Deep learning based urban building cluster seismic resilience capacity prediction system

Abstract

This invention relates to the field of deep learning technology and discloses a deep learning-based system for predicting the seismic resilience of urban building complexes. The system acquires structural attribute data and spatial geographic coordinates of the building complex, maps buildings as graph nodes, uses structural physical parameters including natural vibration period, inter-story yield shear force, and height as node features, and uses the physical dynamic coupling coefficient matrix calculated based on the seismic wave propagation attenuation model and building spatial spacing as edge weights to construct a physically constrained spatial topology graph. A physical constraint graph convolutional temporal network introduces boundary constraint terms from the structural dynamics equations during message passing to filter node feature updates, and combines this with gated recurrent units to extract damage evolution state features. This system preserves the spatial mechanical transmission path of the building complex, suppresses feature updates that violate physical laws, reduces data extrapolation errors, and solves the problem of spatial cascading failure prediction bias.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology and discloses a deep learning-based system for predicting the seismic resilience of urban building complexes. Background Technology

[0002] In the field of seismic toughness prediction for urban building complexes, deep learning models are typically used instead of finite element numerical simulations. Conventional methods acquire structural attribute data and spatial geographic coordinates of the urban building complex, extracting structural physical parameters such as natural vibration period, inter-story yield shear force, and height for each building, directly flattening them into a one-dimensional feature vector. This flattened one-dimensional feature vector, along with the seismic motion time-series input data, is fed into a fully connected network or a long short-term memory network. The network uses a multilayer perceptron to perform linear transformations and nonlinear activations on the one-dimensional feature vector, extracting the temporal evolution features hidden in the data, and ultimately outputting the seismic toughness index of a single building or the entire building complex. In this conventional implementation, each building is treated as an isolated data sample.

[0003] Seismic waves attenuate with energy as they propagate in real physical space, and there are dynamic interactions between adjacent buildings. The conventional deep learning approach described above, which flattens structural physical parameters into one-dimensional feature vectors and inputs them into the network, directly eliminates the physical coupling between the spatial adjacency of buildings and seismic wave propagation during data processing. The network cannot perceive the spatial topology within the building complex during feature extraction, causing the model to fail to capture the actual damage propagation and cascading failure process of the building complex under seismic loads during computation. This results in a technical problem of spatial cascading failure prediction bias. Summary of the Invention

[0004] The purpose of this invention is to provide a deep learning-based system for predicting the seismic resilience of urban building complexes, which can solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A deep learning-based system for predicting the seismic resilience of urban building complexes includes a data acquisition interface, a spatial topology graph construction processor, a physical constraint graph convolutional temporal network processor, and a fully connected mapping processor. The data acquisition interface obtains structural attribute data and spatial geographic coordinates of urban building clusters; The spatial topology graph construction processor maps each building in the building complex to a graph node, sets the node feature vector to structural physical parameters including the building's natural vibration period, inter-story yield shear force, and height, and sets the edge weights between nodes to the physical dynamic coupling coefficient matrix calculated based on the seismic wave propagation attenuation model and the building spatial spacing, thus forming a physically constrained spatial topology graph. The physical constraint graph convolutional temporal network processor includes a physical constraint graph convolutional layer and a gated recurrent unit. The physical constraint graph convolutional layer introduces boundary constraint terms based on structural dynamics equations to filter node feature updates during message passing. The gated recurrent unit extracts the damage evolution state features of the building complex under seismic temporal input. The fully connected mapping processor outputs the seismic toughness index of each node in the building complex based on the damage evolution state characteristics. During the network training phase, a physical information loss function is used. The residual between the network output prediction of inter-layer displacement angle and the theoretical displacement angle limit derived from structural mechanics is calculated and used as a penalty term for backpropagation to update the network weights.

[0006] Preferably, when constructing node feature vectors, the spatial topology map construction processor extracts the number of floors, standard value of concrete compressive strength, standard value of steel bar yield strength, and aspect ratio from the structural attribute data corresponding to each building, and combines the extracted parameters into an initial structural physical feature matrix. The initial structural physical feature matrix is ​​Z-score normalized, and the normalized feature vector is concatenated with the site category features of the building's geographical location to generate an extended node feature vector. The spatial topology graph construction processor assigns the extended node feature vectors to the corresponding graph nodes in the physical constraint spatial topology graph, which serve as the initial input features for the physical constraint graph convolutional temporal network processor.

[0007] Preferably, when calculating the edge weights between nodes, the spatial topology graph construction processor obtains the Euclidean distance between any two adjacent graph nodes in the spatial geographic coordinates, and substitutes the Euclidean distance into the preset seismic wave propagation attenuation model to calculate the spatial attenuation ratio coefficient of the peak ground acceleration. The calculated spatial attenuation ratio coefficient is multiplied by the absolute value of the difference in the natural vibration period of each adjacent graph node, and the result is used as the initial physical-dynamic coupling coefficient between adjacent graph nodes. The spatial topology graph construction processor uses the Sigmoid activation function to perform nonlinear mapping on the initial physical dynamic coupling coefficients, and sets the mapping result as the edge weight of the corresponding edge in the physical constraint spatial topology graph.

[0008] Preferably, when the physical constraint graph convolutional layer performs the message passing process, for the central node in the physical constraint space topology graph, it obtains the node feature vectors and edge weights of the central node and its neighboring nodes that are connected to the central node, calculates the product of the neighboring node feature vectors and edge weights, and accumulates them to generate node aggregate features. The physical constraint diagram convolutional layer extracts the natural period and interlayer yield shear of the central node, and substitutes the extracted parameters into the preset single-degree-of-freedom system dynamic equation to calculate the theoretical acceleration response range of the central node. The physical constraint graph convolutional layer determines whether the predicted acceleration response values ​​contained in the node aggregation features are within the theoretical acceleration response range. It removes node aggregation feature components that are outside the theoretical acceleration response range and then concatenates and updates the filtered node aggregation features with the central node feature vector.

