A highway slope ground surface displacement time series prediction method based on graph attention

Abstract

The application belongs to the technical field of geographic information data processing, and discloses a road slope ground surface displacement time sequence prediction method based on graph attention: ground surface displacement time sequence data and associated environmental influence data of a plurality of monitoring stations are acquired, a weighted adjacent matrix is constructed based on the geographic positions of the monitoring stations, and an initial spatial topological relationship is defined; the displacement data and the environmental data are subjected to feature fusion, and an attribute-enhanced feature matrix is constructed; the weighted adjacent matrix and the feature matrix are respectively input into a graph convolution network and a graph attention network for parallel processing: the GCN extracts structured spatial features through a fixed topological structure, and generates a first feature representation; the GAT adaptively allocates dynamic weights using an attention mechanism, extracts non-uniform spatial dependence features, and generates a second feature representation; the two kinds of feature representations are fused, input into a time sequence modeling module to analyze time dependence, and finally output a future time ground surface displacement prediction result. The method significantly improves the accuracy of ground surface displacement prediction.

Description

Technical Field

[0001] This invention relates to the fields of geographic information data processing and artificial intelligence technology. Specifically, it relates to a method for predicting the time series of surface displacement of highway slopes based on graph attention, which is particularly suitable for early warning of geological disasters based on the Global Navigation Satellite System (GNSS) monitoring network. Background Technology

[0002] Highway slope surface deformation, i.e., displacement of the Earth's surface caused by internal and external forces, is a core indicator for assessing regional geological stability. Severe surface deformation can trigger serious geological disasters such as landslides and ground subsidence, posing a significant threat to people's lives, property, and infrastructure. Global Navigation Satellite Systems (GNSS), with their advantages of all-weather, high-precision, and continuous observation, have become a key technological means for large-scale surface deformation monitoring. Accurately predicting future surface deformation trends based on the massive amounts of time-series data collected by GNSS monitoring stations has immeasurable value for early disaster identification and risk mitigation.

[0003] Existing methods for predicting surface deformation on highway slopes are mainly divided into two categories: physical model-driven and data-driven. While physical models have clear physical meaning, they typically require a large number of difficult-to-obtain geological parameters and are computationally complex, making them difficult to apply to real-time, large-scale predictions. Therefore, data-driven methods, especially deep learning models, have become the mainstream research approach.

[0004] Early data-driven methods often employed time series models such as Long Short-Term Memory (LSTM) networks and Gated Recurrent Units (GRUs). While these models performed well in processing time series data from individual monitoring stations, they treated each station as an isolated entity, completely ignoring the interactions between geographically adjacent or related stations. In large-scale, geologically complex regions, surface deformation often exhibits significant spatial correlations; deformation in one region can affect another. This neglect of spatial dependence severely limits the predictive accuracy of these models.

[0005] To address this issue, researchers have introduced graph neural networks (GNNs), such as graph convolutional networks (GCNs), to model monitoring station networks. For example, the spatiotemporal graph convolutional network (T-GCN) combines GCNs with GRUs, enabling the simultaneous capture of spatiotemporal features. However, these GCN-based methods suffer from a common limitation in modeling spatial relationships: they typically assign equal weights to all neighboring nodes or employ simple, fixed-distance-based weighting methods (such as the inverse distance). This static, homogeneous weighting strategy fails to accurately reflect the complex and heterogeneous spatial dependencies in large-scale monitoring networks. In reality, the influence of different neighboring nodes on the central node is dynamic and should not be treated equally.

[0006] Furthermore, surface deformation of highway slopes is a complex geophysical process driven by a variety of environmental factors, including rainfall, groundwater changes, and tectonic activity. Although some studies have attempted to incorporate these environmental factors as auxiliary variables into models, most have only been conducted on small-scale scenarios and have failed to effectively distinguish and model the complex, potentially lagged, influence mechanisms between dynamic environmental factors (such as rainfall that varies over time) and static geographical factors (such as fixed elevations and fault locations).

[0007] In summary, existing technologies for predicting surface displacement, especially in large-scale and complex scenarios, suffer from problems such as oversimplified spatial dependency modeling, failure to achieve adaptive weighting, and insufficient fusion of multi-source environmental driving factors, which lead to room for improvement in prediction accuracy and model interpretability. Summary of the Invention

[0008] The main objective of this invention is to overcome the aforementioned deficiencies of the prior art and provide a graph attention-based method for predicting the time series of surface displacement on highway slopes. This method can adaptively learn the non-uniform spatial dependencies between monitoring stations in a large-scale monitoring network and effectively integrate multi-source dynamic and static environmental factors, thereby significantly improving the accuracy of surface displacement prediction.

