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

Abstract

The present invention relates to a method and system for predicting the stability of steep slopes based on a manifold graph convolutional network, and belongs to the technical field of geological disaster monitoring and prediction. It includes the following steps: data acquisition and preprocessing; constructing a graph structure that integrates multiple features; building a manifold graph convolutional neural network model; model training; predicting the surface displacement of steep slopes; and evaluating the stability of steep slopes based on the predicted surface displacement results. The present invention integrates multi-source data such as geology and topography to reflect the real-time status of the slope; through multi-dimensional data fusion, it captures key factors and improves the comprehensiveness and accuracy of the prediction. A graph structure that integrates multiple features is constructed, and the manifold graph convolutional network and the neural ordinary differential equation are used to deeply explore spatial correlation and temporal dynamic changes to achieve deep fusion of spatiotemporal features. The model has good adaptability to slight deformations and complex geological conditions, high robustness, and can be applied to monitoring different types of slopes.

Description

Technical Field

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

[0002] With global climate change, extreme weather events are becoming increasingly frequent. Natural disasters such as heavy rainstorms and earthquakes have significantly increased the risk of slope collapse, especially in areas with complex terrain and steep slopes. Traditional slope stability prediction methods often ignore the dynamic changes in terrain, fail to accurately capture the potential risks during slope deformation, and have limited ability to process 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. However, most existing methods are based on static terrain models and lack the full utilization of the dynamic characteristics of the terrain. Therefore, there is an urgent need for an intelligent prediction system that can effectively combine multidimensional data to predict slope stability in real time to improve the prevention and control of slope disasters.

[0003] Because historical data on landslides and collapses is scarce and difficult to obtain, traditional machine learning methods are limited in their training datasets. Therefore, our approach does not rely solely on historical accident data. Instead, it uses InSAR data, combined with multi-dimensional data such as geology, topography, and meteorology, to detect continuous changes in slopes in real time. By treating these changes as a time series, the system can predict slope deformation trends and thus infer potential accident risks. This approach not only addresses the data scarcity issue but also improves prediction accuracy, providing a new solution for the effective prevention and control of slope disasters. Summary of the Invention

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

[0005] To achieve the above-mentioned purpose, the present invention is implemented through the following technical solutions:

[0006] The present invention provides a steep slope stability prediction method based on a manifold graph convolutional network, comprising the following steps:

[0007] 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. Preprocess the data to obtain preprocessed steep slope data, which is then divided into a test set and a training set.

[0008] S2. Construct a graph structure that integrates multiple features: The preprocessed InSAR data I is used as nodes in the graph, and edges between nodes are established based on spatial distance and slope difference to obtain a graph structure. , graph structure Includes the feature vector of each node The adjacency matrix corresponding to the edges between nodes ;

[0009] 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 equations. The feature vector of the node at time Hedi The adjacency matrix corresponding to the edges between nodes at the moment The input is fed into the graph convolutional neural network to extract the spatial features of the steep slope and obtain the potential information representation of the steep slope. , the steep slope of the potential information represents The input is fed into the Godly ordinary differential equation for time dynamic modeling to obtain the predicted surface displacement of the steep slope;

[0010] S4. Model training: The model is trained using mean squared error as the loss function to obtain a trained model.

[0011] S5. Prediction of surface displacement on steep slopes: The test data is input into the trained model to obtain the predicted surface displacement.

[0012] S6. Conduct a stability assessment of steep slopes based on the predicted ground displacement results.

