Method for identifying structural damage of fabricated beam bridge based on differentiable agent model

Abstract

The application discloses a method for identifying damage of an assembled beam bridge structure based on a differential agent model, adopts a chain graph to represent the structural topology and damage state of the assembled beam bridge; a graph neural network integrating an attention mechanism is constructed and trained as an agent model for predicting the structural response of the assembled beam bridge corresponding to the structural topology and damage state parameters of the assembled beam bridge; damage identification is expressed as an optimization inversion problem, and the target is to find a combination of damage state parameters that minimizes the difference between the measured structural response obtained on site and the predicted structural response based on the output of the agent model; the optimization inversion problem is efficiently solved by using a gradient descent algorithm, and the optimal solution obtained by inversion represents the identification result of the damage state of the assembled beam bridge; the application realizes rapid and quantitative inversion of the damage state of multiple components, and provides a new technical route for automatic maintenance and performance evaluation of a large number of assembled beam bridges.

Description

Technical Field

[0001] This invention relates to the field of bridge structure risk identification technology, specifically to a method for identifying damage in prefabricated beam bridge structures based on a differentiable surrogate model. Background Technology

[0002] Precast beam bridges, consisting of precast reinforced concrete beams or precast prestressed concrete beams and cast-in-place joints, have become one of the most widely used types of small- and medium-span bridges in highway transportation systems due to their significant advantages such as simple structure, clear stress distribution, high construction efficiency, and low building height. However, during long-term service, precast beam bridges are highly susceptible to various structural defects due to the combined effects of heavy traffic, environmental erosion, and uneven foundation settlement, such as joint cracking, bottom slab damage, and concrete spalling, leading to a degradation of their structural load-bearing capacity.

[0003] To invert and identify the structural damage status (specific extent of load-bearing performance degradation) of prefabricated beam bridges, existing technologies often update the finite element model based on the measured structural response obtained from monitoring and detection. Specifically, a finite element model of the bridge is established, and the parameters of the model are updated using optimization algorithms such as genetic algorithms and gradient descent algorithms based on finite differences (e.g., adjusting material properties to simulate damage). This ensures that the structural response calculated by the model matches the measured structural response. The updated model parameters (effective section stiffness, material properties, etc.) are then considered to reflect the true damage state, thus completing the damage identification.

[0004] However, due to the enormous computational time required for finite element models, they are prone to slow convergence or the "curse of dimensionality" when facing multi-parameter inversion problems (such as considering the damage level of each main girder and each joint). Using a surrogate model with higher computational efficiency to replace the finite element model can alleviate these problems to some extent. However, traditional surrogate models (such as Kriging or traditional neural networks) often only model a specific bridge and lack the general ability to handle different bridge structures (such as topological information like span and number of main girders, as well as changes in parameters like beam width and material properties).

[0005] Therefore, this invention proposes a graph neural network surrogate model suitable for predicting the structural response of prefabricated beam bridges. This model not only enables efficient prediction of structural response but also has the potential to characterize prefabricated beam bridge structures with arbitrary topological configurations, overcoming the bottleneck of poor generalization of traditional surrogate models. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for identifying damage in prefabricated beam bridge structures based on a differentiable surrogate model to solve the aforementioned problems.

[0007] This invention provides the following technical solution: A method for identifying damage in prefabricated beam bridge structures based on a differentiable surrogate model includes the following steps: Chain diagrams are used to characterize the structural topology and damage state of prefabricated beam bridges; A graph neural network with an attention mechanism is constructed and trained to serve as a surrogate model for predicting the structural response of a prefabricated beam bridge based on its structural topology and damage state parameters. Damage identification is expressed as an optimization inversion problem, with the goal of finding the combination of damage state parameters that minimizes the difference between the measured structural response obtained in the field and the predicted structural response based on the surrogate model. The gradient descent algorithm is used to efficiently solve this optimization inversion problem, and the optimal solution obtained represents the identification result of the damage state of the prefabricated beam bridge.

[0008] Preferably, the measured structural response is a static or dynamic index that reflects the structural performance.

[0009] Preferably, the damage state parameter is a predefined parameter used to represent the structural damage condition.

[0010] Preferably, chain diagrams are used to characterize prefabricated beam bridges, including: If each main girder of a prefabricated beam bridge is considered as a node, and each joint connecting two adjacent main girders is considered as an edge, then a prefabricated beam bridge composed of alternating main girders and joints can be represented by a chain graph G = (V, E); where V is the set of main girders and E is the set of joints.

