Method and device for quickly generating intelligent agent model of mechanical field of concrete dam

Abstract

The application provides a kind of concrete dam mechanics field fast generation intelligent agent model method and device, it is related to data processing technical field, including: constructing historical training sample set, using historical training sample set and global graph structure, representative node physical quantity space-time prediction model is trained;For each node cluster, construct local graph structure based on the spatial position relationship of intra-cluster node, using representative node physical quantity sample in historical training sample set, intra-cluster node physical quantity sample and local graph structure, intra-cluster node physical quantity reconstruction model is trained.The representative node physical quantity space-time prediction model trained in intelligent agent model is used to output representative node physical quantity prediction data according to the target environmental quantity data of input concrete dam, the intra-cluster node physical quantity reconstruction model trained in intelligent agent model is used to output the physical quantity prediction data of all nodes in cluster according to the representative node physical quantity prediction data.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and apparatus for rapidly generating intelligent proxy models of the mechanical field of concrete dams. Background Technology

[0002] As a crucial water conservancy infrastructure, the operational safety of concrete dams directly impacts the safety of life and property and social stability in downstream areas. Under the combined influence of various factors such as water level changes, temperature fluctuations, and time effects, the internal physical fields of the dam exhibit significant time-varying and spatially non-uniformity. Establishing accurate and efficient predictive models for these physical fields is of significant engineering importance for the real-time assessment and trend prediction of the structural safety status of concrete dams.

[0003] Existing methods for analyzing the physical quantities of concrete dams mainly include finite element numerical simulation (FEM) and statistical or machine learning methods based on monitoring data. FEM can comprehensively describe the structural mechanical behavior, but it is computationally expensive and time-consuming, making it difficult to meet the needs of online prediction and real-time analysis. Statistical regression models and traditional machine learning models based on monitoring data typically use environmental quantities such as water level and temperature as input to predict the physical quantities of individual or a few measuring points. While computationally efficient, they often treat each measuring point as an independent entity, ignoring the spatial correlation of physical quantity responses at different locations within the dam body, making it difficult to accurately predict the overall physical quantity field. Summary of the Invention

[0004] This invention provides a method and apparatus for rapidly generating intelligent proxy models of the mechanical field of concrete dams, in order to solve the problem that it is difficult to accurately predict the overall physical field of concrete dams in the prior art.

[0005] This invention provides a method for rapidly generating an intelligent surrogate model of the mechanical field of a concrete dam, comprising: Obtain historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of the concrete dam. Perform time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered to obtain multiple node clusters, and a representative node is selected from each node cluster. A global graph structure is constructed based on the spatial positional relationships of all the representative nodes. An environmental quantity sample, a representative node physical quantity sample, and the global graph structure are used in the historical training sample set to train a spatiotemporal prediction model for the physical quantities of the representative nodes. For each node cluster, a local graph structure is constructed based on the spatial positional relationship of nodes within the cluster. Using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure, a node physical quantity reconstruction model within the cluster is trained. The representative node physical quantity spatiotemporal prediction model and the cluster-internal node physical quantity reconstruction model constitute the intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

[0006] According to the present invention, a method for rapidly generating an intelligent proxy model of the mechanical field of a concrete dam includes training a spatiotemporal prediction model of representative nodal physical quantities, comprising: The environmental quantity sample sequence, the representative node physical quantity sample sequence, and the global graph structure in the historical training sample set are used as inputs to the spatiotemporal prediction model of the representative node physical quantity. Calculate the error between the output value of the spatiotemporal prediction model of the representative node physical quantity and the actual sample value of the representative node physical quantity, and construct the first loss function; The parameters of the spatiotemporal prediction model of the representative node physical quantity are iteratively updated based on the first loss function until the first loss function converges or reaches the first preset number of iterations.

[0007] According to the present invention, a method for rapidly generating an intelligent proxy model of the mechanical field of a concrete dam is provided. The representative node physical quantity spatiotemporal prediction model includes: a graph convolutional layer and a temporal feature extraction layer. The graph convolutional layer receives the adjacency matrix corresponding to the global graph structure. For each representative node, the feature vectors of the neighboring representative nodes adjacent to the representative node are multiplied by the corresponding edge weights in the adjacency matrix and then summed to obtain the neighborhood aggregation feature. The neighborhood aggregation feature is concatenated with the feature vector of the representative node itself and then passed through a nonlinear activation function to output a node embedding vector that integrates spatial association information. The temporal feature extraction layer receives the environmental quantity sample sequence within the historical time window and the node embedding vector, captures the dynamic features of the physical quantity evolution over time through a gated recurrent unit, and outputs the predicted physical quantity values ​​of each representative node at the next moment.

[0008] According to the present invention, a method for rapidly generating an intelligent proxy model of the mechanical field of a concrete dam includes training a cluster-based model for reconstructing the physical quantities of nodes, comprising: The representative node physical quantity samples in the historical training sample set, the spatial coordinate data of the nodes to be reconstructed within the cluster, and the local graph structure are used as inputs to the node physical quantity reconstruction model within the cluster. Calculate the error between the output value of the cluster node physical quantity reconstruction model and the actual sample values ​​of all node physical quantities in the cluster, and construct a second loss function; The parameters of the physical quantity reconstruction model of the nodes within the cluster are iteratively updated based on the second loss function until the second loss function converges or the second preset number of iterations is reached.

[0009] According to the present invention, a method for rapidly generating an intelligent proxy model of the mechanical field of a concrete dam is provided, wherein the physical quantity reconstruction model of the node within the cluster includes a coordinate encoding layer and a feature mapping layer. The coordinate coding layer receives the spatial coordinate data of the node to be reconstructed within the cluster and maps the spatial coordinate data into a high-dimensional coordinate embedding vector. The feature mapping layer copies and expands the physical quantity samples of the representative nodes and concatenates them with the high-dimensional coordinate embedding vectors corresponding to each node to be reconstructed. The concatenated features are then input into a multilayer perceptron, and after multiple linear transformations and nonlinear activations, the predicted physical quantity values ​​of each node to be reconstructed within the cluster are output.

[0010] According to the present invention, a method for rapidly generating an intelligent proxy model of the mechanical field of a concrete dam includes selecting a representative node from each node cluster, comprising: Calculate the variance of the physical quantity of each node in the cluster in the historical training sample set, obtain the maximum and minimum variance values ​​among all the variance values ​​of the nodes in the cluster, calculate the difference between the variance value of each node and the minimum variance value for each node in the cluster, and divide it by the difference between the maximum and minimum variance values ​​to obtain the physical quantity sensitivity index of each node. Calculate the Euclidean distance from each node in the cluster to the geometric center of the cluster, obtain the maximum and minimum Euclidean distance values ​​among all nodes in the cluster, calculate the difference between the maximum distance value and the Euclidean distance of each node in the cluster, and divide the difference between the maximum distance value and the minimum distance value to obtain the spatial centrality index of each node. The physical quantity sensitivity index and the spatial centrality index of each node are weighted and summed to obtain the comprehensive score of each node. The node with the highest comprehensive score is selected as the representative node of the node cluster.

[0011] According to the present invention, a method for rapidly generating an intelligent proxy model of the mechanical field of a concrete dam, wherein the construction of a global graph structure based on the spatial positional relationships of all representative nodes includes: Calculate the Euclidean distance between any two representative nodes, substitute the Euclidean distance into the distance decay function to calculate the connection weight between the two representative nodes, and generate an adjacency matrix based on the connection weights between all representative node pairs. Calculate the degree matrix of the adjacency matrix, where the degree matrix is ​​a diagonal matrix and the diagonal elements are the sum of the connection weights of the corresponding rows of each representative node. Calculate the negative 1 / 2 power matrix of the degree matrix. Multiply the negative 1 / 2 power matrix, the adjacency matrix, and the negative 1 / 2 power matrix in sequence to obtain the symmetric normalized global graph structure.