[0013] Furthermore, step S1 specifically includes:

[0014] S11. The InSAR data I includes the longitude, latitude, and altitude coordinates of each steep slope surface displacement information; the geological data G includes rock type GLT, layer direction GSD, and groundwater level GWL; the topographic data T includes steep slope gradient TSL, aspect TAS, height THG, and length TLG; the environmental data E includes rainfall ERP, temperature ETP, humidity EHM, and wind speed EWS; the mechanical data M includes gravity MDN, shear strength MSS, elastic modulus MEM, slope stress distribution MSD, and deformation MDF; the manual monitoring data D includes surface displacement DSD, underground displacement DUD, and crack development DCF;

[0015] S12. Eliminate abnormal values ​​in the data of step S11. When is an abnormal value, when When is an abnormal value; among them, 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, ;

[0016] S13. Normalize the data after removing outliers. The formula is as follows:

[0017] ,

[0018] in, represents the data after normalization. represents the minimum value of the variable, Indicates the maximum value of a variable;

[0019] S14. Perform format conversion and cleaning on the normalized steep slope data, specifically:

[0020] S141.InSAR data I undergoes phase-to-displacement conversion, converting the radar wave phase information into surface displacement data. The surface displacement data is then unified into the longitude and latitude format of the coordinate points. The formula is as follows:

[0021] ,

[0022] in, Indicates the The surface displacement of each InSAR point, represents the wavelength of the radar signal, Indicates the Phase change of each detection point;

[0023] 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:

[0024] ,

[0025] 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 is shown in Figure 2. and inclination Convert to unit vector form to get the unit vector in three-dimensional space , the formula is as follows:

[0026] ,

[0027] in, 、 、 They represent the x, y, and z components of the layer direction dip θ and dip angle α converted 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 subsequent models;

[0028] Groundwater level It is expressed as a function of space and time, defined as:

[0029]

[0030] 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 and water level elevation The difference between the two 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:

[0031]

[0032] 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;

[0033] S143. Process the slope TSL, height THG, and aspect TAS in the terrain data T. The formula is as follows:

[0034] ,

[0035] ,

[0036] ,

[0037] in, Indicates the slope angle, Indicates altitude, and represent the lowest and highest altitudes of the study area, 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 spatial coordinates to form a unified terrain data format and obtain standardized terrain data , the formula is as follows:

[0038] ,

[0039] in, Indicates the 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 from the digital elevation model (DEM) of the study area, remote sensing mapping or ground measurement; Indicates the total number of terrain sampling points;

[0040] 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. :

[0041] ,

[0042] in, Indicates the timestamp corresponding to the environmental data; Respectively represent the corresponding time rainfall, temperature, humidity, and wind speed; Indicates the number of environmental data records;

[0043] 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:

[0044] ,

[0045] in, Represents the spatial position coordinates corresponding to the mechanical data, which is determined by mapping the mechanical measurement points to the spatial positions corresponding to the InSAR data; 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;

[0046] S146. The manual monitoring data D is converted into a format and unified structure, and organized into multi-dimensional manual monitoring data in time and space. , the formula is as follows:

[0047] ,

[0048] in, Indicates the timestamp corresponding to the manual monitoring data, Represents 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 position respectively; Indicates the number of manual inspection data;

[0049] Through the above processing, we can finally get the feature vector representation of the model input , the formula is as follows:

[0050] ,

[0051] in, Respectively represent The surface displacement corresponding to each InSAR point, the numerical code of the rock type, the x, y, and 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 Gravity, shear strength, elastic modulus, slope stress distribution, and deformation corresponding to each InSAR point; Respectively represent The surface displacement, underground displacement, and crack development corresponding to each InSAR point.

[0052] Furthermore, step S2 specifically includes:

[0053] S21. Take each InSAR point as a node in the graph, and the corresponding node’s eigenvector is ;

[0054] S22. Establish edges between nodes based on spatial distance and slope difference. The formula is as follows:

[0055] ,

[0056] ,

[0057] ,

[0058] 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;

[0059] S23. Build a complete graph structure , the formula is as follows:

[0060] ,

[0061] ,

[0062] ,

[0063] in, Represents a collection of nodes, represents the edge set, represents the total number of InSAR points, Representation node and The edges between Represents the edge weight threshold; further obtain the adjacency matrix , the formula is as follows:

[0064] ,

[0065] in, Representation node and The adjacency matrix between .

[0066] Furthermore, the threshold value in step S22 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.