[0011] Preferably, the graph neural network includes a feature initialization and fusion module, a multi-order crystal graph convolutional encoder, a global context attention encoder, and a decoder.

[0012] Preferably, the feature initialization and fusion module includes the following steps: Obtain the chain graph of the prefabricated beam bridge, extract the local features of each node, the local features of each edge, and the global features that characterize the macroscopic physical properties of the prefabricated beam bridge; broadcast the global features to each node, and splice and fuse them with the local features of each node to generate an initial node embedding matrix, so that the initial embedding vector of each node contains both its own local information and the overall structural information.

[0013] Preferably, the multi-order crystal map convolutional encoder includes the following steps: The initial node embedding matrix and edge features are input into an encoder consisting of stacked multi-layer crystal graph convolutional layers. In each graph convolutional layer, for each edge, its edge feature vector and the current node embedding vectors of the two connected nodes are concatenated and a physical constraint message is generated through a fully connected layer and a gated activation function. Edge features are used as dynamic control valves to regulate information transmission between nodes; the first-order neighborhood aggregation features of each node are calculated, and the higher-order neighborhood aggregation features are calculated iteratively through the adjacency matrix. The neighborhood aggregation features of each order are concatenated and the embedding vector of the node of the graph convolution layer is obtained through linear mapping. After repeating multi-layer graph convolution, the full image features are output.

[0014] Preferably, the global context attention encoder includes the following steps: The full-image features are input into a global contextual attention encoder, which is composed of alternating stacks of multi-head self-attention and feedforward neural networks; In each attention layer, long-range cross-attention weights between all nodes are computed in parallel by multiple attention heads, and weighted aggregation is used to obtain global mixed features. Residual connections and layer normalization are then superimposed. Subsequently, a feedforward neural network containing two linear transformation layers and a nonlinear activation function is used to independently perform nonlinear mapping of feature channels for each node, and residual connections and layer normalization are superimposed again. After multiple layers of attention encoding, an output tensor that integrates global context information is output.

[0015] Preferably, the decoder includes the following steps: Based on the type of structural response to be predicted, the corresponding node feature is selected from the output tensor and embedded, then input into the decoder composed of a multilayer perceptron, and the predicted structural response is output.

[0016] Preferably, the initial values ​​of the damage state parameters of the prefabricated beam bridge are randomly selected; The initial values ​​of the damage state parameters for the current iteration are input into the surrogate model of the graph neural network, and the graph neural network outputs the predicted structural response. The structural response predicted by the output of the graph neural network is compared with the measured structural response obtained on site, and the inversion loss function is calculated. Utilizing the differentiable operation property of the graph neural network, the gradient of the inversion loss function with respect to the damage state parameters is calculated through backpropagation. The gradient calculation relies on the fixed network weights and bias parameters after the surrogate model training converges, and is implemented using automatic differentiation technology. During forward propagation, the operations performed are recorded, and during backpropagation, the chain rule is applied to expand the gradient into the product of the Jacobian matrices of each layer of the surrogate model, thereby obtaining the steepest direction of change of the loss function. Based on the gradient, the damage state parameters are iteratively updated using a gradient descent algorithm according to a preset update step size, so as to reduce the value of the inversion loss function; during this update process, the network weights and bias parameters of the surrogate model remain unchanged. Repeat the above steps until the convergence condition is met, then stop the iteration and use the damage state parameters obtained at convergence as the damage identification result of the prefabricated beam bridge.

[0017] Preferably, the initial values ​​of the damage state parameters of the prefabricated beam bridge can be sampled multiple times (e.g., random sampling or Latin hypercube sampling), and the above-mentioned inversion identification can be performed multiple times accordingly to obtain the statistical characteristics of the damage identification results (e.g., mean, median or mode) as the damage identification results of the prefabricated beam bridge, thereby reducing the uncertainty caused by the randomness of the initial values ​​of the damage state parameters.

