Road slope surface displacement time sequence prediction method based on graph attention

Abstract

The invention belongs to the technical field of geographic information data processing, and discloses a graph attention-based road slope surface displacement time sequence prediction method, which comprises the following steps of: obtaining surface displacement time sequence data of a plurality of monitoring stations and associated environmental influence data, and constructing a weighted adjacency matrix based on geographic positions of the monitoring stations, defining an initial spatial topological relation; carrying out feature fusion on the displacement data and the environment data, and constructing an attribute-enhanced feature matrix; respectively inputting the weighted adjacency matrix and the feature matrix into a graph convolutional network and a graph attention network for parallel processing; extracting structured spatial features by the GCN through a fixed topological structure, and generating a first feature representation; the GAT adaptively allocates a dynamic weight by using an attention mechanism, extracts a non-uniform spatial dependency feature, and generates a second feature representation; and fusing the two feature representations, inputting a time sequence modeling module to analyze time dependence, and finally outputting a surface displacement prediction result at a future moment. According to the method, the accuracy of surface displacement prediction is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of geographic information data processing and artificial intelligence technology, and in particular to a method for predicting time series of highway slope surface displacement 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 Art

[0002] Surface deformation of highway slopes—the displacement of the Earth's surface due to internal and external forces—is a core indicator for assessing regional geological stability. Drastic surface deformation can trigger severe geological disasters such as landslides and ground subsidence, posing a significant threat to public life, property, and infrastructure. The Global Navigation Satellite System (GNSS), with its all-weather, high-precision, and continuous observation capabilities, has become a key technology for large-scale surface deformation monitoring. Accurately predicting future surface deformation trends based on the massive time series data collected by GNSS monitoring stations is invaluable for early disaster identification and risk mitigation.

[0003] Existing methods for predicting highway slope surface deformation are primarily categorized as physical model-driven and data-driven. While physical models offer 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. Consequently, data-driven methods, particularly deep learning models, have become the mainstream of research.

[0004] Early data-driven approaches often employed time series models such as long short-term memory (LSTM) networks and gated recurrent units (GRU). These models performed well when processing time series data from a single monitoring station, but they treated each station as an isolated entity, completely ignoring the interactions between geographically adjacent or related stations. In large, geologically complex areas, surface deformation often exhibits significant spatial correlation, with deformation in one region affecting another. This neglect of spatial dependence significantly limits the model's predictive accuracy.

[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 to capture both temporal and spatial features. However, these GCN-based methods have a common limitation when modeling spatial relationships: they typically assign equal weights to all neighboring nodes, or use a simple, fixed-distance-based weighting method (such as the inverse of the distance). This static, homogenized weight distribution strategy cannot truly reflect the complex and heterogeneous spatial dependencies in large-scale monitoring networks. In reality, the influence of different neighboring nodes on the central node changes dynamically and should not be treated equally.

[0006] Furthermore, highway slope surface deformation is a complex geophysical process, driven by multiple environmental factors, including rainfall, groundwater changes, and tectonic activity. While some studies have attempted to incorporate these environmental factors as auxiliary variables into models, most have been conducted only on a small scale and have failed to effectively distinguish and model the complex, potentially hysteretic, influence mechanisms between dynamic environmental factors (such as time-varying rainfall) and static geographic factors (such as fixed elevation and fault location).

[0007] In summary, existing technologies for surface displacement prediction, especially in large-scale and complex scenarios, have problems such as oversimplification of spatial dependency modeling, failure to implement adaptive weighting, and insufficient integration of multi-source environmental driving factors. As a result, the prediction accuracy and model interpretability need to be improved. Summary of the Invention