[0067] Furthermore, step S3 specifically includes:

[0068] 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:

[0069] ,

[0070] ,

[0071] ,

[0072] ,

[0073] in, Indicates the 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 them, that is, the adjacency matrix No. Row, No. Column elements, Indicates the The node representation of the layer, Indicates the The trainable weight matrix of the layer, Represents the 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 ;

[0074] S32. Time dynamic modeling based on the Neural Ordinary Differential Equation: The time evolution of the ramp state is expressed as follows:

[0075] ,

[0076] in, Indicates the slope at time The hidden state of represents a parameterized dynamic function, Represents a trainable parameter; by the Runge-Kutta method, the slope state is calculated from the moment arrive The evolution of is expressed as follows:

[0077] ,

[0078] in, Indicates the slope at the future time The hidden state of A dynamic function that represents the change of ramp state over time, represents the slope at time The hidden state of is the integration variable, representing time, , from the current moment Integrate into the future ; will slope in the future The hidden state The predicted surface displacement is obtained by linear mapping , the formula is as follows:

[0079] ,

[0080] 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.

[0081] Furthermore, step S4 specifically includes:

[0082] The mean square error is used as the loss function, and the formula is as follows:

[0083] ,

[0084] in, Indicates the total number of nodes, Nodes representing model predictions In the future The surface displacement, Representation node The actual observed surface displacement.

[0085] Furthermore, step S6 specifically includes:

[0086] According to the node At the moment Predicted ground displacement , compared with the observation value at the previous moment or the reference moment Compare and calculate the displacement rate, the formula is as follows:

[0087] ,

[0088] 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 better 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.

[0089] The present invention also provides a steep slope stability prediction system based on a manifold graph convolutional network, which implements the steep slope stability prediction method based on a manifold graph convolutional network, including:

[0090] 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;

[0091] Graph structure construction module integrating multi-features: used to treat pre-processed InSAR data as nodes in a graph, establish edges between nodes based on spatial distance and slope difference, and obtain a graph structure;

[0092] Manifold graph convolutional neural network model construction module: used to build a manifold graph convolutional neural network model, which includes graph convolutional neural network and neural ordinary differential equations;

[0093] Model training module: used to train and optimize the model using mean square error as the loss function to obtain a trained model;

[0094] Steep slope surface displacement prediction module: used to input the test data into the trained model to obtain the predicted surface displacement;

[0095] Steep slope stability assessment module: used to assess the stability of steep slopes based on the predicted surface displacement results.

[0096] The advantages of the present invention are:

[0097] This model comprehensively utilizes multiple sources of data, including geological, topographic, environmental, InSAR, and manual monitoring, to fully reflect the real-time state of the slope. By organically integrating multidimensional data, the model captures key factors influencing slope stability, improving the comprehensiveness and accuracy of the prediction. By constructing a graph structure that integrates multiple features, the model leverages manifold graph convolutional networks and neural ordinary differential equations to deeply explore the spatial correlations and temporal dynamics of the slope. The graph convolutional neural network effectively extracts the complex relationships between monitoring points within the slope, while the neural ordinary differential equations accurately simulate the continuous-time evolution of the slope state, achieving a deep fusion of spatial and temporal features. The model is highly adaptable to slight deformations and complex geological conditions. In experiments, the model was able to detect even minor slope displacements and provide accurate predictions, demonstrating its high robustness and suitability for various types of slope monitoring, with broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0099] Figure 1 is a flow chart of the steps of the method of the present invention; DETAILED DESCRIPTION

[0100] 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. All other embodiments derived by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0101] Example 1

[0102] In this embodiment, Figure 1 As shown, the present invention provides a steep slope stability prediction method based on manifold graph convolutional network, which specifically includes the following steps:

[0103] 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. Preprocess the data to obtain preprocessed steep slope data, which is then divided into a test set and a training set.