[0012] According to the present invention, a method for rapidly generating intelligent surrogate models of the mechanical field of concrete dams is provided, the method further comprising: Obtain the target environmental quantity data of the concrete dam to be predicted at the current moment, and standardize the target environmental quantity data using the same standardized parameters as in the training phase. The standardized target environmental quantity data and the representative node physical quantity data within the historical time window are input into the trained representative node physical quantity spatiotemporal prediction model to obtain the physical quantity prediction data of each representative node at the current moment. For each node cluster, the physical quantity prediction data of the representative node corresponding to the node cluster and the spatial coordinate data of each node in the node cluster are input into the trained node physical quantity reconstruction model within the cluster to obtain the physical quantity prediction data of each node in the node cluster. By summarizing the physical quantity prediction data of all node clusters, the physical quantity prediction data of all nodes of the concrete dam are obtained. Based on the physical quantity prediction data of all nodes of the concrete dam, the radial basis numerical interpolation function is used to interpolate other spatial locations inside the dam body to generate a cloud map of the physical quantity field distribution of the concrete dam. The physical quantity field distribution cloud map of the concrete dam is used to analyze the physical quantity status and changing trend of the dam body.

[0013] This invention also provides a device for rapidly generating intelligent proxy models of the mechanical field of concrete dams, comprising: The acquisition module is used to acquire historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of concrete dam, and to perform time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. The partitioning module is used to cluster all nodes of the concrete dam based on the historical training sample set and the spatial coordinate data of each node, to obtain multiple node clusters, and to select a representative node from each node cluster. The first training module is used to construct a global graph structure based on the spatial positional relationships of all the representative nodes, and to train a spatiotemporal prediction model of the physical quantities of the representative nodes using environmental quantity samples, physical quantity samples of the representative nodes and the global graph structure in the historical training sample set. The second training module is used to construct a local graph structure based on the spatial positional relationship of nodes within each node cluster, and to train a node physical quantity reconstruction model within the cluster using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure. The representative node physical quantity spatiotemporal prediction model and the cluster-internal node physical quantity reconstruction model constitute the intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

[0014] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams as described above.

[0015] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams as described above.

[0016] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams as described above.

[0017] This invention provides a method and apparatus for rapidly generating intelligent proxy models of the mechanical field of concrete dams. It constructs a historical training sample set by acquiring historical physical quantity samples and environmental quantity samples of all nodes in the numerical simulation model of the concrete dam. Based on the historical training sample set and the spatial coordinate data of each node, it clusters all nodes of the concrete dam, selecting representative nodes from each node cluster. This achieves a node-based representation of the concrete dam data, effectively reducing the dimensionality and computational complexity of the full-node physical quantity prediction model. By constructing a global graph structure based on the spatial positional relationships of representative nodes and training a spatiotemporal prediction model for the physical quantities of representative nodes, it can integrate environmental quantity-driven models. The spatial correlation information between dynamic information and representative nodes accurately characterizes the spatiotemporal evolution of physical quantity responses. By constructing a local graph structure for each node cluster and training the physical quantity reconstruction model of nodes within the cluster, a high-fidelity spatial expansion reconstruction from the physical quantity prediction data of representative nodes to the physical quantities of all nodes within the cluster is achieved, ensuring the spatial continuity and consistency of the physical quantity field prediction results. The overall scheme does not require complex finite element solution calculations in the inference stage, and can quickly respond to changes in environmental quantities and output the physical quantity prediction data of all nodes of the concrete dam, providing efficient, stable, and high-precision technical support for the safety monitoring and operation management of concrete dams. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a structural schematic diagram of the intelligent agent model system for the safety of concrete dam structures provided by the present invention; Figure 2 This is a flowchart illustrating the method for predicting the physical quantities of concrete dams provided by this invention. Figure 3 This is a flowchart illustrating the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams provided by the present invention. Figure 4 This invention provides a numerical simulation mesh model of a concrete dam. Figure 5 This is a schematic diagram of the upstream water level curve; Figure 6 This is a schematic diagram of the upstream temperature curve; Figure 7 This is a clustering result diagram of the nodes obtained from solving the displacement field of the dam body; Figure 8 This is a clustering result diagram of the nodes obtained from solving the stress field of the dam body; Figure 9 This is a diagram showing the representative node numbers and locations for solving the dam displacement field; Figure 10 This is a diagram showing the representative node numbers and locations for solving the stress field of the dam body; Figure 11 This is one of the comparison diagrams of the x-direction displacement values ​​of all nodes in the dam body; Figure 12 This is the second comparison chart of the x-direction displacement values ​​of all nodes in the dam body; Figure 13 This is one of the comparison diagrams of the z-axis stress values ​​of all nodes in the dam body; Figure 14 This is the second comparison diagram of the z-axis stress values ​​of all nodes in the dam body; Figure 15 This is one of the comparison images of the x-axis displacement contour plot results; Figure 16 This is the second comparison chart of the x-axis displacement contour plot results; Figure 17 This is one of the schematic diagrams comparing the stress contour plots in the z-direction; Figure 18 This is the second schematic diagram comparing the results of the z-axis stress cloud diagram; Figure 19 This is one of the scatter plots of the predicted values ​​from the finite element-surrogate model provided by the present invention; Figure 20 This is the second scatter plot of the predicted values ​​from the finite element-surrogate model provided by the present invention. Figure 21 A box plot of the response time of the x-direction displacement is generated on the test set provided by this invention. Figure 22 It is a box plot of the response time of generating z-direction stress on the test set; Figure 23 It is the error distribution map for generating the x-direction displacement field map on the test set; Figure 24 It is the error distribution map for generating the z-axis stress field map on the test set; Figure 25 A schematic diagram of the intelligent proxy model device for rapid generation of mechanical field of concrete dam provided by the present invention. Figure 26 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0021] The method for rapidly generating intelligent proxy models of the mechanical field of concrete dams provided in this invention can be executed by a computer device, which can be an electronic device with data processing capabilities, such as a server, workstation, personal computer, or embedded control system. In the following embodiments, a processor is used as the execution entity to describe the technical solution of this invention in detail.

[0022] The core technical idea of ​​this invention is to nominate concrete dam data nodes, that is, to obtain the physical quantity data of each node of the dam body through the numerical simulation model of the concrete dam, and to reduce the modeling dimensionality based on the node clustering and representative node selection strategy; at the same time, to construct a two-layer proxy model architecture including a spatiotemporal prediction model of representative node physical quantities and a node physical quantity reconstruction model within the cluster. The spatiotemporal prediction model of representative node physical quantities takes environmental quantities as input and the physical quantities of representative nodes as output, while the node physical quantity reconstruction model within the cluster takes the physical quantities of representative nodes as input and the physical quantities of each node within the cluster as output, thereby achieving efficient, stable and high-precision prediction of the physical quantity field of the concrete dam.

[0023] Figure 1 This is a structural schematic diagram of the intelligent proxy model system for the safety of concrete dam structures provided by the present invention. Figure 1 As shown, the system includes a data acquisition and preprocessing module, a node clustering and representative node selection module, a representative node physical quantity spatiotemporal prediction module, a cluster node physical quantity reconstruction module, and a physical quantity field generation module. Each module is executed sequentially in the order of number 1 to 5 to form a complete concrete dam physical quantity prediction process.

[0024] The data acquisition and preprocessing module is used to collect various types of data, such as physical quantities and environmental quantities, and divide them into training, validation, and test sets after alignment and standardization. The node clustering and representative node selection module is used to construct physical quantity statistics and spatial feature vectors, cluster them, and select representative nodes according to indicators. The representative node physical quantity spatiotemporal prediction module is used to construct a graph structure and normalize the adjacency matrix, and fuse sequence modeling to predict the physical quantity values ​​of representative nodes. The cluster node physical quantity reconstruction module is used to construct a node graph structure within the cluster, input the physical quantity values ​​of representative nodes, and reconstruct the physical quantity values ​​of all nodes. The physical quantity field generation module is used to visualize and generate the spatial distribution of the physical quantity field based on the prediction results of all node physical quantity values.