[0008] The main purpose of the present invention is to overcome the above-mentioned defects of the prior art and provide a time series prediction method for highway slope surface displacement based on graph attention. 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 highway slope surface displacement time series based on graph attention, comprising the following steps: obtaining time series data of surface displacements of a plurality of monitoring stations and environmental impact data associated with the monitoring stations; Constructing a weighted adjacency matrix based on the geographical location information of the monitoring stations to represent the initial spatial topological relationship between the monitoring stations; fusing the surface displacement time series data with the environmental impact data to construct a feature matrix with enhanced attributes; 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 to perform spatial feature extraction, wherein: The graph convolutional network module extracts structured spatial features based on the fixed topological structure defined by the weighted adjacency matrix and generates a first spatial feature representation; The graph attention network module adaptively assigns dynamic weights to the neighboring monitoring stations of each monitoring station through the attention mechanism, extracts non-uniform spatial dependency features, and generates a second spatial feature representation; fusing the first spatial feature representation and the second spatial feature representation 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, the time dependency of the surface displacement is modeled, and the surface displacement prediction result at the future moment is output.

[0010] As an optional implementation manner of the first aspect of the present 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; 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.

[0011] As an optional implementation of the first aspect of the present application, the step of fusing the first spatial feature representation and the second spatial feature representation is specifically: adopting a feature addition strategy, adding 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, and generating the fused spatial feature representation to retain complementary spatial information.

[0012] As an optional implementation of the first aspect of the present application, the step of extracting non-uniform spatially dependent features includes: adopting a multi-head attention mechanism, wherein each attention head independently calculates the attention coefficient and generates a feature representation; for each attention head, first transforming the node features through a shared learnable linear transformation matrix, and then calculating the unnormalized attention score between any two nodes through a feedforward neural network; using the LeakyReLU activation function to process the unnormalized attention score, and normalizing the scores of all neighbor nodes of a node through the Softmax function to obtain the final attention coefficient; splicing the output feature vectors of multiple attention heads to form the second spatial feature representation, so that the model can learn the importance of neighbor nodes from different representation subspaces.

[0013] As an optional implementation of the first aspect of the present application, the step of constructing a weighted adjacency matrix is ​​specifically: 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 attenuation rate is controlled by a scale parameter to construct a fully connected weighted adjacency matrix that can reflect spatial proximity.

[0014] As an optional implementation of the first aspect of the present application, the step of inputting the fused spatial feature representation into a time series modeling module according to time steps includes: the time series modeling module is a gated recurrent unit; at each time step, the update gate and reset gate inside the gated recurrent unit are used to control the information flow; the update gate determines to what extent the hidden state information of the previous time step is brought into the current state; the reset gate determines to what extent the hidden state information of the previous time step is ignored; through the above-mentioned gating mechanism, the long-term temporal dependency in the surface displacement sequence is captured, and the hidden state is updated to generate a prediction result.

[0015] As an optional implementation of the first aspect of the present application, the method also includes a model training step, which includes: using a sliding window method to divide the time series data, using data containing multiple consecutive time steps in the past as input to predict the surface displacement of one time step in the future; defining a combined loss function for model optimization, the combined loss function includes a mean square 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; using an AdamW optimizer to iteratively update the trainable parameters in the model according to the combined loss function.

[0016] As an optional implementation of the first aspect of the present application, before constructing the attribute-enhanced feature matrix, a data preprocessing step is also included, which includes: for the original surface displacement time series data, the interquartile range method is used to identify and eliminate outliers, the least squares fitting is used to correct step offsets, and the regularized expectation maximization algorithm is used to interpolate missing data points; for input variables including surface displacement, precipitation, humidity, elevation and fault distance, the minimum-maximum normalization method is used to scale their values ​​to a unified interval of [0,1].

[0017] In a second aspect, an embodiment of the present application provides an electronic device, which includes a processor, a memory, and a program or instruction stored in the memory and executable on the processor, wherein the program or instruction, when executed by the processor, implements the steps of the method described in the first aspect.

[0018] In a third aspect, an embodiment of the present application provides a readable storage medium, on which a program or instruction is stored. When the program or instruction is executed by a processor, the steps of the method described in the first aspect are implemented.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 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, homogenized 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 depicting the heterogeneous spatial interactions in large-scale, complex geological environments and significantly improving the expressiveness of spatial features.