[0104] Specifically, S11. The InSAR data I includes the longitude, latitude, and altitude coordinates of each steep slope surface displacement information; the geological data G includes the rock type GLT, the layer direction GSD, and the groundwater level GWL; the topographic 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 slope stress distribution MSD, and the deformation MDF; the manual monitoring data D includes the surface displacement DSD, the underground displacement DUD, and the crack development DCF;

[0105] S12. Eliminate abnormal values ​​in the data of step S11. When is an abnormal value, when When is an abnormal value; among them, 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, ;

[0106] S13. Normalize the data after removing outliers. The formula is as follows:

[0107] ,

[0108] in, represents the data after normalization. represents the minimum value of the variable, Indicates the maximum value of a variable;

[0109] S14. Perform format conversion and cleaning on the normalized steep slope data, specifically:

[0110] S141.InSAR data I undergoes phase-to-displacement conversion, converting the radar wave phase information into surface displacement data. The surface displacement data is then unified into the longitude and latitude format of the coordinate points. The formula is as follows:

[0111] ,

[0112] in, Indicates the The surface displacement of each InSAR point, represents the wavelength of the radar signal, Indicates the Phase change of each detection point;

[0113] 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:

[0114] ,

[0115] 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 is shown in Figure 2. and inclination Convert to unit vector form to get the unit vector in three-dimensional space , the formula is as follows:

[0116] ,

[0117] in, 、 、 They represent the x, y, and z components of the layer direction dip θ and dip angle α converted 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 subsequent models;

[0118] Groundwater level It is expressed as a function of space and time, defined as:

[0119]

[0120] 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 and water level elevation The difference between the two 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:

[0121]

[0122] 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;

[0123] S143. Process the slope TSL, height THG, and aspect TAS in the terrain data T. The formula is as follows:

[0124] ,

[0125] ,

[0126] ,

[0127] in, Indicates the slope angle, Indicates altitude, and represent the lowest and highest altitudes of the study area, 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 spatial coordinates to form a unified terrain data format and obtain standardized terrain data , the formula is as follows:

[0128] ,

[0129] in, Indicates the 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 from the digital elevation model (DEM) of the study area, remote sensing mapping or ground measurement; Indicates the total number of terrain sampling points;

[0130] 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. :

[0131] ,

[0132] in, Indicates the timestamp corresponding to the environmental data; Respectively represent the corresponding time rainfall, temperature, humidity, and wind speed; Indicates the number of environmental data records;

[0133] 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:

[0134] ,

[0135] in, Represents the spatial position coordinates corresponding to the mechanical data, which is determined by mapping the mechanical measurement points to the spatial positions corresponding to the InSAR data; 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;

[0136] S146. The manual monitoring data D is converted into a format and unified structure, and organized into multi-dimensional manual monitoring data in time and space. , the formula is as follows:

[0137] ,

[0138] in, Indicates the timestamp corresponding to the manual monitoring data, Represents 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 position respectively; Indicates the number of manual inspection data;

[0139] Through the above processing, we can finally get the feature vector representation of the model input , the formula is as follows:

[0140] ,

[0141] in, Respectively represent The surface displacement corresponding to each InSAR point, the numerical code of the rock type, the x, y, and 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 Gravity, shear strength, elastic modulus, slope stress distribution, and deformation corresponding to each InSAR point; Respectively represent The surface displacement, underground displacement, and crack development corresponding to each InSAR point.

[0142] S2. Construct a graph structure that integrates multiple features: The preprocessed InSAR data I is used as nodes in the graph, and edges between nodes are established based on spatial distance and slope difference to obtain a graph structure. , graph structure Includes the feature vector of each node The adjacency matrix corresponding to the edges between nodes ;

[0143] Specifically, S21. Each InSAR point is regarded as a node in the graph, and the corresponding node feature vector is ;

[0144] S22. Establish edges between nodes based on spatial distance and slope difference. The formula is as follows:

[0145] ,

[0146] ,

[0147] ,

[0148] 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;

[0149] Specifically, the threshold The specific setting is determined based on the spatial scale of the research 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.

[0150] S23. Build a complete graph structure , the formula is as follows:

[0151] ,

[0152] ,

[0153] ,

[0154] in, Represents a collection of nodes, represents the edge set, represents the total number of InSAR points, Representation node and The edges between Represents the edge weight threshold; further obtain the adjacency matrix , the formula is as follows:

[0155] ,

[0156] in, Representation node and The adjacency matrix between .