[0025] Figure 2 This is a flowchart illustrating the method for predicting the physical quantities of concrete dams provided by this invention. Figure 2 As shown, the method includes: S1 Data Acquisition (Reading node coordinates, dam boundary, environmental quantities, displacement / stress time series data); S2 Data Preprocessing and Alignment (Date Alignment + Filtering Valid Nodes + Splitting Datasets + Standardization); S3 Node Clustering and Representative Node Selection (Construction Features + KMeans Clustering + Representative Node Selection by Score); S4 represents node spatiotemporal prediction training (building an adjacency matrix + sequence modeling + Optuna parameter tuning training model). S5 cluster physical quantity propagation model training (cluster graph construction + ClusterGNN modeling + Optuna parameter tuning), and determining whether to enter online prediction / testing; S6 Online Prediction (Construction Sequence + Predicted Normalized Displacement / Stress of Representative Nodes); S6.1 Global Physical Quantity Prediction (Intra-cluster GNN Output + Summarized Standardized Prediction Values ​​of All Nodes); S6.2 Denormalization and Error Assessment (Denormalization to MPa + Calculation of MAE + Recording of Response Time); S6.3 Visualization output (RBF interpolation generates displacement / stress cloud map + scatter plot of representative nodes); S7 performance statistical analysis (distribution and statistical values ​​of output response time / MAE), etc.

[0026] Figure 3 This is a flowchart illustrating the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams provided by the present invention. Figure 3 As shown, the method includes the following: Step 110: Obtain historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of the concrete dam; perform time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. In this application, the numerical simulation model of a concrete dam refers to a structural model of a concrete dam established based on the finite element method or other numerical calculation methods. This model can simulate the mechanical response of a concrete dam under various working conditions. The numerical simulation model contains multiple discrete calculation nodes, each with a definite spatial coordinate position. The physical quantity values ​​of each node at different times can be obtained through numerical calculation.

[0027] Physical quantities refer to mechanical response parameters that reflect the structural state of a concrete dam, including but not limited to displacement, stress, and strain. In one optional embodiment, the physical quantity can be a displacement component along a specific direction, such as the x-direction displacement along the river along the dam body; in another optional embodiment, the physical quantity can be a stress component, such as the z-direction stress along the elevation direction of the dam body.

[0028] Environmental factors refer to external factors that affect the structural response of concrete dams, including but not limited to upstream water level, air temperature, and time-effect factors. Upstream water level reflects the magnitude of the water load acting on the dam body; air temperature reflects the influence of the temperature field on the thermal stress of the dam body; and time-effect factors reflect time-related effects such as concrete creep and dam foundation settlement.

[0029] Historical physical quantity samples refer to the calculation results of physical quantities at each node extracted from the numerical simulation model of the concrete dam within a historical time period. Environmental quantity samples refer to environmental factor observation data or set data within the time period corresponding to the historical physical quantity samples.

[0030] Time alignment refers to matching historical physical quantity samples with environmental quantity samples according to a unified time benchmark, ensuring that physical quantity data and environmental quantity data at the same moment can correspond one-to-one.

[0031] Time alignment methods can include: resampling at a uniform time interval, using interpolation methods to fill in missing data, and deleting data records with mismatched times.

[0032] Standardization refers to the numerical transformation of raw data to eliminate the impact of differences in units and ranges on model training. Standardization methods can include Z-score standardization, max-min normalization, and mean normalization. In one optional implementation, Z-score standardization can be used, which involves subtracting the mean of the physical quantity data for each node from the mean of that node in the training set, and then dividing by the standard deviation.

[0033] After time alignment and standardization, the processed historical physical quantity samples are combined with environmental quantity samples to form a historical training sample set, which is used for subsequent cluster analysis and model training. In an optional implementation, the historical training sample set can also be divided into a training set, a validation set, and a test set according to a preset ratio, wherein the training set is used for model parameter learning, the validation set is used for model hyperparameter tuning and early stopping detection, and the test set is used to evaluate the model's generalization performance.

[0034] Figure 4 This is a numerical simulation mesh model diagram of a concrete dam provided by the present invention. Figure 4As shown, taking a concrete dam as an example, a finite element numerical simulation model was constructed. This numerical simulation model has a total of 2116 nodes, and the dam body has 7 partitions (labeled with numbers 1-7 in the figure). Different partitions are represented by different colors, and each partition corresponds to different concrete material properties. The material parameters of each partition are shown in Table 1.

[0035] Table 1 Material zoning elastic modulus Poisson's ratio coefficient of linear expansion density 1 41.1 0.167 5.86e-6 2510 2 38.7 0.167 5.86e-6 2460 3 37.0 0.167 5.86e-6 2460 4 40.0 0.167 5.86e-6 2460 5 42.0 0.167 5.86e-6 2470 6 48.2 0.167 5.86e-6 2460 7 48.2 0.167 5.86e-6 2440 Figure 5 This is a schematic diagram of the upstream water level curve. Figure 6 This is a schematic diagram of the upstream temperature curve. (For example...) Figure 5 and Figure 6 As shown in the figure above, the upstream water level time series after splitting the training / validation / test sets is illustrated. The vertical axis represents the upstream water level (unit: m), and the horizontal axis represents the date. The water level fluctuates between 370m and 380m, exhibiting a clear periodic variation. The figure also shows the corresponding temperature time series, with the vertical axis representing the temperature (unit: ℃). The temperature varies periodically between 5℃ and 35℃. In the figure, blue, orange, and green represent the data ranges of the training, validation, and test sets, respectively, with the calculation time span from August 3, 2013 to October 5, 2023.

[0036] Step 120: Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered to obtain multiple node clusters, and a representative node is selected from each node cluster. In this application, node clustering refers to the process of grouping nodes with similar characteristics into the same group based on their physical quantity characteristics and spatial location characteristics. The purpose of clustering is to reduce the dimensionality of the modeling and characterize the global physical quantity response features through a small number of representative nodes.

[0037] The basis for clustering can include: the statistical characteristics of the physical quantities of nodes (such as mean, variance, etc.), the spatial coordinates of nodes, and the temporal response characteristics of nodes.

[0038] In one alternative implementation, a feature vector containing the mean of physical quantities and spatial coordinates can be constructed as clustering input.

[0039] Clustering methods can include K-means clustering, hierarchical clustering, and density clustering. The number of clusters can be determined using methods such as the elbow rule, silhouette coefficient method, and gap statistic method.

[0040] A node cluster refers to a group of nodes output by a clustering algorithm. Nodes within the same node cluster have similar physical quantity response characteristics and spatial proximity relationships.

[0041] A representative node is a node selected from each node cluster that can represent the overall physical quantity response characteristics of that cluster. The selection of a representative node needs to comprehensively consider the node's physical quantity response sensitivity and spatial representativeness.

[0042] Figure 7 This is a node clustering result diagram for solving the dam displacement field. For example... Figure 7 As shown in the figure, the horizontal axis represents the X-coordinate, the vertical axis represents the Y-coordinate, and the black solid line represents the boundary outline of the dam body. The nodes inside the dam body are represented by scatter points of different colors according to the clustering results, and are divided into 13 clusters. The nodes within each cluster have similar displacement response characteristics and spatial proximity. The nodes marked with black circles in the figure are representative nodes selected from each cluster.

[0043] Figure 8 This is a diagram showing the node clustering results for solving the stress field of the dam body. (Example) Figure 8 As shown, the node clustering of the stress field uses the same method as that for the displacement field. However, due to the different spatial characteristics of stress distribution compared to displacement, the clustering results are divided into 15 clusters. The figure also distinguishes each cluster with different colors, and black circles mark the representative node positions of each cluster.

[0044] Figure 9 This is a diagram showing the representative node numbers and locations for solving the dam displacement field. For example... Figure 9 As shown in the figure, the locations and numbers of 13 representative nodes (such as 225, 93, 715, 1137, 3439, 3475, 1875, 2500, 2705, 4009, 4069, 2301, 2311, etc.) are marked within the outline of the dam body. These representative nodes will serve as the prediction targets for the spatiotemporal prediction model of the physical quantities of representative nodes.

[0045] Figure 10 This is a diagram showing the representative node numbers and locations for solving the stress field of the dam body. For example... Figure 10 As shown in the figure, the locations and numbers of 15 representative nodes used for stress field prediction are marked (e.g., 131, 533, 937, 1317, 3475, 1649, 5382, 4065, 4085, 4131, 4179, 1919, 2097, 2223, 2341, etc.). Step 130: Based on the spatial relationships of all the representative nodes, a global graph structure is constructed. Using the environmental quantity samples, representative node physical quantity samples, and the global graph structure from the historical training sample set, a spatiotemporal prediction model for the representative node physical quantities is trained. A global graph structure is a graph data structure built with all representative nodes as graph nodes and the spatial relationships between representative nodes as graph edges. Global graph structures are used to represent the spatial topological relationships between representative nodes, enabling the model to learn the spatial correlations between nodes.