[0009] Preferably, the gated loop unit includes an update gate, a reset gate, and a candidate hidden state calculation layer; The gated recurrent unit receives the updated node feature sequence output from the physical constraint graph convolutional layer and the seismic motion time series input. In the update gate calculation step, the hidden state of the previous time step is concatenated with the updated node feature sequence of the current time step, and the update gate vector is output through the first fully connected layer and the Sigmoid activation function. In the reset gate calculation step, the reset gate vector is output through the second fully connected layer; The candidate hidden state computation layer performs a Hadamard product between the reset gate vector and the hidden state of the previous time step. The product result is then concatenated with the updated node feature sequence of the current time step and input into the third fully connected layer. Finally, the Tanh activation function is used to output the candidate hidden state vector.

[0010] Preferably, the physical information loss function includes a basic prediction loss term and a physical constraint penalty term; The mean square error between the predicted seismic toughness index output by the fully connected mapping processor and the tag toughness index is calculated for the basic prediction loss term. The physical constraint penalty term obtains the predicted value of the intermediate inter-story drift angle generated during the forward propagation of the fully connected mapping processor. Combined with the story height parameter in the structural attribute data, the theoretical drift angle limit of the corresponding building is calculated according to the elastic-plastic inter-story drift angle limit formula in the code. The physical constraint penalty term is calculated as the sum of squares of the differences between the predicted inter-story drift angle and the theoretical drift angle limit. The physical information loss function generates a total loss value by weighting and summing the basic prediction loss term and the physical constraint penalty term according to preset weight coefficients.

[0011] Preferably, after generating the extended node feature vector, the spatial topology graph construction processor obtains the building foundation type parameters and foundation soil shear wave velocity parameters contained in the structural attribute data, converts the building foundation type parameters into one-hot encoded vectors, and performs logarithmic transformation on the foundation soil shear wave velocity parameters. The soil-structure interaction feature vector is generated by concatenating the one-hot encoded vector with the shear wave velocity parameters of the foundation soil after logarithmic transformation. The spatial topology graph construction processor uses the soil-structure interaction feature vector as a bias term and adds it to the tail of the extended node feature vector through vector addition to generate the final node feature vector containing soil-structure interaction features.

[0012] Preferably, before determining whether the predicted acceleration response value contained in the node aggregation feature is within the theoretical acceleration response range, the physical constraint graph convolutional layer obtains the interlayer yield shear force of the neighboring nodes and the interlayer yield shear force of the central node, and calculates the ratio of the interlayer yield shear force of the neighboring nodes to the interlayer yield shear force of the central node. When the calculated ratio is less than the preset load-bearing capacity transmission threshold, the physical constraint graph convolutional layer generates the blocking mask vector of the corresponding neighbor node. When calculating the product of the neighbor node feature vector and the edge weight, the product result is multiplied element by element with the blocking mask vector, and the multiplication result is set to zero vector to prevent the generation of node aggregation features.

[0013] Preferably, after the candidate hidden state calculation layer outputs the candidate hidden state vector, the gated loop unit obtains the peak ground acceleration value of the building group at the current time step, inputs the peak ground acceleration value into the preset continuous damage mechanics evolution equation, and calculates the structural stiffness degradation ratio coefficient corresponding to the current time step. The gated cyclic unit uses the structural stiffness degradation ratio as the exponential decay factor to perform element-wise exponential decay operation on the hidden state of the previous time step, generating a historical state decay vector. The gated loop unit performs a weighted calculation on the historical state decay vector, the update gate vector, and the candidate hidden state vector according to the hidden state update formula to generate the final hidden state vector for the current time step.

[0014] Preferably, when calculating the theoretical displacement angle limit of the corresponding building according to the elastic-plastic inter-story drift angle limit formula in the specification, the physical constraint penalty term obtains the net distance parameter between any two adjacent buildings in the spatial geographic coordinates and the difference value of the floor elevation of the two buildings on the corresponding floor. When the net spacing parameter is less than the sum of the floor elevation difference value and the seismic joint width benchmark value, the physical constraint penalty term uses the net spacing parameter as the collision contact limit between adjacent buildings and calculates the additional inter-story drift angle reduction caused by the collision on the structure based on the seismic joint collision mechanics model. The physical constraint penalty term adds the additional inter-story drift angle reduction to the theoretical drift angle limit, generating a modified theoretical drift angle limit.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention maps buildings as graph nodes and sets the physical dynamic coupling coefficient matrix calculated based on the seismic wave propagation attenuation model and building spatial spacing as the edge weights, constructing a physically constrained spatial topology graph that preserves the spatial mechanical transmission paths between buildings. During graph convolution message passing, boundary constraint terms based on structural dynamic equations are introduced to filter node feature updates. Simultaneously, during the training phase, a physical information loss function is used to calculate the residual between the predicted inter-story drift angle and the theoretical drift angle limit as a penalty term. The above feature extraction and loss calculation mechanism ensures that the network operation process is constrained by structural mechanical laws, overcoming the spatial correlation loss caused by flattening independent vector processing, reducing the data extrapolation error of the prediction model under extreme seismic conditions that violates physical laws, and solving the problem of spatial cascading failure prediction bias.

[0016] 2. This invention transforms building foundation types into uniquely thermal codes and performs a logarithmic transformation on the shear wave velocity of the foundation soil to generate soil-structure interaction feature vectors, which are then superimposed as bias terms, increasing the data dimension of node features. By comparing the inter-story yield shear ratio of adjacent nodes with the bearing capacity transmission threshold to generate a blocking mask vector, message transmission between neighboring nodes that does not conform to the mechanical transmission logic is truncated. In the temporal state update, a continuous damage mechanics evolution equation is introduced to calculate the structural stiffness degradation ratio coefficient and perform exponential decay calculation on the historical state. In the physical constraint penalty term, an additional inter-story displacement angle reduction is calculated based on the seismic joint collision mechanics model to correct the theoretical displacement angle limit, thus limiting the invalid accumulation of temporal feature transmission under complex collision conditions. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the overall operation of the present invention. Figure 2 This is a flowchart illustrating the spatial topology graph construction process of the present invention. Figure 3 This is a flowchart of the physical constraint graph convolutional layer processing of the present invention; Figure 4 This is a flowchart of the gated loop unit processing of the present invention; Figure 5 This is a flowchart illustrating the calculation of the physical information loss function of the present invention; Figure 6 This is a flowchart of the network training and weight update process of the present invention. Detailed Implementation

[0018] Please refer to the attached document. Figure 1 To be continued Figure 6This embodiment provides a deep learning-based system for predicting the seismic resilience of urban building clusters, including a data acquisition interface, a spatial topology map construction processor, a physical constraint graph convolutional temporal network processor, and a fully connected mapping processor. The data acquisition interface interfaces with the urban building information model database and the geographic information system database, and obtains the structural attribute data and spatial geographic coordinates of the urban building clusters through a standardized data communication protocol.