[0009] In a first aspect, the present invention provides a method for predicting the time series of surface displacement of highway slopes based on graph attention, comprising the following steps:

[0010] Acquire time series data of surface displacement from multiple monitoring stations and environmental impact data related to the monitoring stations;

[0011] A weighted adjacency matrix is ​​constructed based on the geographical location information of the monitoring stations to represent the initial spatial topological relationship between the monitoring stations;

[0012] The surface displacement time series data and the environmental impact data are fused to construct an attribute-enhanced feature matrix;

[0013] The weighted adjacency matrix and the attribute-enhanced feature matrix are input in parallel into a graph convolutional network module and a graph attention network module for spatial feature extraction, wherein:

[0014] The graph convolutional network module extracts structured spatial features based on the fixed topology defined by the weighted adjacency matrix, and generates a first spatial feature representation.

[0015] The graph attention network module adaptively assigns dynamic weights to neighboring monitoring stations of each monitoring station through an attention mechanism, extracts non-uniform spatial dependency features, and generates a second spatial feature representation.

[0016] The first spatial feature representation and the second spatial feature representation are fused to generate a fused spatial feature representation;

[0017] The fused spatial feature representation is input into a time-series modeling module according to the time step to model the time dependence of surface displacement and output the predicted surface displacement results for future times.

[0018] As an optional implementation of the first aspect of this application, the environmental impact data includes dynamic environmental data and static geographic data; the step of constructing the attribute-enhanced feature matrix specifically includes: using the surface displacement time series data as the basic feature matrix; constructing the dynamic environmental data into a dynamic feature matrix, wherein the dynamic environmental data includes daily precipitation data and daily humidity data at the location of the monitoring station; constructing the static geographic data into a static feature matrix, wherein the static geographic data includes elevation data of each monitoring station and distance data from each monitoring station to the nearest geological fault zone; and at each time step, combining the basic feature matrix, the dynamic feature matrix, and the static feature matrix to form the attribute-enhanced feature matrix.

[0019] As an optional implementation of the first aspect of this application, the step of fusing the first spatial feature representation and the second spatial feature representation specifically involves: using a feature addition strategy to add the first spatial feature representation output by the graph convolutional network module and the second spatial feature representation output by the graph attention network module element by element to generate the fused spatial feature representation, so as to retain complementary spatial information.

[0020] As an optional implementation of the first aspect of this application, the step of extracting non-uniform spatial dependency features includes: employing a multi-head attention mechanism, wherein each attention head independently calculates attention coefficients and generates a feature representation; for each attention head, firstly, the node features are transformed by a shared learnable linear transformation matrix, and then an unnormalized attention score between any two nodes is calculated by a feedforward neural network; the unnormalized attention score is processed using the LeakyReLU activation function, and the scores of all neighboring nodes of a node are normalized by the Softmax function to obtain the final attention coefficients; the output feature vectors of multiple attention heads are concatenated to form the second spatial feature representation, so that the model can learn the importance of neighboring nodes from different representation subspaces.

[0021] As an optional implementation of the first aspect of this application, the step of constructing the weighted adjacency matrix specifically involves: using a Gaussian similarity function to calculate the connection weight between two monitoring stations based on the Euclidean spatial distance between any two monitoring stations; the connection weight is inversely proportional to the distance between the monitoring stations, and its decay rate is controlled by a scale parameter, so as to construct a fully connected weighted adjacency matrix that can reflect spatial proximity.

[0022] As an optional implementation of the first aspect of this application, the step of inputting the fused spatial feature representation into a time-series modeling module by time step includes: the time-series modeling module is a gated loop unit; at each time step, the information flow is controlled by an update gate and a reset gate inside the gated loop unit; the update gate determines the extent to which the hidden state information of the previous time step is brought into the current state; the reset gate determines the extent to which the hidden state information of the previous time step is ignored; through the above-mentioned gating mechanism, the long-term time dependence in the surface displacement sequence is captured, and the hidden state is updated to generate prediction results.

[0023] As an optional implementation of the first aspect of this application, the method further includes a model training step, which includes: dividing the time series data using a sliding window method, using data containing multiple consecutive past time steps as input, and predicting the surface displacement for a future time step; defining a combined loss function for model optimization, the combined loss function including a mean squared error loss term for measuring the difference between the predicted value and the true value, and an L2 regularization loss term for preventing model overfitting; and using the AdamW optimizer to iteratively update the trainable parameters in the model according to the combined loss function.

