: Level I (safe) The displacement rate or crack expansion is extremely low (e.g., <1 mm / day), indicating that the current deformation of the slope is weak and the overall slope is in a stable state.

[0038] Level II (Attention) The displacement rate is low but shows a slow growth trend (e.g., 1 - 5 mm / day), and there is slight crack expansion. Higher monitoring frequency should be maintained and it should be included in the key observation scope.

[0039] Level III (Warning) The displacement rate or crack expansion rate increases significantly (e.g., 5 - 10 mm / day), indicating that the slope is in the stage of accelerated deformation. The warning mechanism should be activated immediately and measures such as temporary support or drainage and load reduction should be taken.

[0040] Level IV (Emergency) The displacement rate far exceeds the safety level (e.g., >10 mm / day), the crack expansion is significant, and there is a high risk of slope instability. Emergency measures such as immediate evacuation of personnel and traffic closure should be implemented to avoid major disaster consequences.

[0041] 2. Method for Judging the Stability of Steep Slopes The system regards each InSAR node or sensor position as a node in the graph, and summarizes and statistically analyzes the predicted displacement or displacement rate of all nodes. If most of the node indicators are low, it can be determined that the overall slope is basically stable; if significant accelerated deformation occurs in local nodes (or multiple nodes connected in patches), the system will mark this area as a "high-risk area" and automatically issue a local warning.

[0042] 3. Threshold Setting and Dynamic Adjustment (1) Initial Threshold Setting Determine the initial threshold according to historical monitoring data, industry standards or expert experience, and make differential settings for different types of slopes or engineering areas.

[0043] (2) Adaptive Adjustment During extreme weather (heavy rain, typhoon) or special operation periods (blasting construction, post-earthquake), some thresholds can be lowered to improve the warning sensitivity; when the environment is relatively stable, the thresholds can be raised to avoid over-warning.

[0044] (3) Historical Data Retrospection When the system accumulates a certain length of historical monitoring data, the thresholds can be continuously fine-tuned by comparing the actual disaster situation with the warning trigger time to make them more consistent with the actual geological environment.

[0045] 4. Warning and Decision Support Once the risk index of slope instability exceeds the corresponding threshold, the system will send a high-risk signal to the early warning and decision support module and notify the relevant responsible persons and management departments in a timely manner by means of text messages, emails or visual alarms, etc. The system also provides emergency disposal suggestions, including temporary support, drainage measures, traffic control or personnel evacuation plans, etc., providing a scientific decision-making basis for slope disaster prevention and mitigation and the safe operation of the project.

[0046] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A steep slope stability prediction method based on manifold graph convolutional network, characterized in that: The following steps are involved: S1. Data acquisition and preprocessing: Collect steep slope data, including InSAR data I, geological data G, topographic data T, environmental data E, mechanical data M, and manual monitoring data D, and preprocess the data to obtain preprocessed steep slope data, which are divided into test set and training set; S2. Construct a graph structure that integrates multiple features: The preprocessed InSAR data I is used as nodes in the graph, and the edges between nodes are established according to the spatial distance and slope difference to obtain the graph structure , graph structure Includes the feature vector of each node The adjacency matrix corresponding to the edges between nodes ; S3. Constructing a manifold graph convolutional neural network model: The manifold graph convolutional neural network model includes graph convolutional neural network and neural ordinary differential equation. The feature vector of the node at time and The adjacency matrix corresponding to the edges between nodes at the moment The spatial features of the steep slope are extracted by inputting into the graph convolutional neural network to obtain the potential information representation of the steep slope. , the steep slope of the latent information indicates The input is fed into the Godly ordinary differential equation for time dynamic modeling to obtain the predicted surface displacement of the steep slope; S4. Model training: The model is trained using mean square error as the loss function to obtain a trained model; S5. Prediction of surface displacement on steep slopes: The data in the test set are input into the trained model to obtain the predicted surface displacement; S6. Conduct steep slope stability assessment based on the predicted surface displacement results.