[0019] Structural attribute data includes the structural physical parameters of individual buildings, covering three core parameters: building natural period, inter-story yield shear force, and building height. The building natural period is the fundamental natural period of the building structure, obtained through structural dynamics modal analysis. The inter-story yield shear force is the minimum yield shear force of each floor, corresponding to the critical shear force value for overall structural yielding. The building height is the vertical distance from the outdoor ground level to the roof eaves. Spatial geographic coordinates include the two-dimensional geographic coordinates of the center point of the planar projection corresponding to each building. The coordinate system adopts a unified Gauss-Kruger Cartesian coordinate system to ensure a consistent measurement benchmark for the spatial location of different buildings.

[0020] The spatial topology graph construction processor receives structural attribute data and spatial geographic coordinates output from the data acquisition interface. It maps each building in the building complex to an independent graph node in an undirected graph, establishing a corresponding mapping relationship between each building and the graph node. This mapping relationship is bound to the unique identifier of the building and the index value of the graph node. The spatial topology graph construction processor sets the node feature vector of the graph node to include structural physical parameters such as the building's natural vibration period, inter-story yield shear force, and height. The dimension of the node feature vector is consistent with the number of structural physical parameters, with each dimension corresponding to the value of one structural physical parameter. The arrangement order of the node feature vectors is maintained uniformly across all graph nodes to ensure the consistency of parameter dimensions during subsequent feature extraction.

[0021] The spatial topology graph construction processor calculates the edge weights between nodes in the graph. These weights are set as physical-dynamic coupling coefficient matrices calculated based on the seismic wave propagation attenuation model and building spatial spacing. The physical-dynamic coupling coefficient matrix is ​​a symmetric matrix. The weights in the matrix are... Line 1 The elements of the column correspond to the first The graph node and the first The edge weights between graph nodes. The spatial topology graph construction processor generates a physically constrained spatial topology graph based on graph nodes, node feature vectors, and edge weights. The physically constrained spatial topology graph is an undirected weighted graph that fully preserves the spatial positional relationships and physical dynamic coupling of buildings in the building complex.

[0022] In this embodiment, the core constituent parameters of the physical constraint space topology map are defined as shown in Table 1. Through a unified parameter definition specification, the meaning of each physical quantity is clear during the construction of the topology map, the data flow process has a consistent physical benchmark, and the spatial mechanical transmission path within the building complex is fully preserved.

[0023] Table 1 Definition of Core Component Parameters of Physical Constraint Space Topology Diagram ; The Physically Constrained Graph Convolutional Temporal Network Processor receives a spatial topology graph and constructs a physically constrained spatial topology graph output by the processor. The Physically Constrained Graph Convolutional Temporal Network Processor contains physically constrained graph convolutional layers and gated recurrent units. There is at least one physically constrained graph convolutional layer. Each physically constrained graph convolutional layer performs message passing and feature update operations. During message passing, boundary constraint terms based on structural dynamics equations are introduced to filter node feature updates.

[0024] The physical constraint graph convolutional layer performs message aggregation and feature filtering operations on each central node in the physical constraint space topology graph. During message aggregation, it obtains the node feature vector of the central node, the node feature vectors of all neighboring nodes connected to the central node, and the edge weights between the central node and each neighboring node, thus completing the weighted aggregation of neighboring node features and generating node aggregate features. Boundary constraint terms are constructed based on the dynamic equations of a single-degree-of-freedom system architecture. The value range of the boundary constraint terms is the theoretical acceleration response range of the building corresponding to the central node. The physical constraint graph convolutional layer compares the predicted acceleration response values ​​contained in the node aggregate features with the theoretical acceleration response range, eliminating node aggregate feature components outside the theoretical acceleration response range, thus completing the feature filtering operation. The physical constraint graph convolutional layer concatenates the filtered node aggregate features with the original node feature vector of the central node to generate an updated node feature vector, completing the feature update operation for the central node.

[0025] The gated recurrent unit receives the updated node feature sequence output from the physical constraint graph convolutional layer, as well as the seismic ground motion time-series input data. The seismic ground motion time-series input data consists of a sequence of seismic ground acceleration time steps divided into equal time steps, with the time step consistent with the sampling interval of the seismic ground motion records. Each time step corresponds to a set of seismic ground acceleration values ​​and the updated node feature sequence for that time. The gated recurrent unit performs cyclic encoding on the time-series input feature sequence to extract the damage evolution state features of the building complex under the seismic ground motion time-series input. The damage evolution state features are represented by the hidden state vector output by the gated recurrent unit. The dimension of the hidden state vector matches the dimension of the node feature vector, and the hidden state vector at each time step corresponds to the cumulative structural damage state of the building complex at that time.

[0026] The fully connected mapping processor receives damage evolution state features from the physical constraint graph convolutional temporal network processor. The processor contains at least two fully connected layers, with a nonlinear activation function (ReLU) between adjacent layers. The processor performs linear transformations and nonlinear mappings on the input damage evolution state features, outputting seismic toughness indices for each node in the building complex. These indices are quantitative parameters characterizing a building's ability to maintain and recover structural function under seismic loading, including at least one of the following: maximum inter-story drift angle, residual inter-story drift angle, structural failure probability, and functional recovery time. The output layer dimension of the fully connected mapping processor matches the total number of nodes in the physical constraint space topology graph, with each output dimension corresponding to a seismic toughness index value for a graph node.