[0024] As an optional implementation of the first aspect of this application, before constructing the attribute-enhanced feature matrix, a data preprocessing step is also included. This step includes: identifying and removing outliers from the original surface displacement time series data using the quartile interval method, correcting step shifts using least squares fitting, and interpolating missing data points using a regularized expectation-maximization algorithm; scaling the values ​​of input variables, including surface displacement, precipitation, humidity, elevation, and fault distance, to a uniform interval of [0,1] using the min-max normalization method.

[0025] In a second aspect, embodiments of this application provide an electronic device, which includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the steps of the method described in the first aspect.

[0026] Thirdly, embodiments of this application provide a readable storage medium on which a program or instructions are stored, which, when executed by a processor, implement the steps of the method described in the first aspect.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. Adaptive and Refined Spatial Modeling: By using GCN and GAT in parallel and fusing their outputs, this method overcomes the limitations of traditional graph models that rely on fixed, homogeneous spatial weights. The introduction of GAT enables the model to adaptively focus on neighboring nodes that are more important to the current prediction task, thereby more accurately characterizing the non-uniform spatial interactions in large-scale complex geological environments and significantly improving the expressive power of spatial features.

[0029] 2. Comprehensive Multi-Source Information Fusion: By constructing an attribute-enhanced feature matrix, this method seamlessly integrates time-varying dynamic environmental factors and time-invariant static geographic factors into the spatiotemporal prediction framework. This not only provides the model with richer contextual information and enhances the understanding of complex deformation-driving mechanisms, but also improves the physical interpretability of the prediction results. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall structural framework of the GATTGCN model proposed in this embodiment of the invention;

[0031] Figure 2 This is a flowchart of a method for predicting the time series of surface displacement of highway slopes based on graph attention, according to an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram of the weighted graph construction method in an embodiment of the present invention;

[0033] Figure 4 This is a diagram of the parallel spatial feature extraction architecture of the core GATTGCN model in this embodiment of the invention;

[0034] Figure 5 This is a visualization comparing the prediction results of the GATGCN model with those of the GAT, GCN, and GRU models at a representative monitoring station in an embodiment of the present invention.

[0035] Figure 6 This is a visualization comparing the prediction results of the GATTGCN model with those of the T-GCN and LSTM models in an embodiment of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0037] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0038] Example 1

[0039] Please see Figure 1 This invention proposes a time series prediction model for roadside surface displacement based on graph attention, named the GATTGCN model. This model fully considers the spatial dependencies between monitoring points and various factors affecting deformation and displacement prediction in large-scale geographical scenarios.

[0040] In traditional small-scale displacement prediction, non-Euclidean distances are typically used to construct the spatial correlation between monitoring points. Based on and extending this approach, this invention first constructs a fully connected weighted adjacency matrix A to capture the fundamental spatial dependencies between stations. Simultaneously, based on temporal deformation data collected from each monitoring point, a feature matrix X is constructed to characterize the temporal characteristics of each node. Secondly, considering that in large-scale geographical scenarios, in addition to the spatial relationships between stations, there are dynamic environmental factors such as rainfall and humidity, as well as static geographical factors such as monitoring point elevation and fault distance, which can significantly affect surface deformation, rainfall and humidity are considered dynamic features, while DEM and fault distance are used as static features. Then, a dynamic feature matrix D and a static feature matrix S are constructed to describe these external variables. Subsequently, the feature matrix X is combined with the two attribute matrices S and D to form an attribute enhancement matrix T. Finally, using attribute embedding, the features and attributes of matrix T are embedded into Graph Convolutional Network (GCN) and Graph Attention Network (GAT) units, and then combined with Gated Recurrent Units (GRU) to extract the dynamic evolution features of each node along the time dimension. The overall time series prediction method can be implemented using a function... express:

[0041] .

[0042] Please see Figure 2 This is a flowchart illustrating a time series prediction method for roadside surface displacement based on graph attention, provided by an embodiment of the present invention. The method may include the following steps:

[0043] S1: Acquire time series data of surface displacement from multiple monitoring stations and environmental impact data related to the monitoring stations.

[0044] In this embodiment, the monitoring of surface deformation on highway slopes in the Sichuan-Yunnan region of China is used as a specific application scenario. This region, located in southwestern China, is geologically active, has complex topography, and significant surface displacement. It is one of the most earthquake- and geologically hazardous areas in China, making it an ideal region to verify the effectiveness of this method.