[0020] 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, enhancing understanding of complex deformation driving mechanisms, but also improves the physical interpretability of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the overall structural framework of the GATTGCN model proposed in an embodiment of the present invention; Figure 2 This is a flow chart of a method for predicting time series of highway slope surface displacement based on graph attention according to an embodiment of the present invention; Figure 3 Schematic diagram of a weighted graph construction method in an embodiment of the present invention; Figure 4 This is a diagram of the parallel spatial feature extraction architecture of the GATTGCN model core in an embodiment of the present invention; Figure 5 A comparative visualization of the prediction results of the GATTGCN model and the GAT, GCN, and GRU models at a representative monitoring station in an embodiment of the present invention; Figure 6 This is a visualization diagram comparing the prediction results of the GATTGCN model, T-GCN, and LSTM model in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0023] The terms "first", "second", etc. in the specification and claims of this application are used to distinguish similar objects, and are not used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the application can be implemented in a sequence other than those illustrated or described here. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally represents that the objects associated before and after are in a kind of "or" relationship. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically limited.

[0024] Example 1 See also Figure 1 This paper proposes a graph attention-based model for predicting time series displacements of highway slopes, named the GATTGCN model. This model fully considers the spatial dependencies between monitoring points and various factors that affect deformation and displacement prediction in large-scale geographic scenarios.

[0025] In traditional small-scale displacement prediction, non-Euclidean distance is usually used to construct the spatial correlation between monitoring points. Based on and extending this idea, the present invention first constructs a fully connected weighted adjacency matrix A to capture the basic spatial dependency between sites. At the same time, based on the time-series 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 geographic scenarios, in addition to the spatial relationship between sites, there are also dynamic environmental factors such as rainfall and humidity, as well as static geographic factors such as the altitude of the monitoring point and the distance to the fault, these factors may have a significant impact on surface deformation. Therefore, rainfall and humidity are regarded as dynamic features, while DEM and fault distance are used as static features, and then the dynamic feature matrix D and the static feature matrix S are constructed respectively to describe these external variables. Subsequently, the feature matrix X is combined with the two attribute matrices S and D to form the attribute enhancement matrix T. Finally, through the attribute embedding method, the features and attributes in the matrix T are embedded into the graph convolutional network (GCN) and graph attention network (GAT) units, and then combined with the gated recurrent unit (GRU) to extract the dynamic evolution characteristics of each node along the time dimension. The overall time series prediction method can be achieved through the function express: .

[0026] See also Figure 2 , is a flow chart of a method for predicting time series of highway slope surface displacement based on graph attention provided by an embodiment of the present invention. The method may include the following steps: S1: Acquire surface displacement time series data of multiple monitoring stations and environmental impact data related to the monitoring stations.

[0027] In this example, the surface deformation monitoring of highway slopes in the Sichuan-Yunnan region of China was used as a specific application scenario. Located in southwestern China, this region has active geological structures, complex terrain, and significant surface displacement. It is one of the most active areas for earthquakes and geological disasters in China, making it an ideal location for verifying the effectiveness of this method.

[0028] First, we acquired observational data from 74 Global Navigation Satellite System (GNSS) monitoring stations within the study area. The data spanned from January 1, 2011, to December 30, 2022. We used the precise point positioning mode of PANDA software to calculate the daily position of each monitoring station. This example primarily focused on time series data of vertical surface displacement.

[0029] At the same time, multi-source environmental impact data corresponding to the geographical location of each monitoring station is obtained. These data are crucial for understanding and predicting surface deformation and are divided into two categories: Dynamic environmental data refers to factors that change over time, primarily including daily precipitation and humidity data at each monitoring station. These factors, especially heavy rainfall, are the direct cause of geological disasters such as landslides.