[0157] 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 equations. The feature vector of the node at time Hedi The adjacency matrix corresponding to the edges between nodes at the moment The input is fed into the graph convolutional neural network to extract the spatial features of the steep slope and obtain the potential information representation of the steep slope. , the steep slope of the potential information represents The input is fed into the Godly ordinary differential equation for time dynamic modeling to obtain the predicted surface displacement of the steep slope;

[0158] Specifically, 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:

[0159] ,

[0160] ,

[0161] ,

[0162] ,

[0163] in, Indicates the 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 them, that is, the adjacency matrix No. Row, No. Column elements, Indicates the The node representation of the layer, Indicates the The trainable weight matrix of the layer, Represents the 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 ;

[0164] S32. Time dynamic modeling based on the Neural Ordinary Differential Equation: The time evolution of the ramp state is expressed as follows:

[0165] ,

[0166] in, Indicates the slope at time The hidden state of represents a parameterized dynamic function, Represents a trainable parameter; by the Runge-Kutta method, the slope state is calculated from the moment arrive The evolution of is expressed as follows:

[0167] ,

[0168] in, Indicates the slope at the future time The hidden state of A dynamic function that represents the change of ramp state over time, represents the slope at time The hidden state of is the integration variable, representing time, , from the current moment Integrate into the future ; will slope in the future The hidden state The predicted surface displacement is obtained by linear mapping , the formula is as follows:

[0169] ,

[0170] 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.

[0171] S4. Model training: The model is trained using mean squared error as the loss function to obtain a trained model.

[0172] Specifically, the mean square error is used as the loss function, and the formula is expressed as follows:

[0173] ,

[0174] in, Indicates the total number of nodes, Nodes representing model predictions In the future The surface displacement, Representation node The actual observed surface displacement.

[0175] S5. Prediction of surface displacement on steep slopes: The test data is input into the trained model to obtain the predicted surface displacement.

[0176] S6. Conduct a stability assessment of steep slopes based on the predicted ground displacement results.

[0177] Specifically, according to the node At the moment The predicted value of ground displacement , compared with the observation value at the previous moment or the reference moment Compare and calculate the displacement rate, the formula is as follows:

[0178] ,

[0179] 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 better 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.

[0180] Example 2

[0181] In this example, to verify the beneficial effects of the present invention, a comparative experiment was conducted on a steep slope stability prediction model based on a Manifold Graph Convolutional Network (MGCN) and five existing methods. The experimental scenario was a real-world steep slope area that had only minor deformation and no landslides or other accidents.

[0182] Data sources include: geological data: rock type, layer orientation, and fracture distribution are obtained through geological exploration and field surveys; topographic data: Digital elevation models (DEMs) of the slopes are generated using LiDAR and ground surveying techniques, and parameters such as slope gradient, aspect, and height are calculated; environmental data: meteorological data such as rainfall, temperature, humidity, and wind speed are obtained from the local meteorological department; InSAR data: InSAR point cloud data of the slope area is obtained from the Sentinel-1 satellite, providing high-precision surface displacement information; and manual monitoring data: sensors are deployed at key locations on the slope to monitor surface and subsurface displacement and fracture development in real time. Data preprocessing begins with data cleaning to address missing values ​​and outliers to ensure data quality. Numerical data are then normalized to the range [0, 1]. Categorical data such as rock type are numerically encoded to facilitate model processing. Finally, all data types are integrated to form a unified feature vector for model input.

[0183] This experiment compares the following five existing methods:

[0184] Linear Regression (LR): Linear regression analysis based on historical data.

[0185] ARIMA model (Autoregressive Integrated Moving Average, ARIMA): a time series analysis method for predicting slope displacement changes.

[0186] LSTM network (Long Short-Term Memory, LSTM): A deep learning method that captures temporal dependencies.

[0187] Support Vector Regression (SVR): A machine learning method that handles nonlinear relationships.