2. The steep slope stability prediction method based on manifold graph convolutional network according to claim 1 is characterized in that: Step S1 specifically includes: S11. The InSAR data I includes the longitude, latitude and altitude coordinates of the surface displacement information of each steep slope; the geological data G includes the rock type GLT, the layer direction GSD and the groundwater level GWL; the terrain data T includes the steep slope gradient TSL, the slope aspect TAS, the height THG and the length TLG; the environmental data E includes the rainfall ERP, the temperature ETP, the humidity EHM and the wind speed EWS; the mechanical data M includes the gravity MDN, the shear strength MSS, the elastic modulus MEM, the stress distribution MSD and the deformation MDF of the slope; the artificial monitoring data D includes the surface displacement DSD, the underground displacement DUD and the crack development DCF; S12. Eliminate the abnormal values ​​in the data of step S11. When is an abnormal value, when When is an outlier; Indicates the variable value to be tested. represents the first quartile of the data, represents the third quartile of the data, represents the interquartile range, ; S13. Normalize the data after removing outliers. The formula is as follows: ， in, represents the normalized data. represents the minimum value of the variable, Indicates the maximum value of a variable; S14. Perform format conversion and cleaning on the normalized steep slope data, specifically: S141.InSAR data I undergoes phase-to-displacement conversion, converting the phase information of radar waves into surface displacement data, and at the same time unifying the surface displacement data into the longitude and latitude format of coordinate points. The formula is as follows: ， in, Indicates The surface displacement of each InSAR point, represents the wavelength of the radar signal, Indicates Phase change of each detection point; S142. Convert the rock type GLT in the geological data G into a numerical code, and convert the rock type into an integer label by establishing a mapping function. The formula is as follows: ， in, represents the mapping function, The result of numerically converting the rock type GLT into the inclination of the layer direction GSD in the geological data G. and inclination Convert to unit vector form to get the unit vector in three-dimensional space , the formula is as follows: ， in, , , They represent the x, y, and z components after converting the layer direction inclination θ and the dip angle α into three-dimensional space unit vectors, respectively, and are used to represent the spatial orientation of the rock layer in the three-dimensional coordinate system in the subsequent model; The groundwater level It is expressed as a function of space and time, defined as: in, Indicates time, Represents geographic coordinates, Indicates location At the moment The groundwater level elevation, Indicates the initial time The groundwater level elevation, and represent rainfall intensity and evapotranspiration, respectively. Indicates water supply degree or permeability coefficient, represents the integral variable; if the water level depth needs to be evaluated, , using ground elevation With water level The difference between the values ​​of represents the groundwater depth, which is used to evaluate the impact of groundwater on slope stability or pore water pressure changes in subsequent analysis; after discretizing these continuous forms in the data structure, the standardized geological data are finally obtained. , the formula is as follows: ， in, For the The geographical coordinates of the records, Represents the numerical code of rock type, are the three-dimensional unit vector components in the plane direction, Indicates the groundwater level value obtained by monitoring or interpolation, is the total number of geological data records; S143. The slope TSL, height THG, and slope aspect TAS in the terrain data T are processed, and the formula is as follows: ， ， ， in, Indicates the slope angle, Indicates the altitude, and represent the lowest and highest altitudes of the study area, respectively. represents the slope azimuth, represents the slope after processing, Indicates the height after processing, Indicates the processed slope direction; combines the processed slope, height and slope direction data with the spatial coordinates to form a unified terrain data format and obtain standardized terrain data , the formula is as follows: ， in, Indicates The horizontal and vertical coordinates of the spatial coordinates of each terrain sampling point are used to locate the specific position of the point in the study area. The spatial coordinates are provided by the sampling point position obtained by the digital elevation model DEM, remote sensing mapping or ground measurement of the study area; Indicates the total number of terrain sampling points; S144. Organize the environmental data E into a time series format, align the data in time, and unify them to the same time interval. By converting the time format, unit, and data type of the environmental data, standardized environmental data is formed. : ， in, Indicates the timestamp corresponding to the environmental data; Respectively indicate the corresponding time rainfall, temperature, humidity and wind speed; Indicates the number of environmental data records; S145. Associate the mechanical data M with the spatial position and unify them into a standard format to form structured mechanical data , the formula is as follows: ， in, Represents the spatial position coordinates corresponding to the mechanical data, which are determined by mapping the mechanical measurement points to the spatial positions corresponding to the InSAR data; Respectively represent the corresponding spatial position coordinates The weight, shear strength, elastic modulus, stress distribution and deformation of the slope, Indicates the number of mechanical data records; S146. The manual monitoring data D is converted into a multi-dimensional manual monitoring data in time and space through format conversion and structural unification. , the formula is as follows: ， in, Indicates the timestamp corresponding to the manual monitoring data, Respectively represent the horizontal and vertical coordinates of the sensor's geographic coordinates, They represent the surface displacement, underground displacement, and crack development at the corresponding time and location respectively; Indicates the number of manual inspection data; Through the above processing, we finally get the feature vector representation of the model input , the formula is as follows: ， in, Respectively represent The surface displacement corresponding to each InSAR point, the numerical code of the rock type, the x, y, z components of the three-dimensional unit vector in the plane direction, and the groundwater level value; Respectively represent The processed slope, height and aspect corresponding to each InSAR point; Respectively represent Precipitation, temperature, humidity, and wind speed corresponding to each InSAR point; Respectively represent The gravity, shear strength, elastic modulus, stress distribution and deformation of the slope corresponding to each InSAR point; Respectively represent The surface displacement, underground displacement, and crack development corresponding to each InSAR point.