[0027] During the network training phase, the system employs a physical information loss function to optimize and update network parameters. This function, based on conventional prediction loss, introduces a physical constraint penalty term based on structural mechanics principles. During forward propagation, the fully connected mapping processor generates predicted inter-layer displacement angles. The physical information loss function calculates the residual between these predicted values ​​and the theoretical displacement angle limits derived from structural mechanics. This residual is used as the physical constraint penalty term and weighted and summed with the basic prediction loss term to generate the total loss value. Based on this total loss value, the system performs backpropagation. Using a gradient descent optimization algorithm, it calculates the gradient of the total loss value with respect to the weight and bias parameters of each layer. The system then updates the weight and bias parameters along the gradient descent direction, completing one network training iteration. The training process repeats the forward propagation, loss calculation, backpropagation, and parameter update operations until the total loss value converges to a preset convergence threshold, completing the network training process.

[0028] This embodiment achieves a complete representation of the spatial adjacency relationship and physical coupling of building groups by constructing a physical constraint spatial topology graph. Through boundary constraint filtering of the physical constraint graph convolutional layer and the mechanical law constraint of the physical information loss function, the feature extraction and parameter update process of the network always conforms to the basic principles of structural dynamics, avoiding the problem of spatial association loss caused by independent processing of buildings in traditional schemes.

[0029] In a preferred embodiment, when constructing node feature vectors, the spatial topology graph construction processor extracts the number of floors, standard values ​​of concrete compressive strength, standard values ​​of steel yield strength, and aspect ratio from the structural attribute data corresponding to each building. The extracted parameters are then combined into an initial structural physical feature matrix. This initial structural physical feature matrix is ​​a one-dimensional matrix, where each row corresponds to a building and each column corresponds to an extracted structural physical parameter. The column order of the matrix remains fixed across all samples to ensure consistency in parameter dimensions. Specifically, the number of floors represents the total number of floors above ground; the standard value of concrete compressive strength is the standard value of the cubic compressive strength of the concrete used in the main structure of the building; the standard value of steel yield strength is the standard value of the yield strength of the reinforcing steel in the main structure of the building; and the aspect ratio is the ratio of the longer side to the shorter side of the building's plan projection, representing the regularity of the building's plan.

[0030] The spatial topology graph construction processor performs Z-score normalization on the initial structural physical feature matrix to eliminate dimensional and numerical range differences between different structural physical parameters. The normalization calculation formula is as follows:

[0031] in, The first element in the initial structural physical characteristic matrix The original parameter values ​​of each feature dimension. For the training dataset, the first The mean of all samples in each feature dimension. For the training dataset, the first The standard deviation of all samples in each feature dimension For the standardized first The parameter values ​​for each feature dimension. During the standardization process, for feature dimensions with a standard deviation of 0 in the training dataset, all standardized values ​​for that dimension are uniformly set to 0 to avoid division by zero errors.

[0032] The spatial topology graph construction processor concatenates the standardized feature vectors with the site category features of the building's geographical location to generate extended node feature vectors. The site category features are classified according to the site classification standards in the building seismic design code, into five categories: I0, I1, II, III, and IV. The site category features are represented using one-hot encoding, with a dimension of 5 corresponding to the total number of site categories. The position corresponding to a site category has a value of 1, and the remaining positions have values ​​of 0. The vector concatenation operation uses dimensional concatenation, concatenating the standardized feature vectors and the site category one-hot encoded vectors end-to-end in the dimensional direction. The dimension of the resulting extended node feature vector is the sum of the dimensions of the standardized feature vectors and the site category one-hot encoded vectors. The spatial topology graph construction processor assigns the extended node feature vectors to the corresponding graph nodes in the physical constraint spatial topology graph, serving as the initial input features for the physical constraint graph convolutional temporal network processor.

[0033] In this embodiment, the preprocessing rules for various parameters of the node feature vector are shown in Table 2. Through a unified preprocessing process, it is ensured that structural physical parameters of different dimensions and types can be effectively extracted by the network. At the same time, the introduction of multi-dimensional parameters enriches the physical connotation of node features and improves the completeness of feature representation.

[0034] Table 2. Comparison of Node Feature Vector Preprocessing Rules ; Further, after generating the extended node feature vectors, the spatial topology graph construction processor acquires the building foundation type parameters and foundation soil shear wave velocity parameters contained in the structural attribute data. The building foundation type parameters characterize the structural form of the building foundation, including at least two types such as pile foundation, raft foundation, strip foundation, isolated foundation, and box foundation. The foundation soil shear wave velocity parameter is the equivalent shear wave velocity of the soil layer within the site cover layer, characterizing the stiffness property of the site soil. The spatial topology graph construction processor transforms the building foundation type parameters into one-hot encoded vectors. The dimension of the one-hot encoded vector is equal to the total number of building foundation types, with the value corresponding to the foundation type being 1 and the values ​​at other positions being 0. The spatial topology graph construction processor performs a logarithmic transformation on the foundation soil shear wave velocity parameters. The logarithmic transformation uses natural logarithm operations to compress the numerical range of the foundation soil shear wave velocity parameters, reducing the interference of extreme values ​​on the feature extraction process.

[0035] The spatial topology graph construction processor concatenates the one-hot encoded vector with the logarithmically transformed shear wave velocity parameters of the foundation soil to generate a soil-structure interaction feature vector. The dimension of the soil-structure interaction feature vector is the sum of the dimension of the one-hot encoded vector of the building foundation type and the 1D shear wave velocity parameters. The processor uses the soil-structure interaction feature vector as a bias term and adds it to the tail of the extended node feature vector through vector addition, generating a final node feature vector containing soil-structure interaction features. During the vector addition operation, the tail dimension of the extended node feature vector remains consistent with the dimension of the soil-structure interaction feature vector to ensure dimensional matching during addition. The dimension of the final node feature vector after addition remains unchanged from the dimension of the extended node feature vector. Through the superposition of bias terms, the physical characteristics of soil-structure interaction are integrated into the node feature vector.

[0036] This embodiment extracts and standardizes multi-dimensional structural physical parameters, combines them with site category features, and further improves the physical representation capability of node features by superimposing soil-structure interaction feature vectors, providing more comprehensive input information for subsequent graph convolution feature extraction.