[0046] Graph structures can be constructed in various ways, including fully connected graphs based on Euclidean distance, sparse graphs based on K-nearest neighbors, and connected graphs based on threshold distance.

[0047] The edge weights of a graph can be determined based on the distance between nodes; the closer the nodes are, the greater the edge weight.

[0048] A representative nodal physical quantity spatiotemporal prediction model is a prediction model that takes environmental quantity sequences as input and representative nodal physical quantities as output. The function of this model is to learn the spatiotemporal evolution law of representative nodal physical quantities driven by environmental quantities.

[0049] The inputs to the representative node physical quantity spatiotemporal prediction model include: the environmental quantity sequence within the historical time window, the representative node physical quantity sequence within the historical time window, and the global graph structure (adjacency matrix). The model output is the predicted physical quantity values ​​of each representative node at the next time step.

[0050] The model is trained by inputting environmental quantity sample sequences and representative node physical quantity sample sequences into the model, calculating the error between the model output and the actual physical quantity values, and updating the model parameters through the backpropagation algorithm to gradually reduce the error until convergence.

[0051] Step 140: For each node cluster, construct a local graph structure based on the spatial positional relationship of nodes within the cluster, and train a node physical quantity reconstruction model within the cluster using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure. The trained representative node physical quantity spatiotemporal prediction model is used to output representative node physical quantity prediction data based on the input target environmental quantity data of the concrete dam. The trained cluster node physical quantity reconstruction model is used to output physical quantity prediction data of all nodes within the cluster based on the representative node physical quantity prediction data.

[0052] In this application, a local graph structure refers to a graph data structure constructed within a single node cluster, where all nodes within the cluster are graph nodes and the spatial relationships between nodes within the cluster are graph edges. The local graph structure is used to represent the spatial topological relationships between nodes within a cluster.

[0053] The cluster-based node physical quantity reconstruction model is a prediction model that takes the physical quantities of representative nodes as input and outputs the physical quantities of each node within the cluster. The function of this model is to reconstruct the distribution of physical quantities of all nodes within the cluster based on the predicted physical quantity values ​​of the representative nodes.

[0054] The inputs to the cluster-based node physical quantity reconstruction model include: physical quantity values ​​of representative nodes, spatial coordinates of each node to be reconstructed within the cluster, and local graph structure. The model outputs predicted physical quantity values ​​for each node within the cluster.

[0055] The model is trained by inputting representative node physical quantity samples and cluster node spatial coordinates into the model, calculating the error between the model output and the actual cluster node physical quantity values, and updating the model parameters through the backpropagation algorithm.

[0056] During the inference phase, the representative node physical quantity spatiotemporal prediction model receives the target environmental quantity data to be predicted, such as the current upstream water level and temperature, and combines it with the representative node physical quantity data within the historical time window to output the predicted physical quantity values ​​of each representative node at the current moment.

[0057] The cluster-based node physical quantity reconstruction model receives the representative node physical quantity prediction data output by the representative node physical quantity spatiotemporal prediction model, and combines it with the spatial coordinate information of each node in the cluster to output the physical quantity prediction values ​​of all nodes in the cluster.

[0058] By cascading the two models mentioned above, a complete prediction process can be achieved, from inputting environmental quantities to outputting prediction results for all node physical quantities of the concrete dam.

[0059] Figure 11 This is one of the comparison charts of x-direction displacement values ​​for all nodes of the dam body. Figure 12 This is the second comparison chart of the x-direction displacement values ​​of all nodes in the dam body. For example... Figure 11 and Figure 12 As shown in the figure, the horizontal axis is the X-coordinate, the vertical axis is the Y-coordinate, and the color bars represent the displacement values ​​(unit: mm), with the displacement values ​​ranging from approximately 8 mm to 18 mm. It can be seen from the figure that the displacement distribution predicted by the surrogate model is in high agreement with the finite element calculation results, with the largest displacement at the dam crest and gradually decreasing towards the dam foundation; the spatial distribution law of the displacement field has been accurately captured.

[0060] Figure 13 This is one of the comparison diagrams of the z-axis stress values ​​of all nodes in the dam body. Figure 14 This is the second comparison diagram of the z-axis stress values ​​of all nodes in the dam body. For example... Figure 13 and Figure 14 As shown, the stress values ​​range from approximately -12 to 0 (unit: 0.01 MPa), with negative values ​​representing compressive stress. The surrogate model accurately reproduces the spatial distribution characteristics of the stress field, and the stress concentration areas near the dam heel and toe are correctly identified.

[0061] In this application, the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams provided by the embodiments of the present invention discretizes the concrete dam structure into node representations, reduces the modeling dimensionality by clustering nodes and selecting representative nodes, and constructs a two-layer proxy model architecture to realize the prediction of physical quantities of representative nodes and the reconstruction of physical quantities of nodes within clusters, which can significantly improve computational efficiency while ensuring prediction accuracy, and provide reliable technical support for the safety monitoring and risk assessment of concrete dams.

[0062] Optionally, the training of the representative node physical quantity spatiotemporal prediction model includes: The environmental quantity sample sequence, the representative node physical quantity sample sequence, and the global graph structure in the historical training sample set are used as inputs to the spatiotemporal prediction model of the representative node physical quantity. Calculate the error between the output value of the spatiotemporal prediction model of the representative node physical quantity and the actual sample value of the representative node physical quantity, and construct the first loss function; The parameters of the spatiotemporal prediction model of the representative node physical quantity are iteratively updated based on the first loss function until the first loss function converges or reaches the first preset number of iterations.

[0063] In this application, the environmental quantity sample sequence refers to the environmental quantity data sequence within a historical time window L, denoted as This includes observations of environmental factors such as upstream water level and temperature over L consecutive time periods. A representative node physical quantity sample sequence refers to the physical quantity data sequence of representative nodes within the same historical time window, denoted as... .

[0064] The global graph structure is represented in the form of an adjacency matrix, denoted as . This adjacency matrix reflects the spatial association strength between representative nodes.

[0065] The prediction relationship of the representative nodal physical quantity spatiotemporal prediction model can be expressed as: ; In the formula, For historical environmental quantity sequence, A sequence of physical quantities representing historical nodes. This is the physical quantity prediction vector for a representative node at time t+1; (·) is a spatiotemporal prediction function that integrates environmental quantity features and graph structure features.

[0066] The first loss function measures the degree of difference between the model's predicted values ​​and the true values. The first loss function can be constructed in various ways, including mean squared error loss (MSE), mean absolute error loss (MAE), Huber loss, etc.

[0067] The model parameters are updated using a gradient descent optimization algorithm, specifically optimizers such as Adam, SGD, and RMSprop. In each iteration, the gradient of the model parameters is calculated based on the first loss function, and the parameter values ​​are updated according to the learning rate.

[0068] Training termination conditions can include: the value of the first loss function is less than a preset threshold (convergence), the number of training iterations reaches the first preset number of iterations, and the loss on the validation set no longer decreases (early stopping), etc.

[0069] In this application, through the above training process, the representative node physical quantity spatiotemporal prediction model can learn the mapping relationship between environmental quantities and representative node physical quantities, as well as the spatial correlation between representative nodes, thereby achieving accurate prediction of representative node physical quantities.

[0070] Optionally, the representative node physical quantity spatiotemporal prediction model includes: a graph convolutional layer and a temporal feature extraction layer; The graph convolutional layer receives the adjacency matrix corresponding to the global graph structure. For each representative node, the feature vectors of the neighboring representative nodes adjacent to the representative node are multiplied by the corresponding edge weights in the adjacency matrix and then summed to obtain the neighborhood aggregation feature. The neighborhood aggregation feature is concatenated with the feature vector of the representative node itself and then passed through a nonlinear activation function to output a node embedding vector that integrates spatial association information. The temporal feature extraction layer receives the environmental quantity sample sequence within the historical time window and the node embedding vector, captures the dynamic features of the physical quantity evolution over time through a gated recurrent unit, and outputs the predicted physical quantity values ​​of each representative node at the next moment.