[0030] Static geographic data refers to geographic attributes that do not change over time. These primarily include the elevation data reflected by the Digital Elevation Model (DEM) at each monitoring station and the Euclidean distance from each monitoring station to the nearest geological fault. These factors reflect the long-term, disaster-prone environment of surface deformation.

[0031] Before the raw data is fed into the model, a series of rigorous data preprocessing steps are performed to ensure data quality and model performance. The preprocessing steps specifically include: Surface displacement data cleaning: Due to factors such as equipment upgrades and multipath effects, outliers, step offsets, and missing data are unavoidable in raw GNSS time series. This implementation uses the interquartile range method to identify and remove outliers (outliers) from the data series; a least-squares fitting method is used to detect and correct step offsets caused by equipment replacement or events such as earthquakes; and a regularized expectation-maximization algorithm is used to interpolate missing data points in the series to generate a complete, continuous time series.

[0032] Multi-source data standardization: Since the units and numerical ranges of variables such as surface displacement (unit: mm), precipitation (unit: mm), humidity (unit: %), elevation (unit: m), and fault distance (unit: m) are different, this embodiment adopts the Min-Max Standardization method to eliminate the impact of dimensional differences on model training. For all input variables, their values ​​are calculated using the following formula: Scaling to the uniform interval [0,1]: Among them, for time series data such as surface displacement, precipitation and humidity and are the minimum and maximum values ​​of their own independent time series, respectively; for static data such as elevation and fault distance, the global minimum and maximum values ​​of all 74 stations are used for normalization.

[0033] S2: Constructing a weighted adjacency matrix based on the geographical location information of the monitoring stations to represent the initial spatial topological relationship between the monitoring stations.

[0034] like Figure 3 As shown, it is a schematic diagram of the weighted graph construction method in an embodiment of the present invention, which shows the abstraction process from monitoring stations to weighted adjacency matrix: the monitoring stations are abstracted as nodes in the graph structure, and then the Gaussian similarity function is used to calculate the weights between the nodes, and finally a weighted adjacency matrix is ​​constructed.

[0035] In order to effectively represent the spatial correlation between monitoring station networks in the deep learning model, this embodiment abstracts the entire monitoring network into a weighted undirected graph .in is a set of nodes representing monitoring stations, is the number of monitoring stations, is the set of edges connecting each monitoring station, Represents the weight between nodes.

[0036] In this embodiment, the Gaussian similarity function is used to construct the weighted adjacency matrix A. Specifically, based on any two monitoring stations and The geographic coordinates of the two are calculated, the Euclidean distance between them is calculated, and then the connection weight between them is calculated by the following formula : in represents the weight between two monitoring stations, Representative monitoring station and The spatial distance between It is a scale parameter that controls the rate at which the adjacency weight decays.

[0037] The weighted adjacency matrix is ​​shown below: The core idea of ​​this function is the "first law of geography", that is, the closer things are geographically, the stronger their correlation is. Therefore, the weighted adjacency matrix A constructed by this method is a fully connected matrix, and each element in the matrix All reflect the monitoring station and The spatial proximity between them. This matrix provides the initial, fixed-distance-based spatial topological structure information for the subsequent graph neural network module.

[0038] S3: Fusing the surface displacement time series data with the environmental impact data to construct an attribute-enhanced feature matrix.

[0039] In order to enable the model to comprehensively consider the changing patterns of surface displacement itself and the complex driving effects of the external environment, this embodiment uses an attribute embedding mechanism to fuse the various types of data obtained and pre-processed in step S1 to form an attribute-enhanced feature matrix. The specific process is as follows: Basic characteristic matrix: The vertical surface displacement time series data of 74 monitoring stations are constructed into a basic characteristic matrix. At any time step t, the matrix The dimension is 74×1, representing the displacement values ​​of all stations at that moment.