[0045] First, observational data from 74 Global Navigation Satellite System (GNSS) monitoring stations within the study area were acquired. The data spans from January 1, 2011 to December 30, 2022. The daily positions of each monitoring station were calculated using the precise point positioning mode of PANDA software. This embodiment primarily focuses on the time series data of vertical surface displacement.

[0046] Simultaneously, multi-source environmental impact data corresponding to the geographical location of each monitoring station are acquired. This data is crucial for understanding and predicting surface deformation, and is specifically divided into two categories:

[0047] Dynamic environmental data refers to factors that change over time, primarily including daily precipitation and humidity data for each monitoring station's location. These factors, especially heavy rainfall, are direct causes of geological disasters such as landslides.

[0048] Static geographic data refers to geographic attributes that do not change over time. It primarily includes the elevation reflected in the digital elevation model (DEM) data of each monitoring station, and the Euclidean distance data from each monitoring station to the nearest geological fault zone. These factors reflect the long-term disaster-prone environment of surface deformation.

[0049] Before inputting the raw data into the model, a series of rigorous data preprocessing steps are performed to ensure data quality and model performance. These preprocessing steps specifically include:

[0050] Surface displacement data cleaning: Due to factors such as equipment upgrades and multipath effects, outliers, step shifts, and missing data are inevitably present in the original GNSS time series. This embodiment uses the quartile interval method to identify and remove outliers (outliers) from the data series; it uses the least squares fitting method to detect and correct step shifts caused by events such as equipment replacement or earthquakes; and it uses a regularized expectation-maximization algorithm to interpolate missing data points in the series to generate a complete and continuous time series.

[0051] Multi-source data standardization: Since variables such as surface displacement (mm), precipitation (mm), humidity (%), elevation (m), and fault distance (m) have different units and numerical ranges, this embodiment employs min-max standardization to eliminate the impact of these dimensional differences on model training. For all input variables, their values ​​are standardized using the following formula. Scaling to a uniform range of [0,1]:

[0052]

[0053] Among them, time series data such as surface displacement, precipitation, and humidity and These are the minimum and maximum values ​​of their respective independent time series; for static data such as elevation and fault distance, the global minimum and maximum values ​​of all 74 stations are used for normalization.

[0054] S2: Construct a weighted adjacency matrix based on the geographical location information of the monitoring stations to characterize the initial spatial topological relationship between the monitoring stations.

[0055] like Figure 3 The diagram shown illustrates the weighted graph construction method in this embodiment of the invention, demonstrating the abstraction process from monitoring stations to a weighted adjacency matrix: the monitoring stations are abstracted as nodes in a graph structure, and then the Gaussian similarity function is used to calculate the weights between nodes, ultimately constructing a weighted adjacency matrix.

[0056] To effectively represent the spatial correlation between monitoring station networks in a deep learning model, this embodiment abstracts the entire monitoring network as a weighted undirected graph. .in It represents the set of nodes representing monitoring stations. It refers to the number of monitoring stations. It is the set of edges connecting each monitoring station. This represents the weights between nodes.

[0057] In this embodiment, a Gaussian similarity function is used to construct the weighted adjacency matrix A. Specifically, based on any two monitoring stations... and Given the geographic coordinates, calculate the Euclidean spatial distance between them, and then calculate the connection weight between them using the following formula. :

[0058]

[0059] in This indicates the weight between the two monitoring stations. Representative monitoring station and The spatial distance between them, and It is a scale parameter that controls the rate at which adjacency weights decay.

[0060] The weighted adjacency matrix is ​​shown below:

[0061]

[0062] The core idea of ​​this function is the "First Law of Geography," which states that things that are geographically close are more closely related. Therefore, the weighted adjacency matrix A constructed using this method is a fully connected matrix, where each element... All of these reflect the monitoring station and The spatial proximity between them. This matrix provides initial, fixed-distance-based spatial topology information for subsequent graph neural network modules.

[0063] S3: The surface displacement time series data and the environmental impact data are fused to construct an attribute-enhanced feature matrix.

[0064] To enable the model to comprehensively consider both the inherent variation patterns of surface displacement and the complex driving forces of the external environment, this embodiment employs an attribute embedding mechanism to fuse the various data obtained and preprocessed in step S1, forming an attribute-enhanced feature matrix. The specific process is as follows:

[0065] Basic Feature Matrix: The basic feature matrix is ​​constructed using the time series data of vertical surface displacement from 74 monitoring stations. At any time step t, this matrix... The dimension is 74×1, representing the displacement value of all stations at that moment.