[0188] Random Forest Regression (RF): An ensemble learning method that uses multiple decision trees for prediction.

[0189] The experimental steps are as follows:

[0190] First, we collected multi-source data from a slope area spanning six months. We then divided the dataset into a training set and a test set at a ratio of 8:2. We used the training data to train five existing models and the proposed MGCN model.

[0191] Among existing methods, linear regression, ARIMA, and LSTM models primarily build models based on time series data, while SVR and RF methods leverage multivariate features. The MGCN model of our invention extracts spatial features through a manifold graph convolutional network and combines it with neural ordinary differential equations to capture temporal dynamics.

[0192] During the model testing phase, six methods were applied to the test dataset to predict slope stability, recording the predicted surface and subsurface displacements and crack development. The mean squared error (MSE) and mean absolute error (MAE) were used as metrics to assess prediction accuracy. By comparing the predictions of each model with actual observations, their performance was evaluated under different time periods and mild deformation conditions. The experimental results are shown in Table 1.

[0193] Table 1 Comparison results between the MGCN model of the present invention and existing methods

[0194]

[0195] The experimental results clearly demonstrate that the proposed MGCN model achieves the lowest mean squared error (MSE) and mean absolute error (MAE) in predicting surface displacement, crack width, and subsurface displacement, demonstrating its high accuracy and reliability in slope stability prediction. Specifically, the MGCN model achieves an MSE of 0.40 mm² and a MAE of 0.35 mm for surface displacement prediction, significantly lower than other compared models. In crack width prediction, the MGCN model achieves the best performance, with an MSE of 0.36 mm² and a MAE of 0.31 mm. In subsurface displacement prediction, the MGCN model achieves an MSE of 0.38 mm² and a MAE of 0.33 mm, significantly outperforming other models. These figures are significantly lower than those of models such as linear regression (LR), ARIMA, LSTM, support vector regression (SVR), and random forest regression (RF), demonstrating the superior performance of the MGCN model.

[0196] A thorough analysis of the performance differences among the various models reveals that linear regression (LR) and ARIMA models primarily rely on historical time series data of slope displacements, failing to fully utilize the slope's spatial characteristics and multi-source data, resulting in lower prediction accuracy. While the LSTM model can capture both long-term and short-term dependencies in time series data, it lacks spatial modeling and cannot fully account for the interactions and spatial correlations between monitoring points within the slope, resulting in limited performance improvement. Support vector regression (SVR) and random forest regression (RF) models utilize multivariate features, resulting in improved prediction accuracy. However, they still have limitations in handling high-dimensional nonlinear data and complex spatial correlations, preventing them from achieving optimal results.

[0197] The MGCN model of this invention integrates multi-source data, constructs a graph structure, and utilizes graph convolutional networks and neural ordinary differential equations to comprehensively capture the spatial and temporal characteristics of slopes. By treating monitoring points as nodes and establishing a graph structure that reflects the complex spatial relationships within the slope, the model effectively captures the interactions between monitoring points. Even with only slight deformation, the MGCN model can still accurately predict changes in slope stability, demonstrating its sensitivity and adaptability to small displacements and deformations. This provides an advanced technical approach for slope stability monitoring and early warning, with significant theoretical significance and practical application value.

[0198] Experimental results fully demonstrate the effectiveness and superiority of the proposed steep slope stability prediction model based on a manifold graph convolutional network (MGCN) in practical applications. Compared with five existing methods—linear regression (LR), ARIMA, LSTM, support vector regression (SVR), and random forest regression (RF)—the MGCN model significantly improves prediction accuracy and real-time performance. In particular, even when the slope undergoes only minor deformation and no significant hazards, the MGCN model can still accurately capture the dynamic changes of the slope, demonstrating its sensitivity to subtle deformation and adaptability to complex geological conditions.