[0040] Specifically, in order to represent the temporal correlation of monitoring stations, a feature matrix is ​​constructed , which contains the time series information of all monitoring stations. is the number of monitoring stations, and Indicates the total length of the sequence. Indicates time The observation value of each monitoring station at the time. The data of a historical time series data point can be expressed as follows: At the same time, the next forecast The output at this moment can be expressed as: Therefore, suppose Indicates time The characteristic matrix of is the number of monitoring stations.

[0041] Static feature matrix: Two types of static geographic data, elevation (DEM) and fault distance, are constructed into a static feature matrix. The matrix has a dimension of 74×2 and its content does not change over time.

[0042] Since static features such as digital elevation models (DEMs) and fault distances do not change over time, they are organized into a static attribute matrix ,in is the number of static attributes. The static property matrix of is defined as: Dynamic feature matrix: The two types of dynamic environmental data, precipitation and humidity, are constructed into a dynamic feature matrix. At any time step t, the matrix The dimension is 74×2, representing the two dynamic environmental attribute values ​​of all sites at that moment.

[0043] Specifically, dynamic properties such as precipitation and humidity vary over time. Indicates On the time step A dynamic attribute. Indicates time Time In order to capture the time influence and potential lag effect of environmental variables, a dynamic attribute matrix of length Time window. The dynamic property matrix of is defined as: At each time step t, the basic features at that moment , dynamic features and static characteristics that do not change over time Combine (for example, concatenate or connect on the feature dimension) to form the attribute enhancement input matrix at that moment , can be defined as follows: The matrix The dimension is 74 × (1 + 2 + 2) = 74 × 5. In this way, the model input at each time step not only contains surface displacement information, but also incorporates rich dynamic and static environmental background knowledge, greatly enhancing the model's representation ability and ability to understand complex deformation mechanisms.

[0044] S4: 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 topological structure 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 the attention mechanism, extracts non-uniform spatial dependency features, and generates a second spatial feature representation.

[0045] like Figure 4 As shown in Figure 2, the present invention adopts an innovative parallel spatial feature extraction architecture to simultaneously capture structured and adaptive spatial dependencies in monitoring networks. The architecture consists of two parallel core modules: Graph Convolutional Network (GCN) module: After building the aforementioned 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 topology with node features. Through graph convolution operations, GCN effectively extracts the relationships and feature information between nodes, thereby enabling effective learning of graph structure representations.

[0046] like Figure 4 As shown, in order to capture the spatial dependencies between nodes, GCN transforms the adjacency matrix and attribute-enhanced feature matrix As input. The propagation rule of GCN is expressed by the following equation: in, Represents the original adjacency matrix, which is used to describe the connection relationship between nodes in the graph. Represented in the adjacency matrix Add a self-loop (i.e. ,in is the identity matrix), and then normalized; yes The diagonal matrix of Indicates the The trainable weights of the layer; is a nonlinear activation function; Indicates the The node feature matrix of the layer (where is the number of nodes, is the feature dimension of this layer. Note: ).

[0047] GCN performs weighted averaging of neighbor information based on the fixed spatial topology defined by the adjacency matrix A, and can effectively extract structured spatial features based on fixed distance dependencies in the monitoring network. After GCN processing, the first spatial feature representation is generated. .

[0048] Graph Attention Network (GAT) module: When processing graph structures, GCN assigns the same weight to all adjacent nodes, which makes it difficult to capture deeper and more complex spatial relationships between nodes. Therefore, the GAT layer (such as Figure 4As shown in Figure 2), this layer can dynamically aggregate information from neighboring nodes, thereby gradually enriching the feature representation of nodes in the hierarchical structure. Its calculation principle is as follows: in, and Represents nodes respectively and its neighboring nodes The eigenvector of is a learnable linear transformation matrix shared among all nodes; Represents a splicing operation; It is a shared single-layer feed-forward neural network used to calculate the attention score. Representation node The set of neighbor nodes of . This step calculates the unnormalized attention coefficient , which measures the node Feature pair nodes the importance of.