[0018] The present invention has the following beneficial technical effects: This invention defines damage identification as a differentiable optimization inversion problem. Leveraging the automatic differentiation capabilities of deep learning frameworks, the proposed method can directly calculate the accurate gradient of the response bias (the difference between the structural response predicted by the surrogate model and the measured structural response) with respect to damage parameters, thus bypassing the expensive numerical gradient calculations or blind heuristic searches of traditional methods. This "topology-aware surrogate model + gradient-driven optimization" architecture enables rapid and quantitative inversion of the damage state of multiple components, providing a novel technical approach for the automated maintenance and performance evaluation of numerous prefabricated beam bridges.

[0019] Chain graphs are a general data representation form for prefabricated beam bridges, and graph neural network surrogate models can be generalized to any prefabricated beam bridge. A properly trained HG-AttnNet can predict the structural response of any given structural topology and physical parameters (including damage state) without needing to retrain for each new bridge and load condition.

[0020] Compared with traditional finite element model updates, the efficiency of this damage identification method can achieve a significant leap. First, the constructed HG-AttnNet surrogate model can be directly generalized to the prefabricated beam bridge of interest, so the application only involves inversion identification and no longer requires time-consuming modeling. Second, compared with heuristic algorithms or deterministic algorithms based on finite difference indirect gradient calculation that rely on finite element model updates, the differential optimization inversion process has a more explicit and direct adjustment and optimization of damage state parameters, providing support for handling the high-dimensional inversion task of identifying the independent damage state parameters of each joint and each main beam. Attached Figure Description

[0021] Figure 1 This is a framework diagram of the method of the present invention; Figure 2 This is a schematic diagram of the graph neural network of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] A method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model, such as Figures 1-2 As shown, the physical framework of prefabricated beam bridges naturally possesses the graph theory property of "point-line" connections. Therefore, a chain graph is used to characterize the structural topology and damage state of any prefabricated beam bridge.

[0024] A surrogate model incorporating an attention mechanism (HG-AttnNet, abbreviated as Hybrid Graph Attention Network) is constructed and trained to rapidly predict the structural response of any prefabricated beam bridge based on its input structural topology and damage state parameters. In practical bridge applications, damage identification is expressed as an optimization inversion problem, aiming to find the combination of damage state parameters that minimizes the difference between the measured structural response from on-site monitoring or testing and the predicted structural response based on the surrogate model. The gradient descent algorithm is then used to efficiently solve this optimization inversion problem, where the gradient can be easily calculated using the differentiability property of HG-AttnNet. The optimal solution obtained from the inversion represents the identification result of the damage state of the joints and main beams of the prefabricated beam bridge.

[0025] The structural response refers to static or dynamic indicators reflecting structural performance, such as displacement (deflection), strain, acceleration, frequency, and mode shape generated under external static or dynamic excitation. These can be flexibly selected according to the damage identification task of the actual engineering project. The damage state parameters refer to predefined parameters used to represent the structural damage status, such as the stiffness degradation coefficient of the joint (the ratio of the true stiffness of the joint to the stiffness of the intact joint) and the stiffness degradation coefficient of the main beam (the ratio of the true stiffness of the main beam to the stiffness of the intact main beam).

[0026] Chain diagram representation of prefabricated beam bridges: like Figure 1 As shown in (a), if each main girder of the prefabricated beam bridge is considered a node, and each joint connecting two adjacent main girders is considered an edge, then the prefabricated beam bridge composed of alternating main girders and joints can be represented by a chain diagram G = (V, E). Each edge of the chain diagram... e ij Connecting nodes v i and vj Yes, for the special case of a chain graph, each edge only connects nodes. v i and v i+1 It can be simply remembered as e i ; i = 1, 2, …, n The numbering of the main girder along the transverse direction of the bridge. j = 1, 2,…, n 1 is the number of the joint along the transverse direction of the bridge.

[0027] The chain diagram described above can fully represent any prefabricated beam bridge, without being limited by the number of main beams, cross-sectional characteristics, or damage state. In other words, one chain diagram corresponds to a prefabricated beam bridge under a specific damage state, providing a standardized and universal data organization method for this type of structure.