[0199] Example 3

[0200] This embodiment provides a steep slope stability prediction system based on a manifold graph convolutional network, including:

[0201] 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;

[0202] Graph structure construction module integrating multi-features: used to treat pre-processed InSAR data as nodes in a graph, establish edges between nodes based on spatial distance and slope difference, and obtain a graph structure;

[0203] Manifold graph convolutional neural network model construction module: used to build a manifold graph convolutional neural network model, which includes graph convolutional neural network and neural ordinary differential equations;

[0204] Model training module: used to train and optimize the model using mean square error as the loss function to obtain a trained model;

[0205] Steep slope surface displacement prediction module: used to input the test data into the trained model to obtain the predicted surface displacement;

[0206] Steep slope stability assessment module: used to assess the stability of steep slopes based on the predicted surface displacement results.

[0207] In this system, the future surface displacement, underground displacement, and crack expansion results output by the Manifold Graph Convolutional Network (MGCN) model can be used to further quantitatively assess the instability risk of the slope, and stability judgment and early warning can be performed based on risk classification standards. The assessment and judgment process is as follows:

[0208] 1. Risk level classification

[0209] Based on slope monitoring experience, geological conditions, and relevant industry standards, slope instability risk can be divided into several levels (e.g., Levels I to IV), with corresponding thresholds set for each level. The following values ​​are for example purposes only and should be adjusted in practice based on site conditions and expert advice:

[0210] Level I (Safety)

[0211] The displacement rate or crack expansion is extremely low (e.g. <1 mm / day), indicating that the slope is currently deforming slightly and is generally stable.

[0212] Level II (concern)

[0213] The displacement rate is low but has a slow growth trend (such as 1 to 5 mm / day). The cracks are slightly expanding and need to be monitored at a high frequency and included in the key observation range.

[0214] Level III (Warning)

[0215] A significant increase in the displacement rate or crack expansion rate (e.g., 5-10 mm / day) indicates that the slope is in the stage of accelerated deformation. The early warning mechanism should be activated immediately and temporary support or drainage and load reduction measures should be taken.

[0216] Level IV (urgent)

[0217] The displacement rate far exceeds the safe level (e.g. >10 mm / day), the cracks expand significantly, and the slope is at high risk of instability. Emergency measures such as evacuation of personnel and traffic closure should be implemented immediately to avoid major disaster consequences.

[0218] 2. Steep slope stability determination method

[0219] The system treats each InSAR node or sensor location as a node in the graph and aggregates the predicted displacement or displacement rate for all nodes. If the indicators for most nodes are low, the slope is considered generally stable. However, if a local node (or a contiguous area of ​​multiple nodes) shows significant accelerated deformation, the system marks the area as "high-risk" and automatically issues a localized warning.

[0220] 3. Threshold setting and dynamic adjustment

[0221] (1) Initial threshold setting

[0222] The initial threshold is determined based on historical monitoring data, industry standards or expert experience, and is set differently for different types of slopes or project areas.

[0223] (2) Adaptive adjustment

[0224] In extreme weather (heavy rain, typhoon) or special operation periods (blasting construction, post-earthquake disasters), some thresholds can be lowered to increase warning sensitivity; when the environment is relatively stable, the thresholds can be raised to avoid excessive warnings.

[0225] (3) Historical data backtracking

[0226] After the system has accumulated a certain length of historical monitoring data, it can continuously fine-tune the threshold by comparing the actual disaster situation with the warning trigger timing to make it more consistent with the actual geological environment.

[0227] 4. Early warning and decision support

[0228] If the slope instability risk index exceeds the corresponding threshold, the system will send a high-risk signal to the early warning and decision-making support module, and promptly notify the relevant responsible personnel and management departments via SMS, email, or visual alarm. The system also provides emergency response suggestions, including temporary support, drainage measures, traffic control, or personnel evacuation plans, providing a scientific basis for decision-making on slope disaster prevention and mitigation and safe project operations.