[0066] Specifically, a feature matrix was constructed to represent the temporal correlation of the monitoring stations. It contains time-series information from all monitoring stations, here. It refers to the number of monitoring stations, and This indicates the total length of the sequence. Indicates time The observation values ​​at each monitoring station. If the input is a value with... The data of a historical time series data point can be represented as follows:

[0067]

[0068] Meanwhile, the next prediction The output at time t can be represented as:

[0069]

[0070] Therefore, let Indicates time The feature matrix of , where It refers to the number of monitoring stations.

[0071] Static Feature Matrix: A static feature matrix is ​​constructed from two types of static geographic data: elevation (DEM) and fault distance. This matrix has a dimension of 74×2, and its content does not change over time.

[0072] Because static features such as digital elevation models (DEMs) and fault distances remain unchanged over time and are organized into a static attribute matrix. ,in This refers to the number of static properties. (In time...) The static attribute matrix is ​​defined as follows:

[0073]

[0074] Dynamic Feature Matrix: A dynamic feature matrix is ​​constructed from two types of dynamic environmental data: precipitation and humidity. At any time step t, this matrix... The dimension is 74×2, representing the two dynamic environmental attribute values ​​of all stations at that moment.

[0075] Specifically, in contrast, dynamic properties such as precipitation and humidity change over time. Let... Indicates in At each time step A dynamic attribute. Indicates from time Time A dynamic attribute matrix of length is considered. To capture the temporal impact and potential lag effects of environmental variables, a matrix of length is also considered. The time window. Within the time... The dynamic attribute matrix is ​​defined as follows:

[0076]

[0077]

[0078] At each time step t, the fundamental features at that moment are... Dynamic characteristics and static characteristics that do not change over time The components are combined (e.g., concatenated or joined along the feature dimension) to form the attribute-enhanced input matrix at that moment. It can be defined as follows:

[0079]

[0080] The matrix The dimension is 74×(1+2+2)=74×5. In this way, the model's input at each time step not only includes surface displacement information, but also incorporates rich dynamic and static environmental background knowledge, greatly enhancing the model's representation ability and understanding of complex deformation mechanisms.

[0081] S4: The weighted adjacency matrix and the attribute-enhanced feature matrix are input in parallel to a graph convolutional network module and a graph attention network module for spatial feature extraction, wherein: the graph convolutional network module extracts structured spatial features based on the fixed topology defined by the weighted adjacency matrix to generate a first spatial feature representation; the graph attention network module adaptively assigns dynamic weights to the neighboring monitoring stations of each monitoring station through an attention mechanism to extract non-uniform spatial dependency features and generate a second spatial feature representation.

[0082] like Figure 4 As shown, this invention employs an innovative parallel spatial feature extraction architecture designed to simultaneously capture structured and adaptive spatial dependencies in a monitoring network. This architecture comprises two parallel core modules:

[0083] Graph Convolutional Network (GCN) module: After establishing the spatiotemporal data model and embedding attributes, a Graph Convolutional Network (GCN) is used to capture the spatial dependencies between nodes. GCN can operate directly on irregular graph structures and integrate the graph's topology with node features. Through graph convolution operations, GCN effectively extracts the relationships and feature information between nodes, thereby achieving effective learning of graph structure representations.

[0084] like Figure 4 As shown, in order to capture the spatial dependencies between nodes, GCN uses the adjacency matrix... and attribute-enhanced feature matrices As input, the propagation rules of GCN are expressed by the following equation:

[0085]

[0086] in, This represents the original adjacency matrix, used to describe the connection relationships between nodes in the graph. In the adjacency matrix Add self-loop (i.e.) ,in (This is the identity matrix), and then normalization is performed; yes The angle matrix; Indicates the first Trainable weights of the layer; It is a non-linear activation function; Indicates the first The node feature matrix of the layer (where It is the number of nodes. This refers to the feature dimension of this layer. Note: ).

[0087] Based on the fixed spatial topology defined by the adjacency matrix A, GCN performs a weighted average of neighbor information, effectively extracting structured spatial features based on fixed distance dependencies in the monitoring network. After GCN processing, a first spatial feature representation is generated. .