[0028] A graph neural network surrogate model incorporating attention mechanisms (HG-AttnNet): like Figure 1 As shown in (b), after completing the graph representation of the prefabricated beam bridge using the above method, a graph neural network can be constructed as a surrogate model HG-AttnNet for calculating the bridge structural response. The architecture is as follows: Figure 2 As shown, the entire model architecture can be systematically divided into four main modules: feature initialization and fusion module, multi-Hop Crystal Graph Convolution (CGConv) encoder, global context attention encoder, and decoder. The forward computation flow of the model passes sequentially through the multi-Hop Crystal Graph Convolution encoder and the global context attention encoder to extract the topology and global context. Then, appropriate feature embeddings are flexibly selected according to the type of structural response to be predicted and input into the decoder (usually a multilayer perceptron (MLP)) to output the structural response. Each layer of the network in the model is normalized to stabilize the feature distribution, accelerate convergence, and alleviate gradient vanishing. The figure only elaborates on the feature embedding process of a single node, while HG-AttnNet performs this process synchronously on every node.

[0029] Feature initialization and fusion module: In the initial stage, the model needs to align and fuse local and global features. The feature tensor input to the network is defined as follows: (1) Node characteristics The local features of each node are extracted, including normalized damage state parameters of each node (characterizing the damage status of the main beam represented by the node) and relative position encoding, etc.

[0030] (2) Edge features It extracts local features of each edge, including normalized damage state parameters of each edge (characterizing the damage status of the joint represented by the edge), etc.

[0031] (3) Global features It extracts global features that characterize the macroscopic physical properties of prefabricated beam bridges, including the overall prototype parameters of the macrostructure (these features are usually designed to have equal values ​​in the same bridge), such as the stiffness and width of the intact main beam.

[0032] In order to effectively inject the macroscopic physical properties of the structure into local nodes, global features This will be broadcast to every node in the network. This operation generates the merged initial node embedding matrix. Its splicing form can be represented as , , and These are the initial node embedding vector, the node feature vector, and the global feature vector, respectively.

[0033] Multi-order crystal map convolutional encoder: To effectively capture the nonlinear interactions between nodes, a crystal graph convolutional encoder with a neighborhood expansion mechanism is proposed. Assume the total number of graph convolutional layers is... L G For the first l Layered graph convolution, first for each edge e ij Concatenate its edge eigenvectors Nodes connected v i Node embedding vector Input and Nodes v j Node embedding vector input ,get:

[0034] in, To concatenate feature vectors; Then, for any node v i Calculate the physical constraint messages generated by its first-order neighborhood. :

[0035] In the formula, It is a Sigmoid-gated activation function; For element-wise multiplication; and These are two independent, fully connected layers. This allows edge features (joint damage state parameters) to act as a valve-like mechanism to dynamically regulate the information flow between structural components (main beams).

[0036] To further expand the receptive field, the model calculation... k h Propagation and aggregation of neighborhood features of order 1. Definition of order 1 neighborhood aggregation features. The calculation method is as follows:

[0037] In the formula, Represents the first-order neighborhood of a node (nodes directly connected by one edge).

[0038] Similarly, the height can be calculated by iterating through the adjacency matrix. k h Neighborhood aggregation features of order ) :

[0039] In the formula, for k h First-order neighborhood aggregation feature.

[0040] Finally, the aggregated features of each order of neighborhood are concatenated and a dimensionality transformation is performed:

[0041] In the formula, Representing the l Nodes of layer graph convolution v i The embedded vector output; ReLU is the modified linear unit activation function; Representing the l Nodes of a 1-layer graph convolution v i The embedded vector output; These are learnable linear mapping weights.

[0042] L G After the layer convolution is completed, the full image features are output. .

[0043] Global Context Attention Encoder: Since structural responses are often global, relying solely on the local message-passing mechanism of graph neural networks often suffers from oversmoothing or insufficient receptive field for collaborative deformation of distant nodes. To compensate for this deficiency, the system extracts full-graph features from the graph neural network. Then, it is further fed into a cascaded global context attention encoder.

[0044] This encoder is based on the Transformer architecture and stacks... L A Multi-head attention module at layer 1. l There is an attention layer, whose input is... (where the input of the first layer is) Multiple attention heads divide the feature dimensions equally and process them separately. The final result is obtained by concatenating the results from each head. Specifically, the long-sequence cross-influence between nodes is first calculated, and residual connections are used to prevent the decay of physical features or gradient vanishing between local and adjacent nodes in deep networks, resulting in the output of the self-attention layer. :

[0045] In the formula, The operational mechanism of (self-attention) is as follows:

[0046] In the formula, , and It is a learnable linear projection matrix; It is a query vector; It is a key vector; It is a value vector; Softmax represents the normalized exponential function; express transpose; D model Indicates the hidden layer dimension of the model; N head This indicates the number of heads of attention.