[0049] in, is the normalized attention coefficient, which is obtained by calculating the unnormalized attention score After applying the LeakyReLU activation function, all neighbor nodes Softmax exponential normalization is performed. This normalization process ensures that the sum of the attention coefficients of each node's neighbors is 1.

[0050] Finally, through the node The weighted sum of all neighboring node features is obtained Each neighboring node Features First, it undergoes a linear transformation and then multiplies its corresponding attention weight This approach allows the model to selectively aggregate information based on the importance of each neighboring node, thereby more accurately representing the relationships between nodes.

[0051] To further enhance the model's representation capabilities, the Graph Attention Network (GAT) introduces 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 as follows: in, Representation node The final output feature vector of and Represents nodes The output feature vectors of the first and second attention heads; Refers to the operation of concatenating multiple feature vectors into a single feature vector with higher dimensions.

[0052] Finally, the output feature vectors of the two attention heads are concatenated to form the final second space feature representation In this way, GAT is able to extract non-uniform, dynamic, and more physically meaningful spatially dependent features in the monitoring network.

[0053] S5: Fusing the first spatial feature representation and the second spatial feature representation to generate a fused spatial feature representation.

[0054] In order to integrate the spatial features extracted by different types of graph neural networks, the 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, which are denoted as and ,in is the number of nodes, is the feature dimension. Applying the feature addition strategy to combine these two outputs, we get the fused spatial feature representation: The fused representation combines the structural modeling capabilities of the Graph Convolutional Network (GCN) and the adaptability of the Graph Attention Network (GAT). This approach allows the model to retain complementary spatial information while maintaining computational simplicity. The resulting matrix It will serve as input to the temporal modeling part described in the next section.

[0055] S6: Inputting the fused spatial feature representation into a time series modeling module according to the time step, modeling the time dependency of the surface displacement, and outputting the surface displacement prediction result at the future moment.

[0056] In this embodiment, the time series modeling module uses a gated recurrent unit (GRU). GRU is a variant of the recurrent neural network (RNN). By introducing a gating mechanism, it effectively solves the long-term dependency and vanishing gradient problems in traditional RNNs. It also has fewer parameters and higher computational efficiency than the long short-term memory (LSTM) network.

[0057] In order to capture the temporal dependency of node features over time, the fused spatial representation The result is passed to a Gated Recurrent Unit (GRU), a type of Recurrent Neural Network (RNN) designed to simulate sequential data while solving the vanishing gradient problem in traditional RNNs.

[0058] like Figure 4 As shown, GRU maintains a hidden state , the state at each time step Based on the current input and the previous hidden state Update. The GRU unit contains two key gates: reset gate and update gate , which control the flow of information over time. The core calculation of the GRU unit is as follows: Among them, the parameters 、 、 、 、 、 are all weights during training; is the sigmoid activation function; represents element-wise multiplication; and Respectively indicate time The candidate hidden states and final hidden state outputs.

[0059] Through this sophisticated gating mechanism, the GRU is able to learn the complex dynamic evolution patterns of surface displacement sequences over time, including periodicity, trends, and mutations. Ultimately, the GRU module outputs a surface displacement prediction for one future time step based on its hidden state at the last time step, passing through one or more fully connected layers (output layers).

[0060] Optionally, other embodiments also include a complete model training step. The time series data is partitioned using a sliding window approach, with data from the past 16 days (time steps) used as input to predict the surface displacement for one time step in the future (day 17). The loss function for model optimization is a combined loss function defined as follows: in is the mean squared error loss, is the L2 regularization loss. The mean squared error loss measures the size of the model prediction error by calculating the average of the squares of the differences between the predicted values ​​and the actual values. The formula for the mean squared error loss is as follows: in is the actual value, is the predicted value, is the number of samples. In order to reduce the occurrence of overfitting and improve the generalization ability of the model, L2 regularization loss is introduced. The formula is as follows: in is the regularization coefficient, which is used to control the regularization strength. is the weight parameter in the model.