[0088] Graph Attention Network (GAT) module: When processing graph structures, GCN assigns the same weight to all adjacent nodes, making it difficult to capture deeper and more complex spatial relationships between nodes. Therefore, a GAT layer (such as...) is introduced. Figure 4 As shown in the diagram, this layer can dynamically aggregate information from neighboring nodes, thereby progressively enriching the feature representation of nodes within the hierarchical structure. Its computational principle is as follows:

[0089]

[0090] in, and Representing nodes respectively and its neighboring nodes eigenvectors; It is a learnable linear transformation matrix shared among all nodes; Indicates a splicing operation; It is a shared single-layer feedforward neural network used to compute attention scores. Represents a node The set of neighboring nodes. This step calculates the unnormalized attention coefficients. This coefficient measures the nodes Features of nodes The importance of.

[0091]

[0092] in, It is the normalized attention coefficient, obtained by comparing the unnormalized attention score. After applying the LeakyReLU activation function, then apply it to all neighboring nodes. This is obtained by performing Softmax exponential normalization. This normalization process ensures that the sum of the attention coefficients of each node's neighbors is 1.

[0093]

[0094] Finally, through nodes The weighted sum of the features of all neighboring nodes is obtained. Each neighboring node Features First, it undergoes a linear transformation, then it is multiplied by its corresponding attention weight. This approach allows the model to selectively aggregate information based on the importance of each neighboring node, thereby representing the relationships between nodes more accurately.

[0095] To further enhance the model's representational capabilities, Graph Attention Networks (GAT) introduce a multi-head attention mechanism. In this model, attention computation is repeated across two independent attention heads, enabling the model to learn the importance of neighboring nodes from different subspaces. Each attention head generates an independent feature representation, and the outputs of multiple heads are ultimately fused by concatenation. The corresponding formula is shown below:

[0096]

[0097] in, Represents a node The final output feature vector; and Representing nodes respectively The output feature vectors of the first and second attention heads; This refers to the operation of concatenating multiple feature vectors into a single feature vector with a higher dimension.

[0098] Finally, the output feature vectors of the two attention heads are concatenated to form the final second spatial feature representation. In this way, GAT can extract non-uniform, dynamic, and more physically meaningful spatially dependent features in the monitoring network.

[0099] S5: The first spatial feature representation and the second spatial feature representation are fused to generate a fused spatial feature representation.

[0100] To integrate spatial features extracted by different types of graph neural networks, this model fuses the outputs of GCN (Graph Convolutional Network) and GAT (Graph Attention Network) modules. These two modules independently process the same input sequence and produce corresponding feature representations, denoted as […]. and ,in It is the number of nodes. This refers to the feature dimension. A feature addition strategy is applied to combine these two outputs, resulting in a fused spatial feature representation:

[0101]

[0102] The fused representation combines the structural modeling capabilities of Graph Convolutional Networks (GCNs) with the adaptability of Graph Attention Networks (GATs). This approach allows the model to preserve complementary spatial information while maintaining computational simplicity. The resulting matrix... This will serve as input for the time modeling section described in the next section.

[0103] S6: Input the fused spatial feature representation into a time-series modeling module according to the time step to model the time dependence of surface displacement and output the surface displacement prediction results for future times.

[0104] In this embodiment, the temporal modeling module employs a gated recurrent unit (GRU). GRU is a variant of recurrent neural networks (RNNs). By introducing a gating mechanism, it effectively solves the long-term dependency problem and gradient vanishing problem in traditional RNNs, while having fewer parameters and higher computational efficiency than long short-term memory networks (LSTM).

[0105] To capture the temporal dependence of node features over time, the fused spatial representation... It is passed to a gated recurrent unit (GRU). A GRU is a type of recurrent neural network (RNN) designed to simulate sequential data while addressing the vanishing gradient problem in traditional RNNs.

[0106] like Figure 4 As shown, the GRU maintains a hidden state. This state at each time step Based on the current input and the previous hidden state Update. The GRU unit contains two critical gates: the reset gate. and the update gate They control the flow of information over time. The core computation of the GRU unit is as follows:

[0107]

[0108]

[0109]

[0110]

[0111] Among them, parameters , , , , , These are all weights used during the training process; It is the sigmoid activation function; This represents element-wise multiplication; and They represent time. Output the candidate hidden states and the final hidden state.

[0112] Through this ingenious gating mechanism, GRU can learn the complex dynamic evolution patterns of surface displacement sequences over time, including periodicity, trends, and abrupt changes. Finally, based on the hidden state of its last time step, the GRU module outputs the predicted surface displacement for the next time step through one or more fully connected layers (output layers).