[0071] In this application, graph convolutional layers are used to extract spatial association features between representative nodes. The graph convolutional layer receives the adjacency matrix corresponding to the global graph structure and performs neighborhood feature aggregation operations on each representative node.

[0072] Specifically, for each representative node, the graph convolutional layer performs the following operations: obtaining the feature vectors of the neighboring representative nodes adjacent to the representative node; multiplying the feature vectors of each neighboring representative node with the corresponding edge weights in the adjacency matrix and summing the results to obtain the neighborhood aggregated features; concatenating the neighborhood aggregated features with the feature vector of the representative node itself; and passing the concatenated features through a non-linear activation function (such as ReLU, LeakyReLU, Tanh, etc.) to output a node embedding vector that integrates spatial association information.

[0073] The temporal feature extraction layer is used to capture the dynamic features of physical quantities evolving over time. The temporal feature extraction layer receives environmental quantity sample sequences within a historical time window and the node embedding vectors, and models long-term dependencies in the time series using recurrent neural network structures such as gated recurrent units (GRUs) or long short-term memory networks (LSTMs).

[0074] The temporal feature extraction layer outputs the predicted physical quantities of each representative node at the next time step, thereby enabling temporal prediction of the physical quantities of the representative nodes.

[0075] By combining graph convolutional layers with temporal feature extraction layers, the representative node physical quantity spatiotemporal prediction model can simultaneously learn the spatial correlation features between nodes and the temporal evolution features of physical quantity responses, thereby accurately predicting the physical quantity values ​​of representative nodes at future moments.

[0076] Optionally, the training of the intra-cluster node physical quantity reconstruction model includes: The representative node physical quantity samples in the historical training sample set, the spatial coordinate data of the nodes to be reconstructed within the cluster, and the local graph structure are used as inputs to the node physical quantity reconstruction model within the cluster. Calculate the error between the output value of the cluster node physical quantity reconstruction model and the actual sample values ​​of all node physical quantities in the cluster, and construct a second loss function; The parameters of the physical quantity reconstruction model of the nodes within the cluster are iteratively updated based on the second loss function until the second loss function converges or the second preset number of iterations is reached.

[0077] In this application, for each node cluster, the input to the physical quantity reconstruction model of the nodes within the cluster includes: the physical quantity values ​​of the representative nodes corresponding to the cluster. Spatial coordinates of each node to be reconstructed within the cluster ( ), and a local graph structure representing the spatial relationships between nodes within a cluster.

[0078] The predictive relationship of the physical quantity reconstruction model within cluster nodes can be expressed as: ; in, For nodes within a cluster j Predicted values ​​of physical quantities; The predicted physical quantity values ​​for the representative nodes of this cluster; For nodes j Spatial coordinates; It is a nonlinear mapping function based on a graph neural network.

[0079] The second loss function measures the difference between the predicted and actual values ​​of the physical quantity reconstruction model for nodes within a cluster. The second loss function is constructed similarly to the first loss function and can employ methods such as mean squared error loss or mean absolute error loss.

[0080] In this application, the model parameter update process is similar to the training process of the representative nodal physical quantity spatiotemporal prediction model, using a gradient descent optimization algorithm to iteratively update the model parameters. The training termination condition can be the convergence of the second loss function or reaching a second preset number of iterations.

[0081] It should be noted that, for different node clusters, different intra-cluster node physical quantity reconstruction models can be trained, or a model with shared parameters can be trained to process all clusters simultaneously.

[0082] Through the above training process, the cluster-internal node physical quantity reconstruction model can learn the spatial mapping relationship between the physical quantities of representative nodes and the physical quantities of each node in the cluster, and realize the reconstruction of physical quantities from representative nodes to all nodes.

[0083] Optionally, the cluster-internal node physical quantity reconstruction model includes a coordinate encoding layer and a feature mapping layer; The coordinate coding layer receives the spatial coordinate data of the node to be reconstructed within the cluster and maps the spatial coordinate data into a high-dimensional coordinate embedding vector. The feature mapping layer copies and expands the physical quantity samples of the representative nodes and concatenates them with the high-dimensional coordinate embedding vectors corresponding to each node to be reconstructed. The concatenated features are then input into a multilayer perceptron, and after multiple linear transformations and nonlinear activations, the predicted physical quantity values ​​of each node to be reconstructed within the cluster are output.

[0084] In this application, the cluster-internal node physical quantity reconstruction model includes: a coordinate encoding layer and a feature mapping layer.

[0085] The coordinate encoding layer is used to encode the spatial coordinate information of nodes into high-dimensional feature representations. The coordinate encoding layer receives the spatial coordinate data of the nodes to be reconstructed within the cluster. xj,yj The spatial coordinate data is mapped into a high-dimensional coordinate embedding vector.

[0086] Coordinate encoding methods can include: directly using a multilayer perceptron for encoding, using positional encoding methods (such as sinusoidal positional encoding), and using Fourier feature mapping, etc.

[0087] The feature mapping layer is used to fuse representative node physical quantity information and node spatial location information to generate predicted physical quantity values ​​for each node to be reconstructed.

[0088] The processing steps of the feature mapping layer include: copying and expanding the representative node physical quantity samples to match the number of nodes to be reconstructed; concatenating the expanded representative node physical quantities with the high-dimensional coordinate embedding vectors corresponding to each node to be reconstructed; inputting the concatenated features into a multilayer perceptron (MLP); and outputting the predicted physical quantity values ​​of each node to be reconstructed within the cluster after multilayer linear transformation and nonlinear activation.

[0089] In this application, the structure of a multilayer perceptron may include multiple fully connected layers, each followed by a nonlinear activation function (such as ReLU) and an optional batch normalization layer or Dropout layer.

[0090] By combining the coordinate encoding layer and the feature mapping layer, the physical quantity reconstruction model of nodes within a cluster can learn the spatial distribution pattern of representative node physical quantities, predict their physical quantity values ​​based on the spatial location of each node, and achieve fine reconstruction of the physical quantity field within the cluster.

[0091] Optionally, selecting a representative node from each of the node clusters includes: Calculate the variance of the physical quantity of each node in the cluster in the historical training sample set, obtain the maximum and minimum variance values ​​among all the variance values ​​of the nodes in the cluster, calculate the difference between the variance value of each node and the minimum variance value for each node in the cluster, and divide it by the difference between the maximum and minimum variance values ​​to obtain the physical quantity sensitivity index of each node. Calculate the Euclidean distance from each node in the cluster to the geometric center of the cluster, obtain the maximum and minimum Euclidean distance values ​​among all nodes in the cluster, calculate the difference between the maximum distance value and the Euclidean distance of each node in the cluster, and divide the difference between the maximum distance value and the minimum distance value to obtain the spatial centrality index of each node. The physical quantity sensitivity index and the spatial centrality index of each node are weighted and summed to obtain the comprehensive score of each node. The node with the highest comprehensive score is selected as the representative node of the node cluster.

[0092] In this application, firstly, the variance of the physical quantities of each node within the cluster is calculated in the historical training sample set. The variance of the physical quantities reflects the magnitude of change in the node's physical quantity response; the larger the variance, the more sensitive the node is to environmental changes.

[0093] Then, obtain the maximum variance value among all node variance values ​​within the cluster. Var(max) with minimum variance Var (min) .

[0094] For each node i within the cluster, calculate the variance value of that node. Var(σ(i))The difference between the maximum variance value and the minimum variance value is divided by the difference between the maximum variance value and the minimum variance value to obtain the physical quantity sensitivity index of each node.

[0095] The physical quantity sensitivity index ranges from [0,1]. The larger the index value, the more sensitive the physical quantity response of the node is, and the better it can reflect the changes in physical quantities as a representative node.

[0096] Next, the Euclidean distance from each node within the cluster to the geometric center of the cluster is calculated. The geometric center can be defined as the mean of the spatial coordinates of all nodes within the cluster.

[0097] Then, obtain the maximum distance value among all Euclidean distances within the cluster. d(max) The minimum distance value d(min).