[0061] The loss function consists of two parts: the first part is the mean squared error (MSE) loss term, which is used to measure 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 imposing a penalty on the weight parameters in the model, where λ is a coefficient that controls the regularization strength.

[0062] 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 more effectively handle weight decay.

[0063] The key hyperparameters were optimized through comparative experiments to achieve the best performance. By evaluating the model performance under different numbers of hidden units, it was finally determined that the learning rate was set to 1×10 -4 , the batch size is set to 64, the training epochs is set to 200, and the number of hidden units in GCN, GAT and GRU is set to 32.

[0064] In summary, in this embodiment, by systematically acquiring and finely processing multi-source data, using the innovative GCN and GAT parallel architecture to deeply mine and fuse complementary spatial features, and then using GRU for accurate time series modeling, this method constructs an end-to-end deep learning framework that can accurately capture the complex spatiotemporal dependencies in large-scale monitoring networks, thereby achieving high-precision prediction of surface displacements such as highway slopes.

[0065] Alternatively, 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) are used as baseline models for comparison with the model proposed in this paper. For those baselines that rely on spatial correlation, the adjacency matrix is ​​constructed using the same method as 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), coefficient of determination (R 2 ) is used to evaluate the performance of the GATTGCN model.

[0066] Table 1 Prediction results of deformation data in Sichuan and Yunnan regions using the GATTGCN model and other baseline methods Experimental results demonstrate that the proposed model outperforms traditional deep learning methods. In more complex, large-scale scenarios, the traditional model's predictive power is weaker. In contrast, the improved model demonstrates superior 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.

[0067] 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 general trend. GAT performed the worst among graph-based models. GRU and GCN showed similar but lower accuracy, while LSTM tracked the trend better but with significant deviation. T-GCN showed slight improvement. In contrast, GATTGCN achieved the best fit, with predictions closest to the ground truth and greater stability, which is critical for deformation prediction.

[0068] Optionally, an embodiment of the present application also provides an electronic device, including a processor, a memory, and a program or instruction stored in the memory and executable on the processor. When the program or instruction is executed by the processor, each process of the above-mentioned embodiment of the method for predicting the surface displacement of a highway slope based on graph attention is implemented, and the same technical effect can be achieved. To avoid repetition, it will not be described here.

[0069] Optionally, an embodiment of the present application also provides a readable storage medium, which stores a program or instruction. When the program or instruction is executed by a processor, the various processes of the embodiment of the above-mentioned method for predicting the surface displacement time series of highway slopes based on graph attention are implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

[0070] The processor is the processor in the electronic device described in the above embodiment. The readable storage medium includes a computer-readable storage medium, such as a computer read-only memory (ROM), random access memory (RAM), a magnetic disk, or an optical disk.

[0071] It should be noted that, in this article, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the statement "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element. In addition, it should be noted that the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in the opposite order according to the functions involved. For example, the described method may be performed in an order different from that described, and various steps may also be added, omitted, or combined. In addition, the features described with reference to certain examples may be combined in other examples.

[0072] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a more preferred embodiment. Based on this understanding, the technical solution of this application, or the part that contributes to the existing technology, 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 a number of instructions for enabling a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of this application.

[0073] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of this application, ordinary technicians in this field can also make many forms without departing from the purpose of this application and the scope of protection of the claims, all of which are within the protection of this application.