[0047] After completing the spatial information mixing of all nodes in the image, the model further performs a deep feature channel nonlinear mapping on each node individually using a feedforward neural network (FFN). This FFN consists of two linear transformation layers with a nonlinear activation function sandwiched between them, and also includes residual normalization.

[0048] In the formula, and These are the weights and biases of the first linear transformation layer. and These are the weights and biases of the second linear transformation layer, respectively.

[0049] go through L A After layer attention encoding, the final output tensor will be input into the decoder.

[0050] Decoder: The appropriate feature embeddings are flexibly selected from the obtained output tensor based on the type of structural response to be predicted, and then input into a multilayer perceptron (MLP) for processing to output the predicted structural response. Typically, one output corresponds to one decoder. For example, if it is necessary to predict two different structural responses, deflection and frequency, corresponding decoders need to be set separately, and the selection method of the feature embeddings input to the decoders may also be different.

[0051] Model training: Extensive analysis was conducted using finite element models or theoretical models, covering the parameter range of prefabricated beam bridges commonly encountered in practical engineering, generating a dataset in the form of [input bridge features, output structural response]. This dataset was used to train the aforementioned surrogate model, HG-AttnNet.

[0052] Damage identification through differentiable optimization inversion. like Figure 1 As shown in (c), the damage identification task of this invention is to invert (backward infer) unknown damage state parameters by monitoring or testing the measured structural response in the field. This can be expressed as an optimization problem, the objective of which is to find a bridge structural response that can be predicted based on a surrogate model. Measured structural response The optimal solution that minimizes the deviation between As shown in the following formula:

[0053] In the formula, These represent the damage state parameters, which are also part of the input to the surrogate model. This is the inversion loss function.

[0054] To solve this optimization problem, a differentiable optimization inversion method is adopted, and the calculation process is as follows: Figure 1 As shown in the diagram. First, initial values ​​of the damage state parameters of the prefabricated beam bridge are randomly selected and input into the surrogate model. Then, the surrogate model outputs the predicted structural response, which is combined with the measured structural response to calculate the inversion loss function. Finally, the damage state parameters are updated according to the gradient descent of the inversion loss function, as shown in the following formula:

[0055]

[0056] In the formula, The gradient of the loss function, i.e. the steepest direction of change, can be taken advantage of the differentiability property of deep learning surrogate models (all operations in HG-AttnNet are differentiable). Indicates the first L The feature tensor of the layer; Indicates the first L The feature tensor of a 1-layer structure; L This represents the total number of layers in the proxy model, excluding the input layer.

[0057] The gradient calculation shown in the above equation is achieved using automatic differentiation. This involves recording the operations performed during the forward propagation and applying the chain rule to calculate the gradient of each parameter during the backward propagation. This method effectively handles complex composite functions, avoiding the high computational complexity of symbolic differentiation and the rounding errors often associated with numerical differentiation.

[0058] Mode The equation, as shown, expands to the product of Jacobian matrices of each layer using the chain rule. These Jacobian matrices are determined by the network's weights and bias parameters. Since the network parameters are fixed after the surrogate model training converges and will not change during the optimization inversion process, the gradient values ​​can be directly calculated through forward and backward propagation. In the equation, ( l = 0– L ) represents the proxy model. l Features of the layer ; Represents the current iteration round (the 1st iteration) t Damage status parameters (+1 round); Represents the previous iteration round (the 1st iteration) t Damage state parameters of the wheel; λ The update step size representing the damage state parameters; In addition, suitable gradient descent algorithms such as Adaptive Moment Estimation (Adam), Batch Gradient Descent (BGD), and Stochastic Gradient Descent (SGD) can be selected to implement the parameter update shown in the above equation. This inversion optimization process updates the damage state parameters, rather than the weights and biases that are updated only during the training of the surrogate model. This optimization process is repeatedly executed iteratively until it converges to the optimal solution. It represents the identification result of the bridge's damage state.

[0059] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model, characterized in that, Includes the following steps: Chain diagrams are used to characterize the structural topology and damage state of prefabricated beam bridges; A graph neural network with an attention mechanism is constructed and trained to serve as a surrogate model for predicting the structural response of a prefabricated beam bridge based on its structural topology and damage state parameters. Damage identification is expressed as an optimization inversion problem, with the goal of finding the combination of damage state parameters that minimizes the difference between the measured structural response obtained in the field and the predicted structural response based on the surrogate model. The gradient descent algorithm is used to efficiently solve this optimization inversion problem, and the optimal solution obtained represents the identification result of the damage state of the prefabricated beam bridge.

2. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 1, characterized in that, The measured structural response is a static or dynamic index that reflects the structural performance.

3. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 1, characterized in that, The damage state parameters are predefined parameters used to represent the structural damage status.

4. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 1, characterized in that, Chain diagrams are used to represent prefabricated beam bridges, including: If each main girder of a prefabricated beam bridge is considered as a node, and each joint connecting two adjacent main girders is considered as an edge, then a prefabricated beam bridge composed of alternating main girders and joints can be represented by a chain graph G = (V, E); where V is the set of main girders and E is the set of joints.

5. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 1, characterized in that, The graph neural network includes a feature initialization and fusion module, a multi-order crystal graph convolutional encoder, a global context attention encoder, and a decoder.

6. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 5, characterized in that, The feature initialization and fusion module includes the following steps: Obtain the chain graph of the prefabricated beam bridge, extract the local features of each node, the local features of each edge, and the global features that characterize the macroscopic physical properties of the prefabricated beam bridge; broadcast the global features to each node, and splice and fuse them with the local features of each node to generate an initial node embedding matrix, so that the initial embedding vector of each node contains both its own local information and the overall structural information.

7. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 6, characterized in that, The multi-order crystal map convolutional encoder includes the following steps: The initial node embedding matrix and edge features are input into an encoder consisting of stacked multi-layer crystal graph convolutional layers. In each graph convolutional layer, for each edge, its edge feature vector and the current node embedding vectors of the two connected nodes are concatenated and a physical constraint message is generated through a fully connected layer and a gated activation function. Edge features are used as dynamic control valves to regulate information transmission between nodes; the first-order neighborhood aggregation features of each node are calculated, and the higher-order neighborhood aggregation features are calculated iteratively through the adjacency matrix. The neighborhood aggregation features of each order are concatenated and the embedding vector of the node of the graph convolution layer is obtained through linear mapping. After repeating multi-layer graph convolution, the full image features are output.

8. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 7, characterized in that, The global context attention encoder includes the following steps: The full-image features are input into a global contextual attention encoder, which is composed of alternating stacks of multi-head self-attention and feedforward neural networks; In each attention layer, long-range cross-attention weights between all nodes are computed in parallel by multiple attention heads, and weighted aggregation is used to obtain global mixed features. Residual connections and layer normalization are then superimposed. Subsequently, a feedforward neural network containing two linear transformation layers and a nonlinear activation function is used to independently perform nonlinear mapping of feature channels for each node, and residual connections and layer normalization are superimposed again. After multiple layers of attention encoding, an output tensor that integrates global context information is output.

9. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 8, characterized in that, The decoder includes the following steps: Based on the type of structural response to be predicted, the corresponding node feature is selected from the output tensor and embedded, then input into the decoder composed of a multilayer perceptron, and the predicted structural response is output.

10. The method for damage identification of prefabricated beam bridge structures based on a differentiable surrogate model according to claim 1, characterized in that, Initial values ​​of damage state parameters for prefabricated beam bridges were randomly selected; The initial values ​​of the damage state parameters for the current iteration are input into the surrogate model of the graph neural network, and the graph neural network outputs the predicted structural response. The structural response predicted by the output of the graph neural network is compared with the measured structural response obtained in the field, and the inversion loss function is calculated. Utilizing the differentiable operation property of the graph neural network, the gradient of the inversion loss function with respect to the damage state parameters is calculated through backpropagation. The gradient calculation relies on the fixed network weights and bias parameters after the surrogate model training converges, and is implemented using automatic differentiation technology. During forward propagation, the operations performed are recorded, and during backpropagation, the chain rule is applied to expand the gradient into the product of the Jacobian matrices of each layer of the surrogate model, thereby obtaining the steepest direction of change of the loss function. Based on the gradient, the damage state parameters are iteratively updated using a gradient descent algorithm according to a preset update step size, so as to reduce the value of the inversion loss function; during this update process, the network weights and bias parameters of the surrogate model remain unchanged. Repeat the above steps until the convergence condition is met, then stop the iteration and use the damage state parameters obtained at convergence as the damage identification result of the prefabricated beam bridge.

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