[0113] Optionally, in other implementations, a complete model training step is also included. A sliding window method is used to divide the time series data, using data containing the past 16 days (time step) as input to predict the surface displacement at the next time step (day 17). The loss function for model optimization is a combined loss function, defined as follows:

[0114]

[0115] in It is the mean squared error loss. This is the L2 regularization loss. Mean squared error loss measures the magnitude of the model's prediction error by averaging the squared differences between the predicted and actual values. The formula for mean squared error loss is as follows:

[0116]

[0117] in This is the actual value. It is a predicted value. This refers to the number of samples. To reduce overfitting and improve the model's generalization ability, L2 regularization loss is introduced. The formula is as follows:

[0118]

[0119] in It is the regularization coefficient, used to control the strength of regularization. These are the weight parameters in the model.

[0120] The loss function consists of two parts: the first part is the Mean Squared Error (MSE) loss term, which measures the difference between the predicted value and the true value; the second part is the L2 regularization loss term, which prevents the model from overfitting and improves its generalization ability by penalizing the weight parameters in the model, where λ is a coefficient that controls the strength of regularization.

[0121] The AdamW optimizer is used to iteratively update all trainable parameters in the model (including the weight matrices and bias terms in GCN, GAT, and GRU) based on this combined loss function. AdamW is an improved version of the Adam optimizer that can handle weight decay more effectively.

[0122] Key hyperparameters were optimized through comparative experiments to achieve the best performance. By evaluating model performance with different numbers of hidden units, the learning rate was ultimately determined to be 1×10⁻⁶. -4 The batch size was set to 64, the training epochs were set to 200, and the number of hidden units in GCN, GAT, and GRU were all set to 32.

[0123] In summary, this embodiment systematically acquires and refines multi-source data, utilizes an innovative parallel architecture of GCN and GAT to deeply mine and fuse complementary spatial features, and then uses GRU for accurate temporal modeling. This method constructs an end-to-end deep learning framework that can accurately capture complex spatiotemporal dependencies in large-scale monitoring networks, thereby achieving high-precision prediction of surface displacements such as highway slopes.

[0124] Optionally, in this study, Graph Attention Network (GAT), Graph Convolutional Network (GCN), Gated Recurrent Unit (GRU), Spatiotemporal Graph Convolutional Network (T-GCN), and Long Short-Term Memory (LSTM) were used as baseline models for comparison with the proposed model. For those baselines that depend on spatial correlation, the adjacency matrix was constructed using the same method described in this paper. Considering all dynamic and static factors, the prediction accuracy of each model is summarized in Table 1. In this study, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) were used as baselines for comparison. 2 () is used to evaluate the performance of the GATTGCN model.

[0125] Table 1. Prediction results of the GATTGCN model and other baseline methods for deformation data in the Sichuan-Yunnan region.

[0126]

[0127] Experimental results show that the proposed model outperforms traditional deep learning methods. In more complex, large-scale scenarios, the traditional model has weaker predictive power; in contrast, the improved model has stronger predictive power, with RMSE reductions of 28.4%, 12.8%, 15.4%, 12.4%, and 11.5% compared to GAT, GCN, GRU, T-GCN, and LSTM, respectively.

[0128] To further demonstrate the performance of the GATTGCN model, a monitoring station was randomly selected, and the test set prediction results of GATTGCN, GAT, GCN, GRU, T-GCN, and LSTM were visualized. Figure 5 , Figure 6 Despite irregular fluctuations in surface deformation, most models captured the overall trend. GAT performed the worst among graph-based models. GRU and GCN showed similar but lower accuracy, while LSTM tracked the trend better but exhibited significant bias. T-GCN showed a slight improvement. In contrast, GATTGCN achieved the best fit, providing predictions closest to the actual ground conditions and demonstrating higher stability, which is crucial for deformation prediction.

[0129] Optionally, embodiments of this application also provide an electronic device, including a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the various processes of the above-described embodiment of a method for predicting the time series displacement of highway slope based on graph attention, and can achieve the same technical effect. To avoid repetition, they will not be described again here.