Claims

1. A method for predicting time series of highway slope surface displacement based on graph attention, characterized in that: The following steps are involved: obtaining time series data of surface displacements of a plurality of monitoring stations and environmental impact data associated with the monitoring stations; Constructing a weighted adjacency matrix based on the geographical location information of the monitoring stations to represent the initial spatial topological relationship between the monitoring stations; fusing the surface displacement time series data with the environmental impact data to construct a feature matrix with enhanced attributes; 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 to perform spatial feature extraction, wherein: The graph convolutional network module extracts structured spatial features based on the fixed topological structure defined by the weighted adjacency matrix and generates a first spatial feature representation; The graph attention network module adaptively assigns dynamic weights to the neighboring monitoring stations of each monitoring station through the attention mechanism, extracts non-uniform spatial dependency features, and generates a second spatial feature representation; fusing the first spatial feature representation and the second spatial feature representation 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, the time dependency of the surface displacement is modeled, and the surface displacement prediction result at the future moment is output.

2. The method for predicting highway slope surface displacement time series based on graph attention according to claim 1, characterized in that: 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 a 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; At each time step, the basic feature matrix, the dynamic feature matrix and the static feature matrix are combined to form the attribute-enhanced feature matrix.

3. The method for predicting highway slope surface displacement time series based on graph attention according to claim 1, characterized in that: The step of fusing the first spatial feature representation and the second spatial feature representation is specifically: A feature addition strategy is adopted 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 to retain complementary spatial information.

4. The method for predicting highway slope surface displacement time series based on graph attention according to claim 1, characterized in that: The step of extracting non-uniform spatial dependence features comprises: A multi-head attention mechanism is used, where each attention head independently calculates the attention coefficient and generates a feature representation; For each attention head, the node features are first transformed by a shared learnable linear transformation matrix, and then the unnormalized attention score between any two nodes is calculated through a feedforward neural network; The unnormalized attention scores are 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, so that the model can learn the importance of neighbor nodes from different representation subspaces.

5. The method for predicting highway slope surface displacement time series based on graph attention according to claim 1, characterized in that: The steps of constructing a weighted adjacency matrix are specifically as follows: The Gaussian similarity function is used to calculate the connection weight between any two monitoring stations based on the Euclidean space distance between them. The connection weight is inversely proportional to the distance between monitoring stations, and its decay speed is controlled by a scale parameter to construct a fully connected weighted adjacency matrix that can reflect spatial proximity.

6. The method for predicting highway slope surface displacement time series based on graph attention according to claim 1, characterized in that: The step of inputting the fused spatial feature representation into a time series modeling module according to time steps includes: The timing modeling module is a gated recurrent unit that implements the following gating mechanism: At each time step, the update gate and reset gate inside the gated recurrent unit are used to control the information flow; The update gate determines to what extent the hidden state information of the previous time step is brought into the current state; The reset gate determines to what extent the hidden state information of the previous time step is ignored; The above gating mechanism is used to capture the long-term temporal dependencies in the surface displacement sequence and update the hidden state to generate prediction results.

7. The method for predicting highway slope surface displacement time series based on graph attention according to claim 1, characterized in that: The method further includes a model training step, wherein the model training step includes: The sliding window method is used to partition the time series data, and the data containing multiple consecutive time steps in the past are used as input to predict the surface displacement of one time step in the future. Define a combined loss function for model optimization, which includes a mean square 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; The AdamW optimizer is used to iteratively update the trainable parameters in the model according to the combined loss function.

8. The method for predicting highway slope surface displacement time series 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, the interquartile range method is used to identify and remove outliers, the least squares fitting is used to correct step offsets, and the regularized expectation maximization algorithm is used to interpolate missing data points; The input variables including surface displacement, precipitation, humidity, elevation and fault distance are scaled to a uniform interval of [0,1] using the minimum-maximum normalization method.

9. An electronic device, characterized in that: The method comprises a processor, a memory, and a program or instruction stored in the memory and executable on the processor. When the program or instruction is executed by the processor, the method implements the steps of a method for predicting time series of surface displacement of highway slope based on graph attention as described in any one of claims 1 to 8.

10. A readable storage medium, characterized in that: The readable storage medium stores a program or instruction, and when the program or instruction is executed by the processor, the steps of the method for predicting the time series of highway slope surface displacement based on graph attention as described in any one of claims 1 to 8 are implemented.

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