[0037] In another preferred embodiment, when calculating the edge weights between nodes, the spatial topology graph construction processor first obtains the Euclidean distance between any two adjacent graph nodes in the spatial geographic coordinates. Adjacent graph nodes refer to two nodes whose corresponding building spaces have a distance less than a preset adjacency threshold, indicating a connection between the two nodes. The Euclidean distance is calculated based on the two-dimensional planar geographic coordinates of the two nodes, and the formula is: [Formula omitted for brevity]. shaft and The Euclidean distance, calculated by taking the square root of the sum of the squares of the differences along the axes, is the straight-line distance between the center points of the two building plan projections, with units consistent with those of the geographic coordinates.

[0038] The spatial topology map construction processor substitutes the calculated Euclidean distance into a preset seismic wave propagation attenuation model to calculate the spatial attenuation ratio of peak ground acceleration. The seismic wave propagation attenuation model adopts an exponential attenuation model, and the calculation formula is as follows:

[0039] in, For nodes With nodes Spatial attenuation coefficient of peak ground acceleration between the two This is the seismic wave propagation attenuation coefficient, determined by the properties of the propagation medium and the earthquake magnitude. For nodes With nodes The corresponding Euclidean distance between buildings. The spatial attenuation ratio coefficient ranges from (0,1). When the Euclidean distance between two nodes is 0, the spatial attenuation ratio coefficient is 1. As the Euclidean distance increases, the spatial attenuation ratio coefficient decreases exponentially, representing the physical law that the seismic energy attenuates as the propagation distance increases.

[0040] The spatial topology graph construction processor multiplies the calculated spatial attenuation ratio coefficient by the absolute value of the difference in the natural vibration period of each adjacent graph node. The result is used as the initial physical-dynamic coupling coefficient between adjacent graph nodes. The calculation formula is as follows:

[0041] in, For nodes With nodes The initial physical dynamic coupling coefficient between them For nodes The corresponding natural period of the building, For nodes The corresponding natural period of the building. The initial physical-dynamic coupling coefficient takes into account both the spatial attenuation effect of ground motion and the difference in natural periods between buildings. The closer the natural periods of the buildings are, the stronger the dynamic coupling effect and the smaller the value of the initial physical-dynamic coupling coefficient, and vice versa.

[0042] The spatial topology graph construction processor uses the Sigmoid activation function to perform a nonlinear mapping on the initial physical dynamic coupling coefficients. The mapping result is set as the edge weight of the corresponding edge in the physical constraint spatial topology graph. The calculation formula for the nonlinear mapping is as follows:

[0043] in, For nodes With nodes The final edge weights of the connections are determined. Through the nonlinear mapping of the Sigmoid activation function, the range of values ​​for the initial physical dynamic coupling coefficients is mapped to the (0,1) interval, ensuring a uniform range of edge weight values ​​to meet the numerical computation requirements of subsequent graph convolutional layers.

[0044] When performing message passing, the physical constraint graph convolutional layer, for the central node in the physical constraint space topology graph, obtains the node feature vectors and edge weights of the central node and its neighboring nodes connected by edges. It then calculates the product of the neighboring node feature vectors and edge weights and accumulates them to generate the node aggregate feature. The formula for calculating the node aggregate feature is as follows:

[0045] in, As the central node The node aggregation characteristics, As the central node The set of indices of all neighboring nodes, As the central node with neighboring nodes The weight of the edges between them For neighboring nodes The node feature vectors.

[0046] The physical constraint diagram convolutional layer extracts the natural period and interlayer yield shear force of the central node. These extracted parameters are then substituted into the pre-defined dynamic equations of the single-degree-of-freedom system architecture to calculate the theoretical acceleration response range of the central node. The expression for the dynamic equations of the single-degree-of-freedom system architecture is as follows:

[0047] in, The equivalent mass of the building corresponding to the central node. This is the structural equivalent damping coefficient. For the structural equivalent stiffness For the relative acceleration response of the structure, For the structural relative velocity response, This represents the structural relative displacement response. Input acceleration time history for seismic motion. Structural equivalent stiffness. The natural period T of the central node is calculated using the following formula: The yield displacement of the structure Through interlayer yield shear The equivalent stiffness k is calculated using the following formula: Based on the structural dynamics equations, the maximum acceleration response in the elastic stage of the structure is: ,in The natural circular frequency of the structure. Therefore, the theoretical acceleration response range of the central node is determined to be... .

[0048] The physical constraint graph convolutional layer determines whether the predicted acceleration response values ​​contained in the node aggregation features are within the theoretical acceleration response range. It removes node aggregation feature components outside the theoretical acceleration response range and then concatenates the filtered node aggregation features with the central node feature vector to update the feature. Specifically, the node aggregation features contain feature components corresponding to the structural acceleration response. The physical constraint graph convolutional layer extracts the value of this feature component and compares it with the upper and lower limits of the theoretical acceleration response range. When the value of a feature component exceeds the theoretical acceleration response range, its value is set to 0, completing the feature component removal operation. Other feature components within the theoretical acceleration response range remain unchanged. The physical constraint graph convolutional layer concatenates the filtered node aggregation features with the original node feature vector of the central node in the dimensional direction to generate the updated central node feature vector, completing the node feature update operation.

[0049] In this embodiment, the blocking rules for message passing between nodes are shown in Table 3. By using mask control based on the inter-layer yield shear ratio, the message passing process of graph convolution is ensured to conform to the basic law of structural bearing capacity transmission, thus avoiding interference of invalid feature aggregation on node feature updates.

[0050] Table 3. Rules for Determining Inter-Node Message Passing Blockage ; Furthermore, before determining whether the predicted acceleration response values ​​contained in the node aggregation features are within the theoretical acceleration response range, the physical constraint graph convolutional layer obtains the inter-layer yield shear force of neighboring nodes and the inter-layer yield shear force of the central node, and calculates the ratio of the inter-layer yield shear force of neighboring nodes to that of the central node. When the calculated ratio is less than a preset bearing capacity transfer threshold, the physical constraint graph convolutional layer generates a blocking mask vector for the corresponding neighboring node. The dimension of the blocking mask vector is the same as the dimension of the node feature vector of the neighboring node, and all elements of the vector are 0.