[0130] Optionally, embodiments of this application also provide a readable storage medium storing a program or instructions. When the program or instructions are executed by a processor, they implement the various processes of the above-described embodiment of a graph attention-based method for predicting the time series displacement of highway slopes, and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0131] The processor is the processor in the electronic device described in the above embodiments. The readable storage medium includes computer-readable storage media, such as computer read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0132] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0133] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0134] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A method for predicting the time series of surface displacement on highway slopes based on graph attention, characterized in that, Includes the following steps: The surface displacement time series data of multiple monitoring stations and the environmental impact data related to the monitoring stations are acquired. The environmental impact data includes dynamic environmental data such as daily precipitation and daily humidity at the location of the monitoring stations, as well as static geographical data such as the elevation and distance to the nearest geological fault zone of each monitoring station. Based on the geographical location information of the monitoring stations, a Gaussian similarity function is used to calculate the connection weight between two monitoring stations based on the Euclidean spatial distance between any two monitoring stations. The connection weight is inversely proportional to the distance between the monitoring stations and its decay rate is controlled by a scale parameter to construct a fully connected weighted adjacency matrix that can reflect spatial proximity, so as to characterize the initial spatial topological relationship between the monitoring stations. The surface displacement time series data and the environmental impact data are fused to construct an attribute-enhanced feature matrix. Specifically, this includes: using the surface displacement time series data as a basic feature matrix; constructing a dynamic feature matrix from the dynamic environmental data; constructing a static feature matrix from the static geographic data; and combining the basic feature matrix, the dynamic feature matrix, and the static feature matrix at each time step to form the attribute-enhanced feature matrix. The weighted adjacency matrix and the attribute-enhanced feature matrix are input in parallel into a graph convolutional network module and a graph attention network module for spatial feature extraction, wherein: The graph convolutional network module extracts structured spatial features based on the fixed topology defined by the weighted adjacency matrix, and generates a first spatial feature representation. The graph attention network module adaptively assigns dynamic weights to neighboring monitoring stations of each monitoring station through an attention mechanism, extracts non-uniform spatial dependency features, and generates a second spatial feature representation. The first spatial feature representation and the second spatial feature representation are fused, specifically by using a feature addition strategy to add the first spatial feature representation and the second spatial feature representation element by element to generate a fused spatial feature representation. The fused spatial feature representation is input into a time-series modeling module according to the time step to model the time dependency of surface displacement and output the surface displacement prediction result for future time. The time-series modeling module is a gated loop unit that executes the following gating mechanism: at each time step, the update gate and reset gate inside the gated loop unit are used to control the information flow; the update gate determines the extent to which the hidden state information of the previous time step is brought into the current state; the reset gate determines the extent to which the hidden state information of the previous time step is ignored; through the above gating mechanism, the long-term time dependency in the surface displacement sequence is captured, and the hidden state is updated to generate the prediction result.

2. The method for predicting the time series of surface displacement of highway slopes based on graph attention as described in claim 1, characterized in that, The step of extracting non-uniform spatial dependency features includes: A multi-head attention mechanism is adopted, in which each attention head independently calculates the attention coefficient and generates a feature representation; For each attention head, the node features are first transformed using a shared learnable linear transformation matrix, and then the unnormalized attention score between any two nodes is calculated using a feedforward neural network. The unnormalized attention score is processed using the LeakyReLU activation function, and the scores of all neighboring nodes of a node are normalized using the Softmax function to obtain the final attention coefficient. The output feature vectors of multiple attention heads are concatenated to form the second spatial feature representation, enabling the model to learn the importance of neighboring nodes from different representation subspaces.

3. The method for predicting the time series of surface displacement of highway slopes based on graph attention according to claim 1, characterized in that, The method also includes a model training step, which includes: The time series data is divided using a sliding window method, and the surface displacement at the next time step is predicted by using data containing multiple consecutive past time steps as input. Define a combined loss function for model optimization, which includes a mean squared error loss term to measure the difference between the predicted and the true values, and an L2 regularization loss term to prevent the model from overfitting. The AdamW optimizer is used to iteratively update the trainable parameters in the model based on the combined loss function.

4. The method for predicting the time series of surface displacement of highway slopes based on graph attention according to claim 1, characterized in that, Before constructing the attribute-enhanced feature matrix, a data preprocessing step is also included, which includes: For the original surface displacement time series data, outliers were identified and removed using the quartile interval method, step migration was corrected using least squares fitting, and missing data points were interpolated using the regularized expectation-maximization algorithm. For input variables including surface displacement, precipitation, humidity, elevation, and fault distance, the minimum-maximum standardization method is used to scale their values ​​to a uniform interval of [0,1].

5. An electronic device, characterized in that, The method includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the steps of the method for predicting the time series of roadside surface displacement based on graph attention as described in any one of claims 1-4.

6. A readable storage medium, characterized in that, The program or instructions are stored on the readable storage medium, and when the program or instructions are executed by the processor, they implement the steps of the method for predicting the time series of surface displacement of highway slope based on graph attention as described in any one of claims 1-4.

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