[0098] For each node i within the cluster, calculate the Euclidean distance between the maximum distance value and the node. d(i) The difference between the maximum and minimum distance values ​​is used to obtain the spatial centrality index of each node.

[0099] The spatial centrality index ranges from [0,1]. The larger the index value, the closer the node is to the geometric center of the cluster, and the more representative the node is in space.

[0100] The physical quantity sensitivity index and the spatial centrality index of each node are weighted and summed to obtain the comprehensive score of each node. The selection of representative nodes is based on the following comprehensive scoring function: In the formula, Let be the variance of the physical quantity of node i in the training set; is the spatial distance from node i to the geometric center of its cluster; These are the minimum and maximum values ​​within the corresponding clusters, respectively; These are the weighting coefficients.

[0101] Finally, the node with the highest comprehensive score is selected as the representative node of the node cluster.

[0102] In this application, by comprehensively considering two factors, physical quantity sensitivity and spatial centrality, the representative nodes selected in the embodiments of the present invention can not only sensitively reflect the physical quantity response caused by environmental changes, but also have good representativeness in spatial location, which is beneficial for subsequent model learning of the physical quantity response characteristics of the cluster as a whole.

[0103] Optionally, constructing the global graph structure based on the spatial positional relationships of all the representative nodes includes: Calculate the Euclidean distance between any two representative nodes, substitute the Euclidean distance into the distance decay function to calculate the connection weight between the two representative nodes, and generate an adjacency matrix based on the connection weights between all representative node pairs. Calculate the degree matrix of the adjacency matrix, where the degree matrix is ​​a diagonal matrix and the diagonal elements are the sum of the connection weights of the corresponding rows of each representative node. Calculate the negative 1 / 2 power matrix of the degree matrix. Multiply the negative 1 / 2 power matrix, the adjacency matrix, and the negative 1 / 2 power matrix in sequence to obtain the symmetric normalized global graph structure.

[0104] In this application, firstly, the Euclidean distance between any two representative nodes is calculated. d(ij) .

[0105] Then, the Euclidean distance is substituted into the distance decay function to calculate the connection weight between any two representative nodes. The distance decay function converts distance into similarity or connection strength; nodes that are closer together have a greater connection weight.

[0106] The representative node adjacency matrix is ​​constructed as follows: ; In the formula, Representative nodes and The Euclidean distance between them; This is the distance scale parameter.

[0107] An adjacency matrix is ​​generated based on the connection weights between all representative node pairs. A The adjacency matrix is ​​a symmetric matrix with diagonal elements of 1.

[0108] More specifically, the degree matrix of the adjacency matrix is ​​calculated. D The degree matrix is ​​a diagonal matrix, and the diagonal elements are the sum of the connection weights of the corresponding rows of each representative node.

[0109] Then, calculate the negative first power matrix of the degree matrix. .

[0110] Finally, the negative 1 / 2 power matrix, the adjacency matrix, and the negative 1 / 2 power matrix are multiplied sequentially to obtain the symmetric normalized global graph structure.

[0111] The adjacency matrix A By applying symmetric normalization, the normalized adjacency matrix is ​​obtained: ; in, D Adjacency matrix A The degree matrix.

[0112] In this application, the role of symmetric normalization is to limit the range of eigenvalues ​​of the adjacency matrix, which is beneficial to the stable training of the graph neural network, while maintaining the symmetry of the graph structure.

[0113] In this application, by constructing a normalized adjacency matrix based on spatial distance, the global graph structure can accurately represent the spatial topological relationships between representative nodes, providing structured input for the graph convolutional neural network, enabling the model to learn the spatial correlations between nodes.

[0114] Optionally, the method further includes: Obtain the target environmental quantity data of the concrete dam to be predicted at the current moment, and standardize the target environmental quantity data using the same standardized parameters as in the training phase. The standardized target environmental quantity data and the representative node physical quantity data within the historical time window are input into the trained representative node physical quantity spatiotemporal prediction model to obtain the physical quantity prediction data of each representative node at the current moment. For each node cluster, the physical quantity prediction data of the representative node corresponding to the node cluster and the spatial coordinate data of each node in the node cluster are input into the trained node physical quantity reconstruction model within the cluster to obtain the physical quantity prediction data of each node in the node cluster. By summarizing the physical quantity prediction data of all node clusters, the physical quantity prediction data of all nodes of the concrete dam are obtained.

[0115] In this application, target environmental quantity data refers to environmental quantity data input into the model during the inference phase, including observed or set values ​​of environmental factors such as upstream water level and temperature at the current moment.

[0116] The standardization process uses the same standardized parameters (such as mean and standard deviation) as the training phase to ensure that the input data in the inference phase is consistent with the data distribution in the training phase, thus avoiding a decrease in prediction accuracy caused by data distribution shift.

[0117] The standardization method for physical quantity data is as follows: In the formula, For the first i Each node at time... t The original physical quantity value; The value is the standardized physical quantity. and They are nodes i The mean and standard deviation of physical quantities within the training set.

[0118] More specifically, the representative node physical quantity spatiotemporal prediction model receives standardized target environmental quantity data and representative node physical quantity sequences within a historical time window, and outputs the predicted physical quantity values ​​of each representative node at the current moment through forward propagation calculation.

[0119] During the inference phase, representative node physical quantity data within the historical time window can come from previous prediction results (rolling prediction) or from actual observation data.

[0120] For each node cluster, the node physical quantity reconstruction model within the cluster receives the predicted values ​​of the physical quantities of the representative nodes corresponding to the cluster and the spatial coordinates of each node within the cluster. Through forward propagation calculation, it outputs the predicted values ​​of the physical quantities of each node within the cluster.

[0121] The physical quantity prediction results of each node cluster are summarized and integrated according to the node number to obtain the physical quantity prediction results of all nodes in the numerical simulation model of concrete dam.

[0122] Through the prediction process of the above-described reasoning stage, the embodiments of the present invention can quickly and accurately output the prediction results of the physical quantities of all nodes of the concrete dam based on the input environmental data, thus meeting the engineering requirements for real-time safety assessment of concrete dams.

[0123] Optionally, the method further includes: Based on the physical quantity prediction data of all nodes of the concrete dam, the radial basis numerical interpolation function is used to interpolate other spatial locations inside the dam body to generate a cloud map of the physical quantity field distribution of the concrete dam. The physical quantity field distribution cloud map of the concrete dam is used to analyze the physical quantity status and changing trend of the dam body.

[0124] In this application, radial basis function interpolation is a commonly used spatial interpolation method that can estimate data values ​​at any location in continuous space based on data values ​​at discrete points.

[0125] The physical quantity field distribution is generated using radial basis function interpolation, and its expression is: In the formula, The coordinates of the node; For interpolation weights; is the radial basis function; N is the number of nodes.

[0126] The interpolation results of physical quantities of all regular grid points are organized according to spatial location, and the physical quantity values ​​are converted into color values ​​using a color mapping method to generate a cloud map of the physical quantity field distribution of the concrete dam.

[0127] Color mapping methods for cloud maps can include: rainbow color bands, warm and cool tones, and monochrome gradients. Cloud maps can also be overlaid with auxiliary information such as dam boundary outlines, contour lines, and node location markers.

[0128] In this application, by using the radial basis function interpolation method, the embodiments of the present invention can convert the physical quantity prediction results of discrete nodes into a continuous physical quantity field distribution cloud map, which facilitates engineers to intuitively analyze the physical quantity status and change trend of concrete dams and provides visualization support for the safety monitoring of concrete dams.

[0129] In this application, Figure 15 This is one of the comparison images of x-axis displacement contour plot results. Figure 16 This is the second comparison chart of the x-axis displacement contour plot results. For example... Figure 15 and Figure 16 As shown, the horizontal axis represents the X-coordinate, the vertical axis the Y-coordinate, and the color bars indicate the magnitude of the displacement values, ranging from approximately 8 mm to 18 mm. The displacement contour map uses a continuous color gradient to represent the spatial distribution of the displacement field, with the largest displacement values ​​(warm colors) in the dam crest region and gradually decreasing towards the dam foundation (cool colors). The displacement contour map generated by the proxy model is highly consistent with the spatial distribution characteristics of the finite element calculation results.