3. The steep slope stability prediction method based on manifold graph convolutional network according to claim 2 is characterized in that: Step S2 specifically includes: S21. Take each InSAR point as a node in the graph, and the corresponding node feature vector is ; S22. Establish the edges between nodes based on spatial distance and slope difference. The formula is as follows: ， ， ， in, Representation Node and nodes The edge weights between represents the Euclidean distance, represents the distance scale parameter, represents the slope difference scale parameter, represents the spatial distance weight, represents the slope difference weight; when Exceeding the set threshold When, at the node and Create an edge between them; S23. Build a complete graph structure , the formula is as follows: ， ， ， in, Represents a collection of nodes. represents the edge set, represents the total number of InSAR points, Representation Node and The edge between represents the edge weight threshold; further obtain the adjacency matrix , the formula is as follows: ， in, Representation Node and The adjacency matrix between .

4. The steep slope stability prediction method based on manifold graph convolutional network according to claim 3 is characterized in that: Step S3 specifically includes: S31. Spatial feature extraction based on graph convolutional neural network: Perform multi-layer graph convolution operations in graph convolutional neural network, The feature extraction formula of the layer is expressed as follows: ， ， ， ， in, Indicates The node representation of the layer, the initial layer , represents the adjacency matrix after symmetric normalization, represents the degree matrix, Indicates at time Time Node With Node The adjacency relationship weight between No. Row, No. Column elements, Indicates The node representation of the layer, Indicates The trainable weight matrix of the layer, ReLU activation function, when hour, ,when hour, ; After multiple layers of graph convolution operations, the potential information representation of the steep slope is finally obtained ; S32. Time dynamic modeling based on the Godly ordinary differential equation: The time evolution of the ramp state is expressed as follows: ， in, represents the slope at time The hidden state of represents a parameterized dynamic function, Represents a trainable parameter; by using the Runge-Kutta method, the slope state is calculated from the moment arrive The evolution of is expressed as follows: ， in, Indicates the slope at the future time The hidden state of A dynamic function that represents the change of the ramp state over time, represents the slope at time The hidden state of is the integrating variable, representing time, , from the current moment Integrate into the future ; will slope at the future moment The hidden state The predicted surface displacement is obtained by linear mapping , the formula is as follows: ， in, Representation Node At the moment The hidden state vector of represents the trainable weight matrix in the linear mapping process, represents the bias vector in the linear mapping process, Represents the ReLU activation function.

5. The steep slope stability prediction method based on manifold graph convolutional network according to claim 4 is characterized in that: Step S4 specifically includes: The mean square error is used as the loss function, and the formula is as follows: ， in, Indicates the total number of nodes, Nodes representing model predictions In the future The surface displacement of Representation Node The actual observed surface displacement.

6. The steep slope stability prediction method based on manifold graph convolutional network according to claim 5 is characterized in that: Step S6 specifically includes: According to the node At the moment Predicted ground displacement , compared with the observed value at the previous moment or the reference moment Compare and calculate the displacement rate, the formula is as follows: ， in, Representation Node At the moment The displacement rate, It represents the surface displacement value of the node at that moment predicted by the model. The previous moment or the base moment If the measured displacement The larger the difference, the smaller the node The larger the displacement increment within this time period, the higher the risk of slope instability. By comparing the displacement rates of different nodes, local high displacement rate areas can also be identified, providing a scientific basis for slope monitoring and disaster warning.

7. The method for predicting the stability of a steep slope based on a manifold graph convolutional network according to claim 6, characterized in that: In step S22, the threshold The specific setting is determined based on the spatial scale of the study area, the density of monitoring points and the experimental verification results: giving empirical values ​​based on prior knowledge, or Sort and select the top few percentiles as thresholds.

8. A steep slope stability prediction system based on manifold graph convolutional network, executing the steep slope stability prediction method based on manifold graph convolutional network as claimed in claim 1, characterized in that: include Data acquisition and preprocessing module: used to collect steep slope data, including InSAR data, geological data, topographic data, environmental data, mechanical data and manual monitoring data, and preprocess the data to obtain preprocessed steep slope data; Graph structure construction module integrating multi-features: used to take pre-processed InSAR data as nodes in the graph, establish edges between nodes according to spatial distance and slope difference, and obtain the graph structure; Manifold graph convolutional neural network model building module: used to build a manifold graph convolutional neural network model, which includes graph convolutional neural network and neural ordinary differential equations; Model training module: used to train and optimize the model by using mean square error as the loss function to obtain a trained model; Steep slope surface displacement prediction module: used to input the test set data into the trained model to obtain the predicted surface displacement; Steep slope stability assessment module: used to assess the stability of steep slopes based on the predicted surface displacement results.

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