[0051] When calculating the product of the neighbor node's feature vector and the edge weight, the product result is multiplied element-wise with the blocking mask vector, and the result is set to zero, thus preventing the neighbor node's features from participating in the generation of the central node's node aggregation features. When the calculated ratio is greater than or equal to the preset load-bearing capacity transmission threshold, all elements of the blocking mask vector generated by the physical constraint graph convolutional layer are 1, and the product result of the neighbor node's features and the edge weight remains unchanged, allowing it to participate normally in the generation of node aggregation features.

[0052] This embodiment achieves a quantitative characterization of the physical dynamic coupling between buildings by calculating the edge weights based on the seismic wave propagation attenuation model and the difference in natural vibration period. By filtering the boundary constraints of the structural dynamics equations and blocking the bearing capacity transmission threshold through masking, the message passing process of the graph convolutional layer is further standardized, ensuring that the updating of node features always conforms to the basic principles of structural mechanics and improving the physical consistency of feature extraction.

[0053] In another preferred embodiment, the gated recurrent unit includes an update gate, a reset gate, and a candidate hidden state calculation layer. The gated recurrent unit receives the updated node feature sequence output from the physical constraint graph convolutional layer and the seismic motion time series input, and performs time series feature extraction and hidden state update operations. In the update gate calculation step, the gated recurrent unit concatenates the hidden state from the previous time step with the updated node feature sequence from the current time step, and outputs an update gate vector through a first fully connected layer and a sigmoid activation function. The calculation formula for the update gate is:

[0054] in, This is the update gate vector for the current time step t. It is the Sigmoid activation function. To update the weight matrix of the first fully connected layer corresponding to the gate, Let be the hidden state vector of the previous time step t-1. This is the updated node feature sequence output by the convolutional layer of the physical constraint graph at the current time step t. To update the bias vector corresponding to the gate, This is a vector concatenation operation. The update gate vector has a value range of (0,1) and is used to control the proportion of hidden state information from the previous time step that is passed to the current time step. The closer the value of the update gate vector is to 1, the more candidate hidden state information at the current time step is retained. The closer the value is to 0, the more historical hidden state information from the previous time step is retained.

[0055] In the reset gate calculation step, the gated recurrent unit concatenates the hidden state from the previous time step with the updated node feature sequence of the current time step, and outputs the reset gate vector through the second fully connected layer and the Sigmoid activation function. The calculation formula for the reset gate is as follows:

[0056] in, This is the reset gate vector for the current time step t. To reset the weight matrix of the second fully connected layer corresponding to the gate, This is the bias vector corresponding to the reset gate. The value range of the reset gate vector is (0,1), which is used to control the degree to which the hidden state information of the previous time step is retained in the candidate hidden state calculation. The closer the value of the reset gate vector is to 0, the more hidden state information of the previous time step is forgotten. The closer the value is to 1, the more hidden state information of the previous time step is retained.

[0057] The candidate hidden state computation layer performs a Hadamard product between the reset gate vector and the hidden state from the previous time step. The product result is then concatenated with the updated node feature sequence for the current time step and input into the third fully connected layer. The Tanh activation function is then used to output the candidate hidden state vector. The formula for calculating the candidate hidden state is as follows:

[0058] in, Let be the candidate hidden state vector at the current time step t. The hyperbolic tangent activation function is used. The weight matrix of the third fully connected layer corresponding to the candidate hidden state calculation layer. The Hadamard product operation involves multiplying corresponding elements of two vectors element by element. This is the bias vector corresponding to the candidate hidden state calculation layer. The candidate hidden state vector integrates the node feature information of the current time step with the filtered hidden state information of the previous time step, representing the candidate update value of the structural state at the current moment.

[0059] Furthermore, after the candidate hidden state calculation layer outputs the candidate hidden state vector, the gated loop unit obtains the peak ground acceleration (PGA) value of the building complex at the current time step. This PGA value is then input into a preset continuous damage mechanics evolution equation to calculate the structural stiffness degradation ratio coefficient corresponding to the current time step. The continuous damage mechanics evolution equation is constructed based on the structural stiffness degradation law under seismic loading, and its calculation formula is as follows:

[0060] in, For the current time step The corresponding structural stiffness degradation ratio has a value range of [0,1]. The damage evolution coefficient is determined by the material properties and seismic design measures of the structure. For the current time step The corresponding peak ground acceleration value, The peak ground acceleration threshold corresponding to the initial yield of the structure is calculated from the inter-story yield shear force. The structural stiffness degradation ratio increases with the increase of peak ground acceleration, characterizing the degree of stiffness attenuation caused by the accumulation of structural damage under seismic loading.

[0061] The gated cyclic element uses the structural stiffness degradation ratio as an exponential decay factor to perform element-wise exponential decay operations on the hidden states of the previous time step, generating a historical state decay vector. The formula for calculating the historical state decay vector is as follows: ,in The historical state decay vector, The exponential decay factor is used. The gated recurrent unit weights the historical state decay vector, the update gate vector, and the candidate hidden state vector according to the hidden state update formula to generate the final hidden state vector for the current time step. The hidden state update formula is:

[0062] in, This represents the final hidden state vector at the current time step t. By using the structural stiffness degradation ratio coefficient to exponentially decay the historical hidden state, a quantitative characterization of the impact of structural damage accumulation on the historical state under seismic loading is achieved. This avoids the ineffective accumulation of historical state information and ensures that the extraction process of time-series features conforms to the physical laws of structural damage evolution.

[0063] The physical information loss function used in the network training phase includes a basic prediction loss term and a physical constraint penalty term. The basic prediction loss term calculates the mean square error between the predicted seismic toughness index output by the fully connected mapping processor and the labeled toughness index. The calculation formula is as follows:

[0064] in, This represents the total number of nodes in the physical constraint space topology graph. For the first Predicted values ​​of seismic toughness index for each node. For the first The label value of the seismic toughness index of each node is obtained through finite element numerical simulation or shaking table test measured data.