[0130] Figure 17 This is one of the schematic diagrams comparing the stress contour plots in the z-axis. Figure 18 This is the second schematic diagram comparing the stress contour plot results in the z-axis. For example... Figure 17 and Figure 18 As shown, the stress values ​​range from approximately -5 to 0 (unit: 0.01 MPa), with negative values ​​representing compressive stress. The contour map clearly demonstrates the spatial distribution characteristics of the stress field, and the surrogate model can accurately reproduce the stress distribution patterns at key locations such as the dam heel and dam toe.

[0131] Figure 19 This is one of the scatter plots of the predicted values ​​from the finite element-surrogate model provided by the present invention. Figure 20 This is the second scatter plot of the predicted values ​​from the finite element-surrogate model provided by the present invention, as shown below. Figure 19 and Figure 20 As shown, the vertical axis represents the predicted value of the surrogate model (unit: mm), and the scatter points are distributed along the diagonal and are highly concentrated, indicating that the predicted value of the surrogate model and the calculated value of the finite element method have a high correlation. The right figure is a scatter plot of the stress in the z-direction, with the horizontal axis representing the calculated value of the finite element method (unit: 0.01 MPa) and the vertical axis representing the predicted value of the surrogate model (unit: 0.01 MPa), which also shows a good linear correlation.

[0132] Figure 21 Generate a box plot of the response time of the x-direction displacement on the test set provided by this invention, such as Figure 21As shown, the vertical axis represents the response time (unit: s). The box plot shows that the response time is mainly concentrated between 0.48 seconds and 0.58 seconds, with a median of about 0.52 seconds, indicating that the surrogate model can quickly complete the prediction calculation of the displacement field.

[0133] Figure 22 This is a box plot of the response time for generating z-axis stress on the test set. For example... Figure 22 As shown, the response time is mainly concentrated between 0.50 seconds and 0.62 seconds, with a median of about 0.57 seconds, which is comparable to the response time of displacement field prediction.

[0134] Figure 23 This is the error distribution map for generating the x-axis displacement field map on the test set. For example... Figure 23 As shown, the horizontal axis represents the time step MAE (unit: mm), and the vertical axis represents the density. The error distribution is right-skewed, with the peak value located around 0.1 mm to 0.2 mm. Most of the prediction errors are concentrated in a small range, indicating that the surrogate model has high prediction accuracy.

[0135] Figure 24 This is the error distribution map for generating the z-axis stress field map on the test set. For example... Figure 24 As shown, the horizontal axis represents the time step MAE (unit: MPa), and the vertical axis represents the density. The error distribution also exhibits a right-skewed distribution, with the peak value located near 0.02 MPa, indicating a relatively small prediction error.

[0136] To evaluate the performance of the intelligent agent model constructed in this invention, the model was tested on the test set (September 20, 2021 - October 5, 2023), and the test results are shown in Table 2.

[0137] Table 2

[0138] The following describes the device for rapidly generating intelligent proxy models of the mechanical field of concrete dams provided by the present invention. The device for rapidly generating intelligent proxy models of the mechanical field of concrete dams described below can be referred to in correspondence with the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams described above.

[0139] Figure 25 This is a schematic diagram of the intelligent proxy model device for rapid generation of the mechanical field of concrete dams provided by the present invention. Figure 25 As shown, it includes: The acquisition module 11 is used to acquire historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of concrete dam, and to perform time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. The partitioning module 12 is used to perform clustering on all nodes of the concrete dam based on the historical training sample set and the spatial coordinate data of each node, to obtain multiple node clusters, and to select a representative node from each node cluster. The first training module 13 is used to construct a global graph structure based on the spatial positional relationship of all the representative nodes, and to train a spatiotemporal prediction model of representative node physical quantities using environmental quantity samples, representative node physical quantity samples and the global graph structure in the historical training sample set. The second training module 14 is used to construct a local graph structure based on the spatial positional relationship of nodes within each node cluster for each node cluster, and to train a node physical quantity reconstruction model within the cluster using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure; wherein, the spatiotemporal prediction model of representative node physical quantities and the node physical quantity reconstruction model within the cluster constitute an intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

[0140] In this application, a historical training sample set is constructed by acquiring historical physical quantity samples and environmental quantity samples of all nodes in the numerical simulation model of the concrete dam. Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered. Representative nodes are selected from each node cluster, realizing the node-based representation of the concrete dam data, effectively reducing the dimensionality and computational complexity of the whole-node physical quantity prediction model. By constructing a global graph structure based on the spatial positional relationship of representative nodes and training a spatiotemporal prediction model of representative node physical quantities, it is possible to integrate environmental quantity driving information and spatial correlation information between representative nodes, accurately depicting the spatiotemporal evolution law of physical quantity response. By constructing a local graph structure for each node cluster and training a node physical quantity reconstruction model within the cluster, a high-fidelity spatial expansion reconstruction from the physical quantity prediction data of representative nodes to the physical quantities of all nodes within the cluster is achieved, ensuring the spatial continuity and consistency of the physical quantity field prediction results. The overall scheme does not require complex finite element solution calculations in the inference stage, can quickly respond to changes in environmental quantities and output the physical quantity prediction data of all nodes of the concrete dam, providing efficient, stable and high-precision technical support for the safety monitoring and operation management of concrete dams.

[0141] Figure 26 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 26As shown, the electronic device may include: a processor 1210, a communication interface 1220, a memory 1230, and a communication bus 1240, wherein the processor 1210, the communication interface 1220, and the memory 1230 communicate with each other through the communication bus 1240. The processor 1210 can call logical instructions in the memory 1230 to execute a method for rapidly generating a smart proxy model of the mechanical field of a concrete dam. This method includes: acquiring historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of the concrete dam; performing time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered to obtain multiple node clusters, and a representative node is selected from each node cluster. A global graph structure is constructed based on the spatial positional relationships of all the representative nodes. An environmental quantity sample, a representative node physical quantity sample, and the global graph structure are used in the historical training sample set to train a spatiotemporal prediction model for the physical quantities of the representative nodes. For each node cluster, a local graph structure is constructed based on the spatial positional relationship of nodes within the cluster. Using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure, a node physical quantity reconstruction model within the cluster is trained. The representative node physical quantity spatiotemporal prediction model and the node physical quantity reconstruction model within the cluster constitute an intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

[0142] Furthermore, the logical instructions in the aforementioned memory 1230 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0143] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the method for rapidly generating a smart agent model of the mechanical field of a concrete dam provided by the above methods. The method includes: obtaining historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of the concrete dam; performing time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples; and constructing a historical training sample set. Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered to obtain multiple node clusters, and a representative node is selected from each node cluster. A global graph structure is constructed based on the spatial positional relationships of all the representative nodes. An environmental quantity sample, a representative node physical quantity sample, and the global graph structure are used in the historical training sample set to train a spatiotemporal prediction model for the physical quantities of the representative nodes. For each node cluster, a local graph structure is constructed based on the spatial positional relationship of nodes within the cluster. Using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure, a node physical quantity reconstruction model within the cluster is trained. The representative node physical quantity spatiotemporal prediction model and the node physical quantity reconstruction model within the cluster constitute an intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

[0144] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a method for rapidly generating a smart proxy model of the mechanical field of a concrete dam provided by the above methods. The method includes: acquiring historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of the concrete dam; performing time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples; and constructing a historical training sample set. Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered to obtain multiple node clusters, and a representative node is selected from each node cluster. A global graph structure is constructed based on the spatial positional relationships of all the representative nodes. An environmental quantity sample, a representative node physical quantity sample, and the global graph structure are used in the historical training sample set to train a spatiotemporal prediction model for the physical quantities of the representative nodes. For each node cluster, a local graph structure is constructed based on the spatial positional relationship of nodes within the cluster. Using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure, a node physical quantity reconstruction model within the cluster is trained. The representative node physical quantity spatiotemporal prediction model and the node physical quantity reconstruction model within the cluster constitute an intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