[0229] Finally, it should be noted that the above descriptions are merely 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 aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection 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. Preprocess the data to obtain preprocessed steep slope data, which is then divided into a test set and a training set. S2. Construct a graph structure that integrates multiple features: The preprocessed InSAR data I is used as nodes in the graph, and edges between nodes are established based on spatial distance and slope difference to obtain a 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 equations. The feature vector of the node at time Hedi The adjacency matrix corresponding to the edges between nodes at the moment The input is fed into the graph convolutional neural network to extract the spatial features of the steep slope and obtain the potential information representation of the steep slope. , the steep slope of the potential information represents The input is fed into the Godly ordinary differential equation for time dynamic modeling to obtain the predicted surface displacement of the steep slope; The specific steps are as follows: 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 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 them, that is, the adjacency matrix No. Row, No. Column elements, Indicates the The node representation of the layer, Indicates the The trainable weight matrix of the layer, Represents the 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 Neural Ordinary Differential Equation: The time evolution of the ramp state is expressed as follows: ， in, represents a parameterized dynamic function, Represents a trainable parameter; by 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 ramp state over time, represents the slope at time The hidden state of is the integration variable, representing time, , from the current moment Integrate into the future ; will slope in the future 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; S4. Model training: The model is trained using mean squared error as the loss function to obtain a trained model. S5. Prediction of surface displacement on steep slopes: The test data is input into the trained model to obtain the predicted surface displacement. S6. Conduct a stability assessment of steep slopes based on the predicted ground 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 each steep slope surface displacement information; the geological data G includes rock type GLT, layer direction GSD, and groundwater level GWL; the topographic data T includes steep slope gradient TSL, aspect TAS, height THG, and length TLG; the environmental data E includes rainfall ERP, temperature ETP, humidity EHM, and wind speed EWS; the mechanical data M includes gravity MDN, shear strength MSS, elastic modulus MEM, slope stress distribution MSD, and deformation MDF; the manual monitoring data D includes surface displacement DSD, underground displacement DUD, and crack development DCF; S12. Eliminate abnormal values ​​in the data of step S11. When is an abnormal value, when When is an abnormal value; among them, 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 data after normalization. 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 radar wave phase information into surface displacement data. The surface displacement data is then unified into the longitude and latitude format of the coordinate points. The formula is as follows: ， in, Indicates the The surface displacement of each InSAR point, represents the wavelength of the radar signal, Indicates the Phase change of each detection point; 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: ， 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 is shown in Figure 2. 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 of the layer direction dip θ and dip angle α converted 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 subsequent models; 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 and water level elevation The difference between the two 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. Process the slope TSL, height THG, and aspect TAS in the terrain data T. The formula is as follows: ， ， ， in, Indicates the slope angle, Indicates altitude, and represent the lowest and highest altitudes of the study area, 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 spatial coordinates to form a unified terrain data format and obtain standardized terrain data , the formula is as follows: ， in, Indicates the 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 from the digital elevation model (DEM) of the study area, remote sensing mapping or ground measurement; 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 represent 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 is determined by mapping the mechanical measurement points to the spatial positions corresponding to the InSAR data; 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 format and unified structure, and organized into multi-dimensional manual monitoring data in time and space. , the formula is as follows: ， in, Indicates the timestamp corresponding to the manual monitoring data, Represents 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 position respectively; Indicates the number of manual inspection data; Through the above processing, we can 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, and 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 Gravity, shear strength, elastic modulus, slope stress distribution, and deformation 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’s eigenvector is ; S22. Establish 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 edges 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 method for predicting steep slope stability based on manifold graph convolutional network according to claim 3, 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, Representation node The actual observed surface displacement.

5. The method for predicting steep slope stability based on manifold graph convolutional network according to claim 4, characterized in that: Step S6 specifically includes: According to the node At the moment Predicted ground displacement , compared with the observation 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 better 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.

6. The method for predicting steep slope stability based on manifold graph convolutional network according to claim 5, characterized in that: The threshold value in step S22 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.

7. A steep slope stability prediction system based on a manifold graph convolutional network, which executes the steep slope stability prediction method based on a 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 treat pre-processed InSAR data as nodes in a graph, establish edges between nodes based on spatial distance and slope difference, and obtain a graph structure; Manifold graph convolutional neural network model construction 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 using mean square error as the loss function to obtain a trained model; Steep slope surface displacement prediction module: used to input the test 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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