[0065] The physical constraint penalty term obtains the predicted intermediate inter-story drift angles generated during the forward propagation of the fully connected mapping processor. Combined with the story height parameters in the structural attribute data, the theoretical drift angle limit for the corresponding building is calculated according to the elasto-plastic inter-story drift angle limit formula in the code. The elasto-plastic inter-story drift angle limit formula is constructed based on the seismic design code for buildings, and the calculation formula is as follows:

[0066] in, This represents the theoretical limit for the elastoplastic interstory drift angle of the structure. The seismic adjustment coefficient for bearing capacity is determined by the material type and seismic grade of the structure. It is the displacement ductility coefficient of the structure, which is determined by the system type and seismic fortification category of the structure.

[0067] The physical constraint penalty term calculates the sum of squares of the differences between the predicted inter-story drift angle and the theoretical drift angle limit, using the following formula:

[0068] in, The total number of floors in the building. For the first The node corresponds to the building's first... Predicted inter-story drift angle of the layer. For the first Each node corresponds to the theoretical limit of the elastoplastic inter-story drift angle of the building. When the predicted inter-story drift angle is less than or equal to the theoretical limit, the corresponding penalty term is 0. When the predicted inter-story drift angle is greater than the theoretical limit, the square of the excess is included in the penalty term, thus penalizing the prediction results that violate the laws of structural mechanics.

[0069] The physical information loss function generates a total loss value by weighting and summing the basic prediction loss term and the physical constraint penalty term according to preset weight coefficients. The formula for calculating the total loss value is as follows:

[0070] in, This is the total loss value. The weighting coefficients for the basic prediction loss term, These are the weight coefficients for the physical constraint penalty term. The system performs backpropagation based on the total loss value to update the network's weight and bias parameters.

[0071] In this embodiment, the weight coefficient configuration rules of the physical information loss function are shown in Table 4. Through phased weight configuration, the prediction accuracy and physical consistency of the model are balanced, ensuring that the model can fit the labeled data and strictly abide by the basic laws of structural mechanics during the training process.

[0072] Table 4. Rules for configuring weight coefficients of physical information loss function ; Furthermore, when calculating the theoretical displacement angle limit of the corresponding building based on the elastic-plastic inter-story drift angle limit formula in the standard, the physical constraint penalty term obtains the net distance parameter between any two adjacent buildings in the spatial geographic coordinates and the difference in floor elevation between the two buildings at corresponding floors. The net distance parameter between adjacent buildings is the minimum horizontal distance between the adjacent exterior walls of the two buildings, and the difference in floor elevation is the absolute value of the difference in structural floor elevation between the corresponding floors of the two buildings. When the net distance parameter is less than the sum of the difference in floor elevation and the reference value of the seismic joint width, the physical constraint penalty term uses the net distance parameter as the collision contact limit between adjacent buildings and calculates the additional inter-story drift angle reduction caused by the collision based on the seismic joint collision mechanics model. The formula for calculating the additional inter-story drift angle reduction is as follows:

[0073] in, This is for the additional inter-story drift angle reduction. The relative displacement limit caused by collisions between adjacent buildings is determined by the net spacing parameter, where H is the floor height of the building. The physical constraint penalty term adds the additional inter-story drift angle reduction to the theoretical drift angle limit to generate a modified theoretical drift angle limit. The modified theoretical drift angle limit is the difference between the original theoretical drift angle limit and the additional inter-story drift angle reduction, representing the limiting effect of collisions between adjacent buildings on the inter-story displacement of the structure.

[0074] This embodiment uses a gated loop unit to extract the temporal features of structural damage evolution under seismic motion time-series input. By correcting the stiffness degradation of the continuous damage mechanics evolution equation, it achieves reasonable attenuation of historical hidden states, avoiding the accumulation of invalid temporal features. By using a loss function that includes a physical constraint penalty term and a theoretical limit for seismic joint collision correction, it further strengthens the physical constraints in the model training process, reduces the physical extrapolation error of the model prediction under extreme conditions, and improves the accuracy of seismic toughness prediction of building complexes.

Claims

1. A deep learning-based system for predicting the seismic resilience of urban building complexes, characterized in that, This includes a data acquisition interface, a spatial topology graph construction processor, a physical constraint graph convolutional temporal network processor, and a fully connected mapping processor; The data acquisition interface obtains structural attribute data and spatial geographic coordinates of urban building clusters; The spatial topology graph construction processor maps each building in the building complex to a graph node, sets the node feature vector to structural physical parameters including the building's natural vibration period, inter-story yield shear force, and height, and sets the edge weights between nodes to the physical dynamic coupling coefficient matrix calculated based on the seismic wave propagation attenuation model and the building spatial spacing, thus forming a physically constrained spatial topology graph. The physical constraint graph convolutional temporal network processor includes a physical constraint graph convolutional layer and a gated recurrent unit. The physical constraint graph convolutional layer introduces boundary constraint terms based on structural dynamics equations to filter node feature updates during message passing. The gated recurrent unit extracts the damage evolution state features of the building complex under seismic temporal input. The fully connected mapping processor outputs the seismic toughness index of each node in the building complex based on the damage evolution state characteristics. During the network training phase, a physical information loss function is used. The residual between the network output prediction of inter-layer displacement angle and the theoretical displacement angle limit derived from structural mechanics is calculated and used as a penalty term for backpropagation to update the network weights.

2. The deep learning-based urban building complex seismic resilience prediction system according to claim 1, characterized in that, When constructing node feature vectors, the spatial topology graph construction processor extracts the number of floors, standard values ​​of concrete compressive strength, standard values ​​of steel bar yield strength, and aspect ratio from the structural attribute data corresponding to each building, and combines the extracted parameters into an initial structural physical feature matrix. The initial structural physical feature matrix is ​​Z-score normalized, and the normalized feature vector is concatenated with the site category features of the building's geographical location to generate an extended node feature vector. The spatial topology graph construction processor assigns the extended node feature vectors to the corresponding graph nodes in the physical constraint spatial topology graph, which serve as the initial input features for the physical constraint graph convolutional temporal network processor.