[0145] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0146] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, 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 can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for rapidly generating an intelligent surrogate model of the mechanical field of a concrete dam, characterized in that, include: Obtain historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of the concrete dam. Perform time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. Based on the historical training sample set and the spatial coordinate data of each node, all nodes of the concrete dam are clustered to obtain multiple node clusters, and a representative node is selected from each node cluster. A global graph structure is constructed based on the spatial positional relationships of all the representative nodes. An environmental quantity sample, a representative node physical quantity sample, and the global graph structure are used in the historical training sample set to train a spatiotemporal prediction model for the physical quantities of the representative nodes. For each node cluster, a local graph structure is constructed based on the spatial positional relationship of nodes within the cluster. Using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure, a node physical quantity reconstruction model within the cluster is trained. The representative node physical quantity spatiotemporal prediction model and the node physical quantity reconstruction model within the cluster constitute an intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data. The representative node physical quantity spatiotemporal prediction model includes: a graph convolutional layer and a temporal feature extraction layer; The graph convolutional layer receives the adjacency matrix corresponding to the global graph structure. For each representative node, the feature vectors of the neighboring representative nodes adjacent to the representative node are multiplied by the corresponding edge weights in the adjacency matrix and then summed to obtain the neighborhood aggregation feature. The neighborhood aggregation feature is concatenated with the feature vector of the representative node itself and then passed through a nonlinear activation function to output a node embedding vector that integrates spatial association information. The temporal feature extraction layer receives the environmental quantity sample sequence within the historical time window and the node embedding vector, captures the dynamic features of the physical quantity evolution over time through the gated recurrent unit, and outputs the predicted physical quantity values ​​of each representative node at the next moment. The cluster-internal node physical quantity reconstruction model includes a coordinate encoding layer and a feature mapping layer. The coordinate coding layer receives the spatial coordinate data of the node to be reconstructed within the cluster and maps the spatial coordinate data into a high-dimensional coordinate embedding vector. The feature mapping layer copies and expands the physical quantity samples of the representative nodes and concatenates them with the high-dimensional coordinate embedding vectors corresponding to each node to be reconstructed. The concatenated features are then input into a multilayer perceptron, and after multiple linear transformations and nonlinear activations, the predicted physical quantity values ​​of each node to be reconstructed within the cluster are output.

2. The method for rapidly generating intelligent proxy models of the mechanical field of concrete dams according to claim 1, characterized in that, The training of the representative node physical quantity spatiotemporal prediction model includes: The environmental quantity sample sequence, the representative node physical quantity sample sequence, and the global graph structure in the historical training sample set are used as inputs to the spatiotemporal prediction model of the representative node physical quantity. Calculate the error between the output value of the spatiotemporal prediction model of the representative node physical quantity and the actual sample value of the representative node physical quantity, and construct the first loss function; The parameters of the spatiotemporal prediction model of the representative node physical quantity are iteratively updated based on the first loss function until the first loss function converges or reaches the first preset number of iterations.

3. The method for rapidly generating intelligent proxy models of the mechanical field of concrete dams according to claim 1, characterized in that, The training cluster node physical quantity reconstruction model includes: The representative node physical quantity samples in the historical training sample set, the spatial coordinate data of the nodes to be reconstructed within the cluster, and the local graph structure are used as inputs to the node physical quantity reconstruction model within the cluster. Calculate the error between the output value of the cluster node physical quantity reconstruction model and the actual sample values ​​of all node physical quantities in the cluster, and construct a second loss function; The parameters of the physical quantity reconstruction model of the nodes within the cluster are iteratively updated based on the second loss function until the second loss function converges or the second preset number of iterations is reached.

4. The method for rapidly generating intelligent proxy models of the mechanical field of concrete dams according to claim 1, characterized in that, The step of selecting a representative node from each of the node clusters includes: Calculate the variance of the physical quantity of each node in the cluster in the historical training sample set, obtain the maximum and minimum variance values ​​among all the variance values ​​of the nodes in the cluster, calculate the difference between the variance value of each node and the minimum variance value for each node in the cluster, and divide it by the difference between the maximum and minimum variance values ​​to obtain the physical quantity sensitivity index of each node. Calculate the Euclidean distance from each node in the cluster to the geometric center of the cluster, obtain the maximum and minimum Euclidean distance values ​​among all nodes in the cluster, calculate the difference between the maximum distance value and the Euclidean distance of each node in the cluster, and divide the difference between the maximum distance value and the minimum distance value to obtain the spatial centrality index of each node. The physical quantity sensitivity index and the spatial centrality index of each node are weighted and summed to obtain the comprehensive score of each node. The node with the highest comprehensive score is selected as the representative node of the node cluster.

5. The method for rapidly generating intelligent proxy models of the mechanical field of concrete dams according to claim 1, characterized in that, The construction of the global graph structure based on the spatial positional relationships of all the representative nodes includes: Calculate the Euclidean distance between any two representative nodes, substitute the Euclidean distance into the distance decay function to calculate the connection weight between the two representative nodes, and generate an adjacency matrix based on the connection weights between all representative node pairs. Calculate the degree matrix of the adjacency matrix, where the degree matrix is ​​a diagonal matrix and the diagonal elements are the sum of the connection weights of the corresponding rows of each representative node. Calculate the negative 1 / 2 power matrix of the degree matrix. Multiply the negative 1 / 2 power matrix, the adjacency matrix, and the negative 1 / 2 power matrix in sequence to obtain the symmetric normalized global graph structure.

6. The method for rapidly generating intelligent proxy models of the mechanical field of concrete dams according to claim 1, characterized in that, The method further includes: Obtain the target environmental quantity data of the concrete dam to be predicted at the current moment, and standardize the target environmental quantity data using the same standardized parameters as in the training phase. The standardized target environmental quantity data and the representative node physical quantity data within the historical time window are input into the trained representative node physical quantity spatiotemporal prediction model to obtain the physical quantity prediction data of each representative node at the current moment. For each node cluster, the physical quantity prediction data of the representative node corresponding to the node cluster and the spatial coordinate data of each node in the node cluster are input into the trained node physical quantity reconstruction model within the cluster to obtain the physical quantity prediction data of each node in the node cluster. The physical quantity prediction data of all node clusters are summarized to obtain the physical quantity prediction data of all nodes of the concrete dam; based on the physical quantity prediction data of all nodes of the concrete dam, the radial basis numerical interpolation function is used to interpolate other spatial locations inside the dam body to generate a physical quantity field distribution cloud map of the concrete dam. The physical quantity field distribution cloud map of the concrete dam is used to analyze the physical quantity status and changing trend of the dam body.

7. A device for rapidly generating intelligent proxy models of the mechanical field of concrete dams, characterized in that, The apparatus for implementing the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams as described in any one of claims 1-6 includes: The acquisition module is used to acquire historical physical quantity samples and corresponding environmental quantity samples of all nodes in the numerical simulation model of concrete dam, and to perform time alignment and standardization processing on the historical physical quantity samples and the environmental quantity samples to construct a historical training sample set. The partitioning module is used to cluster all nodes of the concrete dam based on the historical training sample set and the spatial coordinate data of each node, to obtain multiple node clusters, and to select a representative node from each node cluster. The first training module is used to construct a global graph structure based on the spatial positional relationships of all the representative nodes, and to train a spatiotemporal prediction model of the physical quantities of the representative nodes using environmental quantity samples, physical quantity samples of the representative nodes and the global graph structure in the historical training sample set. The second training module is used to construct a local graph structure based on the spatial positional relationship of nodes within each node cluster for each node cluster, and to train a node physical quantity reconstruction model within the cluster using representative node physical quantity samples from the historical training sample set, node physical quantity samples within the cluster, and the local graph structure; wherein, the spatiotemporal prediction model of representative node physical quantities and the node physical quantity reconstruction model within the cluster constitute an intelligent agent model. Among them, the representative node physical quantity spatiotemporal prediction model trained in the intelligent agent model is used to output representative node physical quantity prediction data based on the target environmental quantity data of the input concrete dam, and the cluster node physical quantity reconstruction model trained in the intelligent agent model is used to output physical quantity prediction data of all nodes in the cluster based on the representative node physical quantity prediction data.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for rapidly generating intelligent proxy models of the mechanical field of concrete dams as described in any one of claims 1 to 6.

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