3. The deep learning-based urban building complex seismic resilience prediction system according to claim 1, characterized in that, When calculating the edge weights between nodes, the spatial topology graph construction processor obtains the Euclidean distance between any two adjacent graph nodes in the spatial geographic coordinates, and substitutes the Euclidean distance into the preset seismic wave propagation attenuation model to calculate the spatial attenuation ratio coefficient of the peak ground acceleration. The calculated spatial attenuation ratio coefficient is multiplied by the absolute value of the difference in the natural vibration period of each adjacent graph node, and the result is used as the initial physical-dynamic coupling coefficient between adjacent graph nodes. The spatial topology graph construction processor uses the Sigmoid activation function to perform nonlinear mapping on the initial physical dynamic coupling coefficients, and sets the mapping result as the edge weight of the corresponding edge in the physical constraint spatial topology graph.

4. The deep learning-based urban building complex seismic resilience prediction system according to claim 1, characterized in that, When executing the message passing process, the physical constraint graph convolutional layer obtains the node feature vectors and edge weights of the central node and its neighboring nodes that are connected to the central node in the physical constraint space topology graph. It then calculates the product of the neighboring node feature vectors and edge weights and accumulates them to generate node aggregate features. The physical constraint diagram convolutional layer extracts the natural period and interlayer yield shear of the central node, and substitutes the extracted parameters into the preset single-degree-of-freedom system dynamic equation to calculate the theoretical acceleration response range of the central node. The physical constraint graph convolutional layer determines whether the predicted acceleration response values ​​contained in the node aggregation features are within the theoretical acceleration response range. It removes node aggregation feature components that are outside the theoretical acceleration response range and then concatenates and updates the filtered node aggregation features with the central node feature vector.

5. The deep learning-based urban building complex seismic resilience prediction system according to claim 1, characterized in that, The gated loop unit includes an update gate, a reset gate, and a candidate hidden state calculation layer; The gated recurrent unit receives the updated node feature sequence output from the physical constraint graph convolutional layer and the seismic motion time series input. In the update gate calculation step, the hidden state of the previous time step is concatenated with the updated node feature sequence of the current time step, and the update gate vector is output through the first fully connected layer and the Sigmoid activation function. In the reset gate calculation step, the reset gate vector is output through the second fully connected layer; The candidate hidden state computation layer performs a Hadamard product between the reset gate vector and the hidden state of the previous time step. The product result is then concatenated with the updated node feature sequence of the current time step and input into the third fully connected layer. Finally, the Tanh activation function is used to output the candidate hidden state vector.

6. The deep learning-based urban building complex seismic resilience prediction system according to claim 1, characterized in that, The physical information loss function includes a basic prediction loss term and a physical constraint penalty term; The mean square error between the predicted seismic toughness index output by the fully connected mapping processor and the tag toughness index is calculated for the basic prediction loss term. The physical constraint penalty term obtains the predicted value of the intermediate inter-story drift angle generated during the forward propagation of the fully connected mapping processor. Combined with the story height parameter in the structural attribute data, the theoretical drift angle limit of the corresponding building is calculated according to the elastic-plastic inter-story drift angle limit formula in the code. The physical constraint penalty term is calculated as the sum of squares of the differences between the predicted inter-story drift angle and the theoretical drift angle limit. The physical information loss function generates a total loss value by weighting and summing the basic prediction loss term and the physical constraint penalty term according to preset weight coefficients.

7. The deep learning-based urban building complex seismic resilience prediction system according to claim 2, characterized in that, After generating the extended node feature vector, the spatial topology graph construction processor obtains the building foundation type parameters and foundation soil shear wave velocity parameters contained in the structural attribute data, converts the building foundation type parameters into one-hot encoded vectors, and performs logarithmic transformation on the foundation soil shear wave velocity parameters. The soil-structure interaction feature vector is generated by concatenating the one-hot encoded vector with the shear wave velocity parameters of the foundation soil after logarithmic transformation. The spatial topology graph construction processor uses the soil-structure interaction feature vector as a bias term and adds it to the tail of the extended node feature vector through vector addition to generate the final node feature vector containing soil-structure interaction features.

8. The deep learning-based seismic resilience prediction system for urban building complexes according to claim 4, characterized in that, Before determining whether the predicted acceleration response values ​​contained in the node aggregation features are within the theoretical acceleration response range, the physical constraint graph convolutional layer obtains the interlayer yield shear force of the neighboring nodes and the interlayer yield shear force of the central node, and calculates the ratio of the interlayer yield shear force of the neighboring nodes to the interlayer yield shear force of the central node. When the calculated ratio is less than the preset load-bearing capacity transmission threshold, the physical constraint graph convolutional layer generates the blocking mask vector of the corresponding neighbor node. When calculating the product of the neighbor node feature vector and the edge weight, the product result is multiplied element by element with the blocking mask vector, and the multiplication result is set to zero vector to prevent the generation of node aggregation features.

9. The deep learning-based seismic resilience prediction system for urban building complexes according to claim 5, characterized in that, After the candidate hidden state calculation layer outputs the candidate hidden state vector, the gated loop unit obtains the peak ground acceleration value of the building group at the current time step, inputs the peak ground acceleration value into the preset continuous damage mechanics evolution equation, and calculates the structural stiffness degradation ratio coefficient corresponding to the current time step. The gated cyclic unit uses the structural stiffness degradation ratio as the exponential decay factor to perform element-wise exponential decay operation on the hidden state of the previous time step, generating a historical state decay vector. The gated loop unit performs a weighted calculation on the historical state decay vector, the update gate vector, and the candidate hidden state vector according to the hidden state update formula to generate the final hidden state vector for the current time step.

10. The deep learning-based seismic resilience prediction system for urban building complexes according to claim 6, characterized in that, When calculating the theoretical displacement angle limit of the corresponding building according to the elastic-plastic inter-story drift angle limit formula in the specification, the physical constraint penalty term obtains the net distance parameter between any two adjacent buildings in the spatial geographic coordinates and the difference value of the floor elevation of the two buildings on the corresponding floor. When the net spacing parameter is less than the sum of the floor elevation difference value and the seismic joint width benchmark value, the physical constraint penalty term uses the net spacing parameter as the collision contact limit between adjacent buildings and calculates the additional inter-story drift angle reduction caused by the collision on the structure based on the seismic joint collision mechanics model. The physical constraint penalty term adds the additional inter-story drift angle reduction to the theoretical drift angle limit, generating a modified theoretical drift angle